Piezo-optic tensor of crystals from quantum-mechanical calculations.

PubMed

Erba, A; Ruggiero, M T; Korter, T M; Dovesi, R

2015-10-14

An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor of crystals belonging to any space group of symmetry. Elastic stiffness and compliance constants are obtained as numerical first derivatives of analytical energy gradients with respect to the strain and photo-elastic constants as numerical derivatives of analytical dielectric tensor components, which are in turn computed through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach, with respect to the strain. Both point and translation symmetries are exploited at all steps of the calculation, within the framework of periodic boundary conditions. The scheme is applied to the determination of the full set of ten symmetry-independent piezo-optic constants of calcium tungstate CaWO4, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π61 constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.

Piezo-optic tensor of crystals from quantum-mechanical calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Erba, A., E-mail: alessandro.erba@unito.it; Dovesi, R.; Ruggiero, M. T.

2015-10-14

An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor of crystals belonging to any space group of symmetry. Elastic stiffness and compliance constants are obtained as numerical first derivatives of analytical energy gradients with respect to the strain and photo-elastic constants as numerical derivatives of analytical dielectric tensor components, which are in turn computed through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach, with respect to the strain. Both point and translation symmetries are exploited at all steps of the calculation, within the framework of periodic boundary conditions. The scheme is applied to the determination of themore » full set of ten symmetry-independent piezo-optic constants of calcium tungstate CaWO{sub 4}, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π{sub 61} constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.« less

An Orthotropic Model for Composite Materials in EPIC

DTIC Science & Technology

2014-06-06

directions, and fails the material by eliminating the deviatoric stresses when any of the plastic strain components reaches its user-supplied critical...the directions of the fibers, especially in comparison to the non-linear stress -strain curves obtained from off-axis tensile tests. A somewhat...increment in Cauchy stress ; and is the tensor of elastic moduli. In EPIC, this equation is implemented via central differences because the velocity

A high-order strong stability preserving Runge-Kutta method for three-dimensional full waveform modeling and inversion of anelastic models

NASA Astrophysics Data System (ADS)

Wang, N.; Shen, Y.; Yang, D.; Bao, X.; Li, J.; Zhang, W.

2017-12-01

Accurate and efficient forward modeling methods are important for high resolution full waveform inversion. Compared with the elastic case, solving anelastic wave equation requires more computational time, because of the need to compute additional material-independent anelastic functions. A numerical scheme with a large Courant-Friedrichs-Lewy (CFL) condition number enables us to use a large time step to simulate wave propagation, which improves computational efficiency. In this work, we apply the fourth-order strong stability preserving Runge-Kutta method with an optimal CFL coeffiecient to solve the anelastic wave equation. We use a fourth order DRP/opt MacCormack scheme for the spatial discretization, and we approximate the rheological behaviors of the Earth by using the generalized Maxwell body model. With a larger CFL condition number, we find that the computational efficient is significantly improved compared with the traditional fourth-order Runge-Kutta method. Then, we apply the scattering-integral method for calculating travel time and amplitude sensitivity kernels with respect to velocity and attenuation structures. For each source, we carry out one forward simulation and save the time-dependent strain tensor. For each station, we carry out three `backward' simulations for the three components and save the corresponding strain tensors. The sensitivity kernels at each point in the medium are the convolution of the two sets of the strain tensors. Finally, we show several synthetic tests to verify the effectiveness of the strong stability preserving Runge-Kutta method in generating accurate synthetics in full waveform modeling, and in generating accurate strain tensors for calculating sensitivity kernels at regional and global scales.

Subsidence and current strain patterns on Tenerife Island (Canary Archipelago, Spain) derived from continuous GNSS time series (2008-2015)

NASA Astrophysics Data System (ADS)

Sánchez-Alzola, A.; Martí, J.; García-Yeguas, A.; Gil, A. J.

2016-11-01

In this paper we present the current crustal deformation model of Tenerife Island derived from daily CGPS time series processing (2008-2015). Our results include the position time series, a global velocity estimation and the current crustal deformation on the island in terms of strain tensors. We detect a measurable subsidence of 1.5-2 mm/yr. in the proximities of the Cañadas-Teide-Pico Viejo (CTPV) complex. These values are higher in the central part of the complex and could be explained by a lateral spreading of the elastic lithosphere combined with the effect of the drastic descent of the water table in the island experienced during recent decades. The results show that the Anaga massif is stable in both its horizontal and vertical components. The strain tensor analysis shows a 70 nstrain/yr. E-W compression in the central complex, perpendicular to the 2004 sismo-volcanic area, and 50 nstrain/yr. SW-NE extension towards the Northeast ridge. The residual velocity and strain patterns coincide with a decline in volcanic activity since the 2004 unrest.

Direct coordinate-free derivation of the compatibility equation for finite strains

NASA Astrophysics Data System (ADS)

Ryzhak, E. I.

2014-07-01

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness.

Holographic Moire, An Optical Tool For The Determination Of Displacements, Strains, Contours, And Slopes Of Surfaces

NASA Astrophysics Data System (ADS)

Sciammarella, Cesar A.

1982-06-01

In conventional holographic interferometry, the observed fringe patterns are determined by the object displacement and deformation, and by the illumination and observation configurations. The obtained information may not be in the most convenient form for further data processing. To overcome this problem, and to create new possibilities, holographic fringe patterns can be changed by modifying the optical setup. As a result of these modifications, well-known procedures of the moire method can be applied to holographic interferometry. Components of displacement and components of the strain tensor can be isolated and measured separately. Surface contours and slopes can also be determined.

General Rotorcraft Aeromechanical Stability Program (GRASP) - Theory Manual

DTIC Science & Technology

1990-10-01

the A basis. Two symbols frequently encountered in vector operations that use index notation are the Kronecker delta eij and the Levi - Civita epsilon...Blade root cutout fijk Levi - Civita epsilon permutation symbol 0 pretwist angle 0’ pretwist per unit length (d;) Oi Tait-Bryan angles K~i moment strains...the components of the identity tensor in a Cartesian coordinate system, while the Levi Civita epsilon consists of components of the permutation

The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers

NASA Astrophysics Data System (ADS)

Neff, Patrizio; Lankeit, Johannes; Ghiba, Ionel-Dumitrel; Martin, Robert; Steigmann, David

2015-08-01

We consider a family of isotropic volumetric-isochoric decoupled strain energies based on the Hencky-logarithmic (true, natural) strain tensor log U, where μ > 0 is the infinitesimal shear modulus, is the infinitesimal bulk modulus with the first Lamé constant, are dimensionless parameters, is the gradient of deformation, is the right stretch tensor and is the deviatoric part (the projection onto the traceless tensors) of the strain tensor log U. For small elastic strains, the energies reduce to first order to the classical quadratic Hencky energy which is known to be not rank-one convex. The main result in this paper is that in plane elastostatics the energies of the family are polyconvex for , extending a previous finding on its rank-one convexity. Our method uses a judicious application of Steigmann's polyconvexity criteria based on the representation of the energy in terms of the principal invariants of the stretch tensor U. These energies also satisfy suitable growth and coercivity conditions. We formulate the equilibrium equations, and we prove the existence of minimizers by the direct methods of the calculus of variations.

Reducing disk storage of full-3D seismic waveform tomography (F3DT) through lossy online compression

NASA Astrophysics Data System (ADS)

Lindstrom, Peter; Chen, Po; Lee, En-Jui

2016-08-01

Full-3D seismic waveform tomography (F3DT) is the latest seismic tomography technique that can assimilate broadband, multi-component seismic waveform observations into high-resolution 3D subsurface seismic structure models. The main drawback in the current F3DT implementation, in particular the scattering-integral implementation (F3DT-SI), is the high disk storage cost and the associated I/O overhead of archiving the 4D space-time wavefields of the receiver- or source-side strain tensors. The strain tensor fields are needed for computing the data sensitivity kernels, which are used for constructing the Jacobian matrix in the Gauss-Newton optimization algorithm. In this study, we have successfully integrated a lossy compression algorithm into our F3DT-SI workflow to significantly reduce the disk space for storing the strain tensor fields. The compressor supports a user-specified tolerance for bounding the error, and can be integrated into our finite-difference wave-propagation simulation code used for computing the strain fields. The decompressor can be integrated into the kernel calculation code that reads the strain fields from the disk and compute the data sensitivity kernels. During the wave-propagation simulations, we compress the strain fields before writing them to the disk. To compute the data sensitivity kernels, we read the compressed strain fields from the disk and decompress them before using them in kernel calculations. Experiments using a realistic dataset in our California statewide F3DT project have shown that we can reduce the strain-field disk storage by at least an order of magnitude with acceptable loss, and also improve the overall I/O performance of the entire F3DT-SI workflow significantly. The integration of the lossy online compressor may potentially open up the possibilities of the wide adoption of F3DT-SI in routine seismic tomography practices in the near future.

Reducing Disk Storage of Full-3D Seismic Waveform Tomography (F3DT) Through Lossy Online Compression

DOE PAGES

Lindstrom, Peter; Chen, Po; Lee, En-Jui

2016-05-05

Full-3D seismic waveform tomography (F3DT) is the latest seismic tomography technique that can assimilate broadband, multi-component seismic waveform observations into high-resolution 3D subsurface seismic structure models. The main drawback in the current F3DT implementation, in particular the scattering-integral implementation (F3DT-SI), is the high disk storage cost and the associated I/O overhead of archiving the 4D space-time wavefields of the receiver- or source-side strain tensors. The strain tensor fields are needed for computing the data sensitivity kernels, which are used for constructing the Jacobian matrix in the Gauss-Newton optimization algorithm. In this study, we have successfully integrated a lossy compression algorithmmore » into our F3DT SI workflow to significantly reduce the disk space for storing the strain tensor fields. The compressor supports a user-specified tolerance for bounding the error, and can be integrated into our finite-difference wave-propagation simulation code used for computing the strain fields. The decompressor can be integrated into the kernel calculation code that reads the strain fields from the disk and compute the data sensitivity kernels. During the wave-propagation simulations, we compress the strain fields before writing them to the disk. To compute the data sensitivity kernels, we read the compressed strain fields from the disk and decompress them before using them in kernel calculations. Experiments using a realistic dataset in our California statewide F3DT project have shown that we can reduce the strain-field disk storage by at least an order of magnitude with acceptable loss, and also improve the overall I/O performance of the entire F3DT-SI workflow significantly. The integration of the lossy online compressor may potentially open up the possibilities of the wide adoption of F3DT-SI in routine seismic tomography practices in the near future.« less

Computer simulation of thermal conductivity in vulcanized polyisoprene at variable strain and temperature

NASA Astrophysics Data System (ADS)

Engelmann, Sven; Meyer, Jan; Hentschke, Reinhard

2017-08-01

We study the thermal conductivity tensor in an atomistic model of vulcanized cis-1,4-polyisoprene (PI) rubber via molecular dynamics simulations. Our polymer force field is based on V. A. Harmandaris et al. [J. Chem. Phys. 116, 436 (2002), 10.1063/1.1416872], whereas the polymerization algorithm follows the description in J. Hager et al. [Macromolecules 48, 9039 (2015), 10.1021/acs.macromol.5b01864]. The polymer chains are chemically cross linked via sulfur bridges of adjustable cross-link density. A volume-conserving uniaxial strain of up to 200% is applied to the systems. The widely used GROMACS simulation package is adapted to allow using the Green-Kubo approach to calculate the thermal conductivity tensor components. Our analysis of the heat flux autocorrelation functions leads to the conclusion that the thermal conductivity in PI is governed by short-lived phonon modes at low wave numbers due to deformation of the monomers along the polymer backbone. Applying uniaxial strain causes increased orientation of monomers along the strain direction, which enhances the attendant thermal conductivity component. We find an exponential increase of the conductivity in stretch direction in terms of an attendant orientation order parameter. This is accompanied by a simultaneous decline of thermal conductivity in the orthogonal directions. Increase of the cross-link density only has a weak effect on thermal conductivity in the unstrained system, even at high cross-link density. In the strained system we do observed a rising thermal conductivity in the limit of high stress. This increase is attributed to enhanced coupling between chains rather than to their orientation.

Strain Variation along Cimandiri Fault, West Java Based on Continuous and Campaign GPS Observation From 2006-2016

NASA Astrophysics Data System (ADS)

Safitri, A. A.; Meilano, I.; Gunawan, E.; Abidin, H. Z.; Efendi, J.; Kriswati, E.

2018-03-01

The Cimandiri fault which is running in the direction from Pelabuhan Ratu to Padalarang is the longest fault in West Java with several previous shallow earthquakes in the last 20 years. By using continues and campaign GPS observation from 2006-2016, we obtain the deformation pattern along the fault through the variation of strain tensor. We use the velocity vector of GPS station which is fixed in stable International Terrestrial Reference Frame 2008 to calculate horizontal strain tensor. Least Square Collocation is applied to produce widely dense distributed velocity vector and optimum scale factor for the Least Square Weighting matrix. We find that the strain tensor tend to change from dominantly contraction in the west to dominantly extension to the east of fault. Both the maximum shear strain and dilatation show positive value along the fault and increasing from the west to the east. The findings of strain tensor variation along Cimandiri Fault indicate the post seismic effect of the 2006 Java Earthquake.

Moment Inversion of the DPRK Nuclear Tests Using Finite-Difference Three-dimensional Strain Green's Tensors

NASA Astrophysics Data System (ADS)

Bao, X.; Shen, Y.; Wang, N.

2017-12-01

Accurate estimation of the source moment is important for discriminating underground explosions from earthquakes and other seismic sources. In this study, we invert for the full moment tensors of the recent seismic events (since 2016) at the Democratic People's Republic of Korea (PRRK) Punggye-ri test site. We use waveform data from broadband seismic stations located in China, Korea, and Japan in the inversion. Using a non-staggered-grid, finite-difference algorithm, we calculate the strain Green's tensors (SGT) based on one-dimensional (1D) and three-dimensional (3D) Earth models. Taking advantage of the source-receiver reciprocity, a SGT database pre-calculated and stored for the Punggye-ri test site is used in inversion for the source mechanism of each event. With the source locations estimated from cross-correlation using regional Pn and Pn-coda waveforms, we obtain the optimal source mechanism that best fits synthetics to the observed waveforms of both body and surface waves. The moment solutions of the first three events (2016-01-06, 2016-09-09, and 2017-09-03) show dominant isotropic components, as expected from explosions, though there are also notable non-isotropic components. The last event ( 8 minutes after the mb6.3 explosion in 2017) contained mainly implosive component, suggesting a collapse following the explosion. The solutions from the 3D model can better fit observed waveforms than the corresponding solutions from the 1D model. The uncertainty in the resulting moment solution is influenced by heterogeneities not resolved by the Earth model according to the waveform misfit. Using the moment solutions, we predict the peak ground acceleration at the Punggye-ri test site and compare the prediction with corresponding InSAR and other satellite images.

Comparison of magmatic and amagmatic rift zone kinematics using full moment tensor inversions of regional earthquakes

NASA Astrophysics Data System (ADS)

Jaye Oliva, Sarah; Ebinger, Cynthia; Shillington, Donna; Albaric, Julie; Deschamps, Anne; Keir, Derek; Drooff, Connor

2017-04-01

Temporary seismic networks deployed in the magmatic Eastern rift and the mostly amagmatic Western rift in East Africa present the opportunity to compare the depth distribution of strain, and fault kinematics in light of rift age and the presence or absence of surface magmatism. The largest events in local earthquake catalogs (ML > 3.5) are modeled using the Dreger and Ford full moment tensor algorithm (Dreger, 2003; Minson & Dreger, 2008) to better constrain source depth and to investigate non-double-couple components. A bandpass filter of 0.02 to 0.10 Hz is applied to the waveforms prior to inversion. Synthetics are based on 1D velocity models derived during seismic analysis and constrained by reflection and tomographic data where available. Results show significant compensated linear vector dipole (CLVD) and isotropic components for earthquakes in magmatic rift zones, whereas double-couple mechanisms predominate in weakly magmatic rift sectors. We interpret the isotropic components as evidence for fluid-involved faulting in the Eastern rift where volatile emissions are large, and dike intrusions well documented. Lower crustal earthquakes are found in both amagmatic and magmatic sectors. These results are discussed in the context of the growing database of complementary geophysical, geochemical, and geological studies in these regions as we seek to understand the role of magmatism and faulting in accommodating strain during early continental rifting.

Parameterization of subgrid-scale stress by the velocity gradient tensor

NASA Technical Reports Server (NTRS)

Lund, Thomas S.; Novikov, E. A.

1993-01-01

The objective of this work is to construct and evaluate subgrid-scale models that depend on both the strain rate and the vorticity. This will be accomplished by first assuming that the subgrid-scale stress is a function of the strain and rotation rate tensors. Extensions of the Caley-Hamilton theorem can then be used to write the assumed functional dependence explicitly in the form of a tensor polynomial involving products of the strain and rotation rates. Finally, use of this explicit expression as a subgrid-scale model will be evaluated using direct numerical simulation data for homogeneous, isotropic turbulence.

Natural Strain

NASA Technical Reports Server (NTRS)

Freed, Alan D.

1995-01-01

The purpose of this paper is to present a consistent and thorough development of the strain and strain-rate measures affiliated with Hencky. Natural measures for strain and strain-rate, as I refer to them, are first expressed in terms of of the fundamental body-metric tensors of Lodge. These strain and strain-rate measures are mixed tensor fields. They are mapped from the body to space in both the Eulerian and Lagrangian configurations, and then transformed from general to Cartesian fields. There they are compared with the various strain and strain-rate measures found in the literature. A simple Cartesian description for Hencky strain-rate in the Lagrangian state is obtained.

Ferrotoroidial propertiesof Non-Crystallographic Pointgroups

NASA Astrophysics Data System (ADS)

Sireesha, G.; Devi, S. Uma; Yamini Sankar, CH.

2017-08-01

Primary ferroic crystals are the crystals with domain states that are distinguished by properties like spontaneous magnetization, strain, or polarisation. Secondary ferroic crystals are the crystals with domain states that are distinguished by piezoelectric tensor and they are named as Ferromagnetotoroidic (eV2), Ferromagnetoelastic (aeV [V2]) crystals respectively. Here “e” denotes zero rank tensor that changes under spatial inversion, “a” denotes zero rank tensor that changes under time inversion, and “V” denotes a polar vector. Recent observations (Van Aken et al., 2007) identified the fourth type of primary ferroic crystals, a ferrotoroidic crystal with domains distinguished by a toroidial moment. The number of independent constants of quasi crystals is theoretically derived by Wenge Yang et al., (1995). He also formulated the number of independent components of any physical property tensor of quasi crystals using group representation theory. This paper accounts the effect of symmetry on some ferrotoroidial properties of quasi Crystals with 5-fold, 8-fold, 10-fold and 12-fold symmetries using group theoretical methods. Also the number of independent constants is calculated and tabulated that helps in describing the ferrotoroidial properties.

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

NASA Astrophysics Data System (ADS)

Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia

2008-11-01

Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).

Relationship between electrical conductivity anisotropy and fabric anisotropy in granular materials during drained triaxial compressive tests: a numerical approach

NASA Astrophysics Data System (ADS)

Niu, Qifei; Revil, André; Li, Zhaofeng; Wang, Yu-Hsing

2017-07-01

The anisotropy of granular media and its evolution during shearing are important aspects required in developing physics-based constitutive models in Earth sciences. The development of relationships between geoelectrical properties and the deformation of porous media has applications to the monitoring of faulting and landslides. However, such relationships are still poorly understood. In this study, we first investigate the definition of the electrical conductivity anisotropy tensor of granular materials in presence of surface conductivity of the grains. Fabric anisotropy is related to the components of the fabric tensor. We define an electrical anisotropy factor based on the Archie's exponent second-order symmetric tensor m of granular materials. We use numerical simulations to confirm a relationship between the evolution of electrical and fabric anisotropy factors during shearing. To realize the simulations, we build a virtual laboratory in which we can easily perform synthetic experiments. We first simulate drained compressive triaxial tests of loose and dense granular materials (porosity 0.45 and 0.38, respectively) using the discrete element method. Then, the electrical conductivity tensor of a set of deformed synthetic samples is computed using the finite-difference method. The numerical results show that shear strains are responsible for a measurable anisotropy in the bulk conductivity of granular media. The observed electrical anisotropy response, during shearing, is distinct for dense and loose synthetic samples. Electrical and fabric anisotropy factors exhibit however a unique linear correlation, regardless of the shear strain and the initial state (porosity) of the synthetic samples. The practical implication of this finding confirms the usefulness of the electrical conductivity method in studying the fabric tensor of granular media. This result opens the door in using time-lapse electrical resistivity to study non-intrusively the evolution of anisotropy of soils and granular rocks during deformation, for instance during landslides, and to use the evolution of the conductivity tensor to monitor mechanical properties.

Optical ptychographic microscopy for quantitative anisotropic phase imaging

NASA Astrophysics Data System (ADS)

Anthony, N.; Cadenazzi, G.; Nugent, K. A.; Abbey, B.

2016-12-01

Ptychography has recently been adapted for the recovery of the complete Jones matrix of an anisotropic specimen, using a vectorial form of the Ptychographic Iterative Engine (vPIE) for a set of linearly polarized probes. Here we show that this method can be applied to the recovery of the in-plane components of the elastic strain tensor in a diametrically compressed disc. The advantages and disadvantages of vPIE for the recovery of strain information from `real-world' samples is discussed as well as the potential for this approach to be applied to the characterization of the mechanical properties of optically transparent materials

A contribution toward rational modeling of the pressure-strain-rate correlation

NASA Technical Reports Server (NTRS)

Lee, Moon Joo

1990-01-01

A novel method of obtaining an analytical expression of the 'linear part' of the pressure-strain-rate tensor in terms of the anisotropy tensor of the Reynolds stresses has been developed, where the coefficients of the seven independent tensor terms are functions of the invariants of the Reynolds-stress anisotropy. The coefficients are evaluated up to fourth order in the anisotropy of the Reynolds stresses to provide guidance for development of a turbulence model.

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

NASA Astrophysics Data System (ADS)

Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

Search for subgrid scale parameterization by projection pursuit regression

NASA Technical Reports Server (NTRS)

Meneveau, C.; Lund, T. S.; Moin, Parviz

1992-01-01

The dependence of subgrid-scale stresses on variables of the resolved field is studied using direct numerical simulations of isotropic turbulence, homogeneous shear flow, and channel flow. The projection pursuit algorithm, a promising new regression tool for high-dimensional data, is used to systematically search through a large collection of resolved variables, such as components of the strain rate, vorticity, velocity gradients at neighboring grid points, etc. For the case of isotropic turbulence, the search algorithm recovers the linear dependence on the rate of strain (which is necessary to transfer energy to subgrid scales) but is unable to determine any other more complex relationship. For shear flows, however, new systematic relations beyond eddy viscosity are found. For the homogeneous shear flow, the results suggest that products of the mean rotation rate tensor with both the fluctuating strain rate and fluctuating rotation rate tensors are important quantities in parameterizing the subgrid-scale stresses. A model incorporating these terms is proposed. When evaluated with direct numerical simulation data, this model significantly increases the correlation between the modeled and exact stresses, as compared with the Smagorinsky model. In the case of channel flow, the stresses are found to correlate with products of the fluctuating strain and rotation rate tensors. The mean rates of rotation or strain do not appear to be important in this case, and the model determined for homogeneous shear flow does not perform well when tested with channel flow data. Many questions remain about the physical mechanisms underlying these findings, about possible Reynolds number dependence, and, given the low level of correlations, about their impact on modeling. Nevertheless, demonstration of the existence of causal relations between sgs stresses and large-scale characteristics of turbulent shear flows, in addition to those necessary for energy transfer, provides important insight into the relation between scales in turbulent flows.

Irreducible structure, symmetry and average of Eshelby's tensor fields in isotropic elasticity

NASA Astrophysics Data System (ADS)

Zheng, Q.-S.; Zhao, Z.-H.; Du, D.-X.

2006-02-01

The strain field ɛ(x) in an infinitely large, homogenous, and isotropic elastic medium induced by a uniform eigenstrain ɛ0 in a domain ω depends linearly upon ɛ0 : ɛij(x)=Sijklω(x)ɛkl0. It has been a long-standing conjecture that the Eshelby's tensor field Sω(x) is uniform inside ω if and only if ω is ellipsoidally shaped. Because of the minor index symmetry Sijklω=Sjiklω=Sijlkω, Sω might have a maximum of 36 or nine independent components in three or two dimensions, respectively. In this paper, using the irreducible decomposition of Sω, we show that the isotropic part S of Sω vanishes outside ω and is uniform inside ω with the same value as the Eshelby's tensor S0 for 3D spherical or 2D circular domains. We further show that the anisotropic part Aω=Sω-S of Sω is characterized by a second- and a fourth-order deviatoric tensors and therefore have at maximum 14 or four independent components as characteristics of ω's geometry. Remarkably, the above irreducible structure of Sω is independent of ω's geometry (e.g., shape, orientation, connectedness, convexity, boundary smoothness, etc.). Interesting consequences have implication for a number of recently findings that, for example, both the values of Sω at the center of a 2D Cn(n⩾3,n≠4)-symmetric or 3D icosahedral ω and the average value of Sω over such a ω are equal to S0.

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

NASA Technical Reports Server (NTRS)

Jongen, T.; Gatski, T. B.

1997-01-01

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

3D Experimental Measurement of Lattice Strain and Fracture Behavior of Sand Particles Using Synchrotron X-Ray Diffraction and Tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cil, Mehmet B.; Alshibli, Khalid A.; Kenesei, Peter

3D synchrotron X-ray diffraction (3DXRD) and synchrotron micro-computed tomography (SMT) techniques were used to measure and monitor the lattice strain evolution and fracture behavior of natural Ottawa sand particles subjected to 1D compression loading. The particle-averaged lattice strain within sand particles was measured using 3DXRD and then was used to calculate the corresponding lattice stress tensor. In addition, the evolution and mode of fracture of sand particles was investigated using high-resolution 3D SMT images. The results of diffraction data analyses revealed that the major principal component of the lattice strain or stress tensor increased in most of the particles asmore » the global applied compressive load increased until the onset of fracture. Particle fracture and subsequent rearrangements caused significant variation and fluctuations in measured lattice strain/stress values from one particle to another and from one load step to the next one. SMT image analysis at the particle-scale showed that cracks in fractured sand particles generally initiate and propagate along the plane that connects the two contact points. Fractured particles initially split into two or three major fragments followed by disintegration into multiple smaller fragments in some cases. In conclusion, microscale analysis of fractured particles showed that particle position, morphology, the number and location of contact points play a major role in the occurrence of particle fracture in confined comminution of the sand assembly.« less

3D Experimental Measurement of Lattice Strain and Fracture Behavior of Sand Particles Using Synchrotron X-Ray Diffraction and Tomography

DOE PAGES

Cil, Mehmet B.; Alshibli, Khalid A.; Kenesei, Peter

2017-05-27

3D synchrotron X-ray diffraction (3DXRD) and synchrotron micro-computed tomography (SMT) techniques were used to measure and monitor the lattice strain evolution and fracture behavior of natural Ottawa sand particles subjected to 1D compression loading. The particle-averaged lattice strain within sand particles was measured using 3DXRD and then was used to calculate the corresponding lattice stress tensor. In addition, the evolution and mode of fracture of sand particles was investigated using high-resolution 3D SMT images. The results of diffraction data analyses revealed that the major principal component of the lattice strain or stress tensor increased in most of the particles asmore » the global applied compressive load increased until the onset of fracture. Particle fracture and subsequent rearrangements caused significant variation and fluctuations in measured lattice strain/stress values from one particle to another and from one load step to the next one. SMT image analysis at the particle-scale showed that cracks in fractured sand particles generally initiate and propagate along the plane that connects the two contact points. Fractured particles initially split into two or three major fragments followed by disintegration into multiple smaller fragments in some cases. In conclusion, microscale analysis of fractured particles showed that particle position, morphology, the number and location of contact points play a major role in the occurrence of particle fracture in confined comminution of the sand assembly.« less

Modeling Ignition of HMX with the Gibbs Formulation

NASA Astrophysics Data System (ADS)

Lee, Kibaek; Stewart, D. Scott

2017-06-01

We present a HMX model with the Gibbs formulation in which stress tensor and temperature are assumed to be in local equilibrium, but phase/chemical changes are not assumed to be in equilibrium. We assume multi-components for HMX including beta- and delta-phase, liquid, and gas phase of HMX and its gas products. Isotropic small strain solid model, modified Fried Howard liquid EOS, and ideal gas EOS are used for its relevant component. Phase/chemical changes are characterized as reactions and are in individual reaction rate. Maxwell-Stefan model is used for diffusion. Excited gas products in the local domain lead unreacted HMX solid to the ignition event. Density of the mixture, stress, strain, displacement, mass fractions, and temperature are considered in 1D domain with time histories. Office of Naval Research and Air Force Office of Scientific Research.

Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of Newton's iteration

NASA Astrophysics Data System (ADS)

Zhang, Fei; Huang, Weizhang; Li, Xianping; Zhang, Shicheng

2018-03-01

A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the decomposition of the strain tensor into tensile and compressive components is essential for the success of the phase-field modeling of brittle fracture but results in a non-smooth elastic energy and stronger nonlinearity in the governing equation. This makes the governing equation much more difficult to solve and, in particular, Newton's iteration often fails to converge. Three regularization methods are proposed to smooth out the decomposition of the strain tensor. Numerical examples of fracture propagation under quasi-static load demonstrate that all of the methods can effectively improve the convergence of Newton's iteration for relatively small values of the regularization parameter but without compromising the accuracy of the numerical solution. They also show that the moving mesh finite element method is able to adaptively concentrate the mesh elements around propagating cracks and handle multiple and complex crack systems.

On improving the efficiency of tensor voting.

PubMed

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-11-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.

The mathematical formulation of a generalized Hooke's law for blood vessels.

PubMed

Zhang, Wei; Wang, Chong; Kassab, Ghassan S

2007-08-01

It is well known that the stress-strain relationship of blood vessels is highly nonlinear. To linearize the relationship, the Hencky strain tensor is generalized to a logarithmic-exponential (log-exp) strain tensor to absorb the nonlinearity. A quadratic nominal strain potential is proposed to derive the second Piola-Kirchhoff stresses by differentiating the potential with respect to the log-exp strains. The resulting constitutive equation is a generalized Hooke's law. Ten material constants are needed for the three-dimensional orthotropic model. The nondimensional constant used in the log-exp strain definition is interpreted as a nonlinearity parameter. The other nine constants are the elastic moduli with respect to the log-exp strains. In this paper, the proposed linear stress-strain relation is shown to represent the pseudoelastic Fung model very well.

Symmetry classes of the anisotropy tensors of quasielastic materials and a generalized Kelvin approach

NASA Astrophysics Data System (ADS)

Ostrosablin, N. I.

2017-05-01

The anisotropy matrices (tensors) of quasielastic (Cauchy-elastic) materials were obtained for all classes of crystallographic symmetries in explicit form. The fourth-rank anisotropy tensors of such materials do not have the main symmetry, in which case the anisotropy matrix is not symmetric. As a result of introducing various bases in the space of symmetric stress and strain tensors, the linear relationship between stresses and strains is represented in invariant form similar to the form in which generalized Hooke's law is written for the case of anisotropic hyperelastic materials and contains six positive Kelvin eigen moduli. It is shown that the introduction of modified rotation-induced deformation in the strain space can cause a transition to the symmetric anisotropy matrix observed in the case of hyperelasticity. For the case of transverse isotropy, there are examples of determination of the Kelvin eigen moduli and eigen bases and the rotation matrix in the strain space. It is shown that there is a possibility of existence of quasielastic media with a skew-symmetric anisotropy matrix with no symmetric part. Some techniques for the experimental testing of the quasielasticity model are proposed.

Two-dimensional mapping of triaxial strain fields in a multiferroic BiFeO3 thin film using scanning x-ray microdiffraction

NASA Astrophysics Data System (ADS)

Bark, Chung W.; Cho, Kyung C.; Koo, Yang M.; Tamura, Nobumichi; Ryu, Sangwoo; Jang, Hyun M.

2007-03-01

The dramatically enhanced polarizations and saturation magnetizations observed in the epitaxially constrained BiFeO3 (BFO) thin films with their pronounced grain-orientation dependence have attracted much attention and are attributed largely to the constrained in-plane strain. Thus, it is highly desirable to directly obtain information on the two-dimensional (2D) distribution of the in-plane strain and its correlation with the grain orientation of each corresponding microregion. Here the authors report a 2D quantitative mapping of the grain orientation and the local triaxial strain field in a 250nm thick multiferroic BFO film using a synchrotron x-ray microdiffraction technique. This direct scanning measurement demonstrates that the deviatoric component of the in-plane strain tensor is between 5×10-3 and 6×10-3 and that the local triaxial strain is fairly well correlated with the grain orientation in that particular region.

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

NASA Astrophysics Data System (ADS)

Abdoli-Arani, A.; Ramezani-Arani, R.

2012-11-01

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.

Gauge and Non-Gauge Tensor Multiplets in 5D Conformal Supergravity

NASA Astrophysics Data System (ADS)

Kugo, T.; Ohashi, K.

2002-12-01

An off-shell formulation of two distinct tensor multiplets, a massive tensor multiplet and a tensor gauge multiplet, is presented in superconformal tensor calculus in five-dimensional space-time. Both contain a rank 2 antisymmetric tensor field, but there is no gauge symmetry in the former, while it is a gauge field in the latter. Both multiplets have 4 bosonic and 4 fermionic on-shell modes, but the former consists of 16 (boson)+16 (fermion) component fields, while the latter consists of 8 (boson)+8 (fermion) component fields.

Pressure-strain energy redistribution in compressible turbulence: return-to-isotropy versus kinetic-potential energy equipartition

NASA Astrophysics Data System (ADS)

Lee, Kurnchul; Venugopal, Vishnu; Girimaji, Sharath S.

2016-08-01

Return-to-isotropy and kinetic-potential energy equipartition are two fundamental pressure-moderated energy redistributive processes in anisotropic compressible turbulence. Pressure-strain correlation tensor redistributes energy among various Reynolds stress components and pressure-dilatation is responsible for energy reallocation between dilatational kinetic and potential energies. The competition and interplay between these pressure-based processes are investigated in this study. Direct numerical simulations (DNS) of low turbulent Mach number dilatational turbulence are performed employing the hybrid thermal Lattice Boltzman method (HTLBM). It is found that a tendency towards equipartition precedes proclivity for isotropization. An evolution towards equipartition has a collateral but critical effect on return-to-isotropy. The preferential transfer of energy from strong (rather than weak) Reynolds stress components to potential energy accelerates the isotropization of dilatational fluctuations. Understanding of these pressure-based redistributive processes is critical for developing insight into the character of compressible turbulence.

Microstructural Rearrangements and their Rheological Implications in a Model Thixotropic Elastoviscoplastic Fluid

NASA Astrophysics Data System (ADS)

Jamali, Safa; McKinley, Gareth H.; Armstrong, Robert C.

2017-01-01

We identify the sequence of microstructural changes that characterize the evolution of an attractive particulate gel under flow and discuss their implications on macroscopic rheology. Dissipative particle dynamics is used to monitor shear-driven evolution of a fabric tensor constructed from the ensemble spatial configuration of individual attractive constituents within the gel. By decomposing this tensor into isotropic and nonisotropic components we show that the average coordination number correlates directly with the flow curve of the shear stress versus shear rate, consistent with theoretical predictions for attractive systems. We show that the evolution in nonisotropic local particle rearrangements are primarily responsible for stress overshoots (strain-hardening) at the inception of steady shear flow and also lead, at larger times and longer scales, to microstructural localization phenomena such as shear banding flow-induced structure formation in the vorticity direction.

Statistics of pressure fluctuations in decaying isotropic turbulence.

PubMed

Kalelkar, Chirag

2006-04-01

We present results from a systematic direct-numerical simulation study of pressure fluctuations in an unforced, incompressible, homogeneous, and isotropic three-dimensional turbulent fluid. At cascade completion, isosurfaces of low pressure are found to be organized as slender filaments, whereas the predominant isostructures appear sheetlike. We exhibit several results, including plots of probability distributions of the spatial pressure difference, the pressure-gradient norm, and the eigenvalues of the pressure-Hessian tensor. Plots of the temporal evolution of the mean pressure-gradient norm, and the mean eigenvalues of the pressure-Hessian tensor are also exhibited. We find the statistically preferred orientations between the eigenvectors of the pressure-Hessian tensor, the pressure gradient, the eigenvectors of the strain-rate tensor, the vorticity, and the velocity. Statistical properties of the nonlocal part of the pressure-Hessian tensor are also exhibited. We present numerical tests (in the viscous case) of some conjectures of Ohkitani [Phys. Fluids A 5, 2570 (1993)] and Ohkitani and Kishiba [Phys. Fluids 7, 411 (1995)] concerning the pressure-Hessian and the strain-rate tensors, for the unforced, incompressible, three-dimensional Euler equations.

Direct Three-Dimensional Myocardial Strain Tensor Quantification and Tracking using zHARP★

PubMed Central

Abd-Elmoniem, Khaled Z.; Stuber, Matthias; Prince, Jerry L.

2008-01-01

Images of myocardial strain can be used to diagnose heart disease, plan and monitor treatment, and to learn about cardiac structure and function. Three-dimensional (3-D) strain is typically quantified using many magnetic resonance (MR) images obtained in two or three orthogonal planes. Problems with this approach include long scan times, image misregistration, and through-plane motion. This article presents a novel method for calculating cardiac 3-D strain using a stack of two or more images acquired in only one orientation. The zHARP pulse sequence encodes in-plane motion using MR tagging and out-of-plane motion using phase encoding, and has been previously shown to be capable of computing 3D displacement within a single image plane. Here, data from two adjacent image planes are combined to yield a 3-D strain tensor at each pixel; stacks of zHARP images can be used to derive stacked arrays of 3D strain tensors without imaging multiple orientations and without numerical interpolation. The performance and accuracy of the method is demonstrated in-vitro on a phantom and in-vivo in four healthy adult human subjects. PMID:18511332

Strain, magnetic anisotropy, and anisotropic magnetoresistance in (Ga,Mn)As on high-index substrates: Application to (113)A -oriented layers

NASA Astrophysics Data System (ADS)

Dreher, L.; Donhauser, D.; Daeubler, J.; Glunk, M.; Rapp, C.; Schoch, W.; Sauer, R.; Limmer, W.

2010-06-01

Based on a detailed theoretical examination of the lattice distortion in high-index epilayers in terms of continuum mechanics, expressions are deduced that allow the calculation and experimental determination of the strain tensor for (hhl) -oriented (Ga,Mn)As layers. Analytical expressions are derived for the strain-dependent free-energy density and for the resistivity tensor for monoclinic and orthorhombic crystal symmetries, phenomenologically describing the magnetic anisotropy and anisotropic magnetoresistance by appropriate anisotropy and resistivity parameters, respectively. Applying the results to (113)A orientation with monoclinic crystal symmetry, the expressions are used to determine the strain tensor and the shear angle of a series of (113)A -oriented (Ga,Mn)As layers by high-resolution x-ray diffraction and to probe the magnetic anisotropy and anisotropic magnetoresistance at 4.2 K by means of angle-dependent magnetotransport. Whereas the transverse-resistivity parameters are nearly unaffected by the magnetic field, the parameters describing the longitudinal resistivity are strongly field dependent.

On deformation of complex continuum immersed in a plane space

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present paper is devoted to mathematical modelling of complex continua deformations considered as immersed in an external plane space. The complex continuum is defined as a differential manifold supplied with metrics induced by the external space. A systematic derivation of strain tensors by notion of isometric immersion of the complex continuum into a plane space of a higher dimension is proposed. Problem of establishing complete systems of irreducible objective strain and extrastrain tensors for complex continuum immersed in an external plane space is resolved. The solution to the problem is obtained by methods of the field theory and the theory of rational algebraic invariants. Strain tensors of the complex continuum are derived as irreducible algebraic invariants of contravariant vectors of the external space emerging as functional arguments in the complex continuum action density. Present analysis is restricted to rational algebraic invariants. Completeness of the considered systems of rational algebraic invariants is established for micropolar elastic continua. Rational syzygies for non-quadratic invariants are discussed. Objective strain tensors (indifferent to frame rotations in the external plane space) for micropolar continuum are alternatively obtained by properly combining multipliers of polar decompositions of deformation and extra-deformation gradients. The latter is realized only for continua immersed in a plane space of the equal mathematical dimension.

Calculation and Analysis of Magnetic Gradient Tensor Components of Global Magnetic Models

NASA Astrophysics Data System (ADS)

Schiffler, M.; Queitsch, M.; Schneider, M.; Goepel, A.; Stolz, R.; Krech, W.; Meyer, H. G.; Kukowski, N.

2014-12-01

Global Earth's magnetic field models like the International Geomagnetic Reference Field (IGRF), the World Magnetic Model (WMM) or the High Definition Geomagnetic Model (HDGM) are harmonic analysis regressions to available magnetic observations stored as spherical harmonic coefficients. Input data combine recordings from magnetic observatories, airborne magnetic surveys and satellite data. The advance of recent magnetic satellite missions like SWARM and its predecessors like CHAMP offer high resolution measurements while providing a full global coverage. This deserves expansion of the theoretical framework of harmonic synthesis to magnetic gradient tensor components. Measurement setups for Full Tensor Magnetic Gradiometry equipped with high sensitive gradiometers like the JeSSY STAR system can directly measure the gradient tensor components, which requires precise knowledge about the background regional gradients which can be calculated with this extension. In this study we develop the theoretical framework for calculation of the magnetic gradient tensor components from the harmonic series expansion and apply our approach to the IGRF and HDGM. The gradient tensor component maps for entire Earth's surface produced for the IGRF show low gradients reflecting the variation from the dipolar character, whereas maps for the HDGM (up to degree N=729) reveal new information about crustal structure, especially across the oceans, and deeply situated ore bodies. From the gradient tensor components, the rotational invariants, the Eigenvalues, and the normalized source strength (NSS) are calculated. The NSS focuses on shallower and stronger anomalies. Euler deconvolution using either the tensor components or the NSS applied to the HDGM reveals an estimate of the average source depth for the entire magnetic crust as well as individual plutons and ore bodies. The NSS reveals the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

Strain Characterization and Microstructure Evolution Under Deformation in 2060 Alloy

NASA Astrophysics Data System (ADS)

Jin, X.; Zhang, G. D.; Zhao, Y. F.; Xue, F.

2018-05-01

A new method of DIC combined with EBSD is developed for the characterization of strain and microstructure evolution during bending. The traditional microhardness point and DIC methods are used to study the microstructure evolution in 2060 alloy during bending; the interested area suffers under tensile stress, the microstructure evolution is collected by SEM, EBSD, digital image correlation (DIC) method during bending. The results shows that the DIC method can both realize the strain tensor characterization of the interested area, and can also express the local strain tensor in the micro-area even more. The degree of grain division in the process of deformation is related to the strain in this region; the grains have larger strain of small angle grain boundary (SLGBs), which results in a new micro-organizational structure. The misorientation is smaller with larger strain degree while the misorientation is larger with smaller strain.

Relativistic interpretation of the nature of the nuclear tensor force

NASA Astrophysics Data System (ADS)

Zong, Yao-Yao; Sun, Bao-Yuan

2018-02-01

The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

Implementation and application of a gradient enhanced crystal plasticity model

NASA Astrophysics Data System (ADS)

Soyarslan, C.; Perdahcıoǧlu, E. S.; Aşık, E. E.; van den Boogaard, A. H.; Bargmann, S.

2017-10-01

A rate-independent crystal plasticity model is implemented in which description of the hardening of the material is given as a function of the total dislocation density. The evolution of statistically stored dislocations (SSDs) is described using a saturating type evolution law. The evolution of geometrically necessary dislocations (GNDs) on the other hand is described using the gradient of the plastic strain tensor in a non-local manner. The gradient of the incremental plastic strain tensor is computed explicitly during an implicit FE simulation after each converged step. Using the plastic strain tensor stored as state variables at each integration point and an efficient numerical algorithm to find the gradients, the GND density is obtained. This results in a weak coupling of the equilibrium solution and the gradient enhancement. The algorithm is applied to an academic test problem which considers growth of a cylindrical void in a single crystal matrix.

Estimating locations and total magnetization vectors of compact magnetic sources from scalar, vector, or tensor magnetic measurements through combined Helbig and Euler analysis

USGS Publications Warehouse

Phillips, J.D.; Nabighian, M.N.; Smith, D.V.; Li, Y.

2007-01-01

The Helbig method for estimating total magnetization directions of compact sources from magnetic vector components is extended so that tensor magnetic gradient components can be used instead. Depths of the compact sources can be estimated using the Euler equation, and their dipole moment magnitudes can be estimated using a least squares fit to the vector component or tensor gradient component data. ?? 2007 Society of Exploration Geophysicists.

BOOK REVIEW: Nonlinear Continuum Mechanics for Finite Element Analysis

NASA Astrophysics Data System (ADS)

Bialek, James M.

1998-05-01

Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when finite motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the finite element method is a very important field. Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered. This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (Lagrangian) and spatial (Eulerian) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy-Green tensors, the Eulerian or Almansi strain tensor, distortional components, strain rate tensors, rate of deformation tensors, spin tensors and objectivity. The standard Cauchy stress tensor is mentioned in passing, and then virtual work and work conjugacy lead to alternative stress representations such as the Piola-Kirchoff representation. Chapter 5 concentrates on hyperelasticity (where stresses are derived from a stored energy function) and its subvarieties. Chapter 6 proceeds by linearizing the virtual work statement prior to discretization and Chapter 7 deals with approaches to solving the formulation. In Chapter 8 the FORTRAN finite element code written by Bonet (available via the world wide web) is described. In summary this book is written by experts, for future experts, and provides a very fast review of the field for people who already know the topic. The authors assume the reader is familiar with `elementary stress analysis' and has had some exposure to `the principle of the finite element method'. Their goals are summarized by the statement, `If the reader is prepared not to get too hung up on details, it is possible to use the book to obtain a reasonable overview of the subject'. This is a very nice summary of what is going on in the field but as a stand-alone text it is much too terse. The total bibliography is a page and a half. It would be an improvement if there were that much reference material for each chapter.

Anisotropic chemical strain in cubic ceria due to oxygen-vacancy-induced elastic dipoles.

PubMed

Das, Tridip; Nicholas, Jason D; Sheldon, Brian W; Qi, Yue

2018-06-06

Accurate characterization of chemical strain is required to study a broad range of chemical-mechanical coupling phenomena. One of the most studied mechano-chemically active oxides, nonstoichiometric ceria (CeO2-δ), has only been described by a scalar chemical strain assuming isotropic deformation. However, combined density functional theory (DFT) calculations and elastic dipole tensor theory reveal that both the short-range bond distortions surrounding an oxygen-vacancy and the long-range chemical strain are anisotropic in cubic CeO2-δ. The origin of this anisotropy is the charge disproportionation between the four cerium atoms around each oxygen-vacancy (two become Ce3+ and two become Ce4+) when a neutral oxygen-vacancy is formed. Around the oxygen-vacancy, six of the Ce3+-O bonds elongate, one of the Ce3+-O bond shorten, and all seven of the Ce4+-O bonds shorten. Further, the average and maximum chemical strain values obtained through tensor analysis successfully bound the various experimental data. Lastly, the anisotropic, oxygen-vacancy-elastic-dipole induced chemical strain is polarizable, which provides a physical model for the giant electrostriction recently discovered in doped and non-doped CeO2-δ. Together, this work highlights the need to consider anisotropic tensors when calculating the chemical strain induced by dilute point defects in all materials, regardless of their symmetry.

Simulation of Strain Induced Pseudomagnetic Fields in Graphene Suspended on MEMS Chevron Actuators

NASA Astrophysics Data System (ADS)

Vutukuru, Mounika; Christopher, Jason; Bishop, David; Swan, Anna

Graphene has been shown to withstand remarkable levels of mechanical strain an order of magnitude larger than bulk crystalline materials. This exceptional stretchability of graphene allows for the direct tuning of fundamental material properties, as well as for the investigation of novel physics such as generation of strain induced pseudomagnetic fields. However, current methods for strain such as polymer elongation or pressurized wells do not integrate well into devices. We propose microelectromechanical (MEMS) Chevron actuators as a reliable platform for applying strain to graphene. In addition to their advantageous controllable output force, low input power and ease of integration into existing technologies, MEMS allow for different strain orientations to optimize pseudomagnetic field generation in graphene. Here, we model nonuniform strain in suspended graphene on Chevron actuators using COMSOL Multiphysics. By simulating the deformation of the graphene geometry under the device actuation, we explore the pseudomagnetic field map induced by numerically calculating the components of the strain tensor. Our models provide the theoretical framework with which experimental analysis is compared, and optimize our MEMS designs for further exploration of novel physics in graphene. The authors would like to thank NSF DMR 1411008 for their support on this project.

Distribution function of random strains in an elastically anisotropic continuum and defect strengths of T m3 + impurity ions in crystals with zircon structure

NASA Astrophysics Data System (ADS)

Malkin, B. Z.; Abishev, N. M.; Baibekov, E. I.; Pytalev, D. S.; Boldyrev, K. N.; Popova, M. N.; Bettinelli, M.

2017-07-01

We construct a distribution function of the strain-tensor components induced by point defects in an elastically anisotropic continuum, which can be used to account quantitatively for many effects observed in different branches of condensed matter physics. Parameters of the derived six-dimensional generalized Lorentz distribution are expressed through the integrals computed over the array of strains. The distribution functions for the cubic diamond and elpasolite crystals and tetragonal crystals with the zircon and scheelite structures are presented. Our theoretical approach is supported by a successful modeling of specific line shapes of singlet-doublet transitions of the T m3 + ions doped into AB O4 (A =Y , Lu; B =P , V) crystals with zircon structure, observed in high-resolution optical spectra. The values of the defect strengths of impurity T m3 + ions in the oxygen surroundings, obtained as a result of this modeling, can be used in future studies of random strains in different rare-earth oxides.

Shear, principal, and equivalent strains in equal-channel angular deformation

NASA Astrophysics Data System (ADS)

Xia, K.; Wang, J.

2001-10-01

The shear and principal strains involved in equal channel angular deformation (ECAD) were analyzed using a variety of methods. A general expression for the total shear strain calculated by integrating infinitesimal strain increments gave the same result as that from simple geometric considerations. The magnitude and direction of the accumulated principal strains were calculated based on a geometric and a matrix algebra method, respectively. For an intersecting angle of π/2, the maximum normal strain is 0.881 in the direction at π/8 (22.5 deg) from the longitudinal direction of the material in the exit channel. The direction of the maximum principal strain should be used as the direction of grain elongation. Since the principal direction of strain rotates during ECAD, the total shear strain and principal strains so calculated do not have the same meaning as those in a strain tensor. Consequently, the “equivalent” strain based on the second invariant of a strain tensor is no longer an invariant. Indeed, the equivalent strains calculated using the total shear strain and that using the total principal strains differed as the intensity of deformation increased. The method based on matrix algebra is potentially useful in mathematical analysis and computer calculation of ECAD.

Cine phase contrast MRI to measure continuum Lagrangian finite strain fields in contracting skeletal muscle.

PubMed

Zhou, Hehe; Novotny, John E

2007-01-01

To measure the complex mechanics and Lagrangian finite strain of contracting human skeletal muscle in vivo with cine phase contrast MRI (CPC-MRI) applied to the human supraspinatus muscle of the shoulder. Processing techniques are applied to transform velocities from CPC-MRI images to displacements and planar Lagrangian finite strain. An interpolation method describing the continuity of the velocity field and forward-backward and Fourier transform methods were used to track the displacement of regions of interest during a cyclic abduction motion of a subject's arm. The components of the Lagrangian strain tensor were derived during the motion and principal and maximum in-plane shear strain fields calculated. Derived displacement and strain fields are shown that describe the contraction mechanics of the supraspinatus. Strains vary over time during the cyclic motion and are highly nonuniform throughout the muscle. This method presented overcomes the physical resolution of the MRI scanner, which is crucial for the detection of detailed information within muscles, such as the changes that might occur with partial tears of the supraspinatus. These can then be used as input or validation data for modeling human skeletal muscle.

Current density tensors

NASA Astrophysics Data System (ADS)

Lazzeretti, Paolo

2018-04-01

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

Full-wave Moment Tensor and Tomographic Inversions Based on 3D Strain Green Tensor

DTIC Science & Technology

2010-01-31

propagation in three-dimensional (3D) earth, linearizes the inverse problem by iteratively updating the earth model , and provides an accurate way to...self-consistent FD-SGT databases constructed from finite-difference simulations of wave propagation in full-wave tomographic models can be used to...determine the moment tensors within minutes after a seismic event, making it possible for real time monitoring using 3D models . 15. SUBJECT TERMS

Rheologic effects of crystal preferred orientation in upper mantle flow near plate boundaries

NASA Astrophysics Data System (ADS)

Blackman, Donna; Castelnau, Olivier; Dawson, Paul; Boyce, Donald

2016-04-01

Observations of anisotropy provide insight into upper mantle processes. Flow-induced mineral alignment provides a link between mantle deformation patterns and seismic anisotropy. Our study focuses on the rheologic effects of crystal preferred orientation (CPO), which develops during mantle flow, in order to assess whether corresponding anisotropic viscosity could significantly impact the pattern of flow. We employ a coupled nonlinear numerical method to link CPO and the flow model via a local viscosity tensor field that quantifies the stress/strain-rate response of a textured mineral aggregate. For a given flow field, the CPO is computed along streamlines using a self-consistent texture model and is then used to update the viscosity tensor field. The new viscosity tensor field defines the local properties for the next flow computation. This iteration produces a coupled nonlinear model for which seismic signatures can be predicted. Results thus far confirm that CPO can impact flow pattern by altering rheology in directionally-dependent ways, particularly in regions of high flow gradient. Multiple iterations run for an initial, linear stress/strain-rate case (power law exponent n=1) converge to a flow field and CPO distribution that are modestly different from the reference, scalar viscosity case. Upwelling rates directly below the spreading axis are slightly reduced and flow is focused somewhat toward the axis. Predicted seismic anisotropy differences are modest. P-wave anisotropy is a few percent greater in the flow 'corner', near the spreading axis, below the lithosphere and extending 40-100 km off axis. Predicted S-wave splitting differences would be below seafloor measurement limits. Calculations with non-linear stress/strain-rate relation, which is more realistic for olivine, indicate that effects are stronger than for the linear case. For n=2-3, the distribution and strength of CPO for the first iteration are greater than for n=1, although the fast seismic axis directions are similar. The greatest difference in CPO for the nonlinear cases develop at the flow 'corner' at depths of 10-30 km and 20-100 km off-axis. J index values up to 10% greater than the linear case are predicted near the lithosphere base in that region. Viscosity tensor components are notably altered in the nonlinear cases. Iterations between the texture and flow calculations for the non-linear cases are underway this winter; results will be reported in the presentation.

Projector Augmented-Wave formulation of response to strain and electric field perturbation within the density-functional perturbation theory

NASA Astrophysics Data System (ADS)

Martin, Alexandre; Torrent, Marc; Caracas, Razvan

2015-03-01

A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.

Seismic Strain Field in Taiwan

NASA Astrophysics Data System (ADS)

Kao, H.; Liang, W.; Chang, T.; Liu, Y.; Lee, E.

2001-12-01

Centroid-moment-tensor (CMT) solutions determined by inverting waveform data of Broadband Array in Taiwan for Seismology (BATS) are collected for earthquakes that occurred in the Taiwan region. In total, the dataset contains more than 300 events that scattered across an area of 400 km by 400 km, including the devastating 1999 Chi-Chi earthquake sequence. The entire region is divided into 3 layers (0-40 km, 40-70 km, and greater than 70 km) with blocks of 0.2 degree by 0.2 degree in lateral dimension. Seismic moment tensors of all earthquakes that occurred inside each block are summed to give the strain tensor characterizing the corresponding seismic deformation. We calculate the eigenvalues and eigenvectors of the resulted strain tensor for each block and project the normalized maximum compressional (P) and extensional (T) axes on horizontal plane to resolve the strain field in Taiwan associated with regional seismic activities. For the majority of events with depths less than 40 km (i.e., at crustal scale), the strain field is characterized by nearly E-W compression along the eastern coastline and immediately offshore east of Taiwan. Once inland, clear fan-shaped trajectories of P-axes are observed, ranging from NW-SE in the northwest to NE-SW in the southwest. The Ryukyu and Luzon subduction systems show compression in the forearc region and extension in the backarc and outerrise regions. For depths greater than 40 km, a clear pattern of lateral compression is observed within the subducted Philippine Sea plate to the northeast of Taiwan. It is doubtless that the "slab-continent" collision is predominant at deeper depths near the junction between the Ryukyu arc and Taiwan Collision Zone, whereas the "arc-continent" collision is predominant in the central and southern Taiwan.

An Expedient but Fascinating Geophysical Chimera: The Pinyon Flat Seismic Strain Point Array

NASA Astrophysics Data System (ADS)

Langston, C. A.

2016-12-01

The combination of a borehole Gladwin Tensor Strain Meter (GTSM) and a co-located three component broadband seismometer (BB) can theoretically be used to determine the propagation attributes of P-SV waves in vertically inhomogeneous media such as horizontal phase velocity and azimuth of propagation through application of wave gradiometry. A major requirement for this to be successful is to have well-calibrated strain and seismic sensors to be able to rely on using absolute wave amplitude from both systems. A "point" seismic array is constructed using the PBO GTSM station B084 and co-located BB seismic stations from an open array experiment deployed by UCSD as well as PFO station at the Pinyon Flat facility. Site amplitude statics for all three ground motion components are found for the 14-element (13 PY stations + PFO), small aperture seismic array using data from 47 teleseisms recorded from 2014 until present. Precision of amplitude measurement at each site is better than 0.2% for vertical components, 0.5% for EW components, and 1% for NS components. Relative amplitudes among sites of the array are often better than 1% attesting to the high quality of the instrumentation and installation. The wavefield and related horizontal strains are computed for the location of B084 using a second order Taylor's expansion of observed waveforms from moderate ( M4) regional events. The computed seismic array areal, differential, and shear strains show excellent correlation in both phase and amplitude with those recorded by B084 when using the calibration matrix previously determined using teleseismic strains from the entire ANZA seismic network. Use of the GTSM-BB "point" array significantly extends the bandwidth of gradiometry calculations over the small-aperture seismic array by nearly two orders of magnitude from 0.5 Hz to 0.01 Hz. In principle, a seismic strain point array could be constructed from every PBO GTSM with a co-located seismometer to help serve earthquake early warning for large regional events on North America's west coast.

Defects in Nonlinear Elastic Crystals: Differential Geometry, Finite Kinematics, and Second-Order Analytical Solutions

DTIC Science & Technology

2015-04-01

of unit length: da = F L a αδ α Ad A , da = F L−1αaδ A α dA . (2.12) The metric tensor associated with the deformed... A spatial density tensor θ and Frank vector ω̂ of the following forms are consistent with geometry of the problem: θ = θzzgz ⊗ gz = ω̂δ(r)gz ⊗ gz = δ...stress depends quadratically on strain, with the elastic potential cubic in strain and including elastic constants of

On the Prediction of Mechanical Behavior of Particulate Composites Using an Improved Mori-Tanaka Method

DTIC Science & Technology

1997-01-01

perturbed strain, [L/ L] P501263.PDF [Page: 12 of 122] UNCLASSIFIED viii €~j constrained strain, [L/ L] €£j eigenstrain , [L/ L] €£J c corrected... eigenstrain of phase-r material, [L/ L] £iJ u uncorrected eigenstrain of phase~r material, [L/ L] fijkl correction matrix of phase-r material... eigenstrains , [2] wher·e St.jkl is known as the Eshelby tensor. The tensor is a function of the matrix Poisson ratio and the shape of the inclusion

Micro-Stress Bound Estimate Enabled Optimization of Structural Composite Repair for the Next Generation Aircraft

DTIC Science & Technology

2007-02-28

where they exhibited the maximum values, which were the midsurface and 0/-0 surface for two laminates with 0=150 and 0=400. a) 50000 40000 - 0 30000...the first and second invariants of the strain tensor calculated at the midsurface in the x=O cross section as a function of distance from the hole edge...Y Figure 7. Comparison of the distributions of strain tensor invariants predicted in the matrix phase at the midsurface at x=0 as a function of

Simple Derivation of the Maxwell Stress Tensor and Electrostrictive Effects in Crystals

ERIC Educational Resources Information Center

Juretschke, H. J.

1977-01-01

Shows that local equilibrium and energy considerations in an elastic dielectric crystal lead to a simple derivation of the Maxwell stress tensor in anisotropic dielectric solids. The resulting equilibrium stress-strain relations are applied to determine the deformations of a charged parallel plate capacitor. (MLH)

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2003-01-01

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins.

PubMed

Ghose, R; Fushman, D; Cowburn, D

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand. Copyright 2001 Academic Press.

Determination of the Rotational Diffusion Tensor of Macromolecules in Solution from NMR Relaxation Data with a Combination of Exact and Approximate Methods—Application to the Determination of Interdomain Orientation in Multidomain Proteins

NASA Astrophysics Data System (ADS)

Ghose, Ranajeet; Fushman, David; Cowburn, David

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.

Calculation and Analysis of magnetic gradient tensor components of global magnetic models

NASA Astrophysics Data System (ADS)

Schiffler, Markus; Queitsch, Matthias; Schneider, Michael; Stolz, Ronny; Krech, Wolfram; Meyer, Hans-Georg; Kukowski, Nina

2014-05-01

Magnetic mapping missions like SWARM and its predecessors, e.g. the CHAMP and MAGSAT programs, offer high resolution Earth's magnetic field data. These datasets are usually combined with magnetic observatory and survey data, and subject to harmonic analysis. The derived spherical harmonic coefficients enable magnetic field modelling using a potential series expansion. Recently, new instruments like the JeSSY STAR Full Tensor Magnetic Gradiometry system equipped with very high sensitive sensors can directly measure the magnetic field gradient tensor components. The full understanding of the quality of the measured data requires the extension of magnetic field models to gradient tensor components. In this study, we focus on the extension of the derivation of the magnetic field out of the potential series magnetic field gradient tensor components and apply the new theoretical framework to the International Geomagnetic Reference Field (IGRF) and the High Definition Magnetic Model (HDGM). The gradient tensor component maps for entire Earth's surface produced for the IGRF show low values and smooth variations reflecting the core and mantle contributions whereas those for the HDGM gives a novel tool to unravel crustal structure and deep-situated ore bodies. For example, the Thor Suture and the Sorgenfrei-Thornquist Zone in Europe are delineated by a strong northward gradient. Derived from Eigenvalue decomposition of the magnetic gradient tensor, the scaled magnetic moment, normalized source strength (NSS) and the bearing of the lithospheric sources are presented. The NSS serves as a tool for estimating the lithosphere-asthenosphere boundary as well as the depth of plutons and ore bodies. Furthermore changes in magnetization direction parallel to the mid-ocean ridges can be obtained from the scaled magnetic moment and the normalized source strength discriminates the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

2002-01-01

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Study of the velocity gradient tensor in turbulent flow

NASA Technical Reports Server (NTRS)

Cheng, Wei-Ping; Cantwell, Brian

1996-01-01

The behavior of the velocity gradient tensor, A(ij)=delta u(i)/delta x(j), was studied using three turbulent flows obtained from direct numerical simulation The flows studies were: an inviscid calculation of the interaction between two vortex tubes, a homogeneous isotropic flow, and a temporally evolving planar wake. Self-similar behavior for each flow was obtained when A(ij) was normalized with the mean strain rate. The case of the interaction between two vortex tubes revealed a finite sized coherent structure with topological characteristics predictable by a restricted Euler model. This structure was found to evolve with the peak vorticity as the flow approached singularity. Invariants of A(ij) within this structure followed a straight line relationship of the form: gamma(sup 3)+gammaQ+R=0, where Q and R are the second and third invariants of A(ij), and the eigenvalue gamma is nearly constant over the volume of this structure. Data within this structure have local strain topology of unstable-node/saddle/saddle. The characteristics of the velocity gradient tensor and the anisotropic part of a related acceleration gradient tensor H(ij) were also studied for a homogeneous isotropic flow and a temporally evolving planar wake. It was found that the intermediate principal eigenvalue of the rate-of-strain tensor of H(ij) tended to be negative, with local strain topology of the type stable-node/saddle/saddle. There was also a preferential eigenvalue direction. The magnitude of H(ij) in the wake flow was found to be very small when data were conditioned at high local dissipation regions. This result was not observed in the relatively low Reynolds number simulation of homogeneous isotropic flow. A restricted Euler model of the evolution of A(ij) was found to reproduce many of the topological features identified in the simulations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klima, Matej; Kucharik, MIlan; Shashkov, Mikhail Jurievich

We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables.more » We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J 2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J 2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.« less

Right Ventricular Strain, Torsion, and Dyssynchrony in Healthy Subjects using 3D Spiral Cine DENSE Magnetic Resonance Imaging

PubMed Central

Suever, Jonathan D; Wehner, Gregory J; Jing, Linyuan; Powell, David K; Hamlet, Sean M; Grabau, Jonathan D; Mojsejenko, Dimitri; Andres, Kristin N; Haggerty, Christopher M; Fornwalt, Brandon K

2017-01-01

Mechanics of the left ventricle (LV) are important indicators of cardiac function. The role of right ventricular (RV) mechanics is largely unknown due to the technical limitations of imaging its thin wall and complex geometry and motion. By combining 3D Displacement Encoding with Stimulated Echoes (DENSE) with a post-processing pipeline that includes a local coordinate system, it is possible to quantify RV strain, torsion, and synchrony. In this study, we sought to characterize RV mechanics in 50 healthy individuals and compare these values to their LV counterparts. For each cardiac frame, 3D displacements were fit to continuous and differentiable radial basis functions, allowing for the computation of the 3D Cartesian Lagrangian strain tensor at any myocardial point. The geometry of the RV was extracted via a surface fit to manually delineated endocardial contours. Throughout the RV, a local coordinate system was used to transform from a Cartesian strain tensor to a polar strain tensor. It was then possible to compute peak RV torsion as well as peak longitudinal and circumferential strain. A comparable analysis was performed for the LV. Dyssynchrony was computed from the standard deviation of regional activation times. Global circumferential strain was comparable between the RV and LV (−18.0% for both) while longitudinal strain was greater in the RV (−18.1% vs. −15.7%). RV torsion was comparable to LV torsion (6.2 vs. 7.1 degrees, respectively). Regional activation times indicated that the RV contracted later but more synchronously than the LV. 3D spiral cine DENSE combined with a post–processing pipeline that includes a local coordinate system can resolve both the complex geometry and 3D motion of the RV. PMID:28055859

Efficient Computation of Anharmonic Force Constants via q-space, with Application to Graphene

NASA Astrophysics Data System (ADS)

Kornbluth, Mordechai; Marianetti, Chris

We present a new approach for extracting anharmonic force constants from a sparse sampling of the anharmonic dynamical tensor. We calculate the derivative of the energy with respect to q-space displacements (phonons) and strain, which guarantees the absence of supercell image errors. Central finite differences provide a well-converged quadratic error tail for each derivative, separating the contribution of each anharmonic order. These derivatives populate the anharmonic dynamical tensor in a sparse mesh that bounds the Brillouin Zone, which ensures comprehensive sampling of q-space while exploiting small-cell calculations for efficient, high-throughput computation. This produces a well-converged and precisely-defined dataset, suitable for big-data approaches. We transform this sparsely-sampled anharmonic dynamical tensor to real-space anharmonic force constants that obey full space-group symmetries by construction. Machine-learning techniques identify the range of real-space interactions. We show the entire process executed for graphene, up to and including the fifth-order anharmonic force constants. This method successfully calculates strain-based phonon renormalization in graphene, even under large strains, which solves a major shortcoming of previous potentials.

An Integrated Tensorial Approach for Quantifying Porous, Fractured Rocks

NASA Astrophysics Data System (ADS)

Healy, David; Rizzo, Roberto; Harland, Sophie; Farrell, Natalie; Browning, John; Meredith, Phil; Mitchell, Tom; Bubeck, Alodie; Walker, Richard

2017-04-01

The patterns of fractures in deformed rocks are rarely uniform or random. Fracture orientations, sizes, shapes and spatial distributions often exhibit some kind of order. In detail, there may be relationships among the different fracture attributes e.g. small fractures dominated by one orientation, and larger fractures by another. These relationships are important because the mechanical (e.g. strength, anisotropy) and transport (e.g. fluids, heat) properties of rock depend on these fracture patterns and fracture attributes. Based on previously published work (Oda, Cowin, Sayers & Kachanov) this presentation describes an integrated tensorial approach to quantifying fracture networks and predicting the key properties of fractured rock: permeability and elasticity (and in turn, seismic velocities). Each of these properties can be represented as tensors, and these entities capture the essential 'directionality', or anisotropy of the property. In structural geology, we are familiar with using tensors for stress and strain, where these concepts incorporate volume averaging of many forces (in the case of the stress tensor), or many displacements (for the strain tensor), to produce more tractable and more computationally efficient quantities. It is conceptually attractive to formulate both the structure (the fracture network) and the structure-dependent properties (permeability, elasticity) in a consistent way with tensors of 2nd and 4th rank, as appropriate. Examples are provided to highlight the interdependence of the property tensors with the geometry of the fracture network. The fabric tensor (or orientation tensor of Scheidegger, Woodcock) describes the orientation distribution of fractures in the network. The crack tensor combines the fabric tensor (orientation distribution) with information about the fracture density and fracture size distribution. Changes to the fracture network, manifested in the values of the fabric and crack tensors, translate into changes in predicted permeability and elasticity (seismic velocity). Conversely, this implies that measured changes in any of the in situ properties or responses in the subsurface (e.g. permeability, seismic velocity) could be used to predict, or at least constrain, the fracture network. Explicitly linking the fracture network geometry to the permeability and elasticity (seismic velocity) through a tensorial formulation provides an exciting and efficient alternative to existing approaches.

Performance Analysis and Experimental Validation of the Direct Strain Imaging Method

Treesearch

Athanasios Iliopoulos; John G. Michopoulos; John C. Hermanson

2013-01-01

Direct Strain Imaging accomplishes full field measurement of the strain tensor on the surface of a deforming body, by utilizing arbitrarily oriented engineering strain measurements originating from digital imaging. In this paper an evaluation of the method’s performance with respect to its operating parameter space is presented along with a preliminary...

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

NASA Technical Reports Server (NTRS)

Zhao, C. Y.; So, R. M. C.; Gatski, T. B.

2001-01-01

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Fine-scale features in the far-field of a turbulent jet

NASA Astrophysics Data System (ADS)

Buxton, Oliver; Ganapathisubramani, Bharathram

2008-11-01

The structure of a fully turbulent axisymmetric jet, at Reynolds number based on jet exit conditions of 5000, is investigated with cinematographic (1 kHz) stereoscopic PIV in a plane normal to the jet axis. Taylor's hypothesis is employed to calculate all three velocity gradients in the axial direction. The technique's resolution allows all terms of the velocity gradient tensor, hence strain rate tensor and kinetic energy dissipation, to be computed at each point within the plane. The data reveals that the vorticity field is dominated by high enstrophy tube-like structures. Conversely, the dissipation field appears to consist of sheet-like structures. Several criteria for isolating these strongly swirling vortical structures from the background turbulence were employed. One such technique involves isolating points in which the velocity gradient tensor has a real and a pair of complex conjugate eigenvectors. Once identified, the alignment of the various structures with relation to the vorticity vector and the real velocity gradient tensor eigenvector is investigated. The effect of the strain field on the geometry of the structures is also examined.

Paleogeodesy of the Southern Santa Cruz Mountains Frontal Thrusts, Silicon Valley, CA

NASA Astrophysics Data System (ADS)

Aron, F.; Johnstone, S. A.; Mavrommatis, A. P.; Sare, R.; Hilley, G. E.

2015-12-01

We present a method to infer long-term fault slip rate distributions using topography by coupling a three-dimensional elastic boundary element model with a geomorphic incision rule. In particular, we used a 10-m-resolution digital elevation model (DEM) to calculate channel steepness (ksn) throughout the actively deforming southern Santa Cruz Mountains in Central California. We then used these values with a power-law incision rule and the Poly3D code to estimate slip rates over seismogenic, kilometer-scale thrust faults accommodating differential uplift of the relief throughout geologic time. Implicit in such an analysis is the assumption that the topographic surface remains unchanged over time as rock is uplifted by slip on the underlying structures. The fault geometries within the area are defined based on surface mapping, as well as active and passive geophysical imaging. Fault elements are assumed to be traction-free in shear (i.e., frictionless), while opening along them is prohibited. The free parameters in the inversion include the components of the remote strain-rate tensor (ɛij) and the bedrock resistance to channel incision (K), which is allowed to vary according to the mapped distribution of geologic units exposed at the surface. The nonlinear components of the geomorphic model required the use of a Markov chain Monte Carlo method, which simulated the posterior density of the components of the remote strain-rate tensor and values of K for the different mapped geologic units. Interestingly, posterior probability distributions of ɛij and K fall well within the broad range of reported values, suggesting that the joint use of elastic boundary element and geomorphic models may have utility in estimating long-term fault slip-rate distributions. Given an adequate DEM, geologic mapping, and fault models, the proposed paleogeodetic method could be applied to other crustal faults with geological and morphological expressions of long-term uplift.

Advanced Computational Techniques in Regional Wave Studies

DTIC Science & Technology

1990-01-03

UiNCL.ASSIriEDIUNLIMITED C SAME AS RPT. C DTIC USERS CUNCLASSIFIED ; a 𔃾AM OF RE.;PONSIBL- E INOIVIDIJAL 22D. TELEPHCNE NUMBER 22c. OFFICE SYMBOL...this system is right We define the components of the time dependent force handed). Then, e ,, e ., and e , are the unit vectors moment tensor as towards...are constants representing the components of the 1 , ,( ,, - second order seismic moment tensor M, usually termed , M,- "(x,/,,t ,( E ,’ the moment tensor

Full Moment Tensor Analysis Using First Motion Data at The Geysers Geothermal Field

NASA Astrophysics Data System (ADS)

Boyd, O.; Dreger, D. S.; Lai, V. H.; Gritto, R.

2012-12-01

Seismicity associated with geothermal energy production at The Geysers Geothermal Field in northern California has been increasing during the last forty years. We investigate source models of over fifty earthquakes with magnitudes ranging from Mw 3.5 up to Mw 4.5. We invert three-component, complete waveform data from broadband stations of the Berkeley Digital Seismic Network, the Northern California Seismic Network and the USA Array deployment (2005-2007) for the complete, six-element moment tensor. Some solutions are double-couple while others have substantial non-double-couple components. To assess the stability and significance of non-double-couple components, we use a suite of diagnostic tools including the F-test, Jackknife test, bootstrap and network sensitivity solution (NSS). The full moment tensor solutions of the studied events tend to plot in the upper half of the Hudson source type diagram where the fundamental source types include +CLVD, +LVD, tensile-crack, DC and explosion. Using the F-test to compare the goodness-of-fit values between the full and deviatoric moment tensor solutions, most of the full moment tensor solutions do not show a statistically significant improvement in fit over the deviatoric solutions. Because a small isotropic component may not significantly improve the fit, we include first motion polarity data to better constrain the full moment tensor solutions.

Modeling the pressure-strain correlation of turbulence: An invariant dynamical systems approach

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu; Gatski, Thomas B.

1990-01-01

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Modelling the pressure-strain correlation of turbulence - An invariant dynamical systems approach

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu; Gatski, Thomas B.

1991-01-01

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Fluid-Structure Interaction in Continuum Models of Bacterial Biofilms

NASA Astrophysics Data System (ADS)

Hicks, Jared A.

Bacterial biofilms are aggregates of cells that adhere to nearly any solid-fluid interface. While many have harmful effects, such as industrial damage and nosocomial infections, certain biofilm species are now generating renewable energy as the fundamental components of Microbial Fuel Cells (MFCs). In an MFC, bacteria consume organic waste and, as they respire, produce free electrons. To do so efficiently, the bacteria must operate at peak metabolic activity, and so require an ample supply of nutrients. But existing MFC systems face several nutrient delivery problems, including clogging and downstream depletion. Ameliorating these problems will require a better understanding of the interplay between structural development and the surrounding fluid flow. In addition to delivering nutrients that affect biofilm growth, the fluid also exerts stresses that cause erosion, detachment, and deformation. These structural changes, in turn, affect the flow and alter the nutrient distribution. To account for this feedback effect, I have developed a continuum model that couples the growth and deformation processes. My model augments an existing growth model with evolution equations derived from Morphoelasticity Theory, by showing that the growth tensor can be directly related to the biofilm velocity potential. This result helps overcome one of the major practical limitations of Morphoelasticity--there is no physical framework for specifying the growth tensor. Through further analysis of the growth tensor, I define the related adjugate and anisotropic growth tensors, which can be more meaningful measures of growth for some models. Under the assumption of small strain, I show that there exists a small correction to the biofilm growth velocity (the accommodation velocity) that represents the effect of the elastic response on the evolution of the biofilm shape. I derive a solvability condition for the accommodation velocity, and show that it leads to a novel evolution equation for stress and strain in the biofilm, which couples the growth and deformation processes. Furthermore, I show that the introduction of a vorticity allows the accommodation velocity to be described by a system of Poisson equations, and that this vorticity arises naturally from Morphoelasticity theory and is related to the velocity solvability condition. I apply the modeling approach to a one-dimensional biofilm, and show that (a) the coupled growth process affects the evolution of the biofilm shape as expected, and (b) a non-coupled approach to biofilm strain introduces an error that grows over time. Numerical analysis of the one-dimensional strain evolution equation leads to several insights that inform the development of numerical methods for the two-dimensional case, including a split-step approach that reduces the fifth-order PDE to an advection equation for strain and a biharmonic equation for stress. Finally, I discuss some useful numerical methods for the simulation of elastic biofilm growth, particularly the discretization of the strain evolution equation(s). My overall approach is to track the evolving biofilm surface using a combination of the level-set method coupled with the eXtended Finite Element Method (XFEM). The major result is a novel mixed-XFEM discretization of the clamped-plate biharmonic equation, which I show to be first-order accurate for the trace of the solution on the interface.

Advanced Magnetic Resonance Imaging techniques to probe muscle structure and function

NASA Astrophysics Data System (ADS)

Malis, Vadim

Structural and functional Magnetic Resonance Imaging (MRI) studies of skeletal muscle allow the elucidation of muscle physiology under normal and pathological conditions. Continuing on the efforts of the Muscle Imaging and Modeling laboratory, the focus of the thesis is to (i) extend and refine two challenging imaging modalities: structural imaging using Diffusion Tensor Imaging (DTI) and functional imaging based on Velocity Encoded Phase Contrast Imaging (VE-PC) and (ii) apply these methods to explore age related structure and functional differences of the gastrocnemius muscle. Diffusion Tensor Imaging allows the study of tissue microstructure as well as muscle fiber architecture. The images, based on an ultrafast single shot Echo Planar Imaging (EPI) sequence, suffer from geometric distortions and low signal to noise ratio. A processing pipeline was developed to correct for distortions and to improve image Signal to Noise Ratio (SNR). DTI acquired on a senior and young cohort of subjects were processed through the pipeline and differences in DTI derived indices and fiber architecture between the two cohorts were explored. The DTI indices indicated that at the microstructural level, fiber atrophy was accompanied with a reduction in fiber volume fraction. At the fiber architecture level, fiber length and pennation angles decreased with age that potentially contribute to the loss of muscle force with age. Velocity Encoded Phase Contrast imaging provides tissue (e.g. muscle) velocity at each voxel which allows the study of strain and Strain Rate (SR) under dynamic conditions. The focus of the thesis was to extract 2D strain rate tensor maps from the velocity images and apply the method to study age related differences. The tensor mapping can potentially provide unique information on the extracellular matrix and lateral transmission the role of these two elements has recently emerged as important determinants of force loss with age. In the cross sectional study on aging, strain rate during isometric contraction was significantly reduced in the seniors; presumably from decrease in muscle slack and increase in stiffness with age. Other parameters of interest from this study that allow inferences on the ECM and lateral transmission are the asymmetry of deformation in the fiber cross section as well as the angle between the SR and muscle fiber. The last part of thesis, which is a 'work-in-progress', is the extension to 3D SR tensor mapping using a 3D spatial, 3D velocity encoded imaging sequence. This is combined with Diffusion Tensor Imaging to obtain the lead eigenvector (muscle fiber direction) at each voxel. The 3D SR is then rotated to the basis of the DTI to obtain a 'Fiber Aligned Strain rate: FASR'. The off diagonal elements of FASR are shear strain terms. Detailed analysis of the shear strain will provide a unique non-invasive method to probe lateral transmission.

Finite-frequency structural sensitivities of short-period compressional body waves

NASA Astrophysics Data System (ADS)

Fuji, Nobuaki; Chevrot, Sébastien; Zhao, Li; Geller, Robert J.; Kawai, Kenji

2012-07-01

We present an extension of the method recently introduced by Zhao & Chevrot for calculating Fréchet kernels from a precomputed database of strain Green's tensors by normal mode summation. The extension involves two aspects: (1) we compute the strain Green's tensors using the Direct Solution Method, which allows us to go up to frequencies as high as 1 Hz; and (2) we develop a spatial interpolation scheme so that the Green's tensors can be computed with a relatively coarse grid, thus improving the efficiency in the computation of the sensitivity kernels. The only requirement is that the Green's tensors be computed with a fine enough spatial sampling rate to avoid spatial aliasing. The Green's tensors can then be interpolated to any location inside the Earth, avoiding the need to store and retrieve strain Green's tensors for a fine sampling grid. The interpolation scheme not only significantly reduces the CPU time required to calculate the Green's tensor database and the disk space to store it, but also enhances the efficiency in computing the kernels by reducing the number of I/O operations needed to retrieve the Green's tensors. Our new implementation allows us to calculate sensitivity kernels for high-frequency teleseismic body waves with very modest computational resources such as a laptop. We illustrate the potential of our approach for seismic tomography by computing traveltime and amplitude sensitivity kernels for high frequency P, PKP and Pdiff phases. A comparison of our PKP kernels with those computed by asymptotic ray theory clearly shows the limits of the latter. With ray theory, it is not possible to model waves diffracted by internal discontinuities such as the core-mantle boundary, and it is also difficult to compute amplitudes for paths close to the B-caustic of the PKP phase. We also compute waveform partial derivatives for different parts of the seismic wavefield, a key ingredient for high resolution imaging by waveform inversion. Our computations of partial derivatives in the time window where PcP precursors are commonly observed show that the distribution of sensitivity is complex and counter-intuitive, with a large contribution from the mid-mantle region. This clearly emphasizes the need to use accurate and complete partial derivatives in waveform inversion.

Triggering of the Ms = 5.4 Little Skull Mountain, Nevada, earthquake with dynamic strains

USGS Publications Warehouse

Gomberg, Joan; Bodin, Paul

1994-01-01

We have developed an approach to test the viability of dynamic strains as a triggering mechanism by quantifying the dynamic strain tensor at seismogenic depths. We focus on the dynamic strains at the hypocenter of the Ms = 5.4 Little Skull Mountain (LSM), Nevada, earthquake. This event is noteworthy because it is the largest earthquake demonstrably triggered at remote distances (∼280 km) by the Ms = 7.4 Landers, California, earthquake and because of its ambiguous association with magmatic activity. Our analysis shows that, if dynamic strains initiate remote triggering, the orientation and modes of faulting most favorable for being triggered by a given strain transient change with depth. The geometry of the most probable LSM fault plane was favorably oriented with respect to the geometry of the dynamic strain tensor. We estimate that the magnitude of the peak dynamic strains at the hypocentral depth of the LSM earthquake were ∼4 μstrain (∼.2 MPa) which are ∼50% smaller than those estimated from velocity seismograms recorded at the surface. We suggest that these strains are too small to cause Mohr-Coulomb style failure unless the fault was prestrained to near failure levels, the fault was exceptionally weak, and/or the dynamic strains trigger other processes that lead to failure.

Simulation of Anisotropic Rock Damage for Geologic Fracturing

NASA Astrophysics Data System (ADS)

Busetti, S.; Xu, H.; Arson, C. F.

2014-12-01

A continuum damage model for differential stress-induced anisotropic crack formation and stiffness degradation is used to study geologic fracturing in rocks. The finite element-based model solves for deformation in the quasi-linear elastic domain and determines the six component damage tensor at each deformation increment. The model permits an isotropic or anisotropic intact or pre-damaged reference state, and the elasticity tensor evolves depending on the stress path. The damage variable, similar to Oda's fabric tensor, grows when the surface energy dissipated by three-dimensional opened cracks exceeds a threshold defined at the appropriate scale of the representative elementary volume (REV). At the laboratory or wellbore scale (<1m) brittle continuum damage reflects microcracking, grain boundary separation, grain crushing, or fine delamination, such as in shale. At outcrop (1m-100m), seismic (10m-1000m), and tectonic (>1000m) scales the damaged REV reflects early natural fracturing (background or tectonic fracturing) or shear strain localization (fault process zone, fault-tip damage, etc.). The numerical model was recently benchmarked against triaxial stress-strain data from laboratory rock mechanics tests. However, the utility of the model to predict geologic fabric such as natural fracturing in hydrocarbon reservoirs was not fully explored. To test the ability of the model to predict geological fracturing, finite element simulations (Abaqus) of common geologic scenarios with known fracture patterns (borehole pressurization, folding, faulting) are simulated and the modeled damage tensor is compared against physical fracture observations. Simulated damage anisotropy is similar to that derived using fractured rock-mass upscaling techniques for pre-determined fracture patterns. This suggests that if model parameters are constrained with local data (e.g., lab, wellbore, or reservoir domain), forward modeling could be used to predict mechanical fabric at the relevant REV scale. This reference fabric also can be used as the starting material property to pre-condition subsequent deformation or fluid flow. Continuing efforts are to expand the present damage model to couple damage evolution with plasticity and with permeability for more geologically realistic simulation.

Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements: Calculation and application

NASA Astrophysics Data System (ADS)

Luo, Yao; Wu, Mei-Ping; Wang, Ping; Duan, Shu-Ling; Liu, Hao-Jun; Wang, Jin-Long; An, Zhan-Feng

2015-09-01

The full magnetic gradient tensor (MGT) refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

NASA Astrophysics Data System (ADS)

Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.

2013-03-01

A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.

Induced vacuum energy-momentum tensor in the background of a cosmic string

NASA Astrophysics Data System (ADS)

Sitenko, Yu A.; Vlasii, N. D.

2012-05-01

A massive scalar field is quantized in the background of a cosmic string which is generalized to a static flux-carrying codimension-2 brane in the locally flat multidimensional spacetime. We find that the finite energy-momentum tensor is induced in the vacuum. The dependence of the tensor components on the brane flux and tension, as well as on the coupling to the spacetime curvature scalar, is comprehensively analyzed. The tensor components are holomorphic functions of space dimension, decreasing exponentially with the distance from the brane. The case of the massless quantized scalar field is also considered, and the relevance of Bernoulli’s polynomials of even order for this case is discussed.

Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate

NASA Technical Reports Server (NTRS)

Carlson, John R.; Gatski, Thomas B.

2002-01-01

A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.

On the origin independence of the Verdet tensor†

NASA Astrophysics Data System (ADS)

Caputo, M. C.; Coriani, S.; Pelloni, S.; Lazzeretti, P.

2013-07-01

The condition for invariance under a translation of the coordinate system of the Verdet tensor and the Verdet constant, calculated via quantum chemical methods using gaugeless basis sets, is expressed by a vanishing sum rule involving a third-rank polar tensor. The sum rule is, in principle, satisfied only in the ideal case of optimal variational electronic wavefunctions. In general, it is not fulfilled in non-variational calculations and variational calculations allowing for the algebraic approximation, but it can be satisfied for reasons of molecular symmetry. Group-theoretical procedures have been used to determine (i) the total number of non-vanishing components and (ii) the unique components of both the polar tensor appearing in the sum rule and the axial Verdet tensor, for a series of symmetry groups. Test calculations at the random-phase approximation level of accuracy for water, hydrogen peroxide and ammonia molecules, using basis sets of increasing quality, show a smooth convergence to zero of the sum rule. Verdet tensor components calculated for the same molecules converge to limit values, estimated via large basis sets of gaugeless Gaussian functions and London orbitals.

Second rank direction cosine spherical tensor operators and the nuclear electric quadrupole hyperfine structure Hamiltonian of rotating molecules

NASA Astrophysics Data System (ADS)

di Lauro, C.

2018-03-01

Transformations of vector or tensor properties from a space-fixed to a molecule-fixed axis system are often required in the study of rotating molecules. Spherical components λμ,ν of a first rank irreducible tensor can be obtained from the direction cosines between the two axis systems, and a second rank tensor with spherical components λμ,ν(2) can be built from the direct product λ × λ. It is shown that the treatment of the interaction between molecular rotation and the electric quadrupole of a nucleus is greatly simplified, if the coefficients in the axis-system transformation of the gradient of the electric field of the outer charges at the coupled nucleus are arranged as spherical components λμ,ν(2). Then the reduced matrix elements of the field gradient operators in a symmetric top eigenfunction basis, including their dependence on the molecule-fixed z-angular momentum component k, can be determined from the knowledge of those of λ(2) . The hyperfine structure Hamiltonian Hq is expressed as the sum of terms characterized each by a value of the molecule-fixed index ν, whose matrix elements obey the rule Δk = ν. Some of these terms may vanish because of molecular symmetry, and the specific cases of linear and symmetric top molecules, orthorhombic molecules, and molecules with symmetry lower than orthorhombic are considered. Each ν-term consists of a contraction of the rotational tensor λ(2) and the nuclear quadrupole tensor in the space-fixed frame, and its matrix elements in the rotation-nuclear spin coupled representation can be determined by the standard spherical tensor methods.

Polymer stress tensor in turbulent shear flows.

PubMed

L'vov, Victor S; Pomyalov, Anna; Procaccia, Itamar; Tiberkevich, Vasil

2005-01-01

The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence, and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number De > 1. We present analytic results for the suppression of the coil-stretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear high-quality "hydroelastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to the cross-stream component of the elastic stress tensor. This component is smaller than the streamwise component by a factor proportional to De2. Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.

Strain Analysis in Horizontal Geodetic Network of Dams for Control of Stability and Monitoring Deformation

NASA Astrophysics Data System (ADS)

Roohi, S.; Ardalan, A. A.; Khodakarami, M.

2009-04-01

Dams as one of the engineering structures play very important role in human life. Because, from primary human needs such as providing drinking water to professional needs such as water powerhouse creation in order to provide power for industrial centers, hospitals, manufactures and agriculture, have considerable dependent on dams. In addition destruction of a dam can be as dangerous as earthquake. Therefore maintenance, stability control and monitoring deformation of them is indispensable. In order to control stability of dams and their around lands and monitoring deformation a network is created by surveyor, geologist and dam experts on crest and body of dam or on land near the dam. Geodetic observations are done in this network by precise surveying instrument in deferent time then by using linear least square parametric adjustment method, adjusted coordinates with their variance- covariance matrix and error ellipses, redundancy numbers for observation, blunders and … are estimated in each epoch. Then displacement vectors are computed in each point of network, After that by use of Lagrangeian deformation idea and constitution of deformation equations movement, displacement model is determined and strain tensor is computed. we can induce deformation information from strain tensor in different ways such as strain ellipse then interpret deformation that happen in each point of network. Also we can compute rigid rotation from anti-symmetric part of displacement gradient tensor. After processing tow consequence epochs observations of horzontal geodetic network of Hnna dam in southwest of Esfahan, the most semi-major axis of error ellipse is estimated about 0.9mm for point D10, largest displacement is 1.4mm for point C3 that it's semimajor axis of displacement error ellipse is 1.3mm and there is different shear in all of network points exceptional points D2,C3 and C2. There is different dilatation in most of points. These amount of maximum shear and dilatation are justified because of horizontal displacement and subsidence of dam due to pressure of water that conserve behind it. Key word: strain tensor, monitoring deformation, Geodetic network, deformation equation movement, error ellipse, strain ellipse, shear, dilatation

ON THE DECOMPOSITION OF STRESS AND STRAIN TENSORS INTO SPHERICAL AND DEVIATORIC PARTS

PubMed Central

Augusti, G.; Martin, J. B.; Prager, W.

1969-01-01

It is well known that Hooke's law for a linearly elastic, isotropic solid may be written in the form of two relations that involve only the spherical or only the deviatoric parts of the tensors of stress and strain. The example of the linearly elastic, transversely isotropic solid is used to show that this decomposition is not, in general, feasible for linearly elastic, anisotropic solids. The discussion is extended to a large class of work-hardening rigid, plastic solids, and it is shown that the considered decomposition can only be achieved for the incompressible solids of this class. PMID:16591754

Nonlinear motion of cantilevered SWNT and Its Meaning to Phonon Dynamics

NASA Astrophysics Data System (ADS)

Koh, Heeyuen; Cannon, James; Chiashi, Shohei; Shiomi, Junichiro; Maruyama, Shigeo

2013-03-01

Based on the finding that the lowest frequency mode of cantilevered SWNT is described by the continuum beam theory in frequency domain, we considered its effect of the symmetric structure for the coupling of orthogonal transverse modes to explain the nonlinear motion of free thermal vibration. This nonlinear motion calculated by our molecular dynamics simulation, once regarded as noise, is observed to have the periodic order with duffing and beating, which is dependent on aspect ratio and temperature. It could be dictated by the governing equation from the Green Lagrangian strain tensor. The nonlinear beam equation from strain tensor described the motion well for various models which has different aspect ratio in molecular dynamics simulation. Since this motion is nothing but the interaction between 2nd mode of radial, tangential mode and 1st longitudinal mode, it was found that Green Lagrangian strain tensor is capable to deal such coupling. The free thermal motion of suspended SWNT is also considered without temperature gradient. The Q factor measured by this theoretical analysis will be discussed. Part of this work was financially supported by Grant-in-Aid for Scientific Research (19054003 and 22226006), and Global COE Program 'Global Center for Excellence for Mechanical Systems Innovation'

New Methods For Interpretation Of Magnetic Gradient Tensor Data Using Eigenalysis And The Normalized Source Strength

NASA Astrophysics Data System (ADS)

Clark, D.

2012-12-01

In the future, acquisition of magnetic gradient tensor data is likely to become routine. New methods developed for analysis of magnetic gradient tensor data can also be applied to high quality conventional TMI surveys that have been processed using Fourier filtering techniques, or otherwise, to calculate magnetic vector and tensor components. This approach is, in fact, the only practical way at present to analyze vector component data, as measurements of vector components are seriously afflicted by motion noise, which is not as serious a problem for gradient components. In many circumstances, an optimal approach to extracting maximum information from magnetic surveys would be to combine analysis of measured gradient tensor data with vector components calculated from TMI measurements. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for a number of elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, horizontal line current and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalized source strength (NSS), calculated from the eigenvalues, is a particularly useful rotational invariant that peaks directly over 3D compact sources, 2D compact sources, thin sheets and contacts, and is independent of magnetization direction for these sources (and only very weakly dependent on magnetization direction in general). In combination the NSS and its vector gradient enable estimation of the Euler structural index, thereby constraining source geometry, and determine source locations uniquely. NSS analysis can be extended to other useful models, such as vertical pipes, by calculating eigenvalues of the vertical derivative of the gradient tensor. Once source locations are determined, information of source magnetizations can be obtained by simple linear inversion of measured or calculated vector and/or tensor data. Inversions based on the vector gradient of the NSS over the Tallawang magnetite deposit in central New South Wales obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Inverted magnetizations are consistent with magnetic property measurements on drill core samples from this deposit. Similarly, inversions of calculated tensor data over the Mount Leyshold gold-mineralized porphyry system in Queensland yield good estimates of the centroid location, total magnetic moment and magnetization direction of the magnetite-bearing potassic alteration zone that are consistent with geological and petrophysical information.

Tidal calibration of Plate Boundary Observatory borehole strainmeters: Roles of vertical and shear coupling

USGS Publications Warehouse

Roeloffs, Evelyn

2010-01-01

A multicomponent borehole strainmeter directly measures changes in the diameter of its cylindrical housing at several azimuths. To transform these measurements to formation strains requires a calibration matrix, which must be estimated by analyzing the installed strainmeter's response to known strains. Typically, theoretical calculations of Earth tidal strains serve as the known strains. This paper carries out such an analysis for 12 Plate Boundary Observatory (PBO) borehole strainmeters, postulating that each of the strainmeters' four gauges responds ("couples") to all three horizontal components of the formation strain tensor, as well as to vertical strain. Orientation corrections are also estimated. The fourth extensometer in each PBO strainmeter provides redundant information used to reduce the chance that coupling coefficients could be misleadingly fit to inappropriate theoretical tides. Satisfactory fits between observed and theoretically calculated tides were obtained for three PBO strainmeters in California, where the calculated tides are corroborated by other instrumentation, as well as for six strainmeters in Oregon and Washington, where no other instruments have ever recorded Earth tidal strain. Several strainmeters have unexpectedly large coupling coefficients for vertical strain, which increases the strainmeter's response to atmospheric pressure. Vertical coupling diminishes, or even changes the sign of, the apparent response to areal strain caused by Earth tides or deep Earth processes because near the free surface, vertical strains are opposite in sign to areal strain. Vertical coupling does not impair the shear strain response, however. PBO borehole strainmeters can provide calibrated shear strain time series of transient strain associated with tectonic or magmatic processes.

Flexoelectricity as a bulk property

NASA Astrophysics Data System (ADS)

Resta, Raffaele

2010-03-01

Piezoelectric composites can be created using nonpiezoelectric materials, by exploiting flexoelectricity. This is by definition the linear response of polarization to strain gradient, and is symmetry-allowed even in elemental crystals. However, the basic issue whether flexoelectricity is a bulk or a surface material property is open. We mention that the analogous issue about piezoelectricity is nontrivial either.^1 In this first attempt towards a full theory of flexoelectricity we prove that, for a simple class of strain and strain gradients, flexoelectricity is indeed a bulk effect. The key ingredients of the present theory are the long-range perturbations linearly induced by a unit displacement of a single nucleus in an otherwise perfect crystal: to leading order these are dipolar, quadrupolar, and octupolar. The corresponding tensors have rank 2, 3, and 4, respectively. Whereas dipoles and quadrupoles provide the piezoelectric response,^1 we show that dipoles and octupoles provide the flexoelectric response in nonpiezoelectric crystals. We conjecture that the full dipole and octupole tensors provide the flexoelectric response to the most general form of strain gradient. Our problem has a close relationship to the one of the ``absolute'' deformation potentials, which is based on a similar kind of dipolar and octupolar tensors.^2 ^1 R. M. Martin, Phys. Rev. B 5, 1607 (1972). ^2 R. Resta, L. Colombo and S. Baroni, Phys. Rev. B 41, 12538 (1990).

Inversion of gravity gradient tensor data: does it provide better resolution?

NASA Astrophysics Data System (ADS)

Paoletti, V.; Fedi, M.; Italiano, F.; Florio, G.; Ialongo, S.

2016-04-01

The gravity gradient tensor (GGT) has been increasingly used in practical applications, but the advantages and the disadvantages of the analysis of GGT components versus the analysis of the vertical component of the gravity field are still debated. We analyse the performance of joint inversion of GGT components versus separate inversion of the gravity field alone, or of one tensor component. We perform our analysis by inspection of the Picard Plot, a Singular Value Decomposition tool, and analyse both synthetic data and gradiometer measurements carried out at the Vredefort structure, South Africa. We show that the main factors controlling the reliability of the inversion are algebraic ambiguity (the difference between the number of unknowns and the number of available data points) and signal-to-noise ratio. Provided that algebraic ambiguity is kept low and the noise level is small enough so that a sufficient number of SVD components can be included in the regularized solution, we find that: (i) the choice of tensor components involved in the inversion is not crucial to the overall reliability of the reconstructions; (ii) GGT inversion can yield the same resolution as inversion with a denser distribution of gravity data points, but with the advantage of using fewer measurement stations.

Intermittency in small-scale turbulence: a velocity gradient approach

NASA Astrophysics Data System (ADS)

Meneveau, Charles; Johnson, Perry

2017-11-01

Intermittency of small-scale motions is an ubiquitous facet of turbulent flows, and predicting this phenomenon based on reduced models derived from first principles remains an important open problem. Here, a multiple-time scale stochastic model is introduced for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers. This low-dimensional model differs fundamentally from prior shell models and other empirically-motivated models of intermittency because the nonlinear gradient self-stretching and rotation A2 term vital to the energy cascade and intermittency development is represented exactly from the Navier-Stokes equations. With only one adjustable parameter needed to determine the model's effective Reynolds number, numerical solutions of the resulting set of stochastic differential equations show that the model predicts anomalous scaling for moments of the velocity gradient components and negative derivative skewness. It also predicts signature topological features of the velocity gradient tensor such as vorticity alignment trends with the eigen-directions of the strain-rate. This research was made possible by a graduate Fellowship from the National Science Foundation and by a Grant from The Gulf of Mexico Research Initiative.

Evolution of plastic anisotropy for high-strain-rate computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schiferl, S.K.; Maudlin, P.J.

1994-12-01

A model for anisotropic material strength, and for changes in the anisotropy due to plastic strain, is described. This model has been developed for use in high-rate, explicit, Lagrangian multidimensional continuum-mechanics codes. The model handles anisotropies in single-phase materials, in particular the anisotropies due to crystallographic texture--preferred orientations of the single-crystal grains. Textural anisotropies, and the changes in these anisotropies, depend overwhelmingly no the crystal structure of the material and on the deformation history. The changes, particularly for a complex deformations, are not amenable to simple analytical forms. To handle this problem, the material model described here includes a texturemore » code, or micromechanical calculation, coupled to a continuum code. The texture code updates grain orientations as a function of tensor plastic strain, and calculates the yield strength in different directions. A yield function is fitted to these yield points. For each computational cell in the continuum simulation, the texture code tracks a particular set of grain orientations. The orientations will change due to the tensor strain history, and the yield function will change accordingly. Hence, the continuum code supplies a tensor strain to the texture code, and the texture code supplies an updated yield function to the continuum code. Since significant texture changes require relatively large strains--typically, a few percent or more--the texture code is not called very often, and the increase in computer time is not excessive. The model was implemented, using a finite-element continuum code and a texture code specialized for hexagonal-close-packed crystal structures. The results for several uniaxial stress problems and an explosive-forming problem are shown.« less

The cancellous bone multiscale morphology-elasticity relationship.

PubMed

Agić, Ante; Nikolić, Vasilije; Mijović, Budimir

2006-06-01

The cancellous bone effective properties relations are analysed on multiscale across two aspects; properties of representative volume element on micro scale and statistical measure of trabecular trajectory orientation on mesoscale. Anisotropy of the microstructure is described across fabric tensor measure with trajectory orientation tensor as bridging scale connection. The scatter measured data (elastic modulus, trajectory orientation, apparent density) from compression test are fitted by stochastic interpolation procedure. The engineering constants of the elasticity tensor are estimated by last square fitt procedure in multidimensional space by Nelder-Mead simplex. The multiaxial failure surface in strain space is constructed and interpolated by modified super-ellipsoid.

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

DOE PAGES

Mohamed, Mamdouh S.; Larson, Bennett C.; Tischler, Jonathan Z.; ...

2015-05-18

The statistical properties of the elastic distortion fields of dislocations in deforming crystals are investigated using the method of discrete dislocation dynamics to simulate dislocation structures and dislocation density evolution under tensile loading. Probability distribution functions (PDF) and pair correlation functions (PCF) of the simulated internal elastic strains and lattice rotations are generated for tensile strain levels up to 0.85%. The PDFs of simulated lattice rotation are compared with sub-micrometer resolution three-dimensional X-ray microscopy measurements of rotation magnitudes and deformation length scales in 1.0% and 2.3% compression strained Cu single crystals to explore the linkage between experiment and the theoreticalmore » analysis. The statistical properties of the deformation simulations are analyzed through determinations of the Nye and Kr ner dislocation density tensors. The significance of the magnitudes and the length scales of the elastic strain and the rotation parts of dislocation density tensors are demonstrated, and their relevance to understanding the fundamental aspects of deformation is discussed.« less

The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

NASA Astrophysics Data System (ADS)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

2018-04-01

The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

Constitutive equations of a tensorial model for strain-induced damage of metals based on three invariants

NASA Astrophysics Data System (ADS)

Tutyshkin, Nikolai D.; Lofink, Paul; Müller, Wolfgang H.; Wille, Ralf; Stahn, Oliver

2017-01-01

On the basis of the physical concepts of void formation, nucleation, and growth, generalized constitutive equations are formulated for a tensorial model of plastic damage in metals based on three invariants. The multiplicative decomposition of the metric transformation tensor and a thermodynamically consistent formulation of constitutive relations leads to a symmetric second-order damage tensor with a clear physical meaning. Its first invariant determines the damage related to plastic dilatation of the material due to growth of the voids. The second invariant of the deviatoric damage tensor is related to the change in void shape. The third invariant of the deviatoric tensor describes the impact of the stress state on damage (Lode angle), including the effect of rotating the principal axes of the stress tensor (Lode angle change). The introduction of three measures with related physical meaning allows for the description of kinetic processes of strain-induced damage with an equivalent parameter in a three-dimensional vector space, including the critical condition of ductile failure. Calculations were performed by using experimentally determined material functions for plastic dilatation and deviatoric strain at the mesoscale, as well as three-dimensional graphs for plastic damage of steel DC01. The constitutive parameter was determined from tests in tension, compression, and shear by using scanning electron microscopy, which allowed to vary the Lode angle over the full range of its values [InlineEquation not available: see fulltext.]. In order to construct the three-dimensional plastic damage curve for a range of triaxiality parameters -1 ≤ ST ≤ 1 and of Lode angles [InlineEquation not available: see fulltext.], we used our own, as well as systematized published experimental data. A comparison of calculations shows a significant effect of the third invariant (Lode angle) on equivalent damage. The measure of plastic damage, based on three invariants, can be useful for assessing the quality of metal mesostructure produced during metal forming processes. In many processes of metal sheet forming the material experiences, a non-proportional loading accompanied by rotating the principal axes of the stress tensor and a corresponding change of Lode angle.

Spatio-temporal changes of seismic anisotropy in seismogenic zones

NASA Astrophysics Data System (ADS)

Saade, M.; Montagner, J.; Roux, P.; Paul, C.; Brenguier, F.; Enescu, B.; Shiomi, K.

2013-12-01

Seismic anisotropy plays a key role in the study of stress and strain fields in the earth. Potential temporal change of seismic anisotropy can be interpreted as change of the orientation of cracks in seismogenic zones and thus change of the stress field. Such temporal changes have been observed in seismogenic zones before and after earthquakes (Durand et al. , 2011) but are still not well understood. In this study, from a numerical point of view, we investigate the variations of the polarization of surface waves in anisotropic media. These variations are related to the elastic properties of the medium, in particular to anisotropy. The technique used is based on the calculation of the whole cross-correlation tensor (CCT) of ambient seismic noise. If the sources are randomly distributed in homogeneous medium, it allows us to reconstruct the Green's tensor between two stations continuously and to monitor the region through the use of its fluctuations. Therefore, the temporal change of the Green's cross-correlation tensor enables the monitoring of stress and strain fields. This technique is applied to synthetic seismograms computed in a transversally isotropic medium with horizontal symmetry axis (hereafter referred to an HTI medium) using a code RegSEM (Cupillard et al. , 2012) based on the spectral element method. We designed an experiment in order to investigate the influence of anisotropy on the CCT. In homogeneous, isotropic medium the off-diagonal terms of the Green's tensor are null. The CCT is computed between each pair of stations and then rotated in order to approximate the Green's tensor by minimizing the off-diagonal components. This procedure permits the calculation of the polarization angle of quasi-Rayleigh and quasi-Love waves, and to observe the azimuthal variation of their polarization. The results show that even a small variation of the azimuth of seismic anisotropy with respect to a certain pair of stations can induce, in some cases, a large variation in the horizontal polarization of surface waves along the direction of this pair of stations. It depends on the relative azimuth angle between the pair of stations and the direction of anisotropy, on the amplitude of anisotropy and the frequency band of the signal. Therefore, it is now possible to explain the large, rapid and very localized variations of surface waves horizontal polarization observed by Durand et al. (2011) during the Parkfield earthquake of 2004. Furthermore, some preliminary results about the investigation of seismic anisotropy change caused by the June 13, 2008 Iwate-Miyagi Nairiku earthquake (Mw = 6.9) will be presented.

Similar Tensor Arrays - A Framework for Storage of Tensor Array Data

NASA Astrophysics Data System (ADS)

Brun, Anders; Martin-Fernandez, Marcos; Acar, Burak; Munoz-Moreno, Emma; Cammoun, Leila; Sigfridsson, Andreas; Sosa-Cabrera, Dario; Svensson, Björn; Herberthson, Magnus; Knutsson, Hans

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

From Modeling of Plasticity in Single-Crystal Superalloys to High-Resolution X-rays Three-Crystal Diffractometer Peaks Simulation

NASA Astrophysics Data System (ADS)

Jacques, Alain

2016-12-01

The dislocation-based modeling of the high-temperature creep of two-phased single-crystal superalloys requires input data beyond strain vs time curves. This may be obtained by use of in situ experiments combining high-temperature creep tests with high-resolution synchrotron three-crystal diffractometry. Such tests give access to changes in phase volume fractions and to the average components of the stress tensor in each phase as well as the plastic strain of each phase. Further progress may be obtained by a new method making intensive use of the Fast Fourier Transform, and first modeling the behavior of a representative volume of material (stress fields, plastic strain, dislocation densities…), then simulating directly the corresponding diffraction peaks, taking into account the displacement field within the material, chemical variations, and beam coherence. Initial tests indicate that the simulated peak shapes are close to the experimental ones and are quite sensitive to the details of the microstructure and to dislocation densities at interfaces and within the soft γ phase.

Magnetization-induced second-harmonic generation in electrochemically synthesized magnetic films of ternary metal Prussian blue analogs

NASA Astrophysics Data System (ADS)

Ikeda, Katsuyoshi; Ohkoshi, Shin-ichi; Hashimoto, Kazuhito

2003-02-01

We observed magnetic field effects on transmitted second-harmonic generation (SHG) in electrochemically synthesized (FexIICr1-xII)1.5[CrIII(CN)6]ṡ7.5H2O magnetic films. These films showed a variety of temperature dependences for SH intensities below magnetic phase transition temperatures (TC). The SH intensity for x=0.25 increased monotonically with decreasing temperature and that for x=0.13 exhibited a minimum value around the magnetic compensation temperature under a zero magnetic field. These temperature dependences resembled those of the absolute value of magnetization, indicating that the magnetic strain of the films is responsible for the increase in SH below TC. In addition, the polarization of SH light was rotated by an applied external magnetic field. The observed SH rotation angle of 1.3° was much larger than the Faraday rotation angle of 0.079° at 388 nm. This SH rotation can be understood by the mechanism of magnetization-induced SHG caused by interaction between the electric polarization along the out-of-plane of film and spontaneous magnetization. The magnetic linear term [χijkLmagn(1)] contributed particularly to the SH rotation. The value of the magnetic linear tensor component relative to the crystallographic tensor component [|χyyyXmagn(1)|/|χzyycr], which induced the SH rotation, was 0.023 at 50 K under 10 kOe.

Implicit constitutive models with a thermodynamic basis: a study of stress concentration

NASA Astrophysics Data System (ADS)

Bridges, C.; Rajagopal, K. R.

2015-02-01

Motivated by the recent generalization of the class of elastic bodies by Rajagopal (Appl Math 48:279-319, 2003), there have been several recent studies that have been carried out within the context of this new class. Rajagopal and Srinivasa (Proc R Soc Ser A 463:357-367, 2007, Proc R Soc Ser A: Math Phys Eng Sci 465:493-500, 2009) provided a thermodynamic basis for such models and appealing to the idea that rate of entropy production ought to be maximized they developed nonlinear rate equations of the form where T is the Cauchy stress and D is the stretching tensor as well as , where S is the Piola-Kirchhoff stress tensor and E is the Green-St. Venant strain tensor. We follow a similar procedure by utilizing the Gibb's potential and the left stretch tensor V from the Polar Decomposition of the deformation gradient, and we show that when the displacement gradient is small one arrives at constitutive relations of the form . This is, of course, in stark contrast to traditional elasticity wherein one obtains a single model, Hooke's law, when the displacement gradient is small. By solving a classical boundary value problem, with a particular form for f( T), we show that when the stresses are small, the strains are also small which is in agreement with traditional elasticity. However, within the context of our model, when the stress blows up the strains remain small, unlike the implications of Hooke's law. We use this model to study boundary value problems in annular domains to illustrate its efficacy.

Multivariate statistics of the Jacobian matrices in tensor based morphometry and their application to HIV/AIDS.

PubMed

Lepore, Natasha; Brun, Caroline A; Chiang, Ming-Chang; Chou, Yi-Yu; Dutton, Rebecca A; Hayashi, Kiralee M; Lopez, Oscar L; Aizenstein, Howard J; Toga, Arthur W; Becker, James T; Thompson, Paul M

2006-01-01

Tensor-based morphometry (TBM) is widely used in computational anatomy as a means to understand shape variation between structural brain images. A 3D nonlinear registration technique is typically used to align all brain images to a common neuroanatomical template, and the deformation fields are analyzed statistically to identify group differences in anatomy. However, the differences are usually computed solely from the determinants of the Jacobian matrices that are associated with the deformation fields computed by the registration procedure. Thus, much of the information contained within those matrices gets thrown out in the process. Only the magnitude of the expansions or contractions is examined, while the anisotropy and directional components of the changes are ignored. Here we remedy this problem by computing multivariate shape change statistics using the strain matrices. As the latter do not form a vector space, means and covariances are computed on the manifold of positive-definite matrices to which they belong. We study the brain morphology of 26 HIV/AIDS patients and 14 matched healthy control subjects using our method. The images are registered using a high-dimensional 3D fluid registration algorithm, which optimizes the Jensen-Rényi divergence, an information-theoretic measure of image correspondence. The anisotropy of the deformation is then computed. We apply a manifold version of Hotelling's T2 test to the strain matrices. Our results complement those found from the determinants of the Jacobians alone and provide greater power in detecting group differences in brain structure.

Experimental determination of the carboxylate oxygen electric-field-gradient and chemical shielding tensors in L-alanine and L-phenylalanine

NASA Astrophysics Data System (ADS)

Yamada, Kazuhiko; Asanuma, Miwako; Honda, Hisashi; Nemoto, Takahiro; Yamazaki, Toshio; Hirota, Hiroshi

2007-10-01

We report a solid-state 17O NMR study of the 17O electric-field-gradient (EFG) and chemical shielding (CS) tensors for each carboxylate group in polycrystalline L-alanine and L-phenylalanine. The magic angle spinning (MAS) and stationary 17O NMR spectra of these compounds were obtained at 9.4, 14.1, and 16.4 T. Analyzes of these 17O NMR spectra yielded reliable experimental NMR parameters including 17O CS tensor components, 17O quadrupole coupling parameters, and the relative orientations between the 17O CS and EFG tensors. The extensive quantum chemical calculations at both the restricted Hartree-Fock and density-functional theories were carried out with various basis sets to evaluate the quality of quantum chemical calculations for the 17O NMR tensors in L-alanine. For 17O CS tensors, the calculations at the B3LYP/D95 ∗∗ level could reasonably reproduce 17O CS tensors, but they still showed some discrepancies in the δ11 components by approximately 36 ppm. For 17O EFG calculations, it was advantageous to use calibrated Q value to give acceptable CQ values. The calculated results also demonstrated that not only complete intermolecular hydrogen-bonding networks to target oxygen in L-alanine, but also intermolecular interactions around the NH3+ group were significant to reproduce the 17O NMR tensors.

Composite material embedded fiber-optic Fabry-Perot strain rosette

NASA Astrophysics Data System (ADS)

Valis, Thomas; Hogg, Dayle; Measures, Raymond M.

1990-12-01

A fiber-optic strain rosette is embedded in Kevlar/epoxy. The individual arms of the rosette are fiber Fabry-Perot interferometers operated in reflection-mode with gauge (i.e., cavity) lengths of approximately 5 mm. Procedures for manufacturing the cavities, and bending the fibers, to form a strain rosette are described. Experimental results showing 2D interlaminar strain-tensor measurement are presented. The sensor is also tested as a surface adhered device.

Solution of Eshelby's inclusion problem with a bounded domain and Eshelby's tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory

NASA Astrophysics Data System (ADS)

Gao, X.-L.; Ma, H. M.

2010-05-01

A solution for Eshelby's inclusion problem of a finite homogeneous isotropic elastic body containing an inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). An extended Betti's reciprocal theorem and an extended Somigliana's identity based on the SSGET are proposed and utilized to solve the finite-domain inclusion problem. The solution for the disturbed displacement field is expressed in terms of the Green's function for an infinite three-dimensional elastic body in the SSGET. It contains a volume integral term and a surface integral term. The former is the same as that for the infinite-domain inclusion problem based on the SSGET, while the latter represents the boundary effect. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is not considered. The problem of a spherical inclusion embedded concentrically in a finite spherical elastic body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. This Eshelby tensor depends on the position, inclusion size, matrix size, and material length scale parameter, and, as a result, can capture the inclusion size and boundary effects, unlike existing Eshelby tensors. It reduces to the classical Eshelby tensor for the spherical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing as the inclusion becomes large enough, and the boundary effect is vanishing as the inclusion volume fraction gets sufficiently low.

Eshelby's problem of non-elliptical inclusions

NASA Astrophysics Data System (ADS)

Zou, Wennan; He, Qichang; Huang, Mojia; Zheng, Quanshui

2010-03-01

The Eshelby problem consists in determining the strain field of an infinite linearly elastic homogeneous medium due to a uniform eigenstrain prescribed over a subdomain, called inclusion, of the medium. The salient feature of Eshelby's solution for an ellipsoidal inclusion is that the strain tensor field inside the latter is uniform. This uniformity has the important consequence that the solution to the fundamental problem of determination of the strain field in an infinite linearly elastic homogeneous medium containing an embedded ellipsoidal inhomogeneity and subjected to remote uniform loading can be readily deduced from Eshelby's solution for an ellipsoidal inclusion upon imposing appropriate uniform eigenstrains. Based on this result, most of the existing micromechanics schemes dedicated to estimating the effective properties of inhomogeneous materials have been nevertheless applied to a number of materials of practical interest where inhomogeneities are in reality non-ellipsoidal. Aiming to examine the validity of the ellipsoidal approximation of inhomogeneities underlying various micromechanics schemes, we first derive a new boundary integral expression for calculating Eshelby's tensor field (ETF) in the context of two-dimensional isotropic elasticity. The simple and compact structure of the new boundary integral expression leads us to obtain the explicit expressions of ETF and its average for a wide variety of non-elliptical inclusions including arbitrary polygonal ones and those characterized by the finite Laurent series. In light of these new analytical results, we show that: (i) the elliptical approximation to the average of ETF is valid for a convex non-elliptical inclusion but becomes inacceptable for a non-convex non-elliptical inclusion; (ii) in general, the Eshelby tensor field inside a non-elliptical inclusion is quite non-uniform and cannot be replaced by its average; (iii) the substitution of the generalized Eshelby tensor involved in various micromechanics schemes by the average Eshelby tensor for non-elliptical inhomogeneities is in general inadmissible.

Surface‐wave Green’s tensors in the near field

USGS Publications Warehouse

Haney, Matt; Nakahara, Hisashi

2014-01-01

We demonstrate the connection between theoretical expressions for the correlation of ambient noise Rayleigh and Love waves and the exact surface‐wave Green’s tensors for a point force. The surface‐wave Green’s tensors are well known in the far‐field limit. On the other hand, the imaginary part of the exact Green’s tensors, including near‐field effects, arises in correlation techniques such as the spatial autocorrelation (SPAC) method. Using the imaginary part of the exact Green’s tensors from the SPAC method, we find the associated real part using the Kramers–Kronig relations. The application of the Kramers–Kronig relations is not straightforward, however, because the causality properties of the different tensor components vary. In addition to the Green’s tensors for a point force, we also derive expressions for a general point moment tensor source.

On the tidal-energy tensor for two homogeneous coaxial ellipsoids

NASA Astrophysics Data System (ADS)

Caimmi, R.; Secco, L.

2001-10-01

The tidal-energy tensor for two homogeneous and coaxial ellipsoids, one lying completely within the other, is investigated in connection with the tidal action exerted by the outer ellipsoid on the inner one. Making reference to the explicit expression found in a previous paper of ours, it is shown that the generic component of the tidal-energy tensor, (i) may be expressed as the product of the corresponding component of the self-energy tensor related to the inner ellipsoid, by the density ratio, and the shape factor ratio, and (ii) equals the one due to any homogeneous, outer ellipsoid, for which the product of the density and a specified shape factor remains unchanged; in particular, the outer ellipsoid may be similar and similarly placed with respect to the inner one. In addition, an explicit expression for the Clausius-virial tensor is derived. Analogous results for the corresponding scalar quantities are also given. Further attention is paid to the particular case of spheroids.

Nonlocal elasticity tensors in dislocation and disclination cores

DOE PAGES

Taupin, V.; Gbemou, K.; Fressengeas, C.; ...

2017-01-07

We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum andmore » moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.« less

Closed system of coupling effects in generalized thermo-elastoplasticity

NASA Astrophysics Data System (ADS)

Śloderbach, Z.

2016-05-01

In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such materials as rocks, soils, concretes and in some metalic materials. In this paper not only the usual postulate of existence of a dissipation qupotential (the Gyarmati postulate) is used to derive the velocity equation. The plastic flow constitutive equations have the character of non-associated flow laws even when the Gyarmati postulate is assumed. In general formulation, the plastic strain rate tensor is normal to the surface of the generalized function of plastic flow defined in the the space of internal thermodynamic forces Π but is not normal to the yield surface. However, in general formulation and after the use the Gyarmati postulate, the direction of the sum of the plastic strain rate tensor and the coupled elastic strain rate tensor is normal to the yield surface.

Stochastic analysis of transverse dispersion in density‐coupled transport in aquifers

USGS Publications Warehouse

Welty, Claire; Kane, Allen C.; Kauffman, Leon J.

2003-01-01

Spectral perturbation techniques have been used previously to derive integral expressions for dispersive mixing in concentration‐dependent transport in three‐dimensional, heterogeneous porous media, where fluid density and viscosity are functions of solute concentration. Whereas earlier work focused on evaluating longitudinal dispersivity in isotropic media and incorporating the result in a mean one‐dimensional transport model, the emphasis of this paper is on evaluation of the complete dispersion tensor, including the more general case of anisotropic media. Approximate analytic expressions for all components of the macroscopic dispersivity tensor are derived, and the tensor is shown to be asymmetric. The tensor is separated into its symmetric and antisymmetric parts, where the symmetric part is used to calculate the principal components and principal directions of dispersivity, and the antisymmetric part of the tensor is shown to modify the velocity of the solute body compared to that of the background fluid. An example set of numerical simulations incorporating the tensor illustrates the effect of density‐coupled dispersivity on a sinking plume in an aquifer. The simulations show that the effective transverse vertical spreading in a sinking plume to be significantly greater than would be predicted by a standard density‐coupled transport model that does not incorporate the coupling in the dispersivity tensor.

Geometry of Lax pairs: Particle motion and Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-01-01

A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

Transformation volume effect on the magnetic anisotropy of Ni-Mn-Ga thin films

NASA Astrophysics Data System (ADS)

L'vov, V. A.; Golub, V.; Salyuk, O.; Barandiarán, J. M.; Chernenko, V. A.

2015-01-01

Ni-Mn-Ga ferromagnetic shape memory films with similar thickness and chemical composition, deposited onto cold (with a subsequent annealing) and hot MgO(001) substrates exhibit different internal stress and structure giving rise to a different orientation of the magnetic easy axes. A quantitative theoretical analysis of the crystallographic and ferromagnetic resonance (FMR) data shows that the different anisotropies can be caused by the difference in sign between the transformation volume changes in these films, as influenced by the internal stresses. To explain FMR data, the magnetoelastic coupling term of fourth-order in the magnetic vector and linear in the strain tensor components, appearing in the Landau expansion for the free energy, is taken into account. The coefficient of the term, which couples the magnetic vector components with the volume change of the Ni-Mn-Ga alloy, was estimated to be equal to about 10 7 erg cm - 3 .

Separation of specular and diffuse components using tensor voting in color images.

PubMed

Nguyen, Tam; Vo, Quang Nhat; Yang, Hyung-Jeong; Kim, Soo-Hyung; Lee, Guee-Sang

2014-11-20

Most methods for the detection and removal of specular reflections suffer from nonuniform highlight regions and/or nonconverged artifacts induced by discontinuities in the surface colors, especially when dealing with highly textured, multicolored images. In this paper, a novel noniterative and predefined constraint-free method based on tensor voting is proposed to detect and remove the highlight components of a single color image. The distribution of diffuse and specular pixels in the original image is determined using tensors' saliency analysis, instead of comparing color information among neighbor pixels. The achieved diffuse reflectance distribution is used to remove specularity components. The proposed method is evaluated quantitatively and qualitatively over a dataset of highly textured, multicolor images. The experimental results show that our result outperforms other state-of-the-art techniques.

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*

PubMed Central

BARMPOUTIS, ANGELOS; JEFFREY, HO; VEMURI, BABA C.

2012-01-01

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space P02m of 2mth-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on P02m is usually not straightforward computationally because there is no known analytic description of P02m for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone P02m for the cases 0 < m < 3, and presenting an explicit characterization of the approximation Σ2m ⊂ Ω2m for m ≥ 1, using the subset Ω2m⊂P02m of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in Σ2m. Finally, we experimentally validate the proposed approach and we present an application for computing 2mth-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images. PMID:23285313

A Geodetic Strain Rate Model for the East African Rift System.

PubMed

Stamps, D S; Saria, E; Kreemer, C

2018-01-15

Here we describe the new Sub-Saharan Africa Geodetic Strain Rate Model v.1.0 (SSA-GSRM v.1.0), which provides fundamental constraints on long-term tectonic deformation in the region and an improved seismic hazards assessment in Sub-Saharan Africa. Sub-Saharan Africa encompasses the East African Rift System, the active divergent plate boundary between the Nubian and Somalian plates, where strain is largely accommodated along the boundaries of three subplates. We develop an improved geodetic strain rate field for sub-Saharan Africa that incorporates 1) an expanded geodetic velocity field, 2) redefined regions of deforming zones guided by seismicity distribution, and 3) updated constraints on block rotations. SSA-GSRM v.1.0 spans longitudes 22° to 55.5° and latitudes -52° to 20° with 0.25° (longitude) by 0.2° (latitude) spacing. For plates/sub-plates, we assign rigid block rotations as constraints on the strain rate calculation that is determined by fitting bicubic Bessel splines to a new geodetic velocity solution for an interpolated velocity gradient tensor field. We derive strain rates, velocities, and vorticity rates from the velocity gradient tensor field. A comparison with the Global Geodetic Strain Rate model v2.1 reveals regions of previously unresolved spatial heterogeneities in geodetic strain rate distribution, which indicates zones of elevated seismic risk.

Geometrical relationship for the Einstein and Ricci tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sida, D.W.

1976-08-01

Components of the Ricci and Einstein tensors are expressed in terms of the Gaussian curvatures of elementary two-spaces formed by the orthogonal coordinate planes, and the results are applied to some standard metrics.

Full-Wave Tomographic and Moment Tensor Inversion Based on 3D Multigrid Strain Green’s Tensor Databases

DTIC Science & Technology

2014-04-30

grade metamorphic rocks on the southern slope of the Himalaya is imaged as a band of high velocity anomaly...velocity structures closely follow the geological features. As an indication of resolution, the ductile extrusion of high-grade metamorphic rocks on...MATERIEL COMMAND KIRTLAND AIR FORCE BASE, NM 87117-5776 DTIC COPY NOTICE AND SIGNATURE PAGE Using Government drawings, specifications, or other data

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells.

PubMed

Shenoy, Vivek B; Wang, Hailong; Wang, Xiao

2016-02-06

We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature.

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells

PubMed Central

Shenoy, Vivek B.; Wang, Hailong; Wang, Xiao

2016-01-01

We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature. PMID:26855753

Effect of cannula shape on aortic wall and flow turbulence: hydrodynamic study during extracorporeal circulation in mock thoracic aorta.

PubMed

Minakawa, Masahito; Fukuda, Ikuo; Yamazaki, Junichi; Fukui, Kozo; Yanaoka, Hideki; Inamura, Takao

2007-12-01

This study was designed to analyze flow pattern, velocity, and strain on the aortic wall of a glass aortic model during extracorporeal circulation, and to elucidate the characteristics of flow pattern in four aortic cannulas. Different patterns of large vortices and helical flow were made by each cannula. The high-velocity flow (0.6 m/s) was observed in end-hole cannula, causing high strain rate tensor (0.3~0.4 without unit) on the aortic arch. In dispersion cannula, a decreased strain rate tensor (less than 0.1) was found on the outer curvature of the aortic arch. In Soft-flow cannula (3M Cardiovascular, Ann Arbor, MI, USA), further decreased flow velocity (0.2 m/s) and strain (less than 0.2) were observed. In Select 3D cannula (Medtronic, Inc., Minneapolis, MN, USA), a high strain (0.4~0.5) was observed along the inner curvature of the aortic arch. In conclusion, end-hole cannula should not be used in atherosclerotic aorta. Particular attention should be paid both for selection of cannulas and cannulation site based on this result.

Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

NASA Astrophysics Data System (ADS)

Basak, Anup; Levitas, Valery I.

2018-04-01

A thermodynamically consistent, novel multiphase phase field approach for stress- and temperature-induced martensitic phase transformations at finite strains and with interfacial stresses has been developed. The model considers a single order parameter to describe the austenite↔martensitic transformations, and another N order parameters describing N variants and constrained to a plane in an N-dimensional order parameter space. In the free energy model coexistence of three or more phases at a single material point (multiphase junction), and deviation of each variant-variant transformation path from a straight line have been penalized. Some shortcomings of the existing models are resolved. Three different kinematic models (KMs) for the transformation deformation gradient tensors are assumed: (i) In KM-I the transformation deformation gradient tensor is a linear function of the Bain tensors for the variants. (ii) In KM-II the natural logarithms of the transformation deformation gradient is taken as a linear combination of the natural logarithm of the Bain tensors multiplied with the interpolation functions. (iii) In KM-III it is derived using the twinning equation from the crystallographic theory. The instability criteria for all the phase transformations have been derived for all the kinematic models, and their comparative study is presented. A large strain finite element procedure has been developed and used for studying the evolution of some complex microstructures in nanoscale samples under various loading conditions. Also, the stresses within variant-variant boundaries, the sample size effect, effect of penalizing the triple junctions, and twinned microstructures have been studied. The present approach can be extended for studying grain growth, solidifications, para↔ferro electric transformations, and diffusive phase transformations.

Strain Gradient Solution for the Eshelby-Type Polyhedral Inclusion Problem

DTIC Science & Technology

2012-01-01

2011 Available online 6 November 2011 Keywords: Eshelby tensor Polyhedral inclusion Size effect Eigenstrain Strain gradient a b s t r a c t The Eshelby...material containing an ellipsoidal inclusion prescribed with a uniform eigenstrain is a milestone in micromechanics. The solution for the dynamic Eshelby...strain to the prescribed uniform eigenstrain , is constant inside the inclusion. However, this property is true only for ellipsoidal inclusions (and when

Characterizing Atomistic Geometries and Potential Functions Using Strain Functionals

NASA Astrophysics Data System (ADS)

Kober, Edward; Mathew, Nithin; Rudin, Sven

2017-06-01

We demonstrate the use of strain tensor functionals for characterizing arbitrarily ordered atomistic structures. This approach defines a Gaussian-weighted neighborhood around each atom and characterizes that local geometry in terms of n-th order strain tensors, which are equivalent to the n-th order moments/derivatives of the neighborhood. Fourth order expansions can distinguish the cubic structures (and deformations thereof), but sixth order expansions are required to fully characterize hexagonal structures. These functions are continuous and smooth and much less sensitive to thermal fluctuations than other descriptors based on discrete neighborhoods. Reducing these metrics to rotational invariant descriptors allows a large number of defect structures to be readily identified and forms the basis of a classification scheme that allows molecular dynamics simulations to be readily analyzed. Applications to the analysis of shock waves impinging on samples of Cu, Ta and Ti will be presented. The method has been extended to vector fields as well, enabling the local stress to be cast in terms of rotationally invariant functions as well. The stress-strain correlations can then be used as the basis for developing and analyzing potential functions.

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

PubMed

Li, Yi; Chevillard, Laurent; Eyink, Gregory; Meneveau, Charles

2009-01-01

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

NASA Astrophysics Data System (ADS)

Kononova, Olga; Maksudov, Farkhad; Marx, Kenneth A.; Barsegov, Valeri

2018-01-01

A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and C_α -based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid’s mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.

Plastic deformation of B2-NiTi - is it slip or twinning?

NASA Astrophysics Data System (ADS)

Sehitoglu, H.; Wu, Y.; Alkan, S.; Ertekin, E.

2017-06-01

The work addresses two main questions that have baffled the shape memory research community. Firstly, the superb ductility of B2-NiTi cannot be solely attributed to slip on {0 1 1} planes, because there are not a sufficient number of independent slip systems under arbitrary deformations. We show unequivocally, upon diffraction measurements and local strain field traces, that deformation twinning on {1 1 4} planes that can provide additional systems to accommodate plastic flow is activated. Secondly, the slip direction on the {0 1 1} planes has not been established in NiTi with certainty. It is proved precisely to be in ?0 0 1? direction based on crystallographic shear analysis producing the specific strain tensor components (measured at mesoscale with digital image correlation, DIC). Based on the single-crystal experiments, the CRSSs (critical resolved shear stress) are established as 250 and 330 MPa for slip and twinning, respectively. The results have implications in devising correct crystal plasticity formulations for shape memory alloys.

Numerical Estimation of the Elastic Properties of Thin-Walled Structures Manufactured from Short-Fiber-Reinforced Thermoplastics

NASA Astrophysics Data System (ADS)

Altenbach, H.; Naumenko, K.; L'vov, G. I.; Pilipenko, S. N.

2003-05-01

A model which allows us to estimate the elastic properties of thin-walled structures manufactured by injection molding is presented. The starting step is the numerical prediction of the microstructure of a short-fiber-reinforced composite developed during the filling stage of the manufacturing process. For this purpose, the Moldflow Plastic Insight® commercial program is used. As a result of simulating the filling process, a second-rank orientation tensor characterizing the microstructure of the material is obtained. The elastic properties of the prepared material locally depend on the orientational distribution of fibers. The constitutive equation is formulated by means of orientational averaging for a given orientation tensor. The tensor of elastic material properties is computed and translated into the format for a stress-strain analysis based on the ANSYSÒ finite-element code. The numerical procedure and the convergence of results are discussed for a thin strip, a rectangular plate, and a shell of revolution. The influence of manufacturing conditions on the stress-strain state of statically loaded thin-walled elements is illustrated.

Bridging meso- and microscopic anisotropic unilateral damage formulations for microcracked solids

NASA Astrophysics Data System (ADS)

Zhu, Qi-Zhi; Yuan, Shuang-Shuang; Shao, Jian-fu

2017-04-01

A mathematically consistent and unified description of induced anisotropy and unilateral effects constitutes one of the central tasks in the continuum damage theories developed so far. This paper aims at bridging constitutive damage formulations on meso- and micro-scales with an emphasis on a complete mesoscopic determination of material effective properties for microcracked solids. The key is to introduce a new set of invariants in terms of strain tensor and fabric tensor by making use of the Walpole's tensorial base. This invariant set proves to be equivalent to the classical one, while the new one provides great conveniences to high-order orientation-dependent tensor manipulations. When limited to the case of parallel microcracks, potential relations between ten combination coefficients are established by applying continuity conditions. It is found that the dilute approximation with penny-shaped microcracks is a particular case of the present one. By originally introducing effective strain effect, interactions between microcracks are taken into account with comparison to the Mori-Tanaka method as well as the Ponte-Castaneda and Willis scheme. For completeness, discussions are also addressed on macroscopic formulations with high-order damage variables.

Development of a vector-tensor system to measure the absolute magnetic flux density and its gradient in magnetically shielded rooms.

PubMed

Voigt, J; Knappe-Grüneberg, S; Gutkelch, D; Haueisen, J; Neuber, S; Schnabel, A; Burghoff, M

2015-05-01

Several experiments in fundamental physics demand an environment of very low, homogeneous, and stable magnetic fields. For the magnetic characterization of such environments, we present a portable SQUID system that measures the absolute magnetic flux density vector and the gradient tensor. This vector-tensor system contains 13 integrated low-critical temperature (LTc) superconducting quantum interference devices (SQUIDs) inside a small cylindrical liquid helium Dewar with a height of 31 cm and 37 cm in diameter. The achievable resolution depends on the flux density of the field under investigation and its temporal drift. Inside a seven-layer mu-metal shield, an accuracy better than ±23 pT for the components of the static magnetic field vector and ±2 pT/cm for each of the nine components of the gradient tensor is reached by using the shifting method.

Development of a vector-tensor system to measure the absolute magnetic flux density and its gradient in magnetically shielded rooms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Voigt, J.; Knappe-Grüneberg, S.; Gutkelch, D.

2015-05-15

Several experiments in fundamental physics demand an environment of very low, homogeneous, and stable magnetic fields. For the magnetic characterization of such environments, we present a portable SQUID system that measures the absolute magnetic flux density vector and the gradient tensor. This vector-tensor system contains 13 integrated low-critical temperature (LTc) superconducting quantum interference devices (SQUIDs) inside a small cylindrical liquid helium Dewar with a height of 31 cm and 37 cm in diameter. The achievable resolution depends on the flux density of the field under investigation and its temporal drift. Inside a seven-layer mu-metal shield, an accuracy better than ±23more » pT for the components of the static magnetic field vector and ±2 pT/cm for each of the nine components of the gradient tensor is reached by using the shifting method.« less

Symmetry rules for the indirect nuclear spin-spin coupling tensor revisited

NASA Astrophysics Data System (ADS)

Buckingham, A. D.; Pyykkö, P.; Robert, J. B.; Wiesenfeld, L.

The symmetry rules of Buckingham and Love (1970), relating the number of independent components of the indirect spin-spin coupling tensor J to the symmetry of the nuclear sites, are shown to require modification if the two nuclei are exchanged by a symmetry operation. In that case, the anti-symmetric part of J does not transform as a second-rank polar tensor under symmetry operations that interchange the coupled nuclei and may be called an anti-tensor. New rules are derived and illustrated by simple molecular models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez-Ruiz, F. J.; Blas, F. J., E-mail: felipe@uhu.es; Centro de Investigación de Física Teórica y Matemática, Universidad de Huelva, 21071 Huelva

We propose an extension of the improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 110, 6264–6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, r{sub c} = 2.5, 3, 4, and 5σ. In addition,more » we have also considered cutoff distances r{sub c} = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long-range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases, the width of the tangential microscopic component of the pressure tensor profile increases, and the surface tension increases as the cutoff distance is larger. We have also checked the effect of the impulsive contribution to the pressure due to the discontinuity of the intermolecular interaction potential when it is cut. If this contribution is not accounted for in the calculation of the microscopic components of the pressure tensor, incorrect values of both components as well as a wrong structure along the vapour-liquid interface are obtained.« less

Channelling study of La1-xSrxCoO3 films on different substrates

NASA Astrophysics Data System (ADS)

Szilágyi, E.; Kótai, E.; Rata, D.; Németh, Z.; Vankó, G.

2014-08-01

The cobalt oxide system LaCoO3 and its Sr-doped child compounds have been intensively studied for decades due to their intriguing magnetic and electronic properties. Preparing thin La1-xSrxCoO3 (LSCO) films on different substrates allows for studies with a new type of perturbation, as the films are subject to substrate-dependent epitaxial strain. By choosing a proper substrate for a thin film grow, not only compressing but also tensile strain can be applied. The consequences for the fundamental physical properties are dramatic: while compressed films are metallic, as the bulk material, films under tensile strain become insulating. The goal of this work is to determine the strain tensor in LSCO films prepared on LaAlO3 and SrTiO3 substrates by pulsed laser deposition using RBS/channelling methods. Apart from the composition and defect structure of the samples, the depth dependence of the strain tensor, the cell parameters, and the volume of the unit cell are also determined. Asymmetric behaviour of the strained cell parameters is found on both substrates. This asymmetry is rather weak in the case of LSCO film grown on LaAlO3, while stronger on SrTiO3 substrate. The strain is more effective at the interface, some relaxation can be observed near to the surface.

Advanced solid elements for sheet metal forming simulation

NASA Astrophysics Data System (ADS)

Mataix, Vicente; Rossi, Riccardo; Oñate, Eugenio; Flores, Fernando G.

2016-08-01

The solid-shells are an attractive kind of element for the simulation of forming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any additional hypothesis. The present work consists in the improvement of a triangular prism solid-shell originally developed by Flores[2, 3]. The solid-shell can be used in the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation a modified right Cauchy-Green deformation tensor (C) is obtained; in the present work a modified deformation gradient (F) is obtained, which allows to generalise the methodology and allows to employ the Pull-Back and Push-Forwards operations. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow.

Constitutive Modelling and Deformation Band Angle Predictions for High Porosity Sandstones

NASA Astrophysics Data System (ADS)

Richards, M. C.; Issen, K. A.; Ingraham, M. D.

2017-12-01

The development of a field-scale deformation model requires a constitutive framework that is capable of representing known material behavior and able to be calibrated using available mechanical response data. This work employs the principle of hyperplasticity (e.g., Houlsby and Puzrin, 2006) to develop such a constitutive framework for high porosity sandstone. Adapting the works of Zimmerman et al. (1986) and Collins and Houlsby (1997), the mechanical data set of Ingraham et al. (2013 a, b) was used to develop a specific constitutive framework for Castlegate sandstone, a high porosity fluvial-deposited reservoir analog rock. Using the mechanical data set of Ingraham et al. (2013 a, b), explicit expressions and material parameters of the elastic moduli and strain tensors were obtained. With these expressions, analytical and numerical techniques were then employed to partition the total mechanical strain into elastic, coupled, and plastic strain components. With the partitioned strain data, yield surfaces in true-stress space, coefficients of internal friction, dilatancy factors, along with the theorectical predictions of the deformation band angles were obtained. These results were also evaluated against band angle values obtained from a) measurements on specimen jackets (Ingraham et al., 2013a), b) plane fits through located acoustic emissions (AE) events (Ingraham et al. 2013b), and c) X-ray micro-computed tomography (micro-CT) calculations.

Equivalence between short-time biphasic and incompressible elastic material responses.

PubMed

Ateshian, Gerard A; Ellis, Benjamin J; Weiss, Jeffrey A

2007-06-01

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltat

Impact of homogeneous strain on uranium vacancy diffusion in uranium dioxide

DOE PAGES

Goyal, Anuj; Phillpot, Simon R.; Subramanian, Gopinath; ...

2015-03-03

We present a detailed mechanism of, and the effect of homogeneous strains on, the migration of uranium vacancies in UO 2. Vacancy migration pathways and barriers are identified using density functional theory and the effect of uniform strain fields are accounted for using the dipole tensor approach. We report complex migration pathways and noncubic symmetry associated with the uranium vacancy in UO 2 and show that these complexities need to be carefully accounted for to predict the correct diffusion behavior of uranium vacancies. We show that under homogeneous strain fields, only the dipole tensor of the saddle with respect tomore » the minimum is required to correctly predict the change in the energy barrier between the strained and the unstrained case. Diffusivities are computed using kinetic Monte Carlo simulations for both neutral and fully charged state of uranium single and divacancies. We calculate the effect of strain on migration barriers in the temperature range 800–1800 K for both vacancy types. Homogeneous strains as small as 2% have a considerable effect on diffusivity of both single and divacancies of uranium, with the effect of strain being more pronounced for single vacancies than divacancies. In contrast, the response of a given defect to strain is less sensitive to changes in the charge state of the defect. Further, strain leads to anisotropies in the mobility of the vacancy and the degree of anisotropy is very sensitive to the nature of the applied strain field for strain of equal magnitude. Our results indicate that the influence of strain on vacancy diffusivity will be significantly greater when single vacancies dominate the defect structure, such as sintering, while the effects will be much less substantial under irradiation conditions where divacancies dominate.« less

Time-Dependent Moment Tensors of the First Four Source Physics Experiments (SPE) Explosions

NASA Astrophysics Data System (ADS)

Yang, X.

2015-12-01

We use mainly vertical-component geophone data within 2 km from the epicenter to invert for time-dependent moment tensors of the first four SPE explosions: SPE-1, SPE-2, SPE-3 and SPE-4Prime. We employ a one-dimensional (1D) velocity model developed from P- and Rg-wave travel times for Green's function calculations. The attenuation structure of the model is developed from P- and Rg-wave amplitudes. We select data for the inversion based on the criterion that they show consistent travel times and amplitude behavior as those predicted by the 1D model. Due to limited azimuthal coverage of the sources and the mostly vertical-component-only nature of the dataset, only long-period, diagonal components of the moment tensors are well constrained. Nevertheless, the moment tensors, particularly their isotropic components, provide reasonable estimates of the long-period source amplitudes as well as estimates of corner frequencies, albeit with larger uncertainties. The estimated corner frequencies, however, are consistent with estimates from ratios of seismogram spectra from different explosions. These long-period source amplitudes and corner frequencies cannot be fit by classical P-wave explosion source models. The results motivate the development of new P-wave source models suitable for these chemical explosions. To that end, we fit inverted moment-tensor spectra by modifying the classical explosion model using regressions of estimated source parameters. Although the number of data points used in the regression is small, the approach suggests a way for the new-model development when more data are collected.

Myocardial strains from 3D displacement encoded magnetic resonance imaging

PubMed Central

2012-01-01

Background The ability to measure and quantify myocardial motion and deformation provides a useful tool to assist in the diagnosis, prognosis and management of heart disease. The recent development of magnetic resonance imaging methods, such as harmonic phase analysis of tagging and displacement encoding with stimulated echoes (DENSE), make detailed non-invasive 3D kinematic analyses of human myocardium possible in the clinic and for research purposes. A robust analysis method is required, however. Methods We propose to estimate strain using a polynomial function which produces local models of the displacement field obtained with DENSE. Given a specific polynomial order, the model is obtained as the least squares fit of the acquired displacement field. These local models are subsequently used to produce estimates of the full strain tensor. Results The proposed method is evaluated on a numerical phantom as well as in vivo on a healthy human heart. The evaluation showed that the proposed method produced accurate results and showed low sensitivity to noise in the numerical phantom. The method was also demonstrated in vivo by assessment of the full strain tensor and to resolve transmural strain variations. Conclusions Strain estimation within a 3D myocardial volume based on polynomial functions yields accurate and robust results when validated on an analytical model. The polynomial field is capable of resolving the measured material positions from the in vivo data, and the obtained in vivo strains values agree with previously reported myocardial strains in normal human hearts. PMID:22533791

First Search for Nontensorial Gravitational Waves from Known Pulsars

NASA Astrophysics Data System (ADS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Afrough, M.; Agarwal, B.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, G.; Allocca, A.; Altin, P. A.; Amato, A.; Ananyeva, A.; Anderson, S. B.; Anderson, W. G.; Antier, S.; Appert, S.; Arai, K.; Araya, M. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; AultONeal, K.; Avila-Alvarez, A.; Babak, S.; Bacon, P.; Bader, M. K. M.; Bae, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Banagiri, S.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bawaj, M.; Bazzan, M.; Bécsy, B.; Beer, C.; Bejger, M.; Belahcene, I.; Bell, A. S.; Berger, B. K.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Billman, C. R.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blackman, J.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Bode, N.; Boer, M.; Bogaert, G.; Bohe, A.; Bondu, F.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Broida, J. E.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Brunett, S.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cabero, M.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T. A.; Calloni, E.; Camp, J. B.; Canepa, M.; Canizares, P.; Cannon, K. C.; Cao, H.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Carney, M. F.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chatterjee, D.; Cheeseboro, B. D.; Chen, H. Y.; Chen, Y.; Cheng, H.-P.; Chincarini, A.; Chiummo, A.; Chmiel, T.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, A. J. K.; Chua, S.; Chung, A. K. W.; Chung, S.; Ciani, G.; Ciolfi, R.; Cirelli, C. E.; Cirone, A.; Clara, F.; Clark, J. A.; Cleva, F.; Cocchieri, C.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Cominsky, L. R.; Constancio, M.; Conti, L.; Cooper, S. J.; Corban, P.; Corbitt, T. R.; Corley, K. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Covas, P. B.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Creighton, J. D. E.; Creighton, T. D.; Cripe, J.; Crowder, S. G.; Cullen, T. J.; Cumming, A.; Cunningham, L.; Cuoco, E.; Canton, T. Dal; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Dasgupta, A.; Da Silva Costa, C. F.; Dattilo, V.; Dave, I.; Davier, M.; Davis, D.; Daw, E. J.; Day, B.; De, S.; DeBra, D.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Devenson, J.; Devine, R. C.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Girolamo, T.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Renzo, F.; Doctor, Z.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Dorrington, I.; Douglas, R.; Dovale Álvarez, M.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Duncan, J.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Eisenstein, R. A.; Essick, R. C.; Etienne, Z. B.; Etzel, T.; Evans, M.; Evans, T. M.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Farinon, S.; Farr, B.; Farr, W. M.; Fauchon-Jones, E. J.; Favata, M.; Fays, M.; Fehrmann, H.; Feicht, J.; Fejer, M. M.; Fernandez-Galiana, A.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fong, H.; Forsyth, P. W. F.; Forsyth, S. S.; Fournier, J.-D.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fries, E. M.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H.; Gabel, M.; Gadre, B. U.; Gaebel, S. M.; Gair, J. R.; Gammaitoni, L.; Ganija, M. R.; Gaonkar, S. G.; Garufi, F.; Gaudio, S.; Gaur, G.; Gayathri, V.; Gehrels, N.; Gemme, G.; Genin, E.; Gennai, A.; George, D.; George, J.; Gergely, L.; Germain, V.; Ghonge, S.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glover, L.; Goetz, E.; Goetz, R.; Gomes, S.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Grado, A.; Graef, C.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Gruning, P.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannuksela, O. A.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Henry, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hofman, D.; Holt, K.; Holz, D. E.; Hopkins, P.; Horst, C.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Indik, N.; Ingram, D. R.; Inta, R.; Intini, G.; Isa, H. N.; Isac, J.-M.; Isi, M.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Junker, J.; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Karvinen, K. S.; Kasprzack, M.; Katolik, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kawabe, K.; Kéfélian, F.; Keitel, D.; Kemball, A. J.; Kennedy, R.; Kent, C.; Key, J. S.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, Chunglee; Kim, J. C.; Kim, W.; Kim, W. S.; Kim, Y.-M.; Kimbrell, S. J.; King, E. J.; King, P. J.; Kirchhoff, R.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Koch, P.; Koehlenbeck, S. M.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Krämer, C.; Kringel, V.; Krishnan, B.; Królak, A.; Kuehn, G.; Kumar, P.; Kumar, R.; Kumar, S.; Kuo, L.; Kutynia, A.; Kwang, S.; Lackey, B. D.; Lai, K. H.; Landry, M.; Lang, R. N.; Lange, J.; Lantz, B.; Lanza, R. K.; Lartaux-Vollard, A.; Lasky, P. D.; Laxen, M.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, H. W.; Lee, K.; Lehmann, J.; Lenon, A.; Leonardi, M.; Leroy, N.; Letendre, N.; Levin, Y.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Liu, J.; Lo, R. K. L.; Lockerbie, N. A.; London, L. T.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lousto, C. O.; Lovelace, G.; Lück, H.; Lumaca, D.; Lundgren, A. P.; Lynch, R.; Ma, Y.; Macfoy, S.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña Hernandez, I.; Magaña-Sandoval, F.; Magaña Zertuche, L.; Magee, R. M.; Majorana, E.; Maksimovic, I.; Man, N.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markakis, C.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martynov, D. V.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Mastrogiovanni, S.; Matas, A.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McCuller, L.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McRae, T.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Mejuto-Villa, E.; Melatos, A.; Mendell, G.; Mercer, R. A.; Merilh, E. L.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Metzdorff, R.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, A. L.; Miller, A.; Miller, B. B.; Miller, J.; Millhouse, M.; Minazzoli, O.; Minenkov, Y.; Ming, J.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mours, B.; Mow-Lowry, C. M.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Muniz, E. A. M.; Murray, P. G.; Napier, K.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Nelemans, G.; Nelson, T. J. N.; Neri, M.; Nery, M.; Neunzert, A.; Newport, J. M.; Newton, G.; Ng, K. K. Y.; Nguyen, T. T.; Nichols, D.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Noack, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; Ormiston, R.; Ortega, L. F.; O'Shaughnessy, R.; Ottaway, D. J.; Overmier, H.; Owen, B. J.; Pace, A. E.; Page, J.; Page, M. A.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pang, B.; Pang, P. T. H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patricelli, B.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perez, C. J.; Perreca, A.; Perri, L. M.; Pfeiffer, H. P.; Phelps, M.; Piccinni, O. J.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poggiani, R.; Popolizio, P.; Porter, E. K.; Post, A.; Powell, J.; Prasad, J.; Pratt, J. W. W.; Predoi, V.; Prestegard, T.; Prijatelj, M.; Principe, M.; Privitera, S.; Prix, R.; Prodi, G. A.; Prokhorov, L. G.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Qiu, S.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rajan, C.; Rakhmanov, M.; Ramirez, K. E.; Rapagnani, P.; Raymond, V.; Razzano, M.; Read, J.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Reyes, S. D.; Ricci, F.; Ricker, P. M.; Rieger, S.; Riles, K.; Rizzo, M.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, R.; Romel, C. L.; Romie, J. H.; Rosińska, D.; Ross, M. P.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Sakellariadou, M.; Salconi, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sampson, L. M.; Sanchez, E. J.; Sandberg, V.; Sandeen, B.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Scheuer, J.; Schmidt, E.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schulte, B. W.; Schutz, B. F.; Schwalbe, S. G.; Scott, J.; Scott, S. M.; Seidel, E.; Sellers, D.; Sengupta, A. S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Shaddock, D. A.; Shaffer, T. J.; Shah, A. A.; Shahriar, M. S.; Shao, L.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. 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F.; Whittle, C.; Williams, D.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Woehler, J.; Wofford, J.; Wong, K. W. K.; Worden, J.; Wright, J. L.; Wu, D. S.; Wu, G.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, Hang; Yu, Haocun; Yvert, M.; ZadroŻny, A.; Zanolin, M.; Zelenova, T.; Zendri, J.-P.; Zevin, M.; Zhang, L.; Zhang, M.; Zhang, T.; Zhang, Y.-H.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, S. J.; Zhu, X. J.; Zucker, M. E.; Zweizig, J.; Buchner, S.; Cognard, I.; Corongiu, A.; Freire, P. C. C.; Guillemot, L.; Hobbs, G. B.; Kerr, M.; Lyne, A. G.; Possenti, A.; Ridolfi, A.; Shannon, R. M.; Stappers, B. W.; Weltevrede, P.; LIGO Scientific Collaboration; Virgo Collaboration

2018-01-01

We present results from the first directed search for nontensorial gravitational waves. While general relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector, or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200 known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper limits for scalar and vector strains, finding values comparable in magnitude to previously published limits for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.

First Search for Nontensorial Gravitational Waves from Known Pulsars.

PubMed

Abbott, B P; Abbott, R; Abbott, T D; Acernese, F; Ackley, K; Adams, C; Adams, T; Addesso, P; Adhikari, R X; Adya, V B; Affeldt, C; Afrough, M; Agarwal, B; Agathos, M; Agatsuma, K; Aggarwal, N; Aguiar, O D; Aiello, L; Ain, A; Ajith, P; Allen, G; Allocca, A; Altin, P A; Amato, A; Ananyeva, A; Anderson, S B; Anderson, W G; Antier, S; Appert, S; Arai, K; Araya, M C; Areeda, J S; Arnaud, N; Arun, K G; Ascenzi, S; Ashton, G; Ast, M; Aston, S M; Astone, P; Aufmuth, P; Aulbert, C; AultONeal, K; Avila-Alvarez, A; Babak, S; Bacon, P; Bader, M K M; Bae, S; Baker, P T; Baldaccini, F; Ballardin, G; Ballmer, S W; Banagiri, S; Barayoga, J C; Barclay, S E; Barish, B C; Barker, D; Barone, F; Barr, B; Barsotti, L; Barsuglia, M; Barta, D; Bartlett, J; Bartos, I; Bassiri, R; Basti, A; Batch, J C; Baune, C; Bawaj, M; Bazzan, M; Bécsy, B; Beer, C; Bejger, M; Belahcene, I; Bell, A S; Berger, B K; Bergmann, G; Berry, C P L; Bersanetti, D; Bertolini, A; Betzwieser, J; Bhagwat, S; Bhandare, R; Bilenko, I A; Billingsley, G; Billman, C R; Birch, J; Birney, R; Birnholtz, O; Biscans, S; Bisht, A; Bitossi, M; Biwer, C; Bizouard, M A; Blackburn, J K; Blackman, J; Blair, C D; Blair, D G; Blair, R M; Bloemen, S; Bock, O; Bode, N; Boer, M; Bogaert, G; Bohe, A; Bondu, F; Bonnand, R; Boom, B A; Bork, R; Boschi, V; Bose, S; Bouffanais, Y; Bozzi, A; Bradaschia, C; Brady, P R; Braginsky, V B; Branchesi, M; Brau, J E; Briant, T; Brillet, A; Brinkmann, M; Brisson, V; Brockill, P; Broida, J E; Brooks, A F; Brown, D A; Brown, D D; Brown, N M; Brunett, S; Buchanan, C C; Buikema, A; Bulik, T; Bulten, H J; Buonanno, A; Buskulic, D; Buy, C; Byer, R L; Cabero, M; Cadonati, L; Cagnoli, G; Cahillane, C; Calderón Bustillo, J; Callister, T A; Calloni, E; Camp, J B; Canepa, M; Canizares, P; Cannon, K C; Cao, H; Cao, J; Capano, C D; Capocasa, E; Carbognani, F; Caride, S; Carney, M F; Casanueva Diaz, J; Casentini, C; Caudill, S; Cavaglià, M; Cavalier, F; Cavalieri, R; Cella, G; Cepeda, C B; Cerboni Baiardi, L; Cerretani, G; Cesarini, E; Chamberlin, S J; Chan, M; Chao, S; Charlton, P; Chassande-Mottin, E; Chatterjee, D; Cheeseboro, B D; Chen, H Y; Chen, Y; Cheng, H-P; Chincarini, A; Chiummo, A; Chmiel, T; Cho, H S; Cho, M; Chow, J H; Christensen, N; Chu, Q; Chua, A J K; Chua, S; Chung, A K W; Chung, S; Ciani, G; Ciolfi, R; Cirelli, C E; Cirone, A; Clara, F; Clark, J A; Cleva, F; Cocchieri, C; Coccia, E; Cohadon, P-F; Colla, A; Collette, C G; Cominsky, L R; Constancio, M; Conti, L; Cooper, S J; Corban, P; Corbitt, T R; Corley, K R; Cornish, N; Corsi, A; Cortese, S; Costa, C A; Coughlin, M W; Coughlin, S B; Coulon, J-P; Countryman, S T; Couvares, P; Covas, P B; Cowan, E E; Coward, D M; Cowart, M J; Coyne, D C; Coyne, R; Creighton, J D E; Creighton, T D; Cripe, J; Crowder, S G; Cullen, T J; Cumming, A; Cunningham, L; Cuoco, E; Canton, T Dal; Danilishin, S L; D'Antonio, S; Danzmann, K; Dasgupta, A; Da Silva Costa, C F; Dattilo, V; Dave, I; Davier, M; Davis, D; Daw, E J; Day, B; De, S; DeBra, D; Degallaix, J; De Laurentis, M; Deléglise, S; Del Pozzo, W; Denker, T; Dent, T; Dergachev, V; De Rosa, R; DeRosa, R T; DeSalvo, R; Devenson, J; Devine, R C; Dhurandhar, S; Díaz, M C; Di Fiore, L; Di Giovanni, M; Di Girolamo, T; Di Lieto, A; Di Pace, S; Di Palma, I; Di Renzo, F; Doctor, Z; Dolique, V; Donovan, F; Dooley, K L; Doravari, S; Dorrington, I; Douglas, R; Dovale Álvarez, M; Downes, T P; Drago, M; Drever, R W P; Driggers, J C; Du, Z; Ducrot, M; Duncan, J; Dwyer, S E; Edo, T B; Edwards, M C; Effler, A; Eggenstein, H-B; Ehrens, P; Eichholz, J; Eikenberry, S S; Eisenstein, R A; Essick, R C; Etienne, Z B; Etzel, T; Evans, M; Evans, T M; Factourovich, M; Fafone, V; Fair, H; Fairhurst, S; Fan, X; Farinon, S; Farr, B; Farr, W M; Fauchon-Jones, E J; Favata, M; Fays, M; Fehrmann, H; Feicht, J; Fejer, M M; Fernandez-Galiana, A; Ferrante, I; Ferreira, E C; Ferrini, F; Fidecaro, F; Fiori, I; Fiorucci, D; Fisher, R P; Flaminio, R; Fletcher, M; Fong, H; Forsyth, P W F; Forsyth, S S; Fournier, J-D; Frasca, S; Frasconi, F; Frei, Z; 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Heitmann, H; Hello, P; Hemming, G; Hendry, M; Heng, I S; Hennig, J; Henry, J; Heptonstall, A W; Heurs, M; Hild, S; Hoak, D; Hofman, D; Holt, K; Holz, D E; Hopkins, P; Horst, C; Hough, J; Houston, E A; Howell, E J; Hu, Y M; Huerta, E A; Huet, D; Hughey, B; Husa, S; Huttner, S H; Huynh-Dinh, T; Indik, N; Ingram, D R; Inta, R; Intini, G; Isa, H N; Isac, J-M; Isi, M; Iyer, B R; Izumi, K; Jacqmin, T; Jani, K; Jaranowski, P; Jawahar, S; Jiménez-Forteza, F; Johnson, W W; Jones, D I; Jones, R; Jonker, R J G; Ju, L; Junker, J; Kalaghatgi, C V; Kalogera, V; Kandhasamy, S; Kang, G; Kanner, J B; Karki, S; Karvinen, K S; Kasprzack, M; Katolik, M; Katsavounidis, E; Katzman, W; Kaufer, S; Kawabe, K; Kéfélian, F; Keitel, D; Kemball, A J; Kennedy, R; Kent, C; Key, J S; Khalili, F Y; Khan, I; Khan, S; Khan, Z; Khazanov, E A; Kijbunchoo, N; Kim, Chunglee; Kim, J C; Kim, W; Kim, W S; Kim, Y-M; Kimbrell, S J; King, E J; King, P J; Kirchhoff, R; Kissel, J S; Kleybolte, L; Klimenko, S; Koch, P; Koehlenbeck, S M; 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Markosyan, A S; Maros, E; Martelli, F; Martellini, L; Martin, I W; Martynov, D V; Mason, K; Masserot, A; Massinger, T J; Masso-Reid, M; Mastrogiovanni, S; Matas, A; Matichard, F; Matone, L; Mavalvala, N; Mazumder, N; McCarthy, R; McClelland, D E; McCormick, S; McCuller, L; McGuire, S C; McIntyre, G; McIver, J; McManus, D J; McRae, T; McWilliams, S T; Meacher, D; Meadors, G D; Meidam, J; Mejuto-Villa, E; Melatos, A; Mendell, G; Mercer, R A; Merilh, E L; Merzougui, M; Meshkov, S; Messenger, C; Messick, C; Metzdorff, R; Meyers, P M; Mezzani, F; Miao, H; Michel, C; Middleton, H; Mikhailov, E E; Milano, L; Miller, A L; Miller, A; Miller, B B; Miller, J; Millhouse, M; Minazzoli, O; Minenkov, Y; Ming, J; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moggi, A; Mohan, M; Mohapatra, S R P; Montani, M; Moore, B C; Moore, C J; Moraru, D; Moreno, G; Morriss, S R; Mours, B; Mow-Lowry, C M; Mueller, G; Muir, A W; Mukherjee, Arunava; Mukherjee, D; Mukherjee, S; Mukund, N; Mullavey, A; Munch, J; Muniz, E A M; Murray, P G; Napier, K; Nardecchia, I; Naticchioni, L; Nayak, R K; Nelemans, G; Nelson, T J N; Neri, M; Nery, M; Neunzert, A; Newport, J M; Newton, G; Ng, K K Y; Nguyen, T T; Nichols, D; Nielsen, A B; Nissanke, S; Nitz, A; Noack, A; Nocera, F; Nolting, D; Normandin, M E N; Nuttall, L K; Oberling, J; Ochsner, E; Oelker, E; Ogin, G H; Oh, J J; Oh, S H; Ohme, F; Oliver, M; Oppermann, P; Oram, Richard J; O'Reilly, B; Ormiston, R; Ortega, L F; O'Shaughnessy, R; Ottaway, D J; Overmier, H; Owen, B J; Pace, A E; Page, J; Page, M A; Pai, A; Pai, S A; Palamos, J R; Palashov, O; Palomba, C; Pal-Singh, A; Pan, H; Pang, B; Pang, P T H; Pankow, C; Pannarale, F; Pant, B C; Paoletti, F; Paoli, A; Papa, M A; Paris, H R; Parker, W; Pascucci, D; Pasqualetti, A; Passaquieti, R; Passuello, D; Patricelli, B; Pearlstone, B L; Pedraza, M; Pedurand, R; Pekowsky, L; Pele, A; Penn, S; Perez, C J; Perreca, A; Perri, L M; Pfeiffer, H P; Phelps, M; Piccinni, O J; Pichot, M; Piergiovanni, F; Pierro, V; Pillant, G; Pinard, L; Pinto, I M; Pitkin, M; Poggiani, R; Popolizio, P; Porter, E K; Post, A; Powell, J; Prasad, J; Pratt, J W W; Predoi, V; Prestegard, T; Prijatelj, M; Principe, M; Privitera, S; Prix, R; Prodi, G A; Prokhorov, L G; Puncken, O; Punturo, M; Puppo, P; Pürrer, M; Qi, H; Qin, J; Qiu, S; Quetschke, V; Quintero, E A; Quitzow-James, R; Raab, F J; Rabeling, D S; Radkins, H; Raffai, P; Raja, S; Rajan, C; Rakhmanov, M; Ramirez, K E; Rapagnani, P; Raymond, V; Razzano, M; Read, J; Regimbau, T; Rei, L; Reid, S; Reitze, D H; Rew, H; Reyes, S D; Ricci, F; Ricker, P M; Rieger, S; Riles, K; Rizzo, M; Robertson, N A; Robie, R; Robinet, F; Rocchi, A; Rolland, L; Rollins, J G; Roma, V J; Romano, R; Romel, C L; Romie, J H; Rosińska, D; Ross, M P; Rowan, S; Rüdiger, A; Ruggi, P; Ryan, K; Sachdev, S; Sadecki, T; Sadeghian, L; Sakellariadou, M; Salconi, L; Saleem, M; Salemi, F; Samajdar, A; Sammut, L; Sampson, L M; Sanchez, E J; Sandberg, V; Sandeen, B; Sanders, J R; Sassolas, B; 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Wang, G; Wang, H; Wang, J Z; Wang, M; Wang, Y-F; Wang, Y; Ward, R L; Warner, J; Was, M; Watchi, J; Weaver, B; Wei, L-W; Weinert, M; Weinstein, A J; Weiss, R; Wen, L; Wessel, E K; Weßels, P; Westphal, T; Wette, K; Whelan, J T; Whiting, B F; Whittle, C; Williams, D; Williams, R D; Williamson, A R; Willis, J L; Willke, B; Wimmer, M H; Winkler, W; Wipf, C C; Wittel, H; Woan, G; Woehler, J; Wofford, J; Wong, K W K; Worden, J; Wright, J L; Wu, D S; Wu, G; Yam, W; Yamamoto, H; Yancey, C C; Yap, M J; Yu, Hang; Yu, Haocun; Yvert, M; Zadrożny, A; Zanolin, M; Zelenova, T; Zendri, J-P; Zevin, M; Zhang, L; Zhang, M; Zhang, T; Zhang, Y-H; Zhao, C; Zhou, M; Zhou, Z; Zhu, S J; Zhu, X J; Zucker, M E; Zweizig, J; Buchner, S; Cognard, I; Corongiu, A; Freire, P C C; Guillemot, L; Hobbs, G B; Kerr, M; Lyne, A G; Possenti, A; Ridolfi, A; Shannon, R M; Stappers, B W; Weltevrede, P

2018-01-19

We present results from the first directed search for nontensorial gravitational waves. While general relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector, or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200 known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper limits for scalar and vector strains, finding values comparable in magnitude to previously published limits for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.

Volumetric three-component velocimetry measurements of the turbulent flow around a Rushton turbine

NASA Astrophysics Data System (ADS)

Sharp, Kendra V.; Hill, David; Troolin, Daniel; Walters, Geoffrey; Lai, Wing

2010-01-01

Volumetric three-component velocimetry measurements have been taken of the flow field near a Rushton turbine in a stirred tank reactor. This particular flow field is highly unsteady and three-dimensional, and is characterized by a strong radial jet, large tank-scale ring vortices, and small-scale blade tip vortices. The experimental technique uses a single camera head with three apertures to obtain approximately 15,000 three-dimensional vectors in a cubic volume. These velocity data offer the most comprehensive view to date of this flow field, especially since they are acquired at three Reynolds numbers (15,000, 107,000, and 137,000). Mean velocity fields and turbulent kinetic energy quantities are calculated. The volumetric nature of the data enables tip vortex identification, vortex trajectory analysis, and calculation of vortex strength. Three identification methods for the vortices are compared based on: the calculation of circumferential vorticity; the calculation of local pressure minima via an eigenvalue approach; and the calculation of swirling strength again via an eigenvalue approach. The use of two-dimensional data and three-dimensional data is compared for vortex identification; a `swirl strength' criterion is less sensitive to completeness of the velocity gradient tensor and overall provides clearer identification of the tip vortices. The principal components of the strain rate tensor are also calculated for one Reynolds number case as these measures of stretching and compression have recently been associated with tip vortex characterization. Vortex trajectories and strength compare favorably with those in the literature. No clear dependence of trajectory on Reynolds number is deduced. The visualization of tip vortices up to 140° past blade passage in the highest Reynolds number case is notable and has not previously been shown.

Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis Representation Tensor Sparsity Regularization

PubMed Central

Zeng, Dong; Xie, Qi; Cao, Wenfei; Lin, Jiahui; Zhang, Hao; Zhang, Shanli; Huang, Jing; Bian, Zhaoying; Meng, Deyu; Xu, Zongben; Liang, Zhengrong; Chen, Wufan

2017-01-01

Dynamic cerebral perfusion computed tomography (DCPCT) has the ability to evaluate the hemodynamic information throughout the brain. However, due to multiple 3-D image volume acquisitions protocol, DCPCT scanning imposes high radiation dose on the patients with growing concerns. To address this issue, in this paper, based on the robust principal component analysis (RPCA, or equivalently the low-rank and sparsity decomposition) model and the DCPCT imaging procedure, we propose a new DCPCT image reconstruction algorithm to improve low dose DCPCT and perfusion maps quality via using a powerful measure, called Kronecker-basis-representation tensor sparsity regularization, for measuring low-rankness extent of a tensor. For simplicity, the first proposed model is termed tensor-based RPCA (T-RPCA). Specifically, the T-RPCA model views the DCPCT sequential images as a mixture of low-rank, sparse, and noise components to describe the maximum temporal coherence of spatial structure among phases in a tensor framework intrinsically. Moreover, the low-rank component corresponds to the “background” part with spatial–temporal correlations, e.g., static anatomical contribution, which is stationary over time about structure, and the sparse component represents the time-varying component with spatial–temporal continuity, e.g., dynamic perfusion enhanced information, which is approximately sparse over time. Furthermore, an improved nonlocal patch-based T-RPCA (NL-T-RPCA) model which describes the 3-D block groups of the “background” in a tensor is also proposed. The NL-T-RPCA model utilizes the intrinsic characteristics underlying the DCPCT images, i.e., nonlocal self-similarity and global correlation. Two efficient algorithms using alternating direction method of multipliers are developed to solve the proposed T-RPCA and NL-T-RPCA models, respectively. Extensive experiments with a digital brain perfusion phantom, preclinical monkey data, and clinical patient data clearly demonstrate that the two proposed models can achieve more gains than the existing popular algorithms in terms of both quantitative and visual quality evaluations from low-dose acquisitions, especially as low as 20 mAs. PMID:28880164

Tensor gauge condition and tensor field decomposition

NASA Astrophysics Data System (ADS)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory

NASA Astrophysics Data System (ADS)

Hehl, Friedrich W.; Kiefer, Claus

2018-01-01

We perform a short comparison between the local and linear constitutive tensor χ ^{λ ν σ κ } in four-dimensional electrodynamics, the elasticity tensor c^{ijkl} in three-dimensional elasticity theory, and the DeWitt metric G^{abcd} in general relativity, with {a,b,\\ldots =1,2,3}. We find that the DeWitt metric has only six independent components.

Combining Diffusion Tensor Metrics and DSC Perfusion Imaging: Can It Improve the Diagnostic Accuracy in Differentiating Tumefactive Demyelination from High-Grade Glioma?

PubMed

Hiremath, S B; Muraleedharan, A; Kumar, S; Nagesh, C; Kesavadas, C; Abraham, M; Kapilamoorthy, T R; Thomas, B

2017-04-01

Tumefactive demyelinating lesions with atypical features can mimic high-grade gliomas on conventional imaging sequences. The aim of this study was to assess the role of conventional imaging, DTI metrics ( p:q tensor decomposition), and DSC perfusion in differentiating tumefactive demyelinating lesions and high-grade gliomas. Fourteen patients with tumefactive demyelinating lesions and 21 patients with high-grade gliomas underwent brain MR imaging with conventional, DTI, and DSC perfusion imaging. Imaging sequences were assessed for differentiation of the lesions. DTI metrics in the enhancing areas and perilesional hyperintensity were obtained by ROI analysis, and the relative CBV values in enhancing areas were calculated on DSC perfusion imaging. Conventional imaging sequences had a sensitivity of 80.9% and specificity of 57.1% in differentiating high-grade gliomas ( P = .049) from tumefactive demyelinating lesions. DTI metrics ( p : q tensor decomposition) and DSC perfusion demonstrated a statistically significant difference in the mean values of ADC, the isotropic component of the diffusion tensor, the anisotropic component of the diffusion tensor, the total magnitude of the diffusion tensor, and rCBV among enhancing portions in tumefactive demyelinating lesions and high-grade gliomas ( P ≤ .02), with the highest specificity for ADC, the anisotropic component of the diffusion tensor, and relative CBV (92.9%). Mean fractional anisotropy values showed no significant statistical difference between tumefactive demyelinating lesions and high-grade gliomas. The combination of DTI and DSC parameters improved the diagnostic accuracy (area under the curve = 0.901). Addition of a heterogeneous enhancement pattern to DTI and DSC parameters improved it further (area under the curve = 0.966). The sensitivity increased from 71.4% to 85.7% after the addition of the enhancement pattern. DTI and DSC perfusion add profoundly to conventional imaging in differentiating tumefactive demyelinating lesions and high-grade gliomas. The combination of DTI metrics and DSC perfusion markedly improved diagnostic accuracy. © 2017 by American Journal of Neuroradiology.

Effects of Adiabatic Heating on the High Strain Rate Deformation of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Sorini, Chris; Chattopadhyay, Aditi; Goldberg, Robert K.

2017-01-01

Polymer matrix composites (PMCs) are increasingly being used in aerospace structures that are expected to experience complex dynamic loading conditions throughout their lifetime. As such, a detailed understanding of the high strain rate behavior of the constituents, particularly the strain rate, temperature, and pressure dependent polymer matrix, is paramount. In this paper, preliminary efforts in modeling experimentally observed temperature rises due to plastic deformation in PMCs subjected to dynamic loading are presented. To this end, an existing isothermal viscoplastic polymer constitutive formulation is extended to model adiabatic conditions by incorporating temperature dependent elastic properties and modifying the components of the inelastic strain rate tensor to explicitly depend on temperature. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The modified constitutive model is then embedded within a strength of materials based micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700Epon 862 (T700E862) unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for the conversion of plastic work to heat in the polymer matrix in the high strain rate analysis of PMC structures.

DAMAGE ASSESSMENT OF RC BEAMS BY NONLINEAR FINITE ELEMENT ANALYSES

NASA Astrophysics Data System (ADS)

Saito, Shigehiko; Maki, Takeshi; Tsuchiya, Satoshi; Watanabe, Tadatomo

This paper presents damage assessment schemes by using 2-dimensional nonlinear finite element analyses. The second strain invariant of deviatoric strain tensor and consumed strain energy are calculated by local strain at each integration po int of finite elements. Those scalar values are averaged over certain region. The produced nonlocal values are used for indices to verify structural safety by confirming which the ultimate limit state for failure is reached or not. Flexural and shear failure of reinforced concrete beams are estimated by us ing the proposed indices.

Spin and pseudospin symmetric Dirac particles in the field of Tietz—Hua potential including Coulomb tensor interaction

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-09-01

Approximate analytical solutions of the Dirac equation for Tietz—Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin—orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin—orbit coupling terms κ(κ ± 1)r-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov—Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.

Influence of seismic anisotropy on the cross correlation tensor: numerical investigations

NASA Astrophysics Data System (ADS)

Saade, M.; Montagner, J. P.; Roux, P.; Cupillard, P.; Durand, S.; Brenguier, F.

2015-05-01

Temporal changes in seismic anisotropy can be interpreted as variations in the orientation of cracks in seismogenic zones, and thus as variations in the stress field. Such temporal changes have been observed in seismogenic zones before and after earthquakes, although they are still not well understood. In this study, we investigate the azimuthal polarization of surface waves in anisotropic media with respect to the orientation of anisotropy, from a numerical point of view. This technique is based on the observation of the signature of anisotropy on the nine-component cross-correlation tensor (CCT) computed from seismic ambient noise recorded on pairs of three-component sensors. If noise sources are spatially distributed in a homogeneous medium, the CCT allows the reconstruction of the surface wave Green's tensor between the station pairs. In homogeneous, isotropic medium, four off-diagonal terms of the surface wave Green's tensor are null, but not in anisotropic medium. This technique is applied to three-component synthetic seismograms computed in a transversely isotropic medium with a horizontal symmetry axis, using a spectral element code. The CCT is computed between each pair of stations and then rotated, to approximate the surface wave Green's tensor by minimizing the off-diagonal components. This procedure allows the calculation of the azimuthal variation of quasi-Rayleigh and quasi-Love waves. In an anisotropic medium, in some cases, the azimuth of seismic anisotropy can induce a large variation in the horizontal polarization of surface waves. This variation depends on the relative angle between a pair of stations and the direction of anisotropy, the amplitude of the anisotropy, the frequency band of the signal and the depth of the anisotropic layer.

A Magic-Angle Spinning NMR Method for the Site-Specific Measurement of Proton Chemical-Shift Anisotropy in Biological and Organic Solids.

PubMed

Hou, Guangjin; Gupta, Rupal; Polenova, Tatyana; Vega, Alexander J

2014-02-01

Proton chemical shifts are a rich probe of structure and hydrogen bonding environments in organic and biological molecules. Until recently, measurements of 1 H chemical shift tensors have been restricted to either solid systems with sparse proton sites or were based on the indirect determination of anisotropic tensor components from cross-relaxation and liquid-crystal experiments. We have introduced an MAS approach that permits site-resolved determination of CSA tensors of protons forming chemical bonds with labeled spin-1/2 nuclei in fully protonated solids with multiple sites, including organic molecules and proteins. This approach, originally introduced for the measurements of chemical shift tensors of amide protons, is based on three RN -symmetry based experiments, from which the principal components of the 1 H CS tensor can be reliably extracted by simultaneous triple fit of the data. In this article, we expand our approach to a much more challenging system involving aliphatic and aromatic protons. We start with a review of the prior work on experimental-NMR and computational-quantum-chemical approaches for the measurements of 1 H chemical shift tensors and for relating these to the electronic structures. We then present our experimental results on U- 13 C, 15 N-labeled histdine demonstrating that 1 H chemical shift tensors can be reliably determined for the 1 H 15 N and 1 H 13 C spin pairs in cationic and neutral forms of histidine. Finally, we demonstrate that the experimental 1 H(C) and 1 H(N) chemical shift tensors are in agreement with Density Functional Theory calculations, therefore establishing the usefulness of our method for characterization of structure and hydrogen bonding environment in organic and biological solids.

Anisotropic Developments for Homogeneous Shear Flows

NASA Technical Reports Server (NTRS)

Cambon, Claude; Rubinstein, Robert

2006-01-01

The general decomposition of the spectral correlation tensor R(sub ij)(k) by Cambon et al. (J. Fluid Mech., 202, 295; J. Fluid Mech., 337, 303) into directional and polarization components is applied to the representation of R(sub ij)(k) by spherically averaged quantities. The decomposition splits the deviatoric part H(sub ij)(k) of the spherical average of R(sub ij)(k) into directional and polarization components H(sub ij)(sup e)(k) and H(sub ij)(sup z)(k). A self-consistent representation of the spectral tensor in the limit of weak anisotropy is constructed in terms of these spherically averaged quantities. The directional polarization components must be treated independently: models that attempt the same representation of the spectral tensor using the spherical average H(sub ij)(k) alone prove to be inconsistent with Navier-Stokes dynamics. In particular, a spectral tensor consistent with a prescribed Reynolds stress is not unique. The degree of anisotropy permitted by this theory is restricted by realizability requirements. Since these requirements will be less severe in a more accurate theory, a preliminary account is given of how to generalize the formalism of spherical averages to higher expansion of the spectral tensor. Directionality is described by a conventional expansion in spherical harmonics, but polarization requires an expansion in tensorial spherical harmonics generated by irreducible representations of the spatial rotation group SO(exp 3). These expansions are considered in more detail in the special case of axial symmetry.

Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence

NASA Astrophysics Data System (ADS)

Keylock, Christopher J.

2017-08-01

A method is presented for deriving random velocity gradient tensors given a source tensor. These synthetic tensors are constrained to lie within mathematical bounds of the non-normality of the source tensor, but we do not impose direct constraints upon scalar quantities typically derived from the velocity gradient tensor and studied in fluid mechanics. Hence, it becomes possible to ask hypotheses of data at a point regarding the statistical significance of these scalar quantities. Having presented our method and the associated mathematical concepts, we apply it to homogeneous, isotropic turbulence to test the utility of the approach for a case where the behavior of the tensor is understood well. We show that, as well as the concentration of data along the Vieillefosse tail, actual turbulence is also preferentially located in the quadrant where there is both excess enstrophy (Q>0 ) and excess enstrophy production (R<0 ). We also examine the topology implied by the strain eigenvalues and find that for the statistically significant results there is a particularly strong relative preference for the formation of disklike structures in the (Q<0 ,R<0 ) quadrant. With the method shown to be useful for a turbulence that is already understood well, it should be of even greater utility for studying complex flows seen in industry and the environment.

Nuclear-relaxed elastic and piezoelectric constants of materials: Computational aspects of two quantum-mechanical approaches.

PubMed

Erba, Alessandro; Caglioti, Dominique; Zicovich-Wilson, Claudio Marcelo; Dovesi, Roberto

2017-02-15

Two alternative approaches for the quantum-mechanical calculation of the nuclear-relaxation term of elastic and piezoelectric tensors of crystalline materials are illustrated and their computational aspects discussed: (i) a numerical approach based on the geometry optimization of atomic positions at strained lattice configurations and (ii) a quasi-analytical approach based on the evaluation of the force- and displacement-response internal-strain tensors as combined with the interatomic force-constant matrix. The two schemes are compared both as regards their computational accuracy and performance. The latter approach, not being affected by the many numerical parameters and procedures of a typical quasi-Newton geometry optimizer, constitutes a more reliable and robust mean to the evaluation of such properties, at a reduced computational cost for most crystalline systems. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Particle-based solid for nonsmooth multidomain dynamics

NASA Astrophysics Data System (ADS)

Nordberg, John; Servin, Martin

2018-04-01

A method for simulation of elastoplastic solids in multibody systems with nonsmooth and multidomain dynamics is developed. The solid is discretised into pseudo-particles using the meshfree moving least squares method for computing the strain tensor. The particle's strain and stress tensor variables are mapped to a compliant deformation constraint. The discretised solid model thus fit a unified framework for nonsmooth multidomain dynamics simulations including rigid multibodies with complex kinematic constraints such as articulation joints, unilateral contacts with dry friction, drivelines, and hydraulics. The nonsmooth formulation allows for impact impulses to propagate instantly between the rigid multibody and the solid. Plasticity is introduced through an associative perfectly plastic modified Drucker-Prager model. The elastic and plastic dynamics are verified for simple test systems, and the capability of simulating tracked terrain vehicles driving on a deformable terrain is demonstrated.

Interaction of the subduction process and forearc tectonics: An example from the active N - Chilean margin

NASA Astrophysics Data System (ADS)

Victor, P.; Sobiesiak, M.

2005-12-01

Convergent plate boundaries at continental margins belong to the tectonically most active areas on earth and are endangered by devastating earthquakes and tsunamis. The north Chilean margin is a high strain continental margin driven by fast plate convergence rate. The greatest amount of strain is accommodated along the subduction interface. Nevertheless there is extensive crustal deformation obvious by surface ruptures along reactivated segments of large fault systems and vertical surface motions reflecting the interaction between subducting and overriding plates. The historical seismicity record indicates that great earthquakes affect the Chilean Forearc with recurrence intervals of about 112+/- 21 y . The last great event in northern Chile occurred in 1995 near Antofagasta. The Mw= 8.0 event ruptured the subduction interface 180 km along strike with an average slip of about 5m in the depth interval between 10-50 km. From careful evaluation of the aftershock sequence by examining the different catagories of aftershock focal mechanisms we can define three segments of the seismogenic zone affected by the Antofagasta main shock. The non-ruptured northern segment beneath Mejillones Peninsula is seperated by a broad transition zone from the central segment which hosts the earthquakes' rupture plane. The southern fault plane boundary is identified by linear alignment of all apparent aftershock mechanisms. Along this southern boundary the strike slip mechanisms are exclusively left lateral whereas the strike slip mechanisms along the northern transition zone are right lateral. The orientations of summed moment tensors calculated from aftershock fault plane solutions on the northern segment and in the northern transition zone differ from the orientations exhibited by moment tensors on the central segment. This might indicate a rotational component in the coseismic movement of the ruptured segment relative to the non-ruptured segment. The observed segmentation of the downgoing plate correlates well with changes in the coseismic surface displacement field and coseismic rotations derived from GPS data (Allmendinger et al. in press). We can localize a transition zone at Mejillones peninsula (23,5°S) striking approximately N 80°E dominated by clockwise vertical axis rotations also marked by rotations of the summed moment tensors on the downgoing plate. The calculated strain tensor for this transition zone does not correspond with long term surface deformation, implying that coseismic as well as early postseismic effects on the subduction interface do not contribute to long term deformation of crustal fault zones. The Antofagasta earthquake took place just south of the large 1877 gap which extends from southern Peru to Mejillones Peninsula, being the surface expression of a barrier seperating the Antofagasta fault plane from the expected future fault plane. From our studies of the Antofagasta subduction zone and the surface displacement field we hope to find evidences for interface-crust-surface interactions which can be extrapolated also to the 1877 gap.

Normal stresses in semiflexible polymer hydrogels

NASA Astrophysics Data System (ADS)

Vahabi, M.; Vos, Bart E.; de Cagny, Henri C. G.; Bonn, Daniel; Koenderink, Gijsje H.; MacKintosh, F. C.

2018-03-01

Biopolymer gels such as fibrin and collagen networks are known to develop tensile axial stress when subject to torsion. This negative normal stress is opposite to the classical Poynting effect observed for most elastic solids including synthetic polymer gels, where torsion provokes a positive normal stress. As shown recently, this anomalous behavior in fibrin gels depends on the open, porous network structure of biopolymer gels, which facilitates interstitial fluid flow during shear and can be described by a phenomenological two-fluid model with viscous coupling between network and solvent. Here we extend this model and develop a microscopic model for the individual diagonal components of the stress tensor that determine the axial response of semiflexible polymer hydrogels. This microscopic model predicts that the magnitude of these stress components depends inversely on the characteristic strain for the onset of nonlinear shear stress, which we confirm experimentally by shear rheometry on fibrin gels. Moreover, our model predicts a transient behavior of the normal stress, which is in excellent agreement with the full time-dependent normal stress we measure.

A Geodetic Strain Rate Model for the Pacific-North American Plate Boundary, western United States

NASA Astrophysics Data System (ADS)

Kreemer, C.; Hammond, W. C.; Blewitt, G.; Holland, A. A.; Bennett, R. A.

2012-04-01

We present a model of crustal strain rates derived from GPS measurements of horizontal station velocities in the Pacific-North American plate boundary in the western United States. The model reflects a best estimate of present-day deformation from the San Andreas fault system in the west to the Basin and Range province in the east. Of the total 2,846 GPS velocities used in the model, 1,197 are derived by ourselves, and 1,649 are taken from (mostly) published results. The velocities derived by ourselves (the "UNR solution") are estimated from GPS position time-series of continuous and semi-continuous stations for which data are publicly available. We estimated ITRF2005 positions from 2002-2011.5 using JPL's GIPSY-OASIS II software with ambiguity resolution applied using our custom Ambizap software. Only stations with time-series that span at least 2.25 years are considered. We removed from the time-series continental-scale common-mode errors using a spatially-varying filtering technique. Velocity uncertainties (typically 0.1-0.3 mm/yr) assume that the time-series contain flicker plus white noise. We used a subset of stations on the stable parts of the Pacific and North American plates to estimate the Pacific-North American pole of rotation. This pole is applied as a boundary condition to the model and the North American - ITRF2005 pole is used to rotate our velocities into a North America fixed reference frame. We do not include parts of the time-series that show curvature due to post-seismic deformation after major earthquakes and we also exclude stations whose time-series display a significant unexplained non-linearity or that are near volcanic centers. Transient effects longer than the observation period (i.e., slow viscoelastic relaxation) are left in the data. We added to the UNR solution velocities from 12 other studies. The velocities are transformed onto the UNR solution's reference frame by estimating and applying a translation and rotation that minimizes the velocities at collocated stations. We removed obvious outliers and velocities in areas that we identified to undergo subsidence likely due to excessive water pumping. For the strain rate calculations we excluded GPS stations with anomalous vertical motion or annual horizontal periodicity, which are indicators of local site instability. First, we used the stations from the UNR solution to create a Delaunay triangulation and estimated the horizontal strain rate components (and rigid body rotation) for each triangle in a linear least-squares inversion using the horizontal velocities as input. Some level of spatial damping was applied to minimize unnecessary spatial variation in the model parameters. The strain rates estimates were then used as a priori strain rate variances in a method that fits continuous bi-cubic Bessel spline functions through the velocity gradient field while minimizing the weighted misfit to all velocities. A minimal level of spatial smoothing of the variances was applied. The strain rate tensor model is shown by contours of the second invariant of the tensor, which is a measure of the amplitude that is coordinate frame independent. We also show a map of the tensor style and of the signal-to-noise ratio of the model.

LiDAR point classification based on sparse representation

NASA Astrophysics Data System (ADS)

Li, Nan; Pfeifer, Norbert; Liu, Chun

2017-04-01

In order to combine the initial spatial structure and features of LiDAR data for accurate classification. The LiDAR data is represented as a 4-order tensor. Sparse representation for classification(SRC) method is used for LiDAR tensor classification. It turns out SRC need only a few of training samples from each class, meanwhile can achieve good classification result. Multiple features are extracted from raw LiDAR points to generate a high-dimensional vector at each point. Then the LiDAR tensor is built by the spatial distribution and feature vectors of the point neighborhood. The entries of LiDAR tensor are accessed via four indexes. Each index is called mode: three spatial modes in direction X ,Y ,Z and one feature mode. Sparse representation for classification(SRC) method is proposed in this paper. The sparsity algorithm is to find the best represent the test sample by sparse linear combination of training samples from a dictionary. To explore the sparsity of LiDAR tensor, the tucker decomposition is used. It decomposes a tensor into a core tensor multiplied by a matrix along each mode. Those matrices could be considered as the principal components in each mode. The entries of core tensor show the level of interaction between the different components. Therefore, the LiDAR tensor can be approximately represented by a sparse tensor multiplied by a matrix selected from a dictionary along each mode. The matrices decomposed from training samples are arranged as initial elements in the dictionary. By dictionary learning, a reconstructive and discriminative structure dictionary along each mode is built. The overall structure dictionary composes of class-specified sub-dictionaries. Then the sparse core tensor is calculated by tensor OMP(Orthogonal Matching Pursuit) method based on dictionaries along each mode. It is expected that original tensor should be well recovered by sub-dictionary associated with relevant class, while entries in the sparse tensor associated with other classed should be nearly zero. Therefore, SRC use the reconstruction error associated with each class to do data classification. A section of airborne LiDAR points of Vienna city is used and classified into 6classes: ground, roofs, vegetation, covered ground, walls and other points. Only 6 training samples from each class are taken. For the final classification result, ground and covered ground are merged into one same class(ground). The classification accuracy for ground is 94.60%, roof is 95.47%, vegetation is 85.55%, wall is 76.17%, other object is 20.39%.

Raman scattering tensors in thymine molecule from an ab initio MO calculation

NASA Astrophysics Data System (ADS)

Tsuboi, Masamichi; Kumakura, Akiko; Aida, Misako; Kaneko, Motohisa; Dupuis, Michel; Ushizawa, Koichi; Ueda, Toyotoshi

1997-03-01

Ab initio SCF MO calculations have been made of the thymine molecule for the permanent polarizability and the polarizability derivatives with respect to the normal coordinates. The latter correspond to the components of the Raman tensors, and each of these tensors was brought into a visualized form by a transformation of the tensor axes into the principal system. For a comparison with such computational findings, a polarized Raman spectroscopic measurement has been made of a single crystal of thymine with 488.0 nm excitation. For most of the in-plane vibrations, calculated tensors were found to be well correlated with the observed Raman scattering anisotropy. On the basis of such correlations, discussions are given as for the polarizability oscillations caused by the atomic displacements in the molecule.

Source spectra of the first four Source Physics Experiments (SPE) explosions from the frequency-domain moment-tensor inversion

DOE PAGES

Yang, Xiaoning

2016-08-01

In this study, I used seismic waveforms recorded within 2 km from the epicenter of the first four Source Physics Experiments (SPE) explosions to invert for the moment-tensor spectra of these explosions. I employed a one-dimensional (1D) Earth model for Green's function calculations. The model was developed from P- and R g-wave travel times and amplitudes. I selected data for the inversion based on the criterion that they had consistent travel times and amplitude behavior as those predicted by the 1D model. Due to limited azimuthal coverage of the sources and the mostly vertical-component-only nature of the dataset, only long-period,more » volumetric components of the moment-tensor spectra were well constrained.« less

Active tensor magnetic gradiometer system final report for Project MM–1514

USGS Publications Warehouse

Smith, David V.; Phillips, Jeffrey D.; Hutton, S. Raymond

2014-01-01

An interactive computer simulation program, based on physical models of system sensors, platform geometry, Earth environment, and spheroidal magnetically-permeable targets, was developed to generate synthetic magnetic field data from a conceptual tensor magnetic gradiometer system equipped with an active primary field generator. The system sensors emulate the prototype tensor magnetic gradiometer system (TMGS) developed under a separate contract for unexploded ordnance (UXO) detection and classification. Time-series data from different simulation scenarios were analyzed to recover physical dimensions of the target source. Helbig-Euler simulations were run with rectangular and rod-like source bodies to determine whether such a system could separate the induced component of the magnetization from the remanent component for each target. This report concludes with an engineering assessment of a practical system design.

First principle investigation of electronic structure, chemical bonding and optical properties of tetrabarium gallium trinitride oxide single crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khan, Saleem Ayaz, E-mail: sayaz_usb@yahoo.com; Azam, Sikander

The electronic band structure, valence electron charge density and optical susceptibilities of tetrabarium gallium trinitride (TGT) were calculated via first principle study. The electronic band structure calculation describes TGT as semiconductor having direct band gap of 1.38 eV. The valence electronic charge density contour verified the non-polar covalent nature of the bond. The absorption edge and first peak of dielectric tensor components showed electrons transition from N-p state to Ba-d state. The calculated uniaxial anisotropy (0.4842) and birefringence (−0.0061) of present paper is prearranged as follow the spectral components of the dielectric tensor. The first peak in energy loss functionmore » (ELOS) shows the energy loss of fast traveling electrons in the material. The first sharp peak produced in ELOS around 10.5 eV show plasmon loss having plasma frequencies 0.1536, 0.004 and 0.066 of dielectric tensor components. This plasmon loss also cause decrease in reflectivity spectra.« less

Mechanics of deformations in terms of scalar variables

NASA Astrophysics Data System (ADS)

Ryabov, Valeriy A.

2017-05-01

Theory of particle and continuous mechanics is developed which allows a treatment of pure deformation in terms of the set of variables "coordinate-momentum-force" instead of the standard treatment in terms of tensor-valued variables "strain-stress." This approach is quite natural for a microscopic description of atomic system, according to which only pointwise forces caused by the stress act to atoms making a body deform. The new concept starts from affine transformation of spatial to material coordinates in terms of the stretch tensor or its analogs. Thus, three principal stretches and three angles related to their orientation form a set of six scalar variables to describe deformation. Instead of volume-dependent potential used in the standard theory, which requires conditions of equilibrium for surface and body forces acting to a volume element, a potential dependent on scalar variables is introduced. A consistent introduction of generalized force associated with this potential becomes possible if a deformed body is considered to be confined on the surface of torus having six genuine dimensions. Strain, constitutive equations and other fundamental laws of the continuum and particle mechanics may be neatly rewritten in terms of scalar variables. Giving a new presentation for finite deformation new approach provides a full treatment of hyperelasticity including anisotropic case. Derived equations of motion generate a new kind of thermodynamical ensemble in terms of constant tension forces. In this ensemble, six internal deformation forces proportional to the components of Irving-Kirkwood stress are controlled by applied external forces. In thermodynamical limit, instead of the pressure and volume as state variables, this ensemble employs deformation force measured in kelvin unit and stretch ratio.

Nonlinear Viscoelastic Analysis of Orthotropic Beams Using a General Third-Order Theory

DTIC Science & Technology

2012-06-20

Kirchhoff stress tensor, denoted by r and reduced strain tensor E e is given by rxx rzz rxz 8><>: 9>=>;¼ Q11ð0Þ Q13ð0Þ 0 Q13ð0Þ Q33ð0Þ 0 0 0 Q55ð0Þ...0.5 1 −0.5 0 0.5 1 (a) (b) Fig. 1. Graphs of (a) equi-spaced and (b) spectral lagrange interpolation functions for polynomial order of p = 11. 3762 V

Micro-beam Laue alignment of multi-reflection Bragg coherent diffraction imaging measurements

DOE PAGES

Hofmann, Felix; Phillips, Nicholas W.; Harder, Ross J.; ...

2017-08-08

Multi-reflection Bragg coherent diffraction imaging has the potential to allow three-dimensional (3D) resolved measurements of the full lattice strain tensor in specific micro-crystals. Until now such measurements were hampered by the need for laborious, time-intensive alignment procedures. Here, in this paper, a different approach is demonstrated, using micro-beam Laue X-ray diffraction to first determine the lattice orientation of the micro-crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focusedmore » ion beam milled micro-crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Lastly, our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro-crystals are now feasible and can be successfully carried out even in heavily distorted samples.« less

Micro-beam Laue alignment of multi-reflection Bragg coherent diffraction imaging measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hofmann, Felix; Phillips, Nicholas W.; Harder, Ross J.

Multi-reflection Bragg coherent diffraction imaging has the potential to allow three-dimensional (3D) resolved measurements of the full lattice strain tensor in specific micro-crystals. Until now such measurements were hampered by the need for laborious, time-intensive alignment procedures. Here, in this paper, a different approach is demonstrated, using micro-beam Laue X-ray diffraction to first determine the lattice orientation of the micro-crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focusedmore » ion beam milled micro-crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Lastly, our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro-crystals are now feasible and can be successfully carried out even in heavily distorted samples.« less

Micro-beam Laue alignment of multi-reflection Bragg coherent diffraction imaging measurements.

PubMed

Hofmann, Felix; Phillips, Nicholas W; Harder, Ross J; Liu, Wenjun; Clark, Jesse N; Robinson, Ian K; Abbey, Brian

2017-09-01

Multi-reflection Bragg coherent diffraction imaging has the potential to allow three-dimensional (3D) resolved measurements of the full lattice strain tensor in specific micro-crystals. Until now such measurements were hampered by the need for laborious, time-intensive alignment procedures. Here a different approach is demonstrated, using micro-beam Laue X-ray diffraction to first determine the lattice orientation of the micro-crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focused ion beam milled micro-crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro-crystals are now feasible and can be successfully carried out even in heavily distorted samples.

Micro-beam Laue Alignment of Multi-Reflection Bragg Coherent Diffraction Imaging Measurements

PubMed Central

Hofmann, Felix; Phillips, Nicholas W.; Harder, Ross J.; Liu, Wenjun; Clark, Jesse N.; Robinson, Ian K.; Abbey, Brian

2017-01-01

Multi-reflection Bragg coherent diffraction imaging has the potential to allow 3D resolved measurements of the full lattice strain tensor in specific micro-crystals. Until now such measurements were hampered by the need for laborious, time-intensive alignment procedures. Here we demonstrate a different approach, using micro-beam Laue X-ray diffraction to first determine the lattice orientation of the micro-crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focussed ion beam milled micro-crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro-crystals are now feasible and can be successfully carried out even in heavily distorted samples. PMID:28862628

Paleaostress/strain study and its implications for the geodynamic history of the Jabal Akhdar Dome (Oman)

NASA Astrophysics Data System (ADS)

Scharf, Andreas; Amrouch, Khalid; Mattern, Frank

2016-04-01

Field observations, including oolite-, styolite, fracture analyses combined with laboratory measurements using calcite twin analysis show a ductile-to-brittle multiple-phase deformation history of the Arabian carbonate platform, ranging from Late Cretaceous to Neogene times. The Arabian carbonate platform, belonging to a passive continental margin since the Late Permian, was the site of the obduction of Tethyan oceanic lithosphere (Semail Ophiolite) during the Late Cretaceous, caused by the northward drift of Africa (Hanna, 1995). After or during the obduction, large parts of the entire nape pile composed of the Arabian platform and the Hawasina/Semail nappes, where folded and exhumed. This led to the exhumation of the Jabal Akhdar Dome. Our oolite samples from the Jabal Akhdar Dome and from below the ophiolite thrust reveal the strain ellipsoid related to the obduction. This strain ellipsoid shows components of pure and simple shear. In the latter case the longest axes of the strain ellipsoid are parallelly oriented to the direction of obduction (NE to SW), which is in good agreement with the direction of obduction as depicted by Hacker et al. (1996) for the study area. The pure-shear component (flattening) is interpreted to be a result of the overburden of the up to 7 km thick oceanic lithosphere. The oolites that are located approximately 200 m below the ophiolite thrust contact provide evidence for ductile deformation during the Late Cretaceous. These results are compared with strain and stress tensors obtained from styolites, calcite twins and fracture analyses, derived from the uppermost part of the Arabian platform of the Jabal Akhdar Dome. Our results show a complex and detailed structural deformation of the post-obduction history of the Jabal Akhdar Dome, including its folding and exhumation. Hanna, S. (1995) Field guide to the Geology of Oman. Ruwi (Historical Association of Oman. 178 pp. Hacker, B.R., Mosenfelder, J.L. & Gnos, E. (1996) Rapid emplacement of the Oman ophiolite: Thermal and geochronological constraints. Tectonics, 15(6), 1230-1247.

EQUIVALENCE BETWEEN SHORT-TIME BIPHASIC AND INCOMPRESSIBLE ELASTIC MATERIAL RESPONSES

PubMed Central

Ateshian, Gerard A.; Ellis, Benjamin J.; Weiss, Jeffrey A.

2009-01-01

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response δt≪Δ2/‖C4‖||K||, where Δ is a characteristic dimension, C4 is the elasticity tensor and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components. PMID:17536908

Simultaneous determination of mean pressure and deviatoric stress based on numerical tensor analysis: a case study for polycrystalline x-ray diffraction of gold enclosed in a methanol-ethanol mixture.

PubMed

Yoneda, A; Kubo, A

2006-06-28

It is known that the {100} and {111} planes of cubic crystals subjected to uniaxial deviatoric stress conditions have strain responses that are free from the effect of lattice preferred orientation. By utilizing this special character, one can unambiguously and simultaneously determine the mean pressure and deviatoric stress from polycrystalline diffraction data of the cubic sample. Here we introduce a numerical tensor calculation method based on the generalized Hooke's law to simultaneously determine the hydrostatic component of the stress (mean pressure) and deviatoric stress in the sample. The feasibility of this method has been tested by examining the experimental data of the Au pressure marker enclosed in a diamond anvil cell using a pressure medium of methanol-ethanol mixture. The results demonstrated that the magnitude of the deviatoric stress is ∼0.07 GPa at the mean pressure of 10.5 GPa, which is consistent with previous results of Au strength under high pressure. Our results also showed that even a small deviatoric stress (∼0.07 GPa) could yield a ∼0.3 GPa mean pressure error at ∼10 GPa.

Dynamic Creep Buckling: Analysis of Shell Structures Subjected to Time-dependent Mechanical and Thermal Loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1985-01-01

The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.

On the prediction of free turbulent jets with swirl using a quadratic pressure-strain model

NASA Technical Reports Server (NTRS)

Younis, Bassam A.; Gatski, Thomas B.; Speziale, Charles G.

1994-01-01

Data from free turbulent jets both with and without swirl are used to assess the performance of the pressure-strain model of Speziale, Sarkar and Gatski which is quadratic in the Reynolds stresses. Comparative predictions are also obtained with the two versions of the Launder, Reece and Rodi model which are linear in the same terms. All models are used as part of a complete second-order closure based on the solution of differential transport equations for each non-zero component of the Reynolds stress tensor together with an equation for the scalar energy dissipation rate. For non-swirling jets, the quadratic model underestimates the measured spreading rate of the plane jet but yields a better prediction for the axisymmetric case without resolving the plane jet/round jet anomaly. For the swirling axisymmetric jet, the same model accurately reproduces the effects of swirl on both the mean flow and the turbulence structure in sharp contrast with the linear models which yield results that are in serious error. The reasons for these differences are discussed.

Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

NASA Astrophysics Data System (ADS)

Pumir, Alain; Bodenschatz, Eberhard; Xu, Haitao

2013-03-01

We describe the structure and dynamics of turbulence by the scale-dependent perceived velocity gradient tensor as supported by following four tracers, i.e., fluid particles, that initially form a regular tetrahedron. We report results from experiments in a von Kármán swirling water flow and from numerical simulations of the incompressible Navier-Stokes equation. We analyze the statistics and the dynamics of the perceived rate of strain tensor and vorticity for initially regular tetrahedron of size r0 from the dissipative to the integral scale. Just as for the true velocity gradient, at any instant, the perceived vorticity is also preferentially aligned with the intermediate eigenvector of the perceived rate of strain. However, in the perceived rate of strain eigenframe fixed at a given time t = 0, the perceived vorticity evolves in time such as to align with the strongest eigendirection at t = 0. This also applies to the true velocity gradient. The experimental data at the higher Reynolds number suggests the existence of a self-similar regime in the inertial range. In particular, the dynamics of alignment of the perceived vorticity and strain can be rescaled by t0, the turbulence time scale of the flow when the scale r0 is in the inertial range. For smaller Reynolds numbers we found the dynamics to be scale dependent.

Behavior of the Position-Spread Tensor in Diatomic Systems.

PubMed

Brea, Oriana; El Khatib, Muammar; Angeli, Celestino; Bendazzoli, Gian Luigi; Evangelisti, Stefano; Leininger, Thierry

2013-12-10

The behavior of the Position-Spread Tensor (Λ) in a series of light diatomic molecules (either neutral or negative ions) is investigated at a Full Configuration Interaction level. This tensor, which is the second moment cumulant of the total position operator, is invariant with respect to molecular translations, while its trace is also rotationally invariant. Moreover, the tensor is additive in the case of noninteracting subsystems and can be seen as an intrinsic property of a molecule. In the present work, it is shown that the longitudinal component of the tensor, Λ∥, which is small for internuclear distances close to the equilibrium, tends to grow if the bond is stretched. A maximum is reached in the region of the bond breaking, then Λ∥ decreases and converges toward the isolated-atom value. The degenerate transversal components, Λ⊥, on the other hand, usually have a monotonic growth toward the atomic value. The Position Spread is extremely sensitive to reorganization of the molecular wave function, and it becomes larger in the case of an increase of the electron mobility, as illustrated by the neutral-ionic avoided crossing in LiF. For these reasons, the Position Spread can be an extremely useful property that characterizes the nature of the wave function in a molecular system.

Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

PubMed

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

Comparative study of methods for recognition of an unknown person's action from a video sequence

NASA Astrophysics Data System (ADS)

Hori, Takayuki; Ohya, Jun; Kurumisawa, Jun

2009-02-01

This paper proposes a Tensor Decomposition Based method that can recognize an unknown person's action from a video sequence, where the unknown person is not included in the database (tensor) used for the recognition. The tensor consists of persons, actions and time-series image features. For the observed unknown person's action, one of the actions stored in the tensor is assumed. Using the motion signature obtained from the assumption, the unknown person's actions are synthesized. The actions of one of the persons in the tensor are replaced by the synthesized actions. Then, the core tensor for the replaced tensor is computed. This process is repeated for the actions and persons. For each iteration, the difference between the replaced and original core tensors is computed. The assumption that gives the minimal difference is the action recognition result. For the time-series image features to be stored in the tensor and to be extracted from the observed video sequence, the human body silhouette's contour shape based feature is used. To show the validity of our proposed method, our proposed method is experimentally compared with Nearest Neighbor rule and Principal Component analysis based method. Experiments using 33 persons' seven kinds of action show that our proposed method achieves better recognition accuracies for the seven actions than the other methods.

Measuring the quantum geometric tensor in two-dimensional photonic and exciton-polariton systems

NASA Astrophysics Data System (ADS)

Bleu, O.; Solnyshkov, D. D.; Malpuech, G.

2018-05-01

We propose theoretically a method that allows to measure all the components of the quantum geometric tensor (the metric tensor and the Berry curvature) in a photonic system. The method is based on standard optical measurements. It applies to two-band systems, which can be mapped to a pseudospin, and to four-band systems, which can be described by two entangled pseudospins. We apply this method to several specific cases. We consider a 2D planar cavity with two polarization eigenmodes, where the pseudospin measurement can be performed via polarization-resolved photoluminescence. We also consider the s band of a staggered honeycomb lattice with polarization-degenerate modes (scalar photons), where the sublattice pseudospin can be measured by performing spatially resolved interferometric measurements. We finally consider the s band of a honeycomb lattice with polarized (spinor) photons as an example of a four-band model. We simulate realistic experimental situations in all cases. We find the photon eigenstates by solving the Schrödinger equation including pumping and finite lifetime, and then simulate the measurements to finally extract realistic mappings of the k-dependent tensor components.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carvalho, N. C., E-mail: natalia.docarmocarvalho@research.uwa.edu.au; Le Floch, J-M.; Tobar, M. E.

The Y{sub 2}SiO{sub 5} (YSO) crystal is a dielectric material with biaxial anisotropy with known values of refractive index at optical frequencies. It is a well-known rare-earth (RE) host material for optical research and more recently has shown promising performance for quantum-engineered devices. In this paper, we report the first microwave characterization of the real permittivity tensor of a bulk YSO sample, as well as an investigation of the temperature dependence of the tensor components from 296 K down to 6 K. Estimated uncertainties were below 0.26%, limited by the precision of machining the cylindrical dielectric. Also, the electrical Q-factors of amore » few electromagnetic modes were recorded as a way to provide some information about the crystal losses over the temperature range. To solve the tensor components necessary for a biaxial crystal, we developed the multi-mode technique, which uses simultaneous measurement of low order whispering gallery modes. Knowledge of the permittivity tensor offers important data, essential for the design of technologies involving YSO, such as microwave coupling to electron and hyperfine transitions in RE doped samples at low temperatures.« less

Casimir forces on a bi-anisotropic absorbing magneto-dielectric slab between two parallel conducting plates

NASA Astrophysics Data System (ADS)

Amooshahi, Majid; Shoughi, Ali

2018-05-01

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers-Kronig relations. The Maxwell’s equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab.

Strain mapping in TEM using precession electron diffraction

DOEpatents

Taheri, Mitra Lenore; Leff, Asher Calvin

2017-02-14

A sample material is scanned with a transmission electron microscope (TEM) over multiple steps having a predetermined size at a predetermined angle. Each scan at a predetermined step and angle is compared to a template, wherein the template is generated from parameters of the material and the scanning. The data is then analyzed using local mis-orientation mapping and/or Nye's tensor analysis to provide information about local strain states.

The puzzle of the 1996 Bárdarbunga, Iceland, earthquake: no volumetric component in the source mechanism

USGS Publications Warehouse

Tkalcic, Hrvoje; Dreger, Douglas S.; Foulger, Gillian R.; Julian, Bruce R.

2009-01-01

A volcanic earthquake with Mw 5.6 occurred beneath the Bárdarbunga caldera in Iceland on 29 September 1996. This earthquake is one of a decade-long sequence of  events at Bárdarbunga with non-double-couple mechanisms in the Global Centroid Moment Tensor catalog. Fortunately, it was recorded well by the regional-scale Iceland Hotspot Project seismic experiment. We investigated the event with a complete moment tensor inversion method using regional long-period seismic waveforms and a composite structural model. The moment tensor inversion using data from stations of the Iceland Hotspot Project yields a non-double-couple solution with a 67% vertically oriented compensated linear vector dipole component, a 32% double-couple component, and a statistically insignificant (2%) volumetric (isotropic) contraction. This indicates the absence of a net volumetric component, which is puzzling in the case of a large volcanic earthquake that apparently is not explained by shear slip on a planar fault. A possible volcanic mechanism that can produce an earthquake without a volumetric component involves two offset sources with similar but opposite volume changes. We show that although such a model cannot be ruled out, the circumstances under which it could happen are rare.

Green-Kubo relations for the viscosity of biaxial nematic liquid crystals

NASA Astrophysics Data System (ADS)

Sarman, Sten

1996-09-01

We derive Green-Kubo relations for the viscosities of a biaxial nematic liquid crystal. In this system there are seven shear viscosities, three twist viscosities, and three cross coupling coefficients between the antisymmetric strain rate and the symmetric traceless pressure tensor. According to the Onsager reciprocity relations these couplings are equal to the cross couplings between the symmetric traceless strain rate and the antisymmetric pressure. Our method is based on a comparison of the microscopic linear response generated by the SLLOD equations of motion for planar Couette flow (so named because of their close connection to the Doll's tensor Hamiltonian) and the macroscopic linear phenomenological relations between the pressure tensor and the strain rate. In order to obtain simple Green-Kubo relations we employ an equilibrium ensemble where the angular velocities of the directors are identically zero. This is achieved by adding constraint torques to the equations for the molecular angular accelerations. One finds that all the viscosity coefficients can be expressed as linear combinations of time correlation function integrals (TCFIs). This is much simpler compared to the expressions in the conventional canonical ensemble, where the viscosities are complicated rational functions of the TCFIs. The reason for this is, that in the constrained angular velocity ensemble, the thermodynamic forces are given external parameters whereas the thermodynamic fluxes are ensemble averages of phase functions. This is not the case in the canonical ensemble. The simplest way of obtaining numerical estimates of viscosity coefficients of a particular molecular model system is to evaluate these fluctuation relations by equilibrium molecular dynamics simulations.

Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics.

PubMed

Greene, Samuel M; Batista, Victor S

2017-09-12

We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.

A simple scheme for magnetic balance in four-component relativistic Kohn-Sham calculations of nuclear magnetic resonance shielding constants in a Gaussian basis.

PubMed

Olejniczak, Małgorzata; Bast, Radovan; Saue, Trond; Pecul, Magdalena

2012-01-07

We report the implementation of nuclear magnetic resonance (NMR) shielding tensors within the four-component relativistic Kohn-Sham density functional theory including non-collinear spin magnetization and employing London atomic orbitals to ensure gauge origin independent results, together with a new and efficient scheme for assuring correct balance between the large and small components of a molecular four-component spinor in the presence of an external magnetic field (simple magnetic balance). To test our formalism we have carried out calculations of NMR shielding tensors for the HX series (X = F, Cl, Br, I, At), the Xe atom, and the Xe dimer. The advantage of simple magnetic balance scheme combined with the use of London atomic orbitals is the fast convergence of results (when compared with restricted kinetic balance) and elimination of linear dependencies in the basis set (when compared to unrestricted kinetic balance). The effect of including spin magnetization in the description of NMR shielding tensor has been found important for hydrogen atoms in heavy HX molecules, causing an increase of isotropic values of 10%, but negligible for heavy atoms.

Anisotropy of electromagnetically induced left-handedness in atomic three-level media based upon bianisotropic polarizabilities and tensor character

NASA Astrophysics Data System (ADS)

Krowne, Clifford M.

2008-05-01

A three-level atomic system, configured as either a gaseous medium or a solid state material, with a driving field establishing a Rabi frequency of control, is tested by a probe field. The medium has bianisotropic microscopic polarizability and magnetizability, from which the permittivity and permeability tensors are derived. Non-isotropy and polarization dependence for left-handedness (negative index of refraction) is demonstrated through examination of tensor components in the detuning frequency spectrum. These results have important implications for use in optical or electronic devices.

Unified Stress Tensor of the Hydration Water Layer

NASA Astrophysics Data System (ADS)

Kim, Bongsu; Kim, QHwan; Kwon, Soyoung; An, Sangmin; Lee, Kunyoung; Lee, Manhee; Jhe, Wonho

2013-12-01

We present the general stress tensor of the ubiquitous hydration water layer (HWL), based on the empirical hydration force, by combining the elasticity and hydrodynamics theories. The tapping and shear component of the tensor describe the elastic and damping properties of the HWL, respectively, in good agreement with experiments. In particular, a unified understanding of HWL dynamics provides the otherwise unavailable intrinsic parameters of the HWL, which offer additional but unexplored aspects to the supercooled liquidity of the confined HWL. Our results may allow deeper insight on systems where the HWL is critical.

Unified stress tensor of the hydration water layer.

PubMed

Kim, Bongsu; Kim, Qhwan; Kwon, Soyoung; An, Sangmin; Lee, Kunyoung; Lee, Manhee; Jhe, Wonho

2013-12-13

We present the general stress tensor of the ubiquitous hydration water layer (HWL), based on the empirical hydration force, by combining the elasticity and hydrodynamics theories. The tapping and shear component of the tensor describe the elastic and damping properties of the HWL, respectively, in good agreement with experiments. In particular, a unified understanding of HWL dynamics provides the otherwise unavailable intrinsic parameters of the HWL, which offer additional but unexplored aspects to the supercooled liquidity of the confined HWL. Our results may allow deeper insight on systems where the HWL is critical.

A study of the topology of dissipating motions in direct numerical simulations of time-developing compressible and incompressible mixing layers

NASA Technical Reports Server (NTRS)

Chen, J. H.; Chong, M. S.; Soria, J.; Sondergaard, R.; Perry, A. E.; Rogers, M.; Moser, R.; Cantwell, B. J.

1990-01-01

A preliminary investigation of the geometry of flow patterns in numerically simulated compressible and incompressible mixing layers was carried out using 3-D critical point methodology. Motions characterized by high rates of kinetic energy dissipation and/or high enstrophy were of particular interest. In the approach the partial derivatives of the velocity field are determined at every point in the flow. These are used to construct the invariants of the velocity gradient tensor and the rate-of-strain tensor (P, Q, R, and P(sub s), Q(sub s), R(sub s) respectively). For incompressible flow the first invariant is zero. For the conditions of the compressible simulation, the first invariant is found to be everywhere small, relative to the second and third invariants, and so in both cases the local topology at a point is mainly determined by the second and third invariants. The data at every grid point is used to construct scatter plots of Q versus R and Q(sub s) versus R(sub s). Most points map to a cluster near the origin in Q-R space. However, fine scale motions, that is motions which are characterized by velocity derivatives which scale with the square root of R(sub delta), tend to map to regions which lie far from the origin. Definite trends are observed for motions characterized by high enstrophy and/or high dissipation. The observed trends suggest that, for these motions, the second and third invariants of the velocity gradient and rate-of-strain tensors are strongly correlated. The second and third invariants of the rate-of-strain tensor are related by K(-Q(sub s))(exp 3/2), which is consistent with the above scaling of velocity derivatives. The quantity K appears to depend on Reynolds number with an upper limit K = 2(the square root of 3)/9 corresponding to locally axisymmetric flow. For both the compressible and incompressible mixing layer, regions corresponding to high rates of dissipation are found to be characterized by comparable magnitudes of R(sub ij)R(sub ij) and S(sub ij)S(sub ij). For the incompressible mixing layer, regions characterized by the highest values of enstrophy are found to have relatively low strain rates.

White matter damage in primary progressive aphasias: a diffusion tensor tractography study.

PubMed

Galantucci, Sebastiano; Tartaglia, Maria Carmela; Wilson, Stephen M; Henry, Maya L; Filippi, Massimo; Agosta, Federica; Dronkers, Nina F; Henry, Roland G; Ogar, Jennifer M; Miller, Bruce L; Gorno-Tempini, Maria Luisa

2011-10-01

Primary progressive aphasia is a clinical syndrome that encompasses three major phenotypes: non-fluent/agrammatic, semantic and logopenic. These clinical entities have been associated with characteristic patterns of focal grey matter atrophy in left posterior frontoinsular, anterior temporal and left temporoparietal regions, respectively. Recently, network-level dysfunction has been hypothesized but research to date has focused largely on studying grey matter damage. The aim of this study was to assess the integrity of white matter tracts in the different primary progressive aphasia subtypes. We used diffusion tensor imaging in 48 individuals: nine non-fluent, nine semantic, nine logopenic and 21 age-matched controls. Probabilistic tractography was used to identify bilateral inferior longitudinal (anterior, middle, posterior) and uncinate fasciculi (referred to as the ventral pathway); and the superior longitudinal fasciculus segmented into its frontosupramarginal, frontoangular, frontotemporal and temporoparietal components, (referred to as the dorsal pathway). We compared the tracts' mean fractional anisotropy, axial, radial and mean diffusivities for each tract in the different diagnostic categories. The most prominent white matter changes were found in the dorsal pathways in non-fluent patients, in the two ventral pathways and the temporal components of the dorsal pathways in semantic variant, and in the temporoparietal component of the dorsal bundles in logopenic patients. Each of the primary progressive aphasia variants showed different patterns of diffusion tensor metrics alterations: non-fluent patients showed the greatest changes in fractional anisotropy and radial and mean diffusivities; semantic variant patients had severe changes in all metrics; and logopenic patients had the least white matter damage, mainly involving diffusivity, with fractional anisotropy altered only in the temporoparietal component of the dorsal pathway. This study demonstrates that both careful dissection of the main language tracts and consideration of all diffusion tensor metrics are necessary to characterize the white matter changes that occur in the variants of primary progressive aphasia. These results highlight the potential value of diffusion tensor imaging as a new tool in the multimodal diagnostic evaluation of primary progressive aphasia.

Earthquake source tensor inversion with the gCAP method and 3D Green's functions

NASA Astrophysics Data System (ADS)

Zheng, J.; Ben-Zion, Y.; Zhu, L.; Ross, Z.

2013-12-01

We develop and apply a method to invert earthquake seismograms for source properties using a general tensor representation and 3D Green's functions. The method employs (i) a general representation of earthquake potency/moment tensors with double couple (DC), compensated linear vector dipole (CLVD), and isotropic (ISO) components, and (ii) a corresponding generalized CAP (gCap) scheme where the continuous wave trains are broken into Pnl and surface waves (Zhu & Ben-Zion, 2013). For comparison, we also use the waveform inversion method of Zheng & Chen (2012) and Ammon et al. (1998). Sets of 3D Green's functions are calculated on a grid of 1 km3 using the 3-D community velocity model CVM-4 (Kohler et al. 2003). A bootstrap technique is adopted to establish robustness of the inversion results using the gCap method (Ross & Ben-Zion, 2013). Synthetic tests with 1-D and 3-D waveform calculations show that the source tensor inversion procedure is reasonably reliable and robust. As initial application, the method is used to investigate source properties of the March 11, 2013, Mw=4.7 earthquake on the San Jacinto fault using recordings of ~45 stations up to ~0.2Hz. Both the best fitting and most probable solutions include ISO component of ~1% and CLVD component of ~0%. The obtained ISO component, while small, is found to be a non-negligible positive value that can have significant implications for the physics of the failure process. Work on using higher frequency data for this and other earthquakes is in progress.

Determining the coordinate dependence of some components of the cubic susceptibility tensor {chi}-hat{sub yyyy}{sup (3)}(z, {omega}, -{omega}, {omega}, {omega}) of a one-dimensionally inhomogeneous absorbing plate at an arbitrary frequency dispersion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golubkov, A A; Makarov, Vladimir A

The possibility of unique reconstruction of the spatial profile of the cubic nonlinear susceptibility tensor component {chi}-hat{sub yyyy}{sup (3)}(z, {omega}, -{omega}, {omega}, {omega}) of a one-dimensionally inhomogeneous plate whose medium has a symmetry plane m{sub y} perpendicular to its surface is proved for the first time and the unique reconstruction algorithm is proposed. The amplitude complex coefficients of reflection and transmission (measured in some range of angles of incidence) as well as of conversion of an s-polarised plane signal monochromatic wave into two waves propagating on both sides of the plate make it possible to reconstruct the profile. These twomore » waves result from nonlinear interaction of a signal wave with an intense plane wave incident normally on the plate. All the waves under consideration have the same frequency {omega}, and so its variation helps study the frequency dispersion of the cubic nonlinear susceptibility tensor component {chi}-hat{sub yyyy}{sup (3)}(z, {omega}, -{omega}, {omega}, {omega}). For media with additional symmetry axes 2{sub z}, 4{sub z}, 6{sub z}, or {infinity}{sub z} that are perpendicular to the plate surface, the proposed method can be used to reconstruct the profile and to examine the frequency dispersion of about one third of all independent complex components of the tensor {chi}-hat{sup (3)}. (nonlinear-optics phenomena)« less

Superconducting tensor gravity gradiometer for satellite geodesy and inertial navigation

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

A sensitive gravity gradiometer can provide much needed gravity data of the earth and improve the accuracy of inertial navigation. Superconductivity and other properties of materials at low temperatures can be used to obtain a sensitive, low-drift gravity gradiometer; by differencing the outputs of accelerometer pairs using superconducting circuits, it is possible to construct a tensor gravity gradiometer which measures all the in-line and cross components of the tensor simultaneously. Additional superconducting circuits can be provided to determine the linear and angular acceleration vectors. A tensor gravity gradiometer with these features is being developed for satellite geodesy. The device constitutes a complete package of inertial navigation instruments with angular and linear acceleration readouts as well as gravity signals.

The nonlocal elastomagnetoelectrostatics of disordered micropolar media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kabychenkov, A. F.; Lisiovskii, F. V., E-mail: lisf@rambler.ru

The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.

Dispersive transport and symmetry of the dispersion tensor in porous media

NASA Astrophysics Data System (ADS)

Pride, Steven R.; Vasco, Donald W.; Flekkoy, Eirik G.; Holtzman, Ran

2017-04-01

The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010), 10.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor Di j satisfies the flow-reversal symmetry Di j(+q ) =Dj i(-q ) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.

Contribution of the polarization moments of different rank to the integral CPT signal

NASA Astrophysics Data System (ADS)

Taskova, E.; Alipieva, E.; Todorov, G.

2016-01-01

In the present work we investigate the relation of the polarization moments having different ranks with the tensor components which form the observable integral CPT signal, in the presence of a stray magnetic field. A numerical experiment with parameters close to the real ones is performed, using a program based on the irreducible tensor operator formalism1. The integral fluorescent signal is calculated for the non-polarized fluorescence at different laser power excitation. Detailed analysis of the numerical solutions for all tensor components which describe population and alignment allows visualizing the dynamics of their behavior in dependence on the experimental geometry and laboratory magnetic field B'. The dependence of population f00, longitudinal f02 and transverse f22 alignment in the presence of transverse magnetic field is investigated. The shape and sign of the resonance change with laser power.

The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

NASA Astrophysics Data System (ADS)

Li, Huicong; Wang, Xuefeng; Wu, Yanxia

2014-11-01

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone.

Gradients estimation from random points with volumetric tensor in turbulence

NASA Astrophysics Data System (ADS)

Watanabe, Tomoaki; Nagata, Koji

2017-12-01

We present an estimation method of fully-resolved/coarse-grained gradients from randomly distributed points in turbulence. The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3 × 3 matrix determined by a geometric distribution of the points. The coarse grained gradient can be considered as a low pass filtered gradient, whose cutoff is estimated with the eigenvalues of the volumetric tensor. The present method, the volumetric tensor approximation, is tested for velocity and passive scalar gradients in incompressible planar jet and mixing layer. Comparison with a finite difference approximation on a Cartesian grid shows that the volumetric tensor approximation computes the coarse grained gradients fairly well at a moderate computational cost under various conditions of spatial distributions of points. We also show that imposing the solenoidal condition improves the accuracy of the present method for solenoidal vectors, such as a velocity vector in incompressible flows, especially when the number of the points is not large. The volumetric tensor approximation with 4 points poorly estimates the gradient because of anisotropic distribution of the points. Increasing the number of points from 4 significantly improves the accuracy. Although the coarse grained gradient changes with the cutoff length, the volumetric tensor approximation yields the coarse grained gradient whose magnitude is close to the one obtained by the finite difference. We also show that the velocity gradient estimated with the present method well captures the turbulence characteristics such as local flow topology, amplification of enstrophy and strain, and energy transfer across scales.

Tri-Clustered Tensor Completion for Social-Aware Image Tag Refinement.

PubMed

Tang, Jinhui; Shu, Xiangbo; Qi, Guo-Jun; Li, Zechao; Wang, Meng; Yan, Shuicheng; Jain, Ramesh

2017-08-01

Social image tag refinement, which aims to improve tag quality by automatically completing the missing tags and rectifying the noise-corrupted ones, is an essential component for social image search. Conventional approaches mainly focus on exploring the visual and tag information, without considering the user information, which often reveals important hints on the (in)correct tags of social images. Towards this end, we propose a novel tri-clustered tensor completion framework to collaboratively explore these three kinds of information to improve the performance of social image tag refinement. Specifically, the inter-relations among users, images and tags are modeled by a tensor, and the intra-relations between users, images and tags are explored by three regularizations respectively. To address the challenges of the super-sparse and large-scale tensor factorization that demands expensive computing and memory cost, we propose a novel tri-clustering method to divide the tensor into a certain number of sub-tensors by simultaneously clustering users, images and tags into a bunch of tri-clusters. And then we investigate two strategies to complete these sub-tensors by considering (in)dependence between the sub-tensors. Experimental results on a real-world social image database demonstrate the superiority of the proposed method compared with the state-of-the-art methods.

Moment Tensor Analysis of Shallow Sources

NASA Astrophysics Data System (ADS)

Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.; Yoo, S. H.

2015-12-01

A potential issue for moment tensor inversion of shallow seismic sources is that some moment tensor components have vanishing amplitudes at the free surface, which can result in bias in the moment tensor solution. The effects of the free-surface on the stability of the moment tensor method becomes important as we continue to investigate and improve the capabilities of regional full moment tensor inversion for source-type identification and discrimination. It is important to understand these free surface effects on discriminating shallow explosive sources for nuclear monitoring purposes. It may also be important in natural systems that have shallow seismicity such as volcanoes and geothermal systems. In this study, we apply the moment tensor based discrimination method to the HUMMING ALBATROSS quarry blasts. These shallow chemical explosions at approximately 10 m depth and recorded up to several kilometers distance represent rather severe source-station geometry in terms of vanishing traction issues. We show that the method is capable of recovering a predominantly explosive source mechanism, and the combined waveform and first motion method enables the unique discrimination of these events. Recovering the correct yield using seismic moment estimates from moment tensor inversion remains challenging but we can begin to put error bounds on our moment estimates using the NSS technique.

Atomistic determination of flexoelectric properties of crystalline dielectrics

NASA Astrophysics Data System (ADS)

Maranganti, R.; Sharma, P.

2009-08-01

Upon application of a uniform strain, internal sublattice shifts within the unit cell of a noncentrosymmetric dielectric crystal result in the appearance of a net dipole moment: a phenomenon well known as piezoelectricity. A macroscopic strain gradient on the other hand can induce polarization in dielectrics of any crystal structure, even those which possess a centrosymmetric lattice. This phenomenon, called flexoelectricity, has both bulk and surface contributions: the strength of the bulk contribution can be characterized by means of a material property tensor called the bulk flexoelectric tensor. Several recent studies suggest that strain-gradient induced polarization may be responsible for a variety of interesting and anomalous electromechanical phenomena in materials including electromechanical coupling effects in nonuniformly strained nanostructures, “dead layer” effects in nanocapacitor systems, and “giant” piezoelectricity in perovskite nanostructures among others. In this work, adopting a lattice dynamics based microscopic approach we provide estimates of the flexoelectric tensor for certain cubic crystalline ionic salts, perovskite dielectrics, III-V and II-VI semiconductors. We compare our estimates with experimental/theoretical values wherever available and also revisit the validity of an existing empirical scaling relationship for the magnitude of flexoelectric coefficients in terms of material parameters. It is interesting to note that two independent groups report values of flexoelectric properties for perovskite dielectrics that are orders of magnitude apart: Cross and co-workers from Penn State have carried out experimental studies on a variety of materials including barium titanate while Catalan and co-workers from Cambridge used theoretical ab initio techniques as well as experimental techniques to study paraelectric strontium titanate as well as ferroelectric barium titanate and lead titanate. We find that, in the case of perovskite dielectrics, our estimates agree to an order of magnitude with the experimental and theoretical estimates for strontium titanate. For barium titanate however, while our estimates agree to an order of magnitude with existing ab initio calculations, there exists a large discrepancy with experimental estimates. The possible reasons for the observed deviations are discussed.

Validation of micro-mechanical FFT-based simulations using High Energy Diffraction Microscopy on Ti-7Al

DOE PAGES

Tari, Vahid; Lebensohn, Ricardo A.; Pokharel, Reeju; ...

2018-08-01

Here, a validation is reported for micromechanical simulation using a reimplementation of an elasto-viscoplastic FFT-based (EVPFFT) formulation, i.e., the Micromechanical Analysis of Stress-strain Inhomogeneities with fast Fourier transform (MASSIF) code, against experimental data obtained from synchrotron x-ray diffraction. The experimental data was collected during in-situ deformation of a titanium alloy specimen by High Energy Diffraction Microscopy (HEDM), which provided the average elastic strain tensor and orientation of each grain in a polycrystalline sample. MASSIF was used to calculate the local micromechanical fields in a Ti-7Al polycrystalline sample at different load levels. The initially attempted simulation showed that, although the effectivemore » response was calibrated to reproduce the experiment, MASSIF was not able to reproduce the micromechanical fields at the scale of individual grains. The differences between calculated and measured averages at the grain scale were related to initial residual strains resulting from the prior processing of the material, which had not been incorporated in the original calculation. Accordingly, a new simulation was instantiated using information on the measured residual strains to define a set of eigenstrains, calculated via an Eshelby approximation. This initialization significantly improved the correlation between calculated and simulated fields for all strain and stress components, for measurements performed within the elastic regime. For the measurements at the highest load, which was past plastic yield, the correlations deteriorated because of plastic deformation at the grain level and the lack of an accurate enough constitutive description in this deformation regime.« less

Validation of micro-mechanical FFT-based simulations using High Energy Diffraction Microscopy on Ti-7Al

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tari, Vahid; Lebensohn, Ricardo A.; Pokharel, Reeju

Here, a validation is reported for micromechanical simulation using a reimplementation of an elasto-viscoplastic FFT-based (EVPFFT) formulation, i.e., the Micromechanical Analysis of Stress-strain Inhomogeneities with fast Fourier transform (MASSIF) code, against experimental data obtained from synchrotron x-ray diffraction. The experimental data was collected during in-situ deformation of a titanium alloy specimen by High Energy Diffraction Microscopy (HEDM), which provided the average elastic strain tensor and orientation of each grain in a polycrystalline sample. MASSIF was used to calculate the local micromechanical fields in a Ti-7Al polycrystalline sample at different load levels. The initially attempted simulation showed that, although the effectivemore » response was calibrated to reproduce the experiment, MASSIF was not able to reproduce the micromechanical fields at the scale of individual grains. The differences between calculated and measured averages at the grain scale were related to initial residual strains resulting from the prior processing of the material, which had not been incorporated in the original calculation. Accordingly, a new simulation was instantiated using information on the measured residual strains to define a set of eigenstrains, calculated via an Eshelby approximation. This initialization significantly improved the correlation between calculated and simulated fields for all strain and stress components, for measurements performed within the elastic regime. For the measurements at the highest load, which was past plastic yield, the correlations deteriorated because of plastic deformation at the grain level and the lack of an accurate enough constitutive description in this deformation regime.« less

Transversely Isotropic Hyperelastic Constitutive Model of Short Fiber Reinforced EPDM Based on Tensor Function

NASA Astrophysics Data System (ADS)

Feng, Q. L.; Li, C.; Liao, Y. F.

2017-12-01

Short fiber reinforced EPDM is a new kind of composite material used in solid rocket motor winding and coating. It has relatively large deformation under the small stress condition, and the physical non-linear characteristic is obvious. Due to the addition of fiber in the specific direction of the rubber, the macroscopic mechanical properties are expressed as transversely isotropic properties. In order to describe the mechanical behavior under the impact and vibration, the transversely isotropic hyperelastic constitutive model based on tensor function is proposed. The symmetry of the transversely isotropic incompressible material limits the stress tensor ‘ K ’ to be characterized as a function of 5 tensor invariants and 4 scalar invariants. The third power constitutive equations of the model give 12 independent elastic constants of the transversely isotropic nonlinear elastic material. The experimental results show that the non-zero elastic constants are different in the fiber direction and at the different strain rate. Number and value of adiabatic layer and related products R & D has a reference value.

3D tensor-based blind multispectral image decomposition for tumor demarcation

NASA Astrophysics Data System (ADS)

Kopriva, Ivica; Peršin, Antun

2010-03-01

Blind decomposition of multi-spectral fluorescent image for tumor demarcation is formulated exploiting tensorial structure of the image. First contribution of the paper is identification of the matrix of spectral responses and 3D tensor of spatial distributions of the materials present in the image from Tucker3 or PARAFAC models of 3D image tensor. Second contribution of the paper is clustering based estimation of the number of the materials present in the image as well as matrix of their spectral profiles. 3D tensor of the spatial distributions of the materials is recovered through 3-mode multiplication of the multi-spectral image tensor and inverse of the matrix of spectral profiles. Tensor representation of the multi-spectral image preserves its local spatial structure that is lost, due to vectorization process, when matrix factorization-based decomposition methods (such as non-negative matrix factorization and independent component analysis) are used. Superior performance of the tensor-based image decomposition over matrix factorization-based decompositions is demonstrated on experimental red-green-blue (RGB) image with known ground truth as well as on RGB fluorescent images of the skin tumor (basal cell carcinoma).

A study to evaluate non-uniform phase maps in shape memory alloys using finite element method

NASA Astrophysics Data System (ADS)

Motte, Naren

The unique thermo-mechanical behavior of Shape Memory Alloys (SMAs), such as their ability to recover the original shape upon heating or being able to tolerate large deformations without undergoing plastic transformations, makes them a good choice for actuators. This work studies their application in the aerospace and defense industries where SMA components can serve as release mechanisms for gates of enclosures that have to be deployed remotely. This work provides a novel approach in evaluating the stress and heat induced change of phase in a SMA, in terms of the transformation strain tensor. In particular, the FEA tool ANSYS has been used to perform a 2-D analysis of a Cu-Al-Zn-Mn SMA specimen undergoing a nontraditional loading path in two steps with stress and heating loads. In the first load step, tensile displacement is applied, followed by the second load step in which the specimen is heated while the end displacements are held constant. A number of geometric configurations are examined under the two step loading path. Strain results are used to calculate transformation strain which provides a quantitative measure of phase at a material point; when transformation strain is zero, the material point is either twinned martensite, or austenite depending on the temperature. Transformation strain value of unity corresponds to detwinned martensite. A value between zero and one indicates mixed phase. In this study, through two step loading in conjunction with transformation strain calculations, a method for mapping transient non-uniform distribution of phases in an SMA is introduced. Ability to obtain drastically different phase distributions under same loading path by modifying the geometry is demonstrated. The failure behavior of SMAs can be designed such that the load level the crack initiates and the path it propagates can be customized.

Anisotropic strain relaxation in (Ba0.6Sr0.4)TiO3 epitaxial thin films

NASA Astrophysics Data System (ADS)

Simon, W. K.; Akdogan, E. K.; Safari, A.

2005-05-01

We have studied the evolution of anisotropic epitaxial strains in ⟨110⟩-oriented (Ba0.60Sr0.40)TiO3 paraelectric (m3m) thin films grown on orthorhombic (mm2) ⟨100⟩-oriented NdGaO3 by high-resolution x-ray diffractometry. All the six independent components of the three-dimensional strain tensor were measured in films with 25-1200-nm thickness, from which the principal stresses and strains were obtained. Pole figure analysis indicated that the epitaxial relations are [001]m3m‖[001]mm2 and [1¯10]m3m‖[010]mm2 in the plane of the film, and [110]m3m‖[100]mm2 along the growth direction. The dislocation system responsible for strain relief along [001] has been determined to be ∣b ∣(001)=3/4∣b∣. Strain relief along the [1¯10] direction, on the other hand, has been determined to be due to a coupled mechanism given by ∣b∣(1¯10)=∣b∣ and ∣b∣(1¯10)=√3 /4∣b∣. Critical thicknesses, as determined from nonlinear regression using the Matthews-Blakeslee equation, for misfit dislocation formation along [001] and [1¯10] direction were found to be 5 and 7 nm, respectively. The residual strain energy density was calculated as ˜2.9×106J/m3 at 25 nm, which was found to relax an order of magnitude by 200 nm. At 200 nm, the linear dislocation density along [001] and [1¯10] are ˜6.5×105 and ˜6×105cm-1, respectively. For films thicker than 600 nm, additional strain relief occurred through surface undulations, indicating that this secondary strain-relief mechanism is a volume effect that sets in upon cooling from the growth temperature.

A strain energy filter for 3D vessel enhancement with application to pulmonary CT images.

PubMed

Xiao, Changyan; Staring, Marius; Shamonin, Denis; Reiber, Johan H C; Stolk, Jan; Stoel, Berend C

2011-02-01

The traditional Hessian-related vessel filters often suffer from detecting complex structures like bifurcations due to an over-simplified cylindrical model. To solve this problem, we present a shape-tuned strain energy density function to measure vessel likelihood in 3D medical images. This method is initially inspired by established stress-strain principles in mechanics. By considering the Hessian matrix as a stress tensor, the three invariants from orthogonal tensor decomposition are used independently or combined to formulate distinctive functions for vascular shape discrimination, brightness contrast and structure strength measuring. Moreover, a mathematical description of Hessian eigenvalues for general vessel shapes is obtained, based on an intensity continuity assumption, and a relative Hessian strength term is presented to ensure the dominance of second-order derivatives as well as suppress undesired step-edges. Finally, we adopt the multi-scale scheme to find an optimal solution through scale space. The proposed method is validated in experiments with a digital phantom and non-contrast-enhanced pulmonary CT data. It is shown that our model performed more effectively in enhancing vessel bifurcations and preserving details, compared to three existing filters. Copyright © 2010 Elsevier B.V. All rights reserved.

GPS-determined Crustal Deformation of South Korea after the 2011 Tohoku-Oki Earthquake: Straining Heterogeneity and Seismicity

NASA Astrophysics Data System (ADS)

Ree, J. H.; Kim, S.; Yoon, H. S.; Choi, B. K.; Park, P. H.

2017-12-01

The GPS-determined, pre-, co- and post-seismic crustal deformations of the Korean peninsula with respect to the 2011 Tohoku-Oki earthquake (Baek et al., 2012, Terra Nova; Kim et al., 2015, KSCE Jour. of Civil Engineering) are all stretching ones (extensional; horizontal stretching rate larger than horizontal shortening rate). However, focal mechanism solutions of earthquakes indicate that South Korea has been at compressional regime dominated by strike- and reverse-slip faultings. We reevaluated the velocity field of GPS data to see any effect of the Tohoku-Oki earthquake on the Korean crustal deformation and seismicity. To calculate the velocity gradient tensor of GPS sites, we used a gridding method based on least-square collocation (LSC). This LSC method can overcome shortcomings of the segmentation methods including the triangulation method. For example, an undesirable, abrupt change in components of velocity field occurs at segment boundaries in the segmentation methods. It is also known that LSC method is more useful in evaluating deformation patterns in intraplate areas with relatively small displacements. Velocity vectors of South Korea, pointing in general to 113° before the Tohoku-Oki earthquake, instantly changed their direction toward the epicenter (82° on average) during the Tohoku-Oki earthquake, and then gradually returned to the original position about 2 years after the Tohoku-Oki earthquake. Our calculation of velocity gradient tensors after the Tohoku-Oki earthquake shows that the stretching and rotating fields are quite heterogeneous, and that both stretching and shortening areas exist in South Korea. In particular, after the post-seismic relaxation ceased (i.e., from two years after the Tohoku-Oki earthquake), regions with thicker and thinner crusts tend to be shortening and stretching, respectively, in South Korea. Furthermore, the straining rate is larger in the regions with thinner crust. Although there is no meaningful correlation between seismicity and crustal straining pattern of South Korea at present, the seismicity tends to be localized along boundaries between areas with opposite vorticity, particularly for velocity field for one year after the Tohoku-Oki earthquake.

On the energy-momentum tensor of light in strong fields: an all optical view of the Abraham-Minkowski controversy

NASA Astrophysics Data System (ADS)

Macleod, Alexander J.; Noble, Adam; Jaroszynski, Dino A.

2017-05-01

The Abraham-Minkowski controversy is the debate surrounding the "correct" form of the energy-momentum tensor of light in a medium. Over a century of theoretical and experimental studies have consistently produced conflicting results, with no consensus being found on how best to describe the influence of a material on the propagation of light. It has been argued that the total energy-momentum tensor for each of the theories, which includes both wave and material components, are equal. The difficulty in separating the full energy-momentum tensor is generally attributed to the fact that one cannot obtain the energy-momentum tensor of the medium for real materials. Non-linear electrodynamics provides an opportunity to approach the debate from an all optical set up, where the role of the medium is replaced by the vacuum under the influence of a strong background field. We derive, from first principles, the general form of the energy-momentum tensor in such theories, and use our results to shed some light on this long standing issue.

One to Large N Gradiometry

NASA Astrophysics Data System (ADS)

Langston, C. A.

2017-12-01

The seismic wave gradient tensor can be derived from a variety of field observations including measurements of the wavefield by a dense seismic array, strain meters, and rotation meters. Coupled with models of wave propagation, wave gradients along with the original wavefield can give estimates of wave attributes that can be used to infer wave propagation directions, apparent velocities, spatial amplitude behavior, and wave type. Compact geodetic arrays with apertures of 0.1 wavelength or less can be deployed to provide wavefield information at a localized spot similar to larger phased arrays with apertures of many wavelengths. Large N, spatially distributed arrays can provide detailed information over an area to detect structure changes. Key to accurate computation of spatial gradients from arrays of seismic instruments is knowledge of relative instrument responses, particularly component sensitivities and gains, along with relative sensor orientations. Array calibration has been successfully performed for the 14-element Pinyon Flat, California, broadband array using long-period teleseisms to achieve relative precisions as small as 0.2% in amplitude and 0.35o in orientation. Calibration has allowed successful comparison of horizontal seismic strains from local and regional seismic events with the Plate Boundary Observatory (PBO) borehole strainmeter located at the facility. Strains from the borehole strainmeter in conjunction with ground velocity from a co-located seismometer are used as a "point" array in estimating wave attributes for the P-SV components of the wavefield. An effort is underway to verify the calibration of PBO strainmeters in southern California and their co-located borehole seismic sensors to create an array of point arrays for use in studies of regional wave propagation and seismic sources.

Computational aeroelastic analysis of aircraft wings including geometry nonlinearity

NASA Astrophysics Data System (ADS)

Tian, Binyu

The objective of the present study is to show the ability of solving fluid structural interaction problems more realistically by including the geometric nonlinearity of the structure so that the aeroelastic analysis can be extended into the onset of flutter, or in the post flutter regime. A nonlinear Finite Element Analysis software is developed based on second Piola-Kirchhoff stress and Green-Lagrange strain. The second Piola-Kirchhoff stress and Green-Lagrange strain is a pair of energetically conjugated tensors that can accommodate arbitrary large structural deformations and deflection, to study the flutter phenomenon. Since both of these tensors are objective tensors, i.e., the rigid-body motion has no contribution to their components, the movement of the body, including maneuvers and deformation, can be included. The nonlinear Finite Element Analysis software developed in this study is verified with ANSYS, NASTRAN, ABAQUS, and IDEAS for the linear static, nonlinear static, linear dynamic and nonlinear dynamic structural solutions. To solve the flow problems by Euler/Navier equations, the current nonlinear structural software is then embedded into ENSAERO, which is an aeroelastic analysis software package developed at NASA Ames Research Center. The coupling of the two software, both nonlinear in their own field, is achieved by domain decomposition method first proposed by Guruswamy. A procedure has been set for the aeroelastic analysis process. The aeroelastic analysis results have been obtained for fight wing in the transonic regime for various cases. The influence dynamic pressure on flutter has been checked for a range of Mach number. Even though the current analysis matches the general aeroelastic characteristic, the numerical value not match very well with previous studies and needs farther investigations. The flutter aeroelastic analysis results have also been plotted at several time points. The influences of the deforming wing geometry can be well seen in those plots. The movement of shock changes the aerodynamic load distribution on the wing. The effect of viscous on aeroelastic analysis is also discussed. Also compared are the flutter solutions with, or without the structural nonlinearity. As can be seen, linear structural solution goes to infinite, which can not be true in reality. The nonlinear solution is more realistic and can be used to understand the fluid and structure interaction behavior, to control, or prevent disastrous events. (Abstract shortened by UMI.)

Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method

NASA Technical Reports Server (NTRS)

Moghaddam, Masoud Ghorbani; Achuthan, A.; Bednacyk, B. A.; Arnold, S. M.; Pineda, E. J.

2014-01-01

A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.

Acoustics of two-component porous materials with anisotropic tortuosity

NASA Astrophysics Data System (ADS)

Albers, Bettina; Wilmanski, Krzysztof

2012-11-01

The paper is devoted to the analysis of monochromatic waves in two-component poroelastic materials described by a Biot-like model whose stress-strain relations are isotropic but the permeability is anisotropic. This anisotropy is induced by the anisotropy of the tortuosity which is given by a second order symmetric tensor. This is a new feature of the model while in earlier papers only isotropic permeabilities were considered. We show that this new model describes four modes of propagation. For our special choice of orientation of the direction of propagation these are two pseudo longitudinal modes P1 and P2, one pseudo transversal mode S2 and one transversal mode S1. The latter becomes also pseudo transversal in the general case of anisotropy. We analyze the speeds of propagation and the attenuation of these waves as well as the polarization properties in dependence on the orientation of the principal directions of the tortuosity. We indicate the practical importance of different shear (transversal) modes of propagation in a possible new nondestructive test of geophysical materials.

Complex conductivity of organic-rich shales

NASA Astrophysics Data System (ADS)

Woodruff, W. F.; Revil, A.; Torres-Verdin, C.

2013-12-01

We can accurately determine the intrinsic anisotropy and material properties in the laboratory, providing empirical evidence of transverse isotropy and the polarization of the organic and metallic fractions in saturated and unsaturated shales. We develop two distinct approaches to obtain the complex conductivity tensor from spectral induced polarization (SIP) measurements. Experimental results indicate clear anisotropy, and characterize the effects of thermal maturation, TOC, and pyrite, aiding in the calibration and interpretation of geophysical data. SIP is a non-intrusive measurement, sensitive to the surface conductance of mineral grains, frequency-dependent polarization of the electrical double layer, and bulk conductivity of the pore water. The in-phase and quadrature components depend upon parameters of principal importance in unconventional shale formation evaluation (e.g., the distribution of pore throat sizes, formation factor, permeability, salinity and cation exchange capacity (CEC), fluid saturation and wettability). In addition to the contribution of the electrical double layer of non-conducting minerals to surface conductivity, we have observed a clear relaxation associated with kerogen pyrolysis, pyrite distribution, and evidence that the CEC of the kerogen fraction may also contribute, depending on thermal maturation history. We utilize a recent model for anisotropic complex conductivity, and rigorous experimental protocols to quantify the role of kerogen and pyrolysis on surface and quadrature conductivity in mudrocks. The complex conductivity tensor σ* describes the directional dependence of electrical conduction in a porous medium, and accounts for both conduction and polarization. The complex-valued tensor components are given as σ*ij , where σ'ij represents in-phase and σ"ij denotes quadrature conductivities. The directional dependence of the complex conductivity tensor is relegated to the textural properties of the material. The components of the formation factor and connectivity (tortuosity) tensors Fij and Tij (affecting the bulk and surface conductivity, respectively) are correlated as Fij=TijΦ. Both conductivity and connectivity tensors share the same eigenvectors; the anisotropy ratio is equivalent in TI media. At high pore water salinity, surface and quadrature conductivity share the same bulk tortuosity; when surface conductivity dominates (low salinity), conductivity is controlled by the surface conductance, and the tortuosity of electrical current along mineral surfaces usually higher than that of the pore water. We developed two distinct SIP measurement protocols to obtain the tensor: (1) azimuthal sampling and inversion of phasor potentials through the full-field solution of the Laplace equation; (2) direct measurement of complex conductivity eigenvalues by polarized, single-component stimulus current. Experiments also include unsaturated and saturated measurements with three brines of known salinity and pH, at log-distributed frequencies ranging 1 mHz to 45 kHz. Both azimuthal spectra and eigenvalue spectra validate the theoretical model and illustrate the effectiveness of the protocols themselves. We obtain the textural tensors and invert key parameters including Archie exponents and CEC, and characterize the relaxation phenomena associated with kerogen content and maturity for multiphase fluid systems.

Neotectonic activity and parameters of seismotectonic deformations of seismic belts in Northeast Asia

NASA Astrophysics Data System (ADS)

Imaeva, Lyudmila; Gusev, Georgy; Imaev, Valerii; Mel'nikova, Valentina

2017-10-01

The Arctic-Asian and Okhotsk-Chukotka seismic belts bordering the Kolyma-Chukotka crustal plate are the subject of our study aimed at reconstructing the stress-strain state of the crust and defining the types of seismotectonic deformation (STD) in the region. Based on the degrees of activity of geodynamic processes, the regional principles for ranking neotectonic structures were constrained, and the corresponding classes of the discussed neotectonic structures were substantiated. We analyzed the structural tectonic positions of the modern structures, their deep structure parameters, and the systems of active faults in the Laptev, Kharaulakh, Koryak, and Chukotka segments and Chersky seismotectonic zone, as well as the tectonic stress fields revealed by tectonophysical analysis of the Late Cenozoic faults and folds. From the earthquake focal mechanisms, the average seismotectonic strain tensors were estimated. Using the geological, geostructural, geophysical and GPS data, and corresponding average tensors, the directions of the principal stress axes were determined. A regularity in the changes of tectonic settings in the Northeast Arctic was revealed.

The dynamic generalization of the Eshelby inclusion problem and its static limit

PubMed Central

2016-01-01

The dynamic generalization of the celebrated Eshelby inclusion with transformation strain is the (subsonically) self-similarly expanding ellipsoidal inclusion starting from the zero dimension. The solution of the governing system of partial differential equations was obtained recently by Ni & Markenscoff (In press. J. Mech. Phys. Solids (doi:10.1016/j.jmps.2016.02.025)) on the basis of the Radon transformation, while here an alternative method is presented. In the self-similarly expanding motion, the Eshelby property of constant constrained strain is valid in the interior domain of the expanding ellipsoid where the particle velocity vanishes (lacuna). The dynamic Eshelby tensor is obtained in integral form. From it, the static Eshelby tensor is obtained by a limiting procedure, as the axes' expansion velocities tend to zero and time to infinity, while their product is equal to the length of the static axis. This makes the Eshelby problem the limit of its dynamic generalization. PMID:27493574

Strain Rate Tensor Estimation in Cine Cardiac MRI Based on Elastic Image Registration

NASA Astrophysics Data System (ADS)

Sánchez-Ferrero, Gonzalo Vegas; Vega, Antonio Tristán; Grande, Lucilio Cordero; de La Higuera, Pablo Casaseca; Fernández, Santiago Aja; Fernández, Marcos Martín; López, Carlos Alberola

In this work we propose an alternative method to estimate and visualize the Strain Rate Tensor (SRT) in Magnetic Resonance Images (MRI) when Phase Contrast MRI (PCMRI) and Tagged MRI (TMRI) are not available. This alternative is based on image processing techniques. Concretely, image registration algorithms are used to estimate the movement of the myocardium at each point. Additionally, a consistency checking method is presented to validate the accuracy of the estimates when no golden standard is available. Results prove that the consistency checking method provides an upper bound of the mean squared error of the estimate. Our experiments with real data show that the registration algorithm provides a useful deformation field to estimate the SRT fields. A classification between regional normal and dysfunctional contraction patterns, as compared with experts diagnosis, points out that the parameters extracted from the estimated SRT can represent these patterns. Additionally, a scheme for visualizing and analyzing the local behavior of the SRT field is presented.

Harnessing Multivariate Statistics for Ellipsoidal Data in Structural Geology

NASA Astrophysics Data System (ADS)

Roberts, N.; Davis, J. R.; Titus, S.; Tikoff, B.

2015-12-01

Most structural geology articles do not state significance levels, report confidence intervals, or perform regressions to find trends. This is, in part, because structural data tend to include directions, orientations, ellipsoids, and tensors, which are not treatable by elementary statistics. We describe a full procedural methodology for the statistical treatment of ellipsoidal data. We use a reconstructed dataset of deformed ooids in Maryland from Cloos (1947) to illustrate the process. Normalized ellipsoids have five degrees of freedom and can be represented by a second order tensor. This tensor can be permuted into a five dimensional vector that belongs to a vector space and can be treated with standard multivariate statistics. Cloos made several claims about the distribution of deformation in the South Mountain fold, Maryland, and we reexamine two particular claims using hypothesis testing: 1) octahedral shear strain increases towards the axial plane of the fold; 2) finite strain orientation varies systematically along the trend of the axial trace as it bends with the Appalachian orogen. We then test the null hypothesis that the southern segment of South Mountain is the same as the northern segment. This test illustrates the application of ellipsoidal statistics, which combine both orientation and shape. We report confidence intervals for each test, and graphically display our results with novel plots. This poster illustrates the importance of statistics in structural geology, especially when working with noisy or small datasets.

Chemical (knight) shift distortions of quadrupole-split deuteron powder spectra in solids

NASA Astrophysics Data System (ADS)

Torgeson, D. R.; Schoenberger, R. J.; Barnes, R. G.

In strong magnetic fields (e.g., 8 Tesla) anisotropy of the shift tensor (chemical or Knight shift) can alter the spacings of the features of quadrupole-split deuteron spectra of polycrystalline samples. Analysis of powder spectra yields both correct quadrupole coupling and symmetry parameters and all the components of the shift tensor. Synthetic and experimental examples are given to illustrate such behavior.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Finite element analysis of the tetragonal to monoclinic phase transformation during oxidation of zirconium alloys

NASA Astrophysics Data System (ADS)

Platt, P.; Frankel, P.; Gass, M.; Howells, R.; Preuss, M.

2014-11-01

Corrosion is a key limiting factor in the degradation of zirconium alloys in light water reactors. Developing a mechanistic understanding of the corrosion process offers a route towards improving safety and efficiency as demand increases for higher burn-up of fuel. Oxides formed on zirconium alloys are composed of both monoclinic and meta-stable tetragonal phases, and are subject to a number of potential mechanical degradation mechanisms. The work presented investigates the link between the tetragonal to monoclinic oxide phase transformation and degradation of the protective character of the oxide layer. To achieve this, Abaqus finite element analysis of the oxide phase transformation has been carried out. Study of the change in transformation strain energy shows how relaxation of oxidation induced stress and fast fracture at the metal-oxide interface could destabilise the tetragonal phase. Central to this is the identification of the transformation variant most likely to form, and understanding why twinning of the transformed grain is likely to occur. Development of transformation strain tensors and analysis of the strain components allows some separation of dilatation and shear effects. Maximum principal stress is used as an indication of fracture in the surrounding oxide layer. Study of the stress distributions shows the way oxide fracture is likely to occur and the differing effects of dilatation and shape change. Comparison with literature provides qualitative validation of the finite element simulations.

Strain dynamics for vortex ring mixing process

NASA Astrophysics Data System (ADS)

Bouremel, Yann; Yianneskis, Michael; Ducci, Andrea

2009-11-01

Simultaneous PIV-PLIF measurements were carried out to investigate the mixing occurring in a laminar vortex ring flow during the formation stage (Re=357-1072). In the first part of the work a control volume analysis was used to determine the variation in time of the scalar concentration mean, variance, and probability density function. In the second part the advection-diffusion differential equations of the scalar, ξ, and of its energy, 0.5 2̂, were studied in depth to gain insight into the effect of the strain rate tensor, S, on the local scalar concentration for increasing Re. The measurements were obtained with a high spatial resolution (12 μm for the PLIF) in order to resolve the scalar dissipative scales. Reliable estimates of the scalar dissipation rate (∇ξ.∇ξ), and of the symmetric contraction term (∇ξ.S .∇ξ), shown in equation 1, were obtained. ∇ξ.S .∇ξ accounts for the reduction of scalar dissipation due to the straining component directed as the local scalar gradient (see Southerland et al.footnotetextSoutherland K B., Porter III J. R., Dahm, W. J. A., Buch K. A., An experimental study of the molecular mixing process in an axisymmetric laminar vortex ring, Phys. Fluids A 3 (5), May 1991) Equation 1: ( t+u.∇+1ReSc∇^2 )12( ∇ξ.∇ξ )=-( ∇ξ.S.∇ξ )-1ReSc∇(∇ξ):∇(∇ξ)

Berkeley Seismological Laboratory Seismic Moment Tensor Report for the August 6, 2007 M3.9 Seismic event in central Utah

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ford, S; Dreger, D; Hellweg, P

2007-08-08

We have performed a complete moment tensor analysis of the seismic event, which occurred on Monday August 6, 2007 at 08:48:40 UTC 21 km from Mt.Pleasant, Utah. In our analysis we utilized complete three-component seismic records recorded by the USArray, University of Utah, and EarthScope seismic arrays. The seismic waveform data was integrated to displacement and filtered between 0.02 to 0.10 Hz following instrument removal. We used the Song et al. (1996) velocity model to compute Green's functions used in the moment tensor inversion. A map of the stations we used and the location of the event is shown inmore » Figure 1. In our moment tensor analysis we assumed a shallow source depth of 1 km consistent with the shallow depth reported for this event. As shown in Figure 2 the results point to a source mechanism with negligible double-couple radiation and is composed of dominant CLVD and implosive isotropic components. The total scalar seismic moment is 2.12e22 dyne cm corresponding to a moment magnitude (Mw) of 4.2. The long-period records are very well matched by the model (Figure 2) with a variance reduction of 73.4%. An all dilational (down) first motion radiation pattern is predicted by the moment tensor solution, and observations of first motions are in agreement.« less

Fermionic topological quantum states as tensor networks

NASA Astrophysics Data System (ADS)

Wille, C.; Buerschaper, O.; Eisert, J.

2017-06-01

Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.

Magnetic resonance and diffusion tensor imaging analyses indicate heterogeneous strains along human medial gastrocnemius fascicles caused by submaximal plantar-flexion activity.

PubMed

Karakuzu, Agah; Pamuk, Uluç; Ozturk, Cengizhan; Acar, Burak; Yucesoy, Can A

2017-05-24

Sarcomere length changes are central to force production and excursion of skeletal muscle. Previous modeling indicates non-uniformity of that if mechanical interaction of muscle with its surrounding muscular and connective tissues is taken into account. Hence, quantifying length changes along the fascicles of activated human muscle in vivo is crucial, but this is lacking due to technical complexities. Combining magnetic resonance imaging deformation analyses and diffusion tensor imaging tractography, the aim was to test the hypothesis that submaximal plantar flexion activity at 15% MVC causes heterogeneous length changes along the fascicles of human medial gastrocnemius (GM) muscle. A general fascicle strain distribution pattern shown for all subjects indicates that proximal track segments are shortened, whereas distal ones are lengthened (e.g., by 13% and 29%, respectively). Mean fiber direction strains of different tracts also shows heterogeneity (for up to 57.5% of the fascicles). Inter-subject variability of amplitude and distribution of fascicle strains is notable. These findings confirm the hypothesis and are solid indicators for the functionally dependent mechanics of human muscle, in vivo. Heterogeneity of fascicle strains can be explained by epimuscular myofascial force transmission. To the best of our knowledge, this is the first study, which quantified local deformations along human skeletal muscle fascicles caused by sustained submaximal activation. The present approach and indicated fascicle strain heterogeneity has numerous implications for muscle function in health and disease to estimate the muscle's contribution to the joint moment and excursion and to evaluate mechanisms of muscle injury and several treatment techniques. Copyright © 2017 Elsevier Ltd. All rights reserved.

Progress in turbulence modeling for complex flow fields including effects of compressibility

NASA Technical Reports Server (NTRS)

Wilcox, D. C.; Rubesin, M. W.

1980-01-01

Two second-order-closure turbulence models were devised that are suitable for predicting properties of complex turbulent flow fields in both incompressible and compressible fluids. One model is of the "two-equation" variety in which closure is accomplished by introducing an eddy viscosity which depends on both a turbulent mixing energy and a dissipation rate per unit energy, that is, a specific dissipation rate. The other model is a "Reynolds stress equation" (RSE) formulation in which all components of the Reynolds stress tensor and turbulent heat-flux vector are computed directly and are scaled by the specific dissipation rate. Computations based on these models are compared with measurements for the following flow fields: (a) low speed, high Reynolds number channel flows with plane strain or uniform shear; (b) equilibrium turbulent boundary layers with and without pressure gradients or effects of compressibility; and (c) flow over a convex surface with and without a pressure gradient.

Effect of thermal exposure on the residual stress relaxation in a hardened cylindrical sample under creep conditions

NASA Astrophysics Data System (ADS)

Radchenko, V. P.; Saushkin, M. N.; Tsvetkov, V. V.

2016-05-01

This paper describes the effect of thermal exposure (high-temperature exposure) ( T = 675°C) on the residual creep stress relaxation in a surface hardened solid cylindrical sample made of ZhS6UVI alloy. The analysis is carried out with the use of experimental data for residual stresses after micro-shot peening and exposures to temperatures equal to T = 675°C during 50, 150, and 300 h. The paper presents the technique for solving the boundary-value creep problem for the hardened cylindrical sample with the initial stress-strain state under the condition of thermal exposure. The uniaxial experimental creep curves obtained under constant stresses of 500, 530, 570, and 600 MPa are used to construct the models describing the primary and secondary stages of creep. The calculated and experimental data for the longitudinal (axial) tensor components of residual stresses are compared, and their satisfactory agreement is determined.

White matter damage in primary progressive aphasias: a diffusion tensor tractography study

PubMed Central

Galantucci, Sebastiano; Tartaglia, Maria Carmela; Wilson, Stephen M.; Henry, Maya L.; Filippi, Massimo; Agosta, Federica; Dronkers, Nina F.; Henry, Roland G.; Ogar, Jennifer M.; Miller, Bruce L.

2011-01-01

Primary progressive aphasia is a clinical syndrome that encompasses three major phenotypes: non-fluent/agrammatic, semantic and logopenic. These clinical entities have been associated with characteristic patterns of focal grey matter atrophy in left posterior frontoinsular, anterior temporal and left temporoparietal regions, respectively. Recently, network-level dysfunction has been hypothesized but research to date has focused largely on studying grey matter damage. The aim of this study was to assess the integrity of white matter tracts in the different primary progressive aphasia subtypes. We used diffusion tensor imaging in 48 individuals: nine non-fluent, nine semantic, nine logopenic and 21 age-matched controls. Probabilistic tractography was used to identify bilateral inferior longitudinal (anterior, middle, posterior) and uncinate fasciculi (referred to as the ventral pathway); and the superior longitudinal fasciculus segmented into its frontosupramarginal, frontoangular, frontotemporal and temporoparietal components, (referred to as the dorsal pathway). We compared the tracts’ mean fractional anisotropy, axial, radial and mean diffusivities for each tract in the different diagnostic categories. The most prominent white matter changes were found in the dorsal pathways in non-fluent patients, in the two ventral pathways and the temporal components of the dorsal pathways in semantic variant, and in the temporoparietal component of the dorsal bundles in logopenic patients. Each of the primary progressive aphasia variants showed different patterns of diffusion tensor metrics alterations: non-fluent patients showed the greatest changes in fractional anisotropy and radial and mean diffusivities; semantic variant patients had severe changes in all metrics; and logopenic patients had the least white matter damage, mainly involving diffusivity, with fractional anisotropy altered only in the temporoparietal component of the dorsal pathway. This study demonstrates that both careful dissection of the main language tracts and consideration of all diffusion tensor metrics are necessary to characterize the white matter changes that occur in the variants of primary progressive aphasia. These results highlight the potential value of diffusion tensor imaging as a new tool in the multimodal diagnostic evaluation of primary progressive aphasia. PMID:21666264

Tissue signature characterisation of diffusion tensor abnormalities in cerebral gliomas.

PubMed

Price, Stephen J; Peña, Alonso; Burnet, Neil G; Jena, Raj; Green, Hadrian A L; Carpenter, T Adrian; Pickard, John D; Gillard, Jonathan H

2004-10-01

The inherent invasiveness of malignant cells is a major determinant of the poor prognosis of cerebral gliomas. Diffusion tensor MRI (DTI) can identify white matter abnormalities in gliomas that are not seen on conventional imaging. By breaking down DTI into its isotropic (p) and anisotropic (q) components, we can determine tissue diffusion "signatures". In this study we have characterised these abnormalities in peritumoural white matter tracts. Thirty-five patients with cerebral gliomas and seven normal volunteers were imaged with DTI and T2-weighted sequences at 3 T. Displaced, infiltrated and disrupted white matter tracts were identified using fractional anisotropy (FA) maps and directionally encoded colour maps and characterised using tissue signatures. The diffusion tissue signatures were normal in ROIs where the white matter was displaced. Infiltrated white matter was characterised by an increase in the isotropic component of the tensor (p) and a less marked reduction of the anisotropic component (q). In disrupted white matter tracts, there was a marked reduction in q and increase in p. The direction of water diffusion was grossly abnormal in these cases. Diffusion tissue signatures may be a useful method of assessing occult white matter infiltration. Copyright 2004 Springer-Verlag

X-ray Topographic Methods and Application to Analysis of Electronic Materials

NASA Technical Reports Server (NTRS)

Mayo, W. E.; Liu, H. Y.; Chaudhuri, J.

1984-01-01

Three supplementary X-ray techniques new to semiconductor applications are discussed. These are the Computer Aided Rocking Curve Analyzer, the Divergent Beam Method and a new method based on enhanced X-ray flourescence. The first method is used for quantitative mapping of an elastic or plastic strain field while the other two methods are used only to measure elastic strains. The divergent beam method is used for measuring the full strain tensor while the microfluorescence method is useful for monitoring strain uniformity. These methods are discussed in detail and examples of their application is presented. Among these are determination of the full strain ellipsoid in state-of-the-art liquid phase epitaxy deposited III-V epitaxial films; mapping of the plastic strain concentrations in tensile deformed Si; and quantitative determination of damage in V3Si due to ion implantation.

Substrate strain induced interaction of adatoms on W (110)

NASA Astrophysics Data System (ADS)

Kappus, W.

1980-09-01

The interaction of adatoms due to elastic strains created in an elastically isotropic substrate is investigated. For cases where the adatoms occupy sites with low symmetry, an angular dependent interaction results which falls off as s-3 at large distances. An exact expression is given for the long range interaction in terms of an anisotropy parameter of the force dipole tensor. The short range interaction is calculated by introducing a smooth cutoff. Interactions of adatoms on near neighbour sites on W (110) are given.

The exponentiated Hencky energy: anisotropic extension and case studies

NASA Astrophysics Data System (ADS)

Schröder, Jörg; von Hoegen, Markus; Neff, Patrizio

2017-10-01

In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient \\varvec{F} to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies.

Composite Strengthening.

DTIC Science & Technology

1985-01-01

fictitious eigenstrain (2 2 ) which was introduced to connect the present problem to "inclusion problem" and i is the average ij strain disturbance in the...5) and (6), we obtain eij =- Vw(eij - eij) (8) According to Eshelby, eij is related to the total eigenstrain ekZ as e S e (9) ij ijk2. Id w where...tensors of the matrix (D-Q) and fiber (a) are fA ijkt ,ijk respectively. Following Eshelby, the transformation strain(l I ) or eigenstrain ( 2 2) is given

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

NASA Technical Reports Server (NTRS)

Rodal, J. J. A.; Witmer, E. A.

1979-01-01

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

Accommodation by Varying Strain Regimes along the Northern Luzon Arc (Coastal Range, Taiwan) - Insights from Focal Mechanism Strain Inversions

NASA Astrophysics Data System (ADS)

O'Hara, D.; Lee, J.; Lewis, J. C.; Rau, R.

2013-12-01

Taiwan is the product of modern subduction polarity reversal coupled with arc-continent collision. The NW-moving Philippine Sea plate (PSP) subducts beneath the Eurasian plate (EUR) to the northeast of Taiwan at the Ryukyu trench, while overriding EUR south of Taiwan at the Manila trench, bringing the Luzon volcanic arc into collision with the deforming sediments of the Eurasian passive margin. The obliquity between the N-S trending Luzon Arc (LA) and NE-SW trending passive margin is causing the southward, temporal propagation of collision since ~6 Ma. The collided forearc and clastic sediments accreted by the advancing arc created the Coastal Range (CR), whose western-most extent lies at the suture zone between the two plates, the NNE-SSW trending Longitudinal Valley Fault (LVF). In order to understand the change in stress along the northern LA as it docks onto EUR, we inverted over 1900 relocated earthquake focal mechanism solutions within the on-land CR and offshore LA regions for spatial strain tensors. The focal mechanisms cover seismicity from 1991-2013, ranging in depths 0-112 km and magnitudes 2.22-6.92. For our analyses, we grouped the focal mechanisms based on 15' Latitudinal intervals along the study area and inverted the data for best-fit strain tensors using a micropolar continuum model of crustal deformation. Results suggest dominant compression in all regions with accommodation occurring through oblique reverse faults of varying dips. Trends of σ1 rotate clockwise (CW) from 100° in the south to 155° in the north. This CW rotation is also observed in the preferred nodal plane slip vector trends - from E-W orientation in the south to NW-SE in the north. The rotation of σ1 and slip vector trends creates varying degrees of obliquity with the direction normal (DN) to CR (112°). The trends in the southern part of the study area show obliquity counterclockwise (CCW) to DN; trends in the central part are near parallel to DN; and trends in the northern part show obliquity CW to DN. GPS vectors from 2008-2012 using an ITRF reference frame show similar changes in obliquity with GPS velocity trends oblique CCW and CW to DN in the southern and northern areas, respectively, and near parallel to DN in the central area. Our results suggest the accommodation of three varying strain regimes along the northern LA (CR) system - (1) strain partitioning within the Manila forearc basin due to the obliquity between N-S trending LA and NW trending convergence vector; (2) convergence-related strain in the central LVF and CR along NNE trending major thrust faults with a small oblique component due to the obliquity between DN and the convergence vector; and (3) strain partitioning along the Ryukyu trench and forearc basin due to the obliquity between northward subducting plate along the WNW- ESE trending Ryukyu trench and NW convergence vector. As a result, the different subducting characteristics of strain regimes correspond to the different stages of arc accretion/collision, from south to north: pre-collision, present collision, waning collision, and subduction.

A synchrotron study of defect and strain inhomogeneity in laser-assisted three-dimensionally-printed Ni-based superalloy

DOE PAGES

Li, Yao; Qian, Dan; Xue, Jiawei; ...

2015-11-02

Synchrotron X-ray microdiffraction was employed to investigate the inhomogeneous distribution of defect and residual strain in the transitional region between the dendritic and stray grains in a laser-assisted 3D printed Ni-based superalloy. The dendritic region was found to be under tensile strain transversely to the primary dendrite arm directions. The dendrite edges, where high level of strains and geometrically necessary dislocations were detected, were discerned as low angle grain boundaries. Lastly, high angle grain boundaries were observed in the stray grain region, and the orientation of the strain tensor in this region varied dramatically at the micron scale, in contrastmore » with the more or less homogeneous distribution in the dendritic region.« less

The Speech multi features fusion perceptual hash algorithm based on tensor decomposition

NASA Astrophysics Data System (ADS)

Huang, Y. B.; Fan, M. H.; Zhang, Q. Y.

2018-03-01

With constant progress in modern speech communication technologies, the speech data is prone to be attacked by the noise or maliciously tampered. In order to make the speech perception hash algorithm has strong robustness and high efficiency, this paper put forward a speech perception hash algorithm based on the tensor decomposition and multi features is proposed. This algorithm analyses the speech perception feature acquires each speech component wavelet packet decomposition. LPCC, LSP and ISP feature of each speech component are extracted to constitute the speech feature tensor. Speech authentication is done by generating the hash values through feature matrix quantification which use mid-value. Experimental results showing that the proposed algorithm is robust for content to maintain operations compared with similar algorithms. It is able to resist the attack of the common background noise. Also, the algorithm is highly efficiency in terms of arithmetic, and is able to meet the real-time requirements of speech communication and complete the speech authentication quickly.

Off-shell supergravity in five dimensions and supersymmetric brane world scenarios

NASA Astrophysics Data System (ADS)

Zucker, M.

2003-09-01

We review the construction of off-shell Poincaré supergravity in five dimensions. We describe in detail the minimal multiplet, which is the basic building block, containing the propagating fields of supergravity. All matter multiplets containing (8 + 8) components, being the smallest matter multiplets in five dimensions, are constructed. Using these multiplets the complete tensor calculus for supergravity is developed. As expected it turns out, that there exist three distinct minimal (i.e. containing (48 + 48) field components) off-shell supergravities. The lagrangians for these theories and their gauged variants are given explicitly. These results are used in the second part to develop a tensor calculus on the orbifold . Gauged supergravity on the orbifold with additional cosmological constants at the fixpoints, is constructed. This generalizes the work of Randall-Sundrum to local supersymmetry. The developed tensor calculus is used to extend this model to include matter located at the fixpoints. Chiral and super Yang-Mills multiplets at the fixpoints are considered.

Electric Dipole-Magnetic Dipole Polarizability and Anapole Magnetizability of Hydrogen Peroxide as Functions of the HOOH Dihedral Angle.

PubMed

Pelloni, S; Provasi, P F; Pagola, G I; Ferraro, M B; Lazzeretti, P

2017-12-07

The trace of tensors that account for chiroptical response of the H 2 O 2 molecule is a function of the HO-OH dihedral angle. It vanishes at 0° and 180°, due to the presence of molecular symmetry planes, but also for values in the range 90-100° of this angle, in which the molecule is unquestionably chiral. Such an atypical effect is caused by counterbalancing contributions of diagonal tensor components with nearly maximal magnitude but opposite sign, determined by electron flow in open or closed helical paths, and associated with induced electric and magnetic dipole moments and anapole moments. For values of dihedral angle external to the 90-100° interval, the helical paths become smaller in size, thus reducing the amount of cancellation among diagonal components. Shrinking of helical paths determines the appearance of extremum values of tensor traces approximately at 50° and 140° dihedral angles.

Spatial profile reconstruction of individual componentsof the nonlinear susceptibility tensors {chi}-circumflex {sup (3)}(z, {omega}', {omega}' -{omega}, {omega}) and {chi}-circumflex {sup (3)}(z, 2{omega}{+-}{omega}', {+-}{omega}', {omega}, {omega}) of a one-dimensionally inhomogeneous medium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golubkov, A A; Makarov, Vladimir A

We have proved for the first time and proposed an algorithm of unique spatial profile reconstruction of the components {chi}-circumflex {sup (3)}{sub yyyy} of complex tensors {chi}-circumflex {sup (3)}(z, {omega}', {omega}', -{omega}, {omega}) and {chi}-circumflex {sup (3)}(z, 2{omega}{+-}{omega}', {+-}{omega}', {omega}, {omega}), describing four-photon interaction of light waves in a one-dimensionally inhomogeneous plate, whose medium has a symmetry plane m{sub y} that is perpendicular to its surface. For the media with an additional symmetry axis 2{sub z}, 4{sub z}, 6{sub z} or {infinity}{sub z} that is perpendicular to the plate surface, the proposed method can be used to reconstruct about one-fifthmore » of all independent components of the above tensors. (nonlinear optical phenomena)« less

Adsorption-Induced Deformation of Hierarchically Structured Mesoporous Silica—Effect of Pore-Level Anisotropy

PubMed Central

2017-01-01

The goal of this work is to understand adsorption-induced deformation of hierarchically structured porous silica exhibiting well-defined cylindrical mesopores. For this purpose, we performed an in situ dilatometry measurement on a calcined and sintered monolithic silica sample during the adsorption of N2 at 77 K. To analyze the experimental data, we extended the adsorption stress model to account for the anisotropy of cylindrical mesopores, i.e., we explicitly derived the adsorption stress tensor components in the axial and radial direction of the pore. For quantitative predictions of stresses and strains, we applied the theoretical framework of Derjaguin, Broekhoff, and de Boer for adsorption in mesopores and two mechanical models of silica rods with axially aligned pore channels: an idealized cylindrical tube model, which can be described analytically, and an ordered hexagonal array of cylindrical mesopores, whose mechanical response to adsorption stress was evaluated by 3D finite element calculations. The adsorption-induced strains predicted by both mechanical models are in good quantitative agreement making the cylindrical tube the preferable model for adsorption-induced strains due to its simple analytical nature. The theoretical results are compared with the in situ dilatometry data on a hierarchically structured silica monolith composed by a network of mesoporous struts of MCM-41 type morphology. Analyzing the experimental adsorption and strain data with the proposed theoretical framework, we find the adsorption-induced deformation of the monolithic sample being reasonably described by a superposition of axial and radial strains calculated on the mesopore level. The structural and mechanical parameters obtained from the model are in good agreement with expectations from independent measurements and literature, respectively. PMID:28547995

Adsorption-Induced Deformation of Hierarchically Structured Mesoporous Silica-Effect of Pore-Level Anisotropy.

PubMed

Balzer, Christian; Waag, Anna M; Gehret, Stefan; Reichenauer, Gudrun; Putz, Florian; Hüsing, Nicola; Paris, Oskar; Bernstein, Noam; Gor, Gennady Y; Neimark, Alexander V

2017-06-06

The goal of this work is to understand adsorption-induced deformation of hierarchically structured porous silica exhibiting well-defined cylindrical mesopores. For this purpose, we performed an in situ dilatometry measurement on a calcined and sintered monolithic silica sample during the adsorption of N 2 at 77 K. To analyze the experimental data, we extended the adsorption stress model to account for the anisotropy of cylindrical mesopores, i.e., we explicitly derived the adsorption stress tensor components in the axial and radial direction of the pore. For quantitative predictions of stresses and strains, we applied the theoretical framework of Derjaguin, Broekhoff, and de Boer for adsorption in mesopores and two mechanical models of silica rods with axially aligned pore channels: an idealized cylindrical tube model, which can be described analytically, and an ordered hexagonal array of cylindrical mesopores, whose mechanical response to adsorption stress was evaluated by 3D finite element calculations. The adsorption-induced strains predicted by both mechanical models are in good quantitative agreement making the cylindrical tube the preferable model for adsorption-induced strains due to its simple analytical nature. The theoretical results are compared with the in situ dilatometry data on a hierarchically structured silica monolith composed by a network of mesoporous struts of MCM-41 type morphology. Analyzing the experimental adsorption and strain data with the proposed theoretical framework, we find the adsorption-induced deformation of the monolithic sample being reasonably described by a superposition of axial and radial strains calculated on the mesopore level. The structural and mechanical parameters obtained from the model are in good agreement with expectations from independent measurements and literature, respectively.

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array

PubMed Central

Gao, Yu-Fei; Gui, Guan; Xie, Wei; Zou, Yan-Bin; Yang, Yue; Wan, Qun

2017-01-01

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank-(L1,L2,·) BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method. PMID:28448431

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array.

PubMed

Gao, Yu-Fei; Gui, Guan; Xie, Wei; Zou, Yan-Bin; Yang, Yue; Wan, Qun

2017-04-27

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank- ( L 1 , L 2 , · ) BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method.

Low-frequency centroid-moment-tensor inversion from superconducting-gravimeter data: The effect of seismic attenuation

NASA Astrophysics Data System (ADS)

Zábranová, Eliška; Matyska, Ctirad

2014-10-01

After the 2010 Maule and 2011 Tohoku earthquakes the spheroidal modes up to 1 mHz were clearly registered by the Global Geodynamic Project (GGP) network of superconducting gravimeters (SG). Fundamental parameters in synthetic calculations of the signals are the quality factors of the modes. We study the role of their uncertainties in the centroid-moment-tensor (CMT) inversions. First, we have inverted the SG data from selected GGP stations to jointly determine the quality factors of these normal modes and the three low-frequency CMT components, Mrr,(Mϑϑ-Mφφ)/2 and Mϑφ, that generate the observed SG signal. We have used several-days-long records to minimize the trade-off between the quality factors and the CMT but it was not eliminated completely. We have also inverted each record separately to get error estimates of the obtained parameters. Consequently, we have employed the GGP records of 60-h lengths for several published modal-quality-factor sets and inverted only the same three CMT components. The obtained CMT tensors are close to the solution from the joint Q-CMT inversion of longer records and resulting variability of the CMT components is smaller than differences among routine agency solutions. Reliable low-frequency CMT components can thus be obtained for any quality factors from the studied sets.

Strain tensor selection and the elastic theory of incompatible thin sheets.

PubMed

Oshri, Oz; Diamant, Haim

2017-05-01

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids 57, 762 (2009)JMPSA80022-509610.1016/j.jmps.2008.12.004]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.

Strain tensor selection and the elastic theory of incompatible thin sheets

NASA Astrophysics Data System (ADS)

Oshri, Oz; Diamant, Haim

2017-05-01

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids 57, 762 (2009), 10.1016/j.jmps.2008.12.004]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.

Toward an absolute NMR shielding scale using the spin-rotation tensor within a relativistic framework.

PubMed

Aucar, I Agustín; Gomez, Sergio S; Giribet, Claudia G; Aucar, Gustavo A

2016-08-24

One of the most influential articles showing the best way to get the absolute values of NMR magnetic shieldings, σ (non-measurables) from both accurate measurements and theoretical calculations, was published a long time ago by Flygare. His model was shown to break down when heavy atoms are involved. This fact motivated the development of new theories of nuclear spin-rotation (SR) tensors, which consider electronic relativistic effects. One was published recently by some of us. In this article we take another step further and propose three different models that generalize Flygare's model. All of them are written using four-component relativistic expressions, though the two-component relativistic SO-S term also appears in one. The first clues for these developments were built from the relationship among σ and the SR tensors within the two-component relativistic LRESC model. Besides, we had to introduce a few other well defined assumptions: (i) relativistic corrections must be included in a way to best reproduce the relationship among the (e-e) term (called "paramagnetic" within the non-relativistic domain) of σ and its equivalent part of the SR tensor, (ii) as happens in Flygare's rule, the shielding of free atoms shall be included to improve accuracy. In the highest accurate model, a new term known as Spin-orbit due to spin, SO-S (in this mechanism the spin-Zeeman Hamiltonian replaces the orbital-Zeeman Hamiltonian), is included. We show the results of the application of those models to halogen containing linear molecules.

Strain rate orientations near the Coso Geothermal Field

NASA Astrophysics Data System (ADS)

Ogasa, N. T.; Kaven, J. O.; Barbour, A. J.; von Huene, R.

2016-12-01

Many geothermal reservoirs derive their sustained capacity for heat exchange in large part due to continuous deformation of preexisting faults and fractures that permit permeability to be maintained. Similarly, enhanced geothermal systems rely on the creation of suitable permeability from fracture and faults networks to be viable. Stress measurements from boreholes or earthquake source mechanisms are commonly used to infer the tectonic conditions that drive deformation, but here we show that geodetic data can also be used. Specifically, we quantify variations in the horizontal strain rate tensor in the area surrounding the Coso Geothermal Field (CGF) by analyzing more than two decades of high accuracy differential GPS data from a network of 14 stations from the University of Nevada Reno Geodetic Laboratory. To handle offsets in the data, from equipment changes and coseismic deformation, we segment the data, perform a piecewise linear fit and take the average of each segment's strain rate to determine secular velocities at each station. With respect to North America, all stations tend to travel northwest at velocities ranging from 1 to 10 mm/yr. The nearest station to CGF shows anomalous motion compared to regional stations, which otherwise show a coherent increase in network velocity from the northeast to the southwest. We determine strain rates via linear approximation using GPS velocities in Cartesian reference frame due to the small area of our network. Principal strain rate components derived from this inversion show maximum extensional strain rates of 30 nanostrain/a occur at N87W with compressional strain rates of 37nanostrain/a at N3E. These results generally align with previous stress measurements from borehole breakouts, which indicate the least compressive horizontal principal stress is east-west oriented, and indicative of the basin and range tectonic setting. Our results suggest that the CGF represents an anomaly in the crustal deformation field, which may be influenced by the hydrothermal anomaly and possibly by the geothermal reservoir operations as well.

Triangular prismatic solid-shell element with generalised deformation description

NASA Astrophysics Data System (ADS)

Mataix, Vicente; Flores, Fernando G.; Rossi, Riccardo; Oñate, Eugenio

2018-01-01

The solid-shells are an attractive kind of element for the simulation of f orming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any kind of additional modification, besides the thermomechanic problem is formulated without additional assumptions. Additionally, this type of element allows the three-dimensional description of the deformable body, thus contact on both sides of the element can be treated easily. The present work consists in the development of a triangular prism element as a solid-shell, for the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation by Flores, a modified right Cauchy-Green deformation tensor (?) is obtained; in the present work a modified deformation gradient (?) is obtained, which allows to generalise the methodology and allows to employ a wide range of constitutive laws. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow. Some examples have been evaluated to show the good performance of the element and results.

Lattice model calculation of the strain energy density and other properties of crystalline LiCoO{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hart, F.X.; Bates, J.B.

1998-06-01

The strain energy densities for various crystalline planes of LiCoO{sub 2} were calculated from the stiffness tensors obtained from lattice model calculations using the program GULP. In addition to Coulomb and Buckingham potentials, it was necessary to include shell models for the oxygen and cobalt ions in order to obtain acceptable agreement between the observed and calculated structural parameters and high frequency dielectric constant. The strain energy densities u due to differential thermal expansion were calculated using the theoretical stiffness tensors and estimated values for the thermal expansion coefficients of LiCoO{sub 2}. For a temperature change of 675thinsp{degree}C, these rangedmore » from 0.5 to 1.3{times}10{sup 8}thinsperg/cm{sup 3} or 5 to 13thinspJ/m{sup 2} for 1-{mu}m-thick films on alumina substrates. In particular, the energies for the (003), (101), and (104) planes were ordered as u(003){gt}u(104){gt}u(101). This suggests that the strong (101) preferred orientation of LiCoO{sub 2} films ({ge}1thinsp{mu}m thick) is due to the tendency to minimize volume strain energy that arises from differential thermal expansion between the film and the substrate. Additional properties obtained from the GULP calculations include the free energy, heat capacity, and the k=0 vibrational modes. thinsp« less

Influence of the Proton Pressure Tensor on the Turbulent Velocity Spectrum at Ion Kinetic Scales

NASA Astrophysics Data System (ADS)

Vasquez, B. J.; Markovskii, S.

2011-12-01

Numerical hybrid simulations with particle protons and fluid electrons are presented for turbulent fluctuations with spatial variations in a plane perpendicular to the background magnetic field. The steepened portion of the proton bulk velocity spectrum is found at smaller wavenumbers for larger background proton temperature. The velocity spectrum is determined, in part, by the proton pressure tensor. The proton pressure tensor is shown to possess non-gyrotropic and finite off-diagonal components in the places where the turbulent fluctuations have developed strong gradients. Proton demagnetization at these places is a factor in the departure from a Maxwellian velocity distribution function. How demagnetization could connect with both reversible and effectively irreversible aspects of the pressure tensor is considered. The effectively irreversible aspect corresponds to the net heating of the protons and to the dissipation of the turbulent energy cascade.

Fast Approximations of the Rotational Diffusion Tensor and their Application to Structural Assembly of Molecular Complexes

PubMed Central

Berlin, Konstantin; O’Leary, Dianne P.; Fushman, David

2011-01-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. PMID:21604302

Monte Carlo Volcano Seismic Moment Tensors

NASA Astrophysics Data System (ADS)

Waite, G. P.; Brill, K. A.; Lanza, F.

2015-12-01

Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.

Fast approximations of the rotational diffusion tensor and their application to structural assembly of molecular complexes.

PubMed

Berlin, Konstantin; O'Leary, Dianne P; Fushman, David

2011-07-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. Copyright © 2011 Wiley-Liss, Inc.

Influence of N-H...O and C-H...O hydrogen bonds on the 17O NMR tensors in crystalline uracil: computational study.

PubMed

Ida, Ramsey; De Clerk, Maurice; Wu, Gang

2006-01-26

We report a computational study for the 17O NMR tensors (electric field gradient and chemical shielding tensors) in crystalline uracil. We found that N-H...O and C-H...O hydrogen bonds around the uracil molecule in the crystal lattice have quite different influences on the 17O NMR tensors for the two C=O groups. The computed 17O NMR tensors on O4, which is involved in two strong N-H...O hydrogen bonds, show remarkable sensitivity toward the choice of cluster model, whereas the 17O NMR tensors on O2, which is involved in two weak C-H...O hydrogen bonds, show much smaller improvement when the cluster model includes the C-H...O hydrogen bonds. Our results demonstrate that it is important to have accurate hydrogen atom positions in the molecular models used for 17O NMR tensor calculations. In the absence of low-temperature neutron diffraction data, an effective way to generate reliable hydrogen atom positions in the molecular cluster model is to employ partial geometry optimization for hydrogen atom positions using a cluster model that includes all neighboring hydrogen-bonded molecules. Using an optimized seven-molecule model (a total of 84 atoms), we were able to reproduce the experimental 17O NMR tensors to a reasonably good degree of accuracy. However, we also found that the accuracy for the calculated 17O NMR tensors at O2 is not as good as that found for the corresponding tensors at O4. In particular, at the B3LYP/6-311++G(d,p) level of theory, the individual 17O chemical shielding tensor components differ by less than 10 and 30 ppm from the experimental values for O4 and O2, respectively. For the 17O quadrupole coupling constant, the calculated values differ by 0.30 and 0.87 MHz from the experimental values for O4 and O2, respectively.

An optimization approach for fitting canonical tensor decompositions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson

Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methodsmore » have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.« less

Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

Strain distributions and their influence on electronic structures of WSe2-MoS2 laterally strained heterojunctions

NASA Astrophysics Data System (ADS)

Zhang, Chendong; Li, Ming-Yang; Tersoff, Jerry; Han, Yimo; Su, Yushan; Li, Lain-Jong; Muller, David A.; Shih, Chih-Kang

2018-02-01

Monolayer transition metal dichalcogenide heterojunctions, including vertical and lateral p-n junctions, have attracted considerable attention due to their potential applications in electronics and optoelectronics. Lattice-misfit strain in atomically abrupt lateral heterojunctions, such as WSe2-MoS2, offers a new band-engineering strategy for tailoring their electronic properties. However, this approach requires an understanding of the strain distribution and its effect on band alignment. Here, we study a WSe2-MoS2 lateral heterojunction using scanning tunnelling microscopy and image its moiré pattern to map the full two-dimensional strain tensor with high spatial resolution. Using scanning tunnelling spectroscopy, we measure both the strain and the band alignment of the WSe2-MoS2 lateral heterojunction. We find that the misfit strain induces type II to type I band alignment transformation. Scanning transmission electron microscopy reveals the dislocations at the interface that partially relieve the strain. Finally, we observe a distinctive electronic structure at the interface due to hetero-bonding.

Elasticity of phase-Pi (Al3Si2O7(OH)3) - A hydrous aluminosilicate phase

NASA Astrophysics Data System (ADS)

Peng, Ye; Mookherjee, Mainak; Hermann, Andreas; Bajgain, Suraj; Liu, Songlin; Wunder, Bernd

2017-08-01

Phase-Pi (Al3Si2O7(OH)3) is an aluminosilicate hydrous mineral and is likely to be stable in hydrated sedimentary layers of subducting slabs. Phase-Pi is likely to be stable between the depths of 60 and 200 km and is likely to transport water into the Earth's interior. Here, we use first principles simulations based on density functional theory to explore the crystal structure at high-pressure, equation of state, and full elastic stiffness tensor as a function of pressure. We find that the pressure volume results could be described by a finite strain fit with V0 , K0 , and K0‧ being 310.3 Å3, 133 GPa, and 3.6 respectively. At zero pressure, the full elastic stiffness tensor shows significant anisotropy with the diagonal principal components C11 , C22 , and C33 being 235, 292, 266 GPa respectively, the diagonal shear C44 , C55 , and C66 being 86, 92, and 87 GPa respectively, and the off-diagonal stiffness C12 , C13 , C14 ,C15 , C16 , C23 , C24 , C25 , C26 , C34 , C35 , C36 , C45 , C46 , and C56 being 73, 78, 6, -30, 15, 61, 17, 2, 1, -13, -15, 6, 3, 1, and 3 GPa respectively. The zero pressure, shear modulus, G0 and its pressure derivative, G0 ‧ are 90 GPa and 1.9 respectively. Upon compression, hydrogen bonding in phase-Pi shows distinct behavior, with some hydrogen bonds weakening and others strengthening. The latter eventually undergo symmetrization, at pressure greater (>40 GPa) than the thermodynamic stability of phase-Pi. Full elastic constant tensors indicate that phase-Pi is very anisotropic with AVP ∼22.4% and AVS ∼23.7% at 0 GPa. Our results also indicate that the bulk sound velocity of phase-Pi is slower than that of the high-pressure hydrous aluminosilicate phase, topaz-OH.

Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory.

PubMed

Li, Zhendong; Liu, Wenjian

2010-08-14

The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin-flip configuration interaction approaches can easily be spin-adapted via the tensor-coupling scheme.

MO-C-17A-08: Evaluation of Lung Deformation Using Three Dimensional Strain Maps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, T; Huang, Q; Miller, W

2014-06-15

Purpose: To develop a systematic approach to generate three dimensional (3D) strain maps of lung using the displacement vector field (DVF) during the respiratory deformation, and to demonstrate its application in evaluating deformable image registration (DIR). Methods: A DVF based strain tensor at each voxel of interest (VOI) was calculated from the relative displacements between the VOI and each of the six nearest neighbors. The maximum and minimum stretches of a VOI can be determined by the principal strains (E{sub 1}, E{sub 2} and E{sub 3}), which are the eigenvalues and the corresponding strain tensors. Two healthy volunteers enrolled inmore » this study under IRB-approved protocol, each was scanned using 3D Hyperpolarized He-3 tagging-MRI and 3D proton-MRI with TrueFISP sequence at the endof- inhalation (EOI) and the end-of-exhalation (EOE) phases. 3D DVFs of tagging- and proton-MRI were obtained by the direct measurements of the tagging grid trajectory and by the DIR method implemented in commercial software. Results: 3D strain maps were successfully generated for all DVFs. The principal strain E1s were calculated as 0.43±0.05 and 0.17±0.25 for tagging-MRI and proton-MRI, respectively. The large values of E{sub 1} indicate the predominant lung motion in the superior-inferior (SI) direction. Given that the DVFs from the tagging images are considered as the ground truth, the discrepancies in the DIR-based strain maps suggest the inaccuracy of the DIR algorithm. In the E{sub 1} maps of tagging-MRI for subject 1, the fissures were distinguishable by the larger values (0.49±0.02) from the adjacent tissues (0.41±0.03) due to the larger relative displacement between the lung lobes. Conclusion: We have successfully developed a methodology to generate DVF-based 3D strain maps of lung. It can potentially enable us to better understand the pulmonary biomechanics and to evaluate and improve the DIR algorithms for the lung deformation. We are currently studying more subjects to evaluate this tool.« less

Computational modelling of traumatic brain injury predicts the location of chronic traumatic encephalopathy pathology

PubMed Central

Ghajari, Mazdak; Hellyer, Peter J; Sharp, David J

2017-01-01

Abstract Traumatic brain injury can lead to the neurodegenerative disease chronic traumatic encephalopathy. This condition has a clear neuropathological definition but the relationship between the initial head impact and the pattern of progressive brain pathology is poorly understood. We test the hypothesis that mechanical strain and strain rate are greatest in sulci, where neuropathology is prominently seen in chronic traumatic encephalopathy, and whether human neuroimaging observations converge with computational predictions. Three distinct types of injury were simulated. Chronic traumatic encephalopathy can occur after sporting injuries, so we studied a helmet-to-helmet impact in an American football game. In addition, we investigated an occipital head impact due to a fall from ground level and a helmeted head impact in a road traffic accident involving a motorcycle and a car. A high fidelity 3D computational model of brain injury biomechanics was developed and the contours of strain and strain rate at the grey matter–white matter boundary were mapped. Diffusion tensor imaging abnormalities in a cohort of 97 traumatic brain injury patients were also mapped at the grey matter–white matter boundary. Fifty-one healthy subjects served as controls. The computational models predicted large strain most prominent at the depths of sulci. The volume fraction of sulcal regions exceeding brain injury thresholds were significantly larger than that of gyral regions. Strain and strain rates were highest for the road traffic accident and sporting injury. Strain was greater in the sulci for all injury types, but strain rate was greater only in the road traffic and sporting injuries. Diffusion tensor imaging showed converging imaging abnormalities within sulcal regions with a significant decrease in fractional anisotropy in the patient group compared to controls within the sulci. Our results show that brain tissue deformation induced by head impact loading is greatest in sulcal locations, where pathology in cases of chronic traumatic encephalopathy is observed. In addition, the nature of initial head loading can have a significant influence on the magnitude and pattern of injury. Clarifying this relationship is key to understanding the long-term effects of head impacts and improving protective strategies, such as helmet design. PMID:28043957

Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic-Plastic Theories

DTIC Science & Technology

2014-11-01

incorporate the right Cauchy–Green strain tensor E, a function of the ( elas - tic) deformation gradient and its transpose. Such theories have been used...been compared for several anisotropic metallic single crystals (Al, Cu and Mg), with elas - tic constants of up to order four included. Differences

Finite element implementation of a thermo-damage-viscoelastic constitutive model for hydroxyl-terminated polybutadiene composite propellant

NASA Astrophysics Data System (ADS)

Xu, Jinsheng; Han, Long; Zheng, Jian; Chen, Xiong; Zhou, Changsheng

2017-11-01

A thermo-damage-viscoelastic model for hydroxyl-terminated polybutadiene (HTPB) composite propellant with consideration for the effect of temperature was implemented in ABAQUS. The damage evolution law of the model has the same form as the crack growth equation for viscoelastic materials, and only a single damage variable S is considered. The HTPB propellant was considered as an isotropic material, and the deviatoric and volumetric strain-stress relations are decoupled and described by the bulk and shear relaxation moduli, respectively. The stress update equations were expressed by the principal stresses σ_{ii}R and the rotation tensor M, the Jacobian matrix in the global coordinate system J_{ijkl} was obtained according to the fourth-order tensor transformation rules. Two models having complex stress states were used to verify the accuracy of the constitutive model. The test results showed good agreement with the strain responses of characteristic points measured by a contactless optical deformation test system, which illustrates that the thermo-damage-viscoelastic model perform well at describing the mechanical properties of an HTPB propellant.

Development of a Multi-Scale Methodology for Prediction of the Microscopic Anisotropic Stress-Strain Response of Textured Metals under Dynamic Loading

DTIC Science & Technology

2009-01-21

will be denoted by v ⊗ u. Superscript T indicates the transpose operation (AT )ij = Aji for any second-order tensor A while symbol ‘tr‘ denotes the...indicated in red . which was subsequently marked on the plate as shown in Figure 2. Note that the plate exhibits fiber texture resulting from the...specimen deformed to 10% strain reveals that many grains have twinned (twins appear red in Figure 9). The twin volume fraction was estimated to be 17

A new hybrid turbulence modelling strategy for industrial CFD

NASA Astrophysics Data System (ADS)

Basara, B.; Jakirlic, S.

2003-05-01

This paper presents a new strategy for turbulence model employment with emphasis on the model's applicability for industrial computational fluid dynamics (CFD). In the hybrid modelling strategy proposed here, the Reynolds stress and mean rate of strain tensors are coupled via Boussinesq's formula as in the standard k-model. However, the turbulent kinetic energy is calculated as the sum of the normal Reynolds-stress components, representing the solutions of the appropriate transport equations. The equations governing the Reynolds-stress tensor and dissipation rate have been solved in the framework of a background second-moment closure model. Furthermore, the structure parameter C-? has been re-calculated from a newly proposed functional dependency rather than kept constant. This new definition of C-? has been assessed by using direct numerical simulation (DNS) results of several generic flow configurations featuring different phenomena such as separation, reattachment and rotation. Comparisons show a large departure of C-? from the commonly used value of 0.09. The model proposed is computationally validated in a number of well-proven fluid flow benchmarks, e.g. backward-facing step, 180° turn-around duct, rotating pipe, impinging jet and three-dimensional (3D) Ahmed body. The obtained results confirm that the present hybrid model delivers a robust solution procedure while preserving most of the physical advantages of the Reynolds-stress model over simple k-models. A low Reynolds number version of the hybrid model is also proposed and discussed.

Simplified moment tensor analysis and unified decomposition of acoustic emission source: Application to in situ hydrofracturing test

NASA Astrophysics Data System (ADS)

Ohtsu, Masayasu

1991-04-01

An application of a moment tensor analysis to acoustic emission (AE) is studied to elucidate crack types and orientations of AE sources. In the analysis, simplified treatment is desirable, because hundreds of AE records are obtained from just one experiment and thus sophisticated treatment is realistically cumbersome. Consequently, a moment tensor inversion based on P wave amplitude is employed to determine six independent tensor components. Selecting only P wave portion from the full-space Green's function of homogeneous and isotropic material, a computer code named SiGMA (simplified Green's functions for the moment tensor analysis) is developed for the AE inversion analysis. To classify crack type and to determine crack orientation from moment tensor components, a unified decomposition of eigenvalues into a double-couple (DC) part, a compensated linear vector dipole (CLVD) part, and an isotropic part is proposed. The aim of the decomposition is to determine the proportion of shear contribution (DC) and tensile contribution (CLVD + isotropic) on AE sources and to classify cracks into a crack type of the dominant motion. Crack orientations determined from eigenvectors are presented as crack-opening vectors for tensile cracks and fault motion vectors for shear cracks, instead of stereonets. The SiGMA inversion and the unified decomposition are applied to synthetic data and AE waveforms detected during an in situ hydrofracturing test. To check the accuracy of the procedure, numerical experiments are performed on the synthetic waveforms, including cases with 10% random noise added. Results show reasonable agreement with assumed crack configurations. Although the maximum error is approximately 10% with respect to the ratios, the differences on crack orientations are less than 7°. AE waveforms detected by eight accelerometers deployed during the hydrofracturing test are analyzed. Crack types and orientations determined are in reasonable agreement with a predicted failure plane from borehole TV observation. The results suggest that tensile cracks are generated first at weak seams and then shear cracks follow on the opened joints.

Breit interaction effects in relativistic theory of the nuclear spin-rotation tensor.

PubMed

Aucar, I Agustín; Gómez, Sergio S; Giribet, Claudia G; Ruiz de Azúa, Martín C

2013-09-07

In this work, relativistic effects on the nuclear spin-rotation (SR) tensor originated in the electron-nucleus and electron-electron Breit interactions are analysed. To this end, four-component numerical calculations were carried out in model systems HX (X=H,F,Cl,Br,I). The electron-nucleus Breit interaction couples the electrons and nuclei dynamics giving rise to a purely relativistic contribution to the SR tensor. Its leading order in 1/c is of the same value as that of relativistic corrections on the usual second order expression of the SR tensor considered in previous work [I. A. Aucar, S. S. Gómez, J. I. Melo, C. G. Giribet, and M. C. Ruiz de Azúa, J. Chem. Phys. 138, 134107 (2013)], and therefore it is absolutely necessary to establish its relative importance. For the sake of completeness, the corresponding effect originating in the electron-electron Breit interaction is also considered. It is verified that in all cases these Breit interactions yield only very small corrections to the SR tensors of both the X and H nuclei in the present series of compounds. Results of the present work strongly suggest that in order to achieve experimental accuracy in the theoretical study of the SR tensor both electron-nucleus and electron-electron Breit effects can be safely neglected.

Mechanical signals in plant development: a new method for single cell studies

NASA Technical Reports Server (NTRS)

Lynch, T. M.; Lintilhac, P. M.

1997-01-01

Cell division, which is critical to plant development and morphology, requires the orchestration of hundreds of intracellular processes. In the end, however, cells must make critical decisions, based on a discrete set of mechanical signals such as stress, strain, and shear, to divide in such a way that they will survive the mechanical loads generated by turgor pressure and cell enlargement within the growing tissues. Here we report on a method whereby tobacco protoplasts swirled into a 1.5% agarose entrapment medium will survive and divide. The application of a controlled mechanical load to agarose blocks containing protoplasts orients the primary division plane of the embedded cells. Photoelastic analysis of the agarose entrapment medium can identify the lines of principal stress within the agarose, confirming the hypothesis that cells divide either parallel or perpendicular to the principal stress tensors. The coincidence between the orientation of the new division wall and the orientation of the principal stress tensors suggests that the perception of mechanical stress is a characteristic of individual plant cells. The ability of a cell to determine a shear-free orientation for a new partition wall may be related to the applied load through the deformation of the matrix material. In an isotropic matrix a uniaxial load will produce a rotationally symmetric strain field, which will define a shear-free plane. Where high stress intensities combine with the loading geometry to produce multiaxial loads there will be no axis of rotational symmetry and hence no shear free plane. This suggests that two mechanisms may be orienting the division plane, one a mechanism that works in rotationally symmetrical fields, yielding divisions perpendicular to the compressive tensor, parallel to the long axis of the cell, and one in asymmetric fields, yielding divisions parallel to the short axis of the cell and the compressive tensor.

Werner-Wheeler mass tensor for fusionlike configuration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gherghescu, R.A.; Poenaru, D.N.

2005-08-01

The Werner-Wheeler approach is used to calculate the components of the mass tensor for a binary configuration of two intersected spheroids. Four free coordinates form the deformation space: the small semiaxis of the projectile, the two semiaxis ratios of the spheroids, and the distance between centers. A correction term is also calculated, due to the center of mass motion. Final results are presented for the fusion channel {sup 54}Cr+{sup 240}Pu, and all possible couplings are analyzed.

Nonzero Ideal Gas Contribution to the Surface Tension of Water.

PubMed

Sega, Marcello; Fábián, Balázs; Jedlovszky, Pál

2017-06-15

Surface tension, the tendency of fluid interfaces to behave elastically and minimize their surface, is routinely calculated as the difference between the lateral and normal components of the pressure or, invoking isotropy in momentum space, of the virial tensor. Here we show that the anisotropy of the kinetic energy tensor close to a liquid-vapor interface can be responsible for a large part of its surface tension (about 15% for water, independent from temperature).

Critical Analysis of Cluster Models and Exchange-Correlation Functionals for Calculating Magnetic Shielding in Molecular Solids.

PubMed

Holmes, Sean T; Iuliucci, Robbie J; Mueller, Karl T; Dybowski, Cecil

2015-11-10

Calculations of the principal components of magnetic-shielding tensors in crystalline solids require the inclusion of the effects of lattice structure on the local electronic environment to obtain significant agreement with experimental NMR measurements. We assess periodic (GIPAW) and GIAO/symmetry-adapted cluster (SAC) models for computing magnetic-shielding tensors by calculations on a test set containing 72 insulating molecular solids, with a total of 393 principal components of chemical-shift tensors from 13C, 15N, 19F, and 31P sites. When clusters are carefully designed to represent the local solid-state environment and when periodic calculations include sufficient variability, both methods predict magnetic-shielding tensors that agree well with experimental chemical-shift values, demonstrating the correspondence of the two computational techniques. At the basis-set limit, we find that the small differences in the computed values have no statistical significance for three of the four nuclides considered. Subsequently, we explore the effects of additional DFT methods available only with the GIAO/cluster approach, particularly the use of hybrid-GGA functionals, meta-GGA functionals, and hybrid meta-GGA functionals that demonstrate improved agreement in calculations on symmetry-adapted clusters. We demonstrate that meta-GGA functionals improve computed NMR parameters over those obtained by GGA functionals in all cases, and that hybrid functionals improve computed results over the respective pure DFT functional for all nuclides except 15N.

Anisotropic Poroelasticity in a Rock With Cracks

NASA Astrophysics Data System (ADS)

Wong, Teng-Fong

2017-10-01

Deformation of a saturated rock in the field and laboratory may occur in a broad range of conditions, ranging from undrained to drained. The poromechanical response is often anisotropic, and in a brittle rock, closely related to preexisting and stress-induced cracks. This can be modeled as a rock matrix embedded with an anisotropic system of cracks. Assuming microisotropy, expressions for three of the poroelastic coefficients of a transversely isotropic rock were derived in terms of the crack density tensor. Together with published results for the five effective elastic moduli, this provides a complete micromechanical description of the eight independent poroelastic coefficients of such a cracked rock. Relatively simple expressions were obtained for the Skempton pore pressure tensor, which allow one to infer the crack density tensor from undrained measurement in the laboratory, and also to infer the Biot-Willis effective stress coefficients. The model assumes a dilute concentration of noninteractive penny-shaped cracks, and it shows good agreement with experimental data for Berea sandstone, with crack density values up to 0.6. Whereas predictions on the storage coefficient and normal components of the elastic stiffness tensor also seem reasonable, significant discrepancy between model and measurement was observed regarding the off-diagonal and shear components of the stiffness. A plausible model had been proposed for development of very strong anisotropy in the undrained response of a fault zone, and the model here placed geometric constraints on the associated fracture system.

Cosmic Ray Diffusion Tensor throughout the Heliosphere on the basis of Nearly Incompressible Magnetohydrodynamic Turbulence Model

NASA Astrophysics Data System (ADS)

Zhao, L.; Zank, G. P.; Adhikari, L.

2017-12-01

The radial and rigidity dependence of cosmic ray (CR) diffusion tensor is investigated on the basis of the recently developed 2D and slab turbulence transport model using nearly incompressible (NI) theory (Zank et al. 2017; Adhikari et al. 2017). We use the energy in forward propagating modes from 0.29 to 1 AU and in backward propagating modes from 1 to 75 AU. We employ the quasi-linear theory (QLT) and nonlinear guiding center (NLGC) theory, respectively, to determine the parallel and perpendicular elements of CR diffusion tensor. We also present the effect of both weak and moderately strong turbulence on the drift element of CR diffusion tensor. We find that (1) from 0.29 to 1 AU the radial mean free path (mfp) is dominated by the parallel component, both increase slowly after 0.4 AU; (2) from 1 to 75 AU the radial mfp starts with a rapid increase and then decreases after a peak at about 3.5 AU, mainly caused by pick-up ion sources of turbulence model; (3) after 20 AU the perpendicular mfp is nearly constant and begin to dominate the radial mfp; (4) the rigidity dependence of the parallel mfp is proportional to at 1 AU from 0.1 to 10 GV and the perpendicular mfp is weakly influenced by the rigidity; (5) turbulence does more than suppress the traditional drift element but introduces a new component normal to the magnetic field. This study shows that a proper two-component turbulence model is necessary to produce the complexity of diffusion coefficient for CR modulation throughout the heliosphere.

Moment tensor inversion of ground motion from mining-induced earthquakes, Trail Mountain, Utah

USGS Publications Warehouse

Fletcher, Joe B.; McGarr, A.

2005-01-01

A seismic network was operated in the vicinity of the Trail Mountain mine, central Utah, from the summer of 2000 to the spring of 2001 to investigate the seismic hazard to a local dam from mining-induced events that we expect to be triggered by future coal mining in this area. In support of efforts to develop groundmotion prediction relations for this situation, we inverted ground-motion recordings for six mining-induced events to determine seismic moment tensors and then to estimate moment magnitudes M for comparison with the network coda magnitudes Mc. Six components of the tensor were determined, for an assumed point source, following the inversion method of McGarr (1992a), which uses key measurements of amplitude from obvious features of the displacement waveforms. When the resulting moment tensors were decomposed into implosive and deviatoric components, we found that four of the six events showed a substantial volume reduction, presumably due to coseismic closure of the adjacent mine openings. For these four events, the volume reduction ranges from 27% to 55% of the shear component (fault area times average slip). Radiated seismic energy, computed from attenuation-corrected body-wave spectra, ranged from 2.4 ?? 105 to 2.4 ?? 106 J for events with M from 1.3 to 1.8, yielding apparent stresses from 0.02 to 0.06 MPa. The energy released for each event, approximated as the product of volume reduction and overburden stress, when compared with the corresponding seismic energies, revealed seismic efficiencies ranging from 0.5% to 7%. The low apparent stresses are consistent with the shallow focal depths of 0.2 to 0.6 km and rupture in a low stress/low strength regime compared with typical earthquake source regions at midcrustal depths.

Finsler geometry of nonlinear elastic solids with internal structure

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

Concepts from Finsler differential geometry are applied towards a theory of deformable continua with internal structure. The general theory accounts for finite deformation, nonlinear elasticity, and various kinds of structural features in a solid body. The general kinematic structure of the theory includes macroscopic and microscopic displacement fields-i.e., a multiscale representation-whereby the latter are represented mathematically by the director vector of pseudo-Finsler space, not necessarily of unit magnitude. A physically appropriate fundamental (metric) tensor is introduced, leading to affine and nonlinear connections. A deformation gradient tensor is defined via differentiation of the macroscopic motion field, and another metric indicative of strain in the body is a function of this gradient. A total energy functional of strain, referential microscopic coordinates, and horizontal covariant derivatives of the latter is introduced. Variational methods are applied to derive Euler-Lagrange equations and Neumann boundary conditions. The theory is shown to encompass existing continuum physics models such as micromorphic, micropolar, strain gradient, phase field, and conventional nonlinear elasticity models, and it can reduce to such models when certain assumptions on geometry, kinematics, and energy functionals are imposed. The theory is applied to analyze two physical problems in crystalline solids: shear localization/fracture in a two-dimensional body and cavitation in a spherical body. In these examples, a conformal or Weyl-type transformation of the fundamental tensor enables a description of dilatation associated, respectively, with cleavage surface roughness and nucleation of voids or vacancies. For the shear localization problem, the Finsler theory is able to accurately reproduce the surface energy of Griffith's fracture mechanics, and it predicts dilatation-induced toughening as observed in experiments on brittle crystals. For the cavitation problem, the Finsler theory is able to accurately reproduce the vacancy formation energy at a nanoscale resolution, and various solutions describe localized cavitation at the core of the body and/or distributed dilatation and softening associated with amorphization as observed in atomic simulations, with relative stability of solutions depending on the regularization length.

A direct numerical simulation-based re-examination of coefficients in the pressure-strain models in second-moment closures

NASA Astrophysics Data System (ADS)

Jakirlić, S.; Hanjalić, K.

2013-10-01

The most challenging task in closing the Reynolds-averaged Navier-Stokes equations at the second-moment closure (SMC) level is to model the pressure-rate-of-strain correlation in the transport equation for the Reynolds-stress tensor. The accurate modelling of this term, commonly denoted as Φij, is the key prerequisite for the correct capturing of the stress anisotropy, which potentially gives SMCs a decisive advantage over the ‘anisotropy-blind’ eddy-viscosity models. A variety of models for Φij proposed in the literature can all be expressed as a function of the stress-anisotropy-, rate-of-strain- and rate-of-rotation second-rank tensors, so that the modelling task is reduced to determining the model coefficients. It is, thus, the coefficients, associated with various terms in the expression, which differ from one model to another. The model coefficients have been traditionally determined with reference to the available data for sets of generic flows while being forced to satisfying the known values at flow boundaries. We evaluated the coefficients up to the second-order terms (in stress-anisotropy aij) directly from the DNS database for Φij and the turbulence variables involved in its modelling. The variations of the coefficients across the flow in a plane channel over a range of Reynolds numbers are compared with several popular models. The analysis provided a reasonable support for the common tensor-expansion representation of both the slow and rapid terms. Apart from the near-wall region and the channel centre, most coefficients for higher Re numbers showed themselves to be reasonably uniform, with the values closest to those proposed by Sarkar et al (1991 J. Fluid Mech. 227 245-72). An illustration of the coefficient variation for the ‘quasi-linear’ model is also presented for flow over a backward-facing step.

Investigating source processes of isotropic events

NASA Astrophysics Data System (ADS)

Chiang, Andrea

This dissertation demonstrates the utility of the complete waveform regional moment tensor inversion for nuclear event discrimination. I explore the source processes and associated uncertainties for explosions and earthquakes under the effects of limited station coverage, compound seismic sources, assumptions in velocity models and the corresponding Green's functions, and the effects of shallow source depth and free-surface conditions. The motivation to develop better techniques to obtain reliable source mechanism and assess uncertainties is not limited to nuclear monitoring, but they also provide quantitative information about the characteristics of seismic hazards, local and regional tectonics and in-situ stress fields of the region . This dissertation begins with the analysis of three sparsely recorded events: the 14 September 1988 US-Soviet Joint Verification Experiment (JVE) nuclear test at the Semipalatinsk test site in Eastern Kazakhstan, and two nuclear explosions at the Chinese Lop Nor test site. We utilize a regional distance seismic waveform method fitting long-period, complete, three-component waveforms jointly with first-motion observations from regional stations and teleseismic arrays. The combination of long period waveforms and first motion observations provides unique discrimination of these sparsely recorded events in the context of the Hudson et al. (1989) source-type diagram. We examine the effects of the free surface on the moment tensor via synthetic testing, and apply the moment tensor based discrimination method to well-recorded chemical explosions. These shallow chemical explosions represent rather severe source-station geometry in terms of the vanishing traction issues. We show that the combined waveform and first motion method enables the unique discrimination of these events, even though the data include unmodeled single force components resulting from the collapse and blowout of the quarry face immediately following the initial explosion. In contrast, recovering the announced explosive yield using seismic moment estimates from moment tensor inversion remains challenging but we can begin to put error bounds on our moment estimates using the NSS technique. The estimation of seismic source parameters is dependent upon having a well-calibrated velocity model to compute the Green's functions for the inverse problem. Ideally, seismic velocity models are calibrated through broadband waveform modeling, however in regions of low seismicity velocity models derived from body or surface wave tomography may be employed. Whether a velocity model is 1D or 3D, or based on broadband seismic waveform modeling or the various tomographic techniques, the uncertainty in the velocity model can be the greatest source of error in moment tensor inversion. These errors have not been fully investigated for the nuclear discrimination problem. To study the effects of unmodeled structures on the moment tensor inversion, we set up a synthetic experiment where we produce synthetic seismograms for a 3D model (Moschetti et al., 2010) and invert these data using Green's functions computed with a 1D velocity mode (Song et al., 1996) to evaluate the recoverability of input solutions, paying particular attention to biases in the isotropic component. The synthetic experiment results indicate that the 1D model assumption is valid for moment tensor inversions at periods as short as 10 seconds for the 1D western U.S. model (Song et al., 1996). The correct earthquake mechanisms and source depth are recovered with statistically insignificant isotropic components as determined by the F-test. Shallow explosions are biased by the theoretical ISO-CLVD tradeoff but the tectonic release component remains low, and the tradeoff can be eliminated with constraints from P wave first motion. Path-calibration to the 1D model can reduce non-double-couple components in earthquakes, non-isotropic components in explosions and composite sources and improve the fit to the data. When we apply the 3D model to real data, at long periods (20-50 seconds), we see good agreement in the solutions between the 1D and 3D models and slight improvement in waveform fits when using the 3D velocity model Green's functions. (Abstract shortened by ProQuest.).

Strain-rate dependence of ramp-wave evolution and strength in tantalum

DOE PAGES

Lane, J. Matthew D.; Foiles, Stephen M.; Lim, Hojun; ...

2016-08-25

We have conducted molecular dynamics (MD) simulations of quasi-isentropic ramp-wave compression to very high pressures over a range of strain rates from 10 11 down to 10 8 1/s. Using scaling methods, we collapse wave profiles from various strain rates to a master profile curve, which shows deviations when material response is strain-rate dependent. Thus, we can show with precision where, and how, strain-rate dependence affects the ramp wave. We find that strain rate affects the stress-strain material response most dramatically at strains below 20%, and that above 30% strain the material response is largely independent of strain rate. Wemore » show good overall agreement with experimental stress-strain curves up to approximately 30% strain, above which simulated response is somewhat too stiff. We postulate that this could be due to our interatomic potential or to differences in grain structure and/or size between simulation and experiment. Strength is directly measured from per-atom stress tensor and shows significantly enhanced elastic response at the highest strain rates. As a result, this enhanced elastic response is less pronounced at higher pressures and at lower strain rates.« less

A model for origin of self-rotation in a protoplanetary cloud under action of exterior periodic force

NASA Astrophysics Data System (ADS)

Tkachova, P. P.; Krot, A. M.

2009-04-01

This work investigates condition for origin of increasing rotational disturbance in a gas-liquid protoplanetary cloud under action of a periodic force. The model (based on Reynolds equations [1]) describing self-organization of rotational disturbance of viscous gas-liquid substance into a protoplanetary cloud is proposed. The Reynolds equations as well as continuity equation in cylindrical frame of reference (r, e, z) as basis relations for this analytical model are used. The mean velocity is supposed to be equal to zero from the beginning action of an exterior periodic force. The Reynolds' tensor of turbulent strain of velocity disturbances in a becoming fluid flow is sought for (besides, z-component of velocity disturbance is supposed to be equal to zero). In assumption that z-components of turbulent strains are equal to zero, the (r, e)-turbulent strain components are found. After all considerations the Reynolds equations and continuity one (in the cylindrical coordinate system) are reduced to the system of two differential equations in partial derivatives relatively to (r, e)-cylindrical components of turbulent strain of velocity disturbance. A common solution of these two equations permits us to reduce this task to solution of one differential equation relatively to (r, e)-turbulent strain. This homogeneous differential equation is solved with usage of the variables separation method. As a result, a superposition of two cosine's and sine's waves gives us (r, e)-turbulent strain wave with an elliptic (or circular) polarization. Moreover, this paper shows that amplitude of cosine-wave as well as sine-wave is an increasing function as r**(n**2-2). This paper finds that oscillations are intensified with growing a frequency of becoming oscillations. The computational experiments based on STAR-CD package [2] confirm the main analytical statements of the proposed model for becoming self-rotation in a gas-liquid protoplanetary cloud. This work develops also the nonlinear analysis of an attractor describing hydrodynamic state of rotating flows based on the matrix decomposition [3]. This analysis permits to estimate the values of characteristic parameters (including control one) of the attractor and predict its evolution in time analogously to the stated in [4]. References: [1] Loytsyansky, L.G. Mechanics of Fluid and Gas, Nauka: Moscow, 1973 (in Russian). [2] Methodology for STAR-CD: Version 3.24. Computational Dynamics Limited, 2004. [3] Krot, A.M. Matrix decompositions of vector functions and shift operators on the trajectories of a nonlinear dynamical system, Nonlinear Phenomena in Complex Systems, vol.4, no. 2, pp.106-115, 2001. [4] Krot, A.M. and Tkachova, P.P. Investigation of geometrical shapes of hydrodynamic structures for identification of dynamical states of convective liquid, in: Lecture Notes in Computer Sciences, Berlin, Germany: Springer, Part 1, vol. 2667, pp. 398-406, 2003.

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

NASA Technical Reports Server (NTRS)

Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming

1996-01-01

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.

Contribution to the development of low frequency terahertz coherent Raman micro-spectroscopy and microscopy

NASA Astrophysics Data System (ADS)

Ujj, Laszlo

2018-06-01

We report the construction and characterization of a coherent Raman tabletop system utilizing a novel astigmatic optical focusing geometry, a broadband nanosecond optical parametric oscillator and volumetric Bragg filters assisting 3CBCRS measuring system for the first time. In order to illustrate the versatility of the measurements and reveal the molecular information obtainable, two well-characterized chemicals were selected. Polarization sensitive epi-detected 3CBCRS spectra of liquid CCl4 and calcite crystal were recorded and analyzed. An unexpected polarization dependence of the signals of the lowest frequency modes of CCl4 was observed. The 1122 third order susceptibility component was phase flipped. The non-resonant susceptibility normalized 1122 component was found to be larger than the 1111 component for the lowest vibrational modes. This anomalous comportment was attributable to the anisotropy Raman tensor invariant in the third order nonlinear susceptibility tensor.

Modelling Dynamic Behaviour and Spall Failure of Aluminium Alloy AA7010

NASA Astrophysics Data System (ADS)

Ma'at, N.; Nor, M. K. Mohd; Ismail, A. E.; Kamarudin, K. A.; Jamian, S.; Ibrahim, M. N.; Awang, M. K.

2017-10-01

A finite strain constitutive model to predict the dynamic deformation behaviour of Aluminium Alloy 7010 including shockwaves and spall failure is developed in this work. The important feature of this newly hyperelastic-plastic constitutive formulation is a new Mandel stress tensor formulated using new generalized orthotropic pressure. This tensor is combined with a shock equation of state (EOS) and Grady spall failure. The Hill’s yield criterion is adopted to characterize plastic orthotropy by means of the evolving structural tensors that is defined in the isoclinic configuration. This material model was developed and integration into elastic and plastic parts. The elastic anisotropy is taken into account through the newly stress tensor decomposition of a generalized orthotropic pressure. Plastic anisotropy is considered through yield surface and an isotropic hardening defined in a unique alignment of deviatoric plane within the stress space. To test its ability to describe shockwave propagation and spall failure, the new material model was implemented into the LLNL-DYNA3D code of UTHM’s. The capability of this newly constitutive model were compared against published experimental data of Plate Impact Test at 234m/s, 450m/s and 895m/s impact velocities. A good agreement is obtained between experimental and simulation in each test.

Bayesian inference and interpretation of centroid moment tensors of the 2016 Kumamoto earthquake sequence, Kyushu, Japan

NASA Astrophysics Data System (ADS)

Hallo, Miroslav; Asano, Kimiyuki; Gallovič, František

2017-09-01

On April 16, 2016, Kumamoto prefecture in Kyushu region, Japan, was devastated by a shallow M JMA7.3 earthquake. The series of foreshocks started by M JMA6.5 foreshock 28 h before the mainshock. They have originated in Hinagu fault zone intersecting the mainshock Futagawa fault zone; hence, the tectonic background for this earthquake sequence is rather complex. Here we infer centroid moment tensors (CMTs) for 11 events with M JMA between 4.8 and 6.5, using strong motion records of the K-NET, KiK-net and F-net networks. We use upgraded Bayesian full-waveform inversion code ISOLA-ObsPy, which takes into account uncertainty of the velocity model. Such an approach allows us to reliably assess uncertainty of the CMT parameters including the centroid position. The solutions show significant systematic spatial and temporal variations throughout the sequence. Foreshocks are right-lateral steeply dipping strike-slip events connected to the NE-SW shear zone. Those located close to the intersection of the Hinagu and Futagawa fault zones are dipping slightly to ESE, while those in the southern area are dipping to WNW. Contrarily, aftershocks are mostly normal dip-slip events, being related to the N-S extensional tectonic regime. Most of the deviatoric moment tensors contain only minor CLVD component, which can be attributed to the velocity model uncertainty. Nevertheless, two of the CMTs involve a significant CLVD component, which may reflect complex rupture process. Decomposition of those moment tensors into two pure shear moment tensors suggests combined right-lateral strike-slip and normal dip-slip mechanisms, consistent with the tectonic settings of the intersection of the Hinagu and Futagawa fault zones.[Figure not available: see fulltext.

On the simplest scale invariant tree-tensor-states preserving the quantum symmetries of the antiferromagnetic XXZ chain

NASA Astrophysics Data System (ADS)

Monthus, Cécile

2018-03-01

For the line of critical antiferromagnetic XXZ chains with coupling J  >  0 and anisotropy 0<Δ ≤slant 1 , we describe how the block-spin renormalization procedure preserving the SU q (2) symmetry introduced by Martin-Delgado and Sierra (1996 Phys. Rev. Lett. 76 1146) can be reformulated as the translation-invariant scale-invariant tree-tensor-state of the smallest dimension that is compatible with the quantum symmetries of the model. The properties of this tree-tensor-state are studied in detail via the ground-state energy, the magnetizations and the staggered magnetizations, as well as the Shannon-Renyi entropies characterizing the multifractality of the components of the wave function.

Effect of complex configurations on the description of properties of {sup 132}Sn beta decay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Severyukhin, A. P., E-mail: sever@theor.jinr.ru; Sushenok, E. O.

2015-07-15

Gamow–Teller transitions in the beta decay of the {sup 132}Sn neutron-rich nucleus was described microscopically. The coupling of one- and two-phonon components of the wave functions was taken into account on the basis of Skyrme interactions featuring various contributions of the tensor component. A separable approximation of the particle—hole interaction made it possible tohole interaction perform calculations in a large configuration space. It was shown that an increase in the strength of the neutron—proton tensor interaction led to an increase in the energy of Gamow—Teller transitions. In addition, a decrease in the {sup 132}Sn half-life with respect to beta decaymore » was obtained.« less

Inversion of calcite twin data for paleostress (1) : improved Etchecopar technique tested on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Daniel, Jean-Marc; Schueller, Sylvie

2015-04-01

Inversion of calcite twin data are known to be a powerful tool to reconstruct the past-state of stress in carbonate rocks of the crust, especially in fold-and-thrust belts and sedimentary basins. This is of key importance to constrain results of geomechanical modelling. Without proposing a new inversion scheme, this contribution reports some recent improvements of the most efficient stress inversion technique to date (Etchecopar, 1984) that allows to reconstruct the 5 parameters of the deviatoric paleostress tensors (principal stress orientations and differential stress magnitudes) from monophase and polyphase twin data sets. The improvements consist in the search of the possible tensors that account for the twin data (twinned and untwinned planes) and the aid to the user to define the best stress tensor solution, among others. We perform a systematic exploration of an hypersphere in 4 dimensions by varying different parameters, Euler's angles and the stress ratio. We first record all tensors with a minimum penalization function accounting for 20% of the twinned planes. We then define clusters of tensors following a dissimilarity criterion based on the stress distance between the 4 parameters of the reduced stress tensors and a degree of disjunction of the related sets of twinned planes. The percentage of twinned data to be explained by each tensor is then progressively increased and tested using the standard Etchecopar procedure until the best solution that explains the maximum number of twinned planes and the whole set of untwinned planes is reached. This new inversion procedure is tested on monophase and polyphase numerically-generated as well as natural calcite twin data in order to more accurately define the ability of the technique to separate more or less similar deviatoric stress tensors applied in sequence on the samples, to test the impact of strain hardening through the change of the critical resolved shear stress for twinning as well as to evaluate the possible bias due to measurement uncertainties or clustering of grain optical axes in the samples.

Multiview robotic microscope reveals the in-plane kinematics of amphibian neurulation.

PubMed

Veldhuis, Jim H; Brodland, G Wayne; Wiebe, Colin J; Bootsma, Gregory J

2005-06-01

A new robotic microscope system, called the Frogatron 3000, was developed to collect time-lapse images from arbitrary viewing angles over the surface of live embryos. Embryos are mounted at the center of a horizontal, fluid-filled, cylindrical glass chamber around which a camera with special optics traverses. To hold them at the center of the chamber and revolve them about a vertical axis, the embryos are placed on the end of a small vertical glass tube that is rotated under computer control. To demonstrate operation of the system, it was used to capture time-lapse images of developing axolotl (amphibian) embryos from 63 viewing angles during the process of neurulation and the in-plane kinematics of the epithelia visible at the center of each view was calculated. The motions of points on the surface of the embryo were determined by digital tracking of their natural surface texture, and a least-squares algorithm was developed to calculate the deformation-rate tensor from the motions of these surface points. Principal strain rates and directions were extracted from this tensor using decomposition and eigenvector techniques. The highest observed principal true strain rate was 28 +/- 5% per hour, along the midline of the neural plate during developmental stage 14, while the greatest contractile true strain rate was--35 +/- 5% per hour, normal to the embryo midline during stage 15.

Explicit robust schemes for implementation of a class of principal value-based constitutive models: Theoretical development

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Arnold, S. M.

1991-01-01

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, explicit forms for the corresponding material tangent stiffness tensors are developed, and these are valid for the entire deformation range; i.e., with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.

Nonlinear temperature dependent failure analysis of finite width composite laminates

NASA Technical Reports Server (NTRS)

Nagarkar, A. P.; Herakovich, C. T.

1979-01-01

A quasi-three dimensional, nonlinear elastic finite element stress analysis of finite width composite laminates including curing stresses is presented. Cross-ply, angle-ply, and two quasi-isotropic graphite/epoxy laminates are studied. Curing stresses are calculated using temperature dependent elastic properties that are input as percent retention curves, and stresses due to mechanical loading in the form of an axial strain are calculated using tangent modulii obtained by Ramberg-Osgood parameters. It is shown that curing stresses and stresses due to tensile loading are significant as edge effects in all types of laminate studies. The tensor polynomial failure criterion is used to predict the initiation of failure. The mode of failure is predicted by examining individual stress contributions to the tensor polynomial.

Stress field models from Maxwell stress functions: southern California

NASA Astrophysics Data System (ADS)

Bird, Peter

2017-08-01

The lithospheric stress field is formally divided into three components: a standard pressure which is a function of elevation (only), a topographic stress anomaly (3-D tensor field) and a tectonic stress anomaly (3-D tensor field). The boundary between topographic and tectonic stress anomalies is somewhat arbitrary, and here is based on the modeling tools available. The topographic stress anomaly is computed by numerical convolution of density anomalies with three tensor Green's functions provided by Boussinesq, Cerruti and Mindlin. By assuming either a seismically estimated or isostatic Moho depth, and by using Poisson ratio of either 0.25 or 0.5, I obtain four alternative topographic stress models. The tectonic stress field, which satisfies the homogeneous quasi-static momentum equation, is obtained from particular second derivatives of Maxwell vector potential fields which are weighted sums of basis functions representing constant tectonic stress components, linearly varying tectonic stress components and tectonic stress components that vary harmonically in one, two and three dimensions. Boundary conditions include zero traction due to tectonic stress anomaly at sea level, and zero traction due to the total stress anomaly on model boundaries at depths within the asthenosphere. The total stress anomaly is fit by least squares to both World Stress Map data and to a previous faulted-lithosphere, realistic-rheology dynamic model of the region computed with finite-element program Shells. No conflict is seen between the two target data sets, and the best-fitting model (using an isostatic Moho and Poisson ratio 0.5) gives minimum directional misfits relative to both targets. Constraints of computer memory, execution time and ill-conditioning of the linear system (which requires damping) limit harmonically varying tectonic stress to no more than six cycles along each axis of the model. The primary limitation on close fitting is that the Shells model predicts very sharp shallow stress maxima and discontinuous horizontal compression at the Moho, which the new model can only approximate. The new model also lacks the spatial resolution to portray the localized stress states that may occur near the central surfaces of weak faults; instead, the model portrays the regional or background stress field which provides boundary conditions for weak faults. Peak shear stresses in one registered model and one alternate model are 120 and 150 MPa, respectively, while peak vertically integrated shear stresses are 2.9 × 1012 and 4.1 × 1012 N m-1. Channeling of deviatoric stress along the strong Great Valley and the western slope of the Peninsular Ranges is evident. In the neotectonics of southern California, it appears that deviatoric stress and long-term strain rate have a negative correlation, because regions of low heat flow are strong and act as stress guides, while undergoing very little internal deformation. In contrast, active faults lie preferentially in areas with higher heat flow, and their low strength keeps deviatoric stresses locally modest.

Super-Laplacians and their symmetries

NASA Astrophysics Data System (ADS)

Howe, P. S.; Lindström, U.

2017-05-01

A super-Laplacian is a set of differential operators in superspace whose highestdimensional component is given by the spacetime Laplacian. Symmetries of super-Laplacians are given by linear differential operators of arbitrary finite degree and are determined by superconformal Killing tensors. We investigate these in flat superspaces. The differential operators determining the symmetries give rise to algebras which can be identified in many cases with the tensor algebras of the relevant superconformal Lie algebras modulo certain ideals. They have applications to Higher Spin theories.

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

NASA Technical Reports Server (NTRS)

Avis, L. M.

1976-01-01

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

Uncovering the local inelastic interactions during manufacture of ductile cast iron: How the substructure of the graphite particles can induce residual stress concentrations in the matrix

NASA Astrophysics Data System (ADS)

Andriollo, Tito; Hellström, Kristina; Sonne, Mads Rostgaard; Thorborg, Jesper; Tiedje, Niels; Hattel, Jesper

2018-02-01

Recent X-ray diffraction (XRD) measurements have revealed that plastic deformation and a residual elastic strain field can be present around the graphite particles in ductile cast iron after manufacturing, probably due to some local mismatch in thermal contraction. However, as only one component of the elastic strain tensor could be obtained from the XRD data, the shape and magnitude of the associated residual stress field have remained unknown. To compensate for this and to provide theoretical insight into this unexplored topic, a combined experimental-numerical approach is presented in this paper. First, a material equivalent to the ductile cast iron matrix is manufactured and subjected to dilatometric and high-temperature tensile tests. Subsequently, a two-scale hierarchical top-down model is devised, calibrated on the basis of the collected data and used to simulate the interaction between the graphite particles and the matrix during manufacturing of the industrial part considered in the XRD study. The model indicates that, besides the viscoplastic deformation of the matrix, the effect of the inelastic deformation of the graphite has to be considered to explain the magnitude of the XRD strain. Moreover, the model shows that the large elastic strain perturbations recorded with XRD close to the graphite-matrix interface are not artifacts due to e.g. sharp gradients in chemical composition, but correspond to residual stress concentrations induced by the conical sectors forming the internal structure of the graphite particles. In contrast to common belief, these results thus suggest that ductile cast iron parts cannot be considered, in general, as stress-free at the microstructural scale.

Borehole strainmeter measurements spanning the 2014, Mw6.0 South Napa Earthquake, California: The effect from instrument calibration

USGS Publications Warehouse

Langbein, John O.

2015-01-01

The 24 August 2014 Mw6.0 South Napa, California earthquake produced significant offsets on 12 borehole strainmeters in the San Francisco Bay area. These strainmeters are located between 24 and 80 km from the source and the observed offsets ranged up to 400 parts-per-billion (ppb), which exceeds their nominal precision by a factor of 100. However, the observed offsets of tidally calibrated strains differ by up to 130 ppb from predictions based on a moment tensor derived from seismic data. The large misfit can be attributed to a combination of poor instrument calibration and better modeling of the strain fit from the earthquake. Borehole strainmeters require in-situ calibration, which historically has been accomplished by comparing their measurements of Earth tides with the strain-tides predicted by a model. Although the borehole strainmeter accurately measure the deformation within the borehole, the long-wavelength strain signals from tides or other tectonic processes recorded in the borehole are modified by the presence of the borehole and the elastic properties of the grout and the instrument. Previous analyses of surface-mounted, strainmeter data and their relationship with the predicted tides suggest that tidal models could be in error by 30%. The poor fit of the borehole strainmeter data from this earthquake can be improved by simultaneously varying the components of the model tides up to 30% and making small adjustments to the point-source model of the earthquake, which reduces the RMS misfit from 130 ppb to 18 ppb. This suggests that relying on tidal models to calibrate borehole strainmeters significantly reduces their accuracy.

Waveform-based Bayesian full moment tensor inversion and uncertainty determination for the induced seismicity in an oil/gas field

NASA Astrophysics Data System (ADS)

Gu, Chen; Marzouk, Youssef M.; Toksöz, M. Nafi

2018-03-01

Small earthquakes occur due to natural tectonic motions and are induced by oil and gas production processes. In many oil/gas fields and hydrofracking processes, induced earthquakes result from fluid extraction or injection. The locations and source mechanisms of these earthquakes provide valuable information about the reservoirs. Analysis of induced seismic events has mostly assumed a double-couple source mechanism. However, recent studies have shown a non-negligible percentage of non-double-couple components of source moment tensors in hydraulic fracturing events, assuming a full moment tensor source mechanism. Without uncertainty quantification of the moment tensor solution, it is difficult to determine the reliability of these source models. This study develops a Bayesian method to perform waveform-based full moment tensor inversion and uncertainty quantification for induced seismic events, accounting for both location and velocity model uncertainties. We conduct tests with synthetic events to validate the method, and then apply our newly developed Bayesian inversion approach to real induced seismicity in an oil/gas field in the sultanate of Oman—determining the uncertainties in the source mechanism and in the location of that event.

A new validation technique for estimations of body segment inertia tensors: Principal axes of inertia do matter.

PubMed

Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J

2016-12-08

The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

The dual boundary element formulation for elastoplastic fracture mechanics

NASA Astrophysics Data System (ADS)

Leitao, V.; Aliabadi, M. H.; Rooke, D. P.

1993-08-01

The extension of the dual boundary element method (DBEM) to the analysis of elastoplastic fracture mechanics (EPFM) problems is presented. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied to one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. In order to avoid collocation at crack tips, crack kinks, and crack-edge corners, both crack surfaces are discretized with discontinuous quadratic boundary elements. The elastoplastic behavior is modeled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral, and/or triangular cells. A center-cracked plate and a slant edge-cracked plate subjected to tensile load are analyzed and the results are compared with others available in the literature. J-type integrals are calculated.

LES versus DNS: A comparative study

NASA Technical Reports Server (NTRS)

Shtilman, L.; Chasnov, J. R.

1992-01-01

We have performed Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of forced isotropic turbulence at moderate Reynolds numbers. The subgrid scale model used in the LES is based on an eddy viscosity which adjusts instantaneously the energy spectrum of the LES to that of the DNS. The statistics of the large scales of the DNS (filtered DNS field or fDNS) are compared to that of the LES. We present results for the transfer spectra, the skewness and flatness factors of the velocity components, the PDF's of the angle between the vorticity and the eigenvectors of the rate of strain, and that between the vorticity and the vorticity stretching tensor. The above LES statistics are found to be in good agreement with those measured in the fDNS field. We further observe that in all the numerical measurements, the trend was for the LES field to be more gaussian than the fDNS field. Future research on this point is planned.

Experimental investigation of cyclic thermomechanical deformation in torsion

NASA Technical Reports Server (NTRS)

Ellis, John R.; Castelli, Michael G.; Bakis, Charles E.

1992-01-01

An investigation of thermomechanical testing and deformation behavior of tubular specimens under torsional loading is described. Experimental issues concerning test accuracy and control specific to thermomechanical loadings under a torsional regime are discussed. A series of shear strain-controlled tests involving the nickel-base superalloy Hastelloy X were performed with various temperature excursions and compared to similar thermomechanical uniaxial tests. The concept and use of second invariants of the deviatoric stress and strain tensors as a means of comparing uniaxial and torsional specimens is also briefly presented and discussed in light of previous thermomechanical tests conducted under uniaxial conditions.

Finite element model for brittle fracture and fragmentation

DOE PAGES

Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin; ...

2016-06-01

A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.

Finite element model for brittle fracture and fragmentation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin

A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.

Can a pure vector gravitational wave mimic a pure tensor one?

NASA Astrophysics Data System (ADS)

Allen, Bruce

2018-06-01

In the general theory of relativity, gravitational waves have two possible polarizations, which are transverse and traceless with helicity ±2 . Some alternative theories contain additional helicity 0 and helicity ±1 polarization modes. Here, we consider a hypothetical "pure vector" theory in which gravitational waves have only two possible polarizations, with helicity ±1 . We show that if these polarizations are allowed to rotate as the wave propagates, then for certain source locations on the sky, the strain outputs of three ideal interferometric gravitational wave detectors can exactly reproduce the strain outputs predicted by general relativity.

Hencky's model for elastomer forming process

NASA Astrophysics Data System (ADS)

Oleinikov, A. A.; Oleinikov, A. I.

2016-08-01

In the numerical simulation of elastomer forming process, Henckys isotropic hyperelastic material model can guarantee relatively accurate prediction of strain range in terms of large deformations. It is shown, that this material model prolongate Hooke's law from the area of infinitesimal strains to the area of moderate ones. New representation of the fourth-order elasticity tensor for Hencky's hyperelastic isotropic material is obtained, it possesses both minor symmetries, and the major symmetry. Constitutive relations of considered model is implemented into MSC.Marc code. By calculating and fitting curves, the polyurethane elastomer material constants are selected. Simulation of equipment for elastomer sheet forming are considered.

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

NASA Technical Reports Server (NTRS)

Shay, R. M., Jr.; Caruthers, J. M.

1987-01-01

Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

Simulation of creep effects in framework of a geometrically nonlinear endochronic theory of inelasticity

NASA Astrophysics Data System (ADS)

Zabavnikova, T. A.; Kadashevich, Yu. I.; Pomytkin, S. P.

2018-05-01

A geometric non-linear endochronic theory of inelasticity in tensor parametric form is considered. In the framework of this theory, the creep strains are modelled. The effect of various schemes of applying stresses and changing of material properties on the development of creep strains is studied. The constitutive equations of the model are represented by non-linear systems of ordinary differential equations which are solved in MATLAB environment by implicit difference method. Presented results demonstrate a good qualitative agreement of theoretical data and experimental observations including the description of the tertiary creep and pre-fracture of materials.

Non-double-couple earthquakes. 1. Theory

USGS Publications Warehouse

Julian, B.R.; Miller, A.D.; Foulger, G.R.

1998-01-01

Historically, most quantitative seismological analyses have been based on the assumption that earthquakes are caused by shear faulting, for which the equivalent force system in an isotropic medium is a pair of force couples with no net torque (a 'double couple,' or DC). Observations of increasing quality and coverage, however, now resolve departures from the DC model for many earthquakes and find some earthquakes, especially in volcanic and geothermal areas, that have strongly non-DC mechanisms. Understanding non-DC earthquakes is important both for studying the process of faulting in detail and for identifying nonshear-faulting processes that apparently occur in some earthquakes. This paper summarizes the theory of 'moment tensor' expansions of equivalent-force systems and analyzes many possible physical non-DC earthquake processes. Contrary to long-standing assumption, sources within the Earth can sometimes have net force and torque components, described by first-rank and asymmetric second-rank moment tensors, which must be included in analyses of landslides and some volcanic phenomena. Non-DC processes that lead to conventional (symmetric second-rank) moment tensors include geometrically complex shear faulting, tensile faulting, shear faulting in an anisotropic medium, shear faulting in a heterogeneous region (e.g., near an interface), and polymorphic phase transformations. Undoubtedly, many non-DC earthquake processes remain to be discovered. Progress will be facilitated by experimental studies that use wave amplitudes, amplitude ratios, and complete waveforms in addition to wave polarities and thus avoid arbitrary assumptions such as the absence of volume changes or the temporal similarity of different moment tensor components.

Uncertainties for seismic moment tensors and applications to nuclear explosions, volcanic events, and earthquakes

NASA Astrophysics Data System (ADS)

Tape, C.; Alvizuri, C. R.; Silwal, V.; Tape, W.

2017-12-01

When considered as a point source, a seismic source can be characterized in terms of its origin time, hypocenter, moment tensor, and source time function. The seismologist's task is to estimate these parameters--and their uncertainties--from three-component ground motion recorded at irregularly spaced stations. We will focus on one portion of this problem: the estimation of the moment tensor and its uncertainties. With magnitude estimated separately, we are left with five parameters describing the normalized moment tensor. A lune of normalized eigenvalue triples can be used to visualize the two parameters (lune longitude and lune latitude) describing the source type, while the conventional strike, dip, and rake angles can be used to characterize the orientation. Slight modifications of these five parameters lead to a uniform parameterization of moment tensors--uniform in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. For a moment tensor m that we have inferred from seismic data for an earthquake, we define P(V) to be the probability that the true moment tensor for the earthquake lies in the neighborhood of m that has fractional volume V. The average value of P(V) is then a measure of our confidence in our inference of m. The calculation of P(V) requires knowing both the probability P(w) and the fractional volume V(w) of the set of moment tensors within a given angular radius w of m. We apply this approach to several different data sets, including nuclear explosions from the Nevada Test Site, volcanic events from Uturuncu (Bolivia), and earthquakes. Several challenges remain: choosing an appropriate misfit function, handling time shifts between data and synthetic waveforms, and extending the uncertainty estimation to include more source parameters (e.g., hypocenter and source time function).

Interrogating the origin and behavior of magnetic resonance diffusion tensor scalar parameters in the myocardium

NASA Astrophysics Data System (ADS)

Abdullah, Osama Mahmoud

Myocardial microstructure plays an important role in sustaining the orchestrated beating motion of the heart. Several microstructural components, including myocytes and auxiliary cells, extracellular space, and blood vessels provide the infrastructure for normal heart function, including excitation propagation, myocyte contraction, delivery of oxygen and nutrients, and removing byproduct wastes. Cardiac diseases cause deleterious changes to some or all of these microstructural components in the detrimental process of cardiac remodeling. Since heart failure is among the leading causes of death in the world, new and novel tools to noninvasively characterize heart microstructure are needed for monitoring and staging of cardiac disease. In this regards, diffusion magnetic resonance imaging (MRI) provides a promising framework to probe and quantify tissue microstructure without the need for exogenous contrast agent. As diffusion in 3-dimensional space is characterized by the diffusion tensor, MR diffusion tensor imaging (DTI) is being used to noninvasively measure anisotropic diffusion, and thus the magnitude and spatial orientation of microstructural organization of tissues, including the heart. However, even though in vivo cardiac DTI has become more clinically available, to date the origin and behavior of different microstructural components on the measured DTI signal remain to be explicitly specified. The presented studies in this work demonstrate that DTI can be used as a noninvasive and contrast-free imaging modality to characterize myocyte size and density, extracellular collagen content, and the directional magnitude of blood flow. The identified applications are expected to provide metrics to enable physicians to detect, quantify, and stage different microstructural components during progression of cardiac disease.

Mid-Crustal Stress Magnitude and Rotation Transients Related to the Seismic Cycle

NASA Astrophysics Data System (ADS)

Nüchter, J. A.; Ellis, S.

2008-12-01

Seismic slip causes a stress drop in the upper crust, and a major stress increase at the lower termination of the fault in the middle crust. Previous numerical models show how these stresses relax during an episode of postseismic creep. Natural evidence for postseismic stress and strain transients at depth is provided by 1) the geological record of exhumed metamorphic rocks, and 2) from postseismic surface deformation transients. In the present study, we use numerical models to investigate the changes in the geometry of the mid-crustal stress field caused by seismic slip along normal faults within an extensional tectonic setting. We model a 100x30km crustal section, with a fault reaching down to 20km and dipping at 60°. A non-linear thermal gradient and constant elastic parameters are applied. Thermally activated creep is described by values derived from laboratory creep experiments on wet quartzite. The crust is loaded by horizontal extension at a constant rate, and earthquakes are triggered by a short term decrease in the frictional coefficient of the fault. During the interseismic period, this coefficient is set to high values to lock the fault. A sequence of 30 earthquakes with a constant recurrence interval of 500y is simulated, and the results for the last seismic cycle are analyzed. In such a tectonic setting, the Anderson theory predicts that the maximum principal stress is vertical. A stress field consistent to this theory is reached after an initial stage of 15ka extension without earthquake activity. The results for the 30th seismic cycle imply that seismic slip causes a major stress increase of at least 50MPa at a depth level below the brittle ductile transition, which is in accordance to reports on seismic stress increase derived from the record of metamorphic rocks. In the hanging wall, the stress increase results mainly from an increase in the maximum principal stress and the stress tensor rotates counter-clockwise by 10-30°. In the footwall the stress increase results mainly from a drop in the minimum principal stress, and the stress tensor rotates clockwise by 45-60°. A change in the magnitude of differential stress can be addressed by the addition of an incremental stress tensor resulting from elastic strain to the preexisting stress tensor. In an isotropic medium, the orientation of the maximum and the minimum principal stress changes are controlled by the directions of maximum compression and maximum extension, respectively. The magnitude and the orientation of the resulting stress tensor depend: 1) on the absolute magnitudes and on the ratio of the magnitudes of pre-existing stress and incremental change in the stress tensor; and 2) on the mis-orientation between existing stress and stress change principal directions. The zone of coseismic loading correlates to the interval in which seismic slip tapers off with depth. For a normal fault, the crust here is subjected to fault-parallel compression in the hanging wall, and to extension in the footwall. The resulting orientation of the seismic principal compressive stress change parallel to the fault in the hanging wall and normal to the fault in the footwall causes the particular deflection of the resulting stress tensor . During the interseismic period, the stress peak relaxes by thermally activated creep, while the deflection of the stress tensor is persistent. We show that significant mis- orientations of the stress tensor can be preserved over timescales typical for a seismic cycle, in dependence on the far field extension rate. We conclude that seismic activity causes 1) a non-steady state mid-crustal stress field, and 2) a persistent deflection of the stress tensor orientation from the predictions of the Anderson theory.

Precursory, Nucleation and Propagation of Ruptures Along Heterogeneously Loaded, Circular Experimental Faults

NASA Astrophysics Data System (ADS)

Reches, Z.; Zu, X.; Jeffers, J.

2017-12-01

We explored the evolution of dynamic rupture along a circular experimental fault composed of clear acrylic blocks. The ring-shaped fault surface has inner and outer diameters of 7.72 and 10.16 cm, respectively. An array of ten rossette strain-gauges is attached to the outer rim of one block that provide the 2D strain tensor in a plane normal to the fault. The 30 components of the gauges are monitored at 10^6 samples/second. One 3D miniature accelerometer is attached to the fault block. The initial asperities of the fault surface generated a non-uniform strain (=stress) distribution that was recorded, and indicated local deviations of ±30% from the mean stress. The mean normal stress was up to 3.5 MPa, the remotely applied velocity was up to .002 m/s, and the slip velocities during rupture were not measured. The rupture characteristics, namely propagation velocity and rupture front strain-field, were determined from strain-gauge outputs. The analysis of tens of stick-slip events revealed the following preliminary results: (1) The ruptures consistently nucleated at sites of high local strains (=stresses) that were formed by the pre-shear, normal stress loading. (2) The pre-rupture nucleation process was recognized a by temporal (< 0.1 s), local (<20 mm) reduction of the shear strain. (3) Commonly, the initiation of nucleation was associated with micro acoustic emissions, whereas the initiation of rupture was associated with intense acoustic activity. (4) Nucleation could occur quasi-simultaneously at two, highly stressed sites. (5) From the nucleation site, the ruptures propagated in two directions along the ring-shaped fault, and the collision between the two fronts led to rupture `shut-off'. (5) The strain-field of rupture fronts was well-recognized for ruptures propagating faster than 50 m/s, and the fastest fronts propagated at 1000 m/s. (7) It appears that the rupture front strain-field close to the nucleation site differs from the front strain-field far from nucleation site. (8) Post-shear examination of the fault surfaces revealed evidence of brittle wear of the acrylic including gouge formation, ploughing, and powder smearing. (9) Work in progress includes attempts to achieve faster dynamic ruptures, and the utilization of the existing monitoring system to rupture granite faults.

Influences of the Darrieus-Landau instability on premixed turbulent flames

NASA Astrophysics Data System (ADS)

Patyal, Advitya; Matalon, Moshe

2017-11-01

The propagation of turbulent flames in three-dimensional turbulent flows is studied within the context of the hydrodynamic theory. The flame is treated as a surface of density discontinuity with the flow modified by gas expansion resulting from heat released during combustion. The flame is tracked using a level-set method with a propagation speed that depends on the local flame stretch, modulated by a Markstein length. Impact of the Darrieus-Landau instability on the topology of the flame surface is studied. It is shown that similar to passive interfaces, flames under the influence of the hydrodynamic instability resort to cylindrical structures with increasing turbulence intensity, even in 3D. The mechanism of modification of vortical structures in the burned gas is identified in terms of the alignments between the vorticity vector, flame surface normal and eigenvectors of the strain rate tensor. The results indicate that the strain rate tensor is intricately coupled with the normal to the flame surface and creates anisotropy in the orientation of vortical structures, which begins to weaken as the turbulent intensity increases. Furthermore, vorticity budgets are used to highlight the relative importance of baroclinic torque due to Darrieus-Landau instability.

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure.

PubMed

Muhlestein, Michael B; Haberman, Michael R

2016-08-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

PubMed Central

Haberman, Michael R.

2016-01-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed. PMID:27616932

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

NASA Astrophysics Data System (ADS)

Muhlestein, Michael B.; Haberman, Michael R.

2016-08-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

24 +24 real scalar multiplet in four dimensional N =2 conformal supergravity

NASA Astrophysics Data System (ADS)

Hegde, Subramanya; Lodato, Ivano; Sahoo, Bindusar

2018-03-01

Starting from the 48 +48 component multiplet of supercurrents for a rigid N =2 tensor multiplet in four spacetime dimensions, we obtain the transformation of the linearized supergravity multiplet which couples to this supercurrent multiplet. At the linearized level, this 48 +48 component supergravity multiplet decouples into the 24 +24 component linearized standard Weyl multiplet and a 24 +24 component irreducible matter multiplet containing a real scalar field. By a consistent application of the supersymmetry algebra with field-dependent structure constants appropriate to N =2 conformal supergravity, we find the full transformation law for this multiplet in a conformal supergravity background. By performing a suitable field redefinition, we find that the multiplet is a generalization of the flat space multiplet, obtained by Howe et al. in Nucl. Phys. B214, 519 (1983), 10.1016/0550-3213(83)90249-3, to a conformal supergravity background. We also present a set of constraints which can be consistently imposed on this multiplet to obtain a restricted minimal 8 +8 off-shell matter multiplet. We also show, as an example, the precise embedding of the tensor multiplet inside this multiplet.

Temperature dependent elastic properties of γ-phase U – 8 wt% Mo

DOE PAGES

Steiner, M. A.; Garlea, E.; Creasy, J.; ...

2017-12-28

Polycrystalline elastic moduli and stiffness tensor components of γ-phase U – 8 wt% Mo have been determined by resonant ultrasound spectroscopy in the temperature range of 25-650°C. The ambient temperature elastic properties are compared to results measured via other experimental methods and show reasonable agreement, though there is considerable variation of these properties within the literature at both the U – 8 wt% Mo composition and as a function of Mo concentration. The Young’s modulus of U – 8 wt% Mo measured in this study decreases steadily with temperature at a rate that is slower than trends previously observed atmore » similar Mo concentrations, though the difference is not statistically significant. This first measurement of the temperature dependent elastic stiffness tensor of a polycrystalline U-Mo alloy clarifies that the behavior of the Young’s modulus is due to a strongly weakening C 11 polycrystalline stiffness tensor component, along with milder decreases in C 12 and C 44. The unique partially auxetic properties recently predicted for singlecrystalline U-Mo are discussed in regard to their possible impact on the polycrystalline behavior of the alloy.« less

Temperature dependent elastic properties of γ-phase U – 8 wt% Mo

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steiner, M. A.; Garlea, E.; Creasy, J.

Polycrystalline elastic moduli and stiffness tensor components of γ-phase U – 8 wt% Mo have been determined by resonant ultrasound spectroscopy in the temperature range of 25-650°C. The ambient temperature elastic properties are compared to results measured via other experimental methods and show reasonable agreement, though there is considerable variation of these properties within the literature at both the U – 8 wt% Mo composition and as a function of Mo concentration. The Young’s modulus of U – 8 wt% Mo measured in this study decreases steadily with temperature at a rate that is slower than trends previously observed atmore » similar Mo concentrations, though the difference is not statistically significant. This first measurement of the temperature dependent elastic stiffness tensor of a polycrystalline U-Mo alloy clarifies that the behavior of the Young’s modulus is due to a strongly weakening C 11 polycrystalline stiffness tensor component, along with milder decreases in C 12 and C 44. The unique partially auxetic properties recently predicted for singlecrystalline U-Mo are discussed in regard to their possible impact on the polycrystalline behavior of the alloy.« less

Spin correlations in the {Lambda}{Lambda} and {Lambda}{Lambda}-bar systems generated in relativistic heavy-ion collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lyuboshitz, V. L.; Lyuboshitz, V. V., E-mail: Valery.Lyuboshitz@jinr.r

2010-05-15

Spin correlations for the {Lambda}{Lambda} and {Lambda}{Lambda}-bar pairs, generated in relativistic heavy-ion collisions, and related angular correlations at the joint registration of hadronic decays of two hyperons, in which space parity is not conserved, are analyzed. The correlation tensor components can be derived from the double angular distribution of products of two decays by the method of 'moments'. The properties of the 'trace' of the correlation tensor (a sum of three diagonal components), determining the relative fractions of the triplet states and singlet state of respective pairs, are discussed. Spin correlations for two identical particles ({Lambda}{Lambda}) and two nonidentical particlesmore » ({Lambda}{Lambda}-bar) are considered from the viewpoint of the conventional model of one-particle sources. In the framework of this model, correlations vanish at sufficiently large relative momenta. However, under these conditions, in the case of two nonidentical particles ({Lambda}{Lambda}-bar) a noticeable role is played by two-particle annihilation (two-quark, two-gluon) sources, which lead to the difference of the correlation tensor from zero. In particular, such a situation may arise when the system passes through the 'mixed phase.'« less

On the role of the transformation eigenstrain in the growth or shrinkage of spheroidal isotropic precipitations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fischer, F.D.; Boehm, H.J.

The jumps of the strain and stress tensors on the surface of elastic homogeneous or inhomogeneous ellipsoidal inclusions embedded in an elastic matrix are obtained from results reported in the literature. They are used to derive closed-form expressions for the thermodynamic force in such matrix-inclusion systems that are subjected to a generally defined homogeneous transformation eigenstrain. A detailed study is presented for an isotropic spheroidal inclusion in an isotropic matrix in which the most important parameters are the inclusion's aspect ratio {alpha} and an eigenstrain triaxiality parameter d-bar. The fluctuations of the thermodynamic force are investigated for a set ofmore » specific transformation eigenstrain tensors and are presented for inclusion shapes ranging from disk-like to fiber-like spheroids.« less

Yield Scaling of Frequency Domain Moment Tensors from Contained Chemical Explosions Detonated in Granite

NASA Astrophysics Data System (ADS)

MacPhail, M. D.; Stump, B. W.; Zhou, R.

2017-12-01

The Source Phenomenology Experiment (SPE - Arizona) was a series of nine, contained and partially contained chemical explosions within the porphyry granite at the Morenci Copper mine in Arizona. Its purpose was to detonate, record and analyze seismic waveforms from these single-fired explosions. Ground motion data from the SPE is analyzed in this study to assess the uniqueness of the time domain moment tensor source representation and its ability to quantify containment and yield scaling. Green's functions were computed for each of the explosions based on a 1D velocity model developed for the SPE. The Green's functions for the sixteen, near-source stations focused on observations from 37 to 680 m. This study analyzes the three deepest, fully contained explosions with a depth of burial of 30 m and yields of 0.77e-3, 3.08e-3 and 6.17e-3 kt. Inversions are conducted within the frequency domain and moment tensors are decomposed into deviatoric and isotropic components to evaluate the effects of containment and yield on the resulting source representation. Isotropic moments are compared to those for other contained explosions as reported by Denny and Johnson, 1991, and are in good agreement with their scaling results. The explosions in this study have isotropic moments of 1.2e12, 3.1e12 and 6.1e13 n*m. Isotropic and Mzz moment tensor spectra are compared to Mueller-Murphy, Denny-Johnson and revised Heard-Ackerman (HA) models and suggest that the larger explosions fit the HA model better. Secondary source effects resulting from free surface interactions including the effects of spallation contribute to the resulting moment tensors which include a CLVD component. Hudson diagrams, using frequency domain moment tensor data, are computed as a tool to assess how these containment scenarios affect the source representation. Our analysis suggests that, within our band of interest (2-20 Hz), as the frequency increases, the source representation becomes more explosion like, peaking at around 20 Hz. These results guide additional analysis of the observational data and the practical resolution of physical phenomenology accompanying underground explosions.

Scalar Casimir densities and forces for parallel plates in cosmic string spacetime

NASA Astrophysics Data System (ADS)

Bezerra de Mello, E. R.; Saharian, A. A.; Abajyan, S. V.

2018-04-01

We analyze the Green function, the Casimir densities and forces associated with a massive scalar quantum field confined between two parallel plates in a higher dimensional cosmic string spacetime. The plates are placed orthogonal to the string, and the field obeys the Robin boundary conditions on them. The boundary-induced contributions are explicitly extracted in the vacuum expectation values (VEVs) of the field squared and of the energy-momentum tensor for both the single plate and two plates geometries. The VEV of the energy-momentum tensor, in additional to the diagonal components, contains an off diagonal component corresponding to the shear stress. The latter vanishes on the plates in special cases of Dirichlet and Neumann boundary conditions. For points outside the string core the topological contributions in the VEVs are finite on the plates. Near the string the VEVs are dominated by the boundary-free part, whereas at large distances the boundary-induced contributions dominate. Due to the nonzero off diagonal component of the vacuum energy-momentum tensor, in addition to the normal component, the Casimir forces have nonzero component parallel to the boundary (shear force). Unlike the problem on the Minkowski bulk, the normal forces acting on the separate plates, in general, do not coincide if the corresponding Robin coefficients are different. Another difference is that in the presence of the cosmic string the Casimir forces for Dirichlet and Neumann boundary conditions differ. For Dirichlet boundary condition the normal Casimir force does not depend on the curvature coupling parameter. This is not the case for other boundary conditions. A new qualitative feature induced by the cosmic string is the appearance of the shear stress acting on the plates. The corresponding force is directed along the radial coordinate and vanishes for Dirichlet and Neumann boundary conditions. Depending on the parameters of the problem, the radial component of the shear force can be either positive or negative.

Methods and computer program documentation for determining anisotropic transmissivity tensor components of two-dimensional ground-water flow

USGS Publications Warehouse

Maslia, M.L.; Randolph, R.B.

1986-01-01

The theory of anisotropic aquifer hydraulic properties and a computer program, written in Fortran 77, developed to compute the components of the anisotropic transmissivity tensor of two-dimensional groundwater flow are described. To determine the tensor components using one pumping well and three observation wells, the type-curve and straight-line approximation methods are developed. These methods are based on the equation of drawdown developed for two-dimensional nonsteady flow in an infinite anisotropic aquifer. To determine tensor components using more than three observation wells, a weighted least squares optimization procedure is described for use with the type-curve and straight-line approximation methods. The computer program described in this report allows the type-curve, straight-line approximation, and weighted least squares optimization methods to be used in conjunction with data from observation and pumping wells. Three example applications using the computer program and field data gathered during geohydrologic investigations at a site near Dawsonville, Georgia , are provided to illustrate the use of the computer program. The example applications demonstrate the use of the type-curve method using three observation wells, the weighted least squares optimization method using eight observation wells and equal weighting, and the weighted least squares optimization method using eight observation wells and unequal weighting. Results obtained using the computer program indicate major transmissivity in the range of 347-296 sq ft/day, minor transmissivity in the range of 139-99 sq ft/day, aquifer anisotropy in the range of 3.54 to 2.14, principal direction of flow in the range of N. 45.9 degrees E. to N. 58.7 degrees E., and storage coefficient in the range of 0.0063 to 0.0037. The numerical results are in good agreement with field data gathered on the weathered crystalline rocks underlying the investigation site. Supplemental material provides definitions of variables, data requirements and corresponding formats, input data and output results for the example applications, and a listing of the Fortran 77 computer code. (Author 's abstract)

Nature of the tensor order in Cd 2 Re 2 O 7

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di Matteo, S.; Norman, M. R.

The pyrochlore metal Cd 2Re 2O 7 has been recently investigated by second-harmonic generation (SHG) reflectivity. In this paper, we develop a general formalism that allows for the identification of the relevant tensor components of the SHG from azimuthal scans. We demonstrate that the secondary order parameter identified by SHG at the structural phase transition is the x 2 - y 2 component of the axial toroidal quadrupole. This differs from the 3z 2 - r 2 symmetry of the atomic displacements associated with the I4m2 crystal structure that was previously thought to be its origin. Within the same formalism,more » we suggest that the primary order parameter detected in the SHG experiment is the 3z 2 - r 2 component of the magnetic quadrupole. We discuss the general mechanism driving the phase transition in our proposed framework, and suggest experiments, particularly resonant x-ray scattering ones, that could clarify this issue.« less

Non-Double-Couple Component Analysis of Induced Microearthquakes in the Val D'Agri Basin (Italy)

NASA Astrophysics Data System (ADS)

Roselli, P.; Improta, L.; Saccorotti, G.

2017-12-01

In recent years it has become accepted that earthquake source can attain significant Non-Double-Couple (NDC) components. Among the driving factors of deviation from normal double-couple (DC) mechanisms there is the opening/closing of fracture networks and the activation of pre-existing faults by pore fluid pressure perturbations. This observation makes the thorough analysis of source mechanism of key importance for the understanding of withdrawal/injection induced seismicity from geothermal and hydrocarbon reservoirs, as well as of water reservoir induced seismicity. In addition to the DC component, seismic moment tensor can be decomposed into isotropic (ISO) and compensated linear vector dipole (CLVD) components. In this study we performed a careful analysis of the seismic moment tensor of induced microseismicity recorded in the Val d'Agri (Southern Apennines, Italy) focusing our attention on the NDC component. The Val d'Agri is a Quaternary extensional basin that hosts the largest onshore European oil field and a water reservoir (Pertusillo Lake impoundment) characterized by severe seasonal level oscillations. Our input data-set includes swarm-type induced micro-seismicity recorded between 2005-2006 by a high-performance network and accurately localized by a reservoir-scale local earthquake tomography. We analyze two different seismicity clusters: (i) a swarm of 69 earthquakes with 0.3 ≤ ML ≤ 1.8 induced by a wastewater disposal well of the oilfield during the initial daily injection tests (10 days); (ii) 526 earthquakes with -0.2 ≤ ML ≤ 2.7 induced by seasonal volume changes of the artificial lake. We perform the seismic moment tensor inversion by using HybridMT code. After a very accurate signal-to-noise selection and hand-made picking of P-pulses, we obtain %DC, %ISO, %CLVD for each event. DC and NDC components are analyzed and compared with the spatio-temporal distribution of seismicity, the local stress field, the injection parameters and the water level in the impoundment. We find significant NDC components and abrupt temporal variations in the %DC and %ISO components that appear linked to the extremely variable parameters of the injection tests into the disposal well.

EEG Classification for Hybrid Brain-Computer Interface Using a Tensor Based Multiclass Multimodal Analysis Scheme

PubMed Central

Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang

2016-01-01

Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI. PMID:26880873

A metamodel for the apparent permeability tensor of three-dimensional porous media in the inertial regime

NASA Astrophysics Data System (ADS)

Luminari, Nicola; Airiau, Christophe; Bottaro, Alessandro

2017-11-01

In the description of the homogenized flow through a porous medium saturated by a fluid, the apparent permeability tensor is one of the most important parameters to evaluate. In this work we compute numerically the apparent permeability tensor for a 3D porous medium constituted by rigid cylinder using the VANS (Volume-Averaged Navier-Stokes) theory. Such a tensor varies with the Reynolds number, the mean pressure gradient orientation and the porosity. A database is created exploring the space of the above parameters. Including the two Euler angles that define the mean pressure gradient is extremely important to capture well possible 3D effects. Based on the database, a kriging interpolation metamodel is used to obtain an estimate of all the tensor components for any input parameters. Preliminary results of the flow in a porous channel based on the metamodel and the VANS closure are shown; the use of such a reduced order model together with a numerical code based on the equations at the macroscopic scale permit to maintain the computational times to within reasonable levels. The authors acknowledge the IDEX Foundation of the University of Toulouse 570 for the financial support Granted to the last author under the project Attractivity Chairs.

Waveform inversion of oscillatory signatures in long-period events beneath volcanoes

USGS Publications Warehouse

Kumagai, H.; Chouet, B.A.; Nakano, M.

2002-01-01

The source mechanism of long-period (LP) events is examined using synthetic waveforms generated by the acoustic resonance of a fluid-filled crack. We perform a series of numerical tests in which the oscillatory signatures of synthetic LP waveforms are used to determine the source time functions of the six moment tensor components from waveform inversions assuming a point source. The results indicate that the moment tensor representation is valid for the odd modes of crack resonance with wavelengths 2L/n, 2W/n, n = 3, 5, 7, ..., where L and W are the crack length and width, respectively. For the even modes with wavelengths 2L/n, 2W/n, n = 2, 4, 6,..., a generalized source representation using higher-order tensors is required, although the efficiency of seismic waves radiated by the even modes is expected to be small. We apply the moment tensor inversion to the oscillatory signatures of an LP event observed at Kusatsu-Shirane Volcano, central Japan. Our results point to the resonance of a subhorizontal crack located a few hundred meters beneath the summit crater lakes. The present approach may be useful to quantify the source location, geometry, and force system of LP events, and opens the way for moment tensor inversions of tremor.

EEG Classification for Hybrid Brain-Computer Interface Using a Tensor Based Multiclass Multimodal Analysis Scheme.

PubMed

Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang

2016-01-01

Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI.

Reconstruction of apparent orthotropic conductivity tensor image using magnetic resonance electrical impedance tomography

NASA Astrophysics Data System (ADS)

Sajib, Saurav Z. K.; Kim, Ji Eun; Jeong, Woo Chul; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je

2015-03-01

Magnetic resonance electrical impedance tomography visualizes current density and/or conductivity distributions inside an electrically conductive object. Injecting currents into the imaging object along at least two different directions, induced magnetic flux density data can be measured using a magnetic resonance imaging scanner. Without rotating the object inside the scanner, we can measure only one component of the magnetic flux density denoted as Bz. Since the biological tissues such as skeletal muscle and brain white matter show strong anisotropic properties, the reconstruction of anisotropic conductivity tensor is indispensable for the accurate observations in the biological systems. In this paper, we propose a direct method to reconstruct an axial apparent orthotropic conductivity tensor by using multiple Bz data subject to multiple injection currents. To investigate the anisotropic conductivity properties, we first recover the internal current density from the measured Bz data. From the recovered internal current density and the curl-free condition of the electric field, we derive an over-determined matrix system for determining the internal absolute orthotropic conductivity tensor. The over-determined matrix system is designed to use a combination of two loops around each pixel. Numerical simulations and phantom experimental results demonstrate that the proposed algorithm stably determines the orthotropic conductivity tensor.

Spacetime encodings. III. Second order Killing tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brink, Jeandrew

2010-01-15

This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture ofmore » what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.« less

Interaction of Strain and Nuclear Spins in Silicon: Quadrupolar Effects on Ionized Donors

NASA Astrophysics Data System (ADS)

Franke, David P.; Hrubesch, Florian M.; Künzl, Markus; Becker, Hans-Werner; Itoh, Kohei M.; Stutzmann, Martin; Hoehne, Felix; Dreher, Lukas; Brandt, Martin S.

2015-07-01

The nuclear spins of ionized donors in silicon have become an interesting quantum resource due to their very long coherence times. Their perfect isolation, however, comes at a price, since the absence of the donor electron makes the nuclear spin difficult to control. We demonstrate that the quadrupolar interaction allows us to effectively tune the nuclear magnetic resonance of ionized arsenic donors in silicon via strain and determine the two nonzero elements of the S tensor linking strain and electric field gradients in this material to S11=1.5 ×1022 V /m2 and S44=6 ×1022 V /m2 . We find a stronger benefit of dynamical decoupling on the coherence properties of transitions subject to first-order quadrupole shifts than on those subject to only second-order shifts and discuss applications of quadrupole physics including mechanical driving of magnetic resonance, cooling of mechanical resonators, and strain-mediated spin coupling.

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

NASA Astrophysics Data System (ADS)

Jiang, Li; Liu, Jie; Zhang, Jianzhong; Feng, Zhibing

2017-12-01

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.

Measuring in-vivo and in-situ ex-vivo the 3D deformation of the lamina cribrosa microstructure under elevated intraocular pressure

NASA Astrophysics Data System (ADS)

Wei, Junchao; Yang, Bin; Voorhees, Andrew P.; Tran, Huong; Brazile, Bryn; Wang, Bo; Schuman, Joel; Smith, Matthew A.; Wollstein, Gadi; Sigal, Ian A.

2018-02-01

Elevated intraocular pressure (IOP) deforms the lamina cribrosa (LC), a structure within the optic nerve head (ONH) in the back of the eye. Evidence suggests that these deformations trigger events that eventually cause irreversible blindness, and have therefore been studied in-vivo using optical coherence tomography (OCT), and ex-vivo using OCT and a diversity of techniques. To the best of our knowledge, there have been no in-situ ex-vivo studies of LC mechanics. Our goal was two-fold: to introduce a technique for measuring 3D LC deformations from OCT, and to determine whether deformations of the LC induced by elevated IOP differ between in-vivo and in-situ ex-vivo conditions. A healthy adult rhesus macaque monkey was anesthetized and IOP was controlled by inserting a 27- gauge needle into the anterior chamber of the eye. Spectral domain OCT was used to obtain volumetric scans of the ONH at normal and elevated IOPs. To improve the visibility of the LC microstructure the scans were first processed using a novel denoising technique. Zero-normalized cross-correlation was used to find paired corresponding locations between images. For each location pair, the components of the 3D strain tensor were determined using non-rigid image registration. A mild IOP elevation from 10 to 15mmHg caused LC effective strains as large as 3%, and about 50% larger in-vivo than in-situ ex-vivo. The deformations were highly heterogeneous, with substantial 3D components, suggesting that accurate measurement of LC microstructure deformation requires high-resolution volumes. This technique will help improve understanding of LC biomechanics and how IOP contributes to glaucoma.

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

NASA Technical Reports Server (NTRS)

Howard, J. C.

1975-01-01

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Flexible Force Field Parameterization through Fitting on the Ab Initio-Derived Elastic Tensor

PubMed Central

2017-01-01

Constructing functional forms and their corresponding force field parameters for the metal–linker interface of metal–organic frameworks is challenging. We propose fitting these parameters on the elastic tensor, computed from ab initio density functional theory calculations. The advantage of this top-down approach is that it becomes evident if functional forms are missing when components of the elastic tensor are off. As a proof-of-concept, a new flexible force field for MIL-47(V) is derived. Negative thermal expansion is observed and framework flexibility has a negligible effect on adsorption and transport properties for small guest molecules. We believe that this force field parametrization approach can serve as a useful tool for developing accurate flexible force field models that capture the correct mechanical behavior of the full periodic structure. PMID:28661672

Synthesis of Creep Measurements from Strainmeters and Creepmeters along the San Andreas Fault: Implications for Seismic vs. Aseismic Partitioning

NASA Astrophysics Data System (ADS)

Mencin, D.; Gottlieb, M. H.; Hodgkinson, K. M.; Bilham, R. G.; Mattioli, G. S.; Johnson, W.; Van Boskirk, E.; Meertens, C. M.

2015-12-01

Strainmeters and creepmeters have been operated along the San Andreas Fault, observing creep events for decades. In particular, the EarthScope Plate Boundary Observatory (PBO) has added a significant number of borehole strainmeters along the San Andreas Fault (SAF) over the last decade. The geodetic data cover a significant temporal portion of the inferred earthquake cycle along this portion of the SAF. Creepmeters measure the surface displacement over time (creep) with short apertures and have the ability to capture slow slip, coseismic rupture, and afterslip. Modern creepmeters deployed by the authors have a resolution of 5 µm over a range of 10 mm and a dynamic sensor with a resolution 25 µm over a range 2.2 m. Borehole strainmeters measure local deformation some distance from the fault with a broader aperture. Borehole tensor strainmeters principally deployed as part of the PBO, measure the horizontal strain tensor at a depth of 100-200 m with a resolution of 10-11 strain and are located 4 - 10 km from the fault with the ability to image a 1 mm creep event acting on an area of ~500 m2 from over 4 km away (fault perpendicular). A single borehole tensor strainmeter is capable of providing broad constraints on the creep event asperity size, location, direction and depth of a single creep event. The synthesis of these data from all the available geodetic instruments proximal to the SAF presents a unique opportunity to constrain the partitioning between aseismic and seismic slip on the central SAF. We show that simple elastic half-space models allow us to loosely constrain the location and depth of any individual creep event on the fault, even with a single instrument, and to image the accumulation of creep with time.

Airborne full tensor magnetic gradiometry surveys in the Thuringian basin, Germany

NASA Astrophysics Data System (ADS)

Queitsch, M.; Schiffler, M.; Goepel, A.; Stolz, R.; Meyer, M.; Meyer, H.; Kukowski, N.

2013-12-01

In this contribution we introduce a newly developed fully operational full tensor magnetic gradiometer (FTMG) instrument based on Superconducting Quantum Interference Devices (SQUIDs) and show example data acquired in 2012 within the framework of the INFLUINS (Integrated Fluid Dynamics in Sedimentary basins) project. This multidisciplinary project aims for a better understanding of movements and interaction between shallow and deep fluids in the Thuringian Basin in the center of Germany. In contrast to mapping total magnetic field intensity (TMI) in conventional airborne magnetic surveys for industrial exploration of mineral deposits and sedimentary basins, our instrument measures all components of the magnetic field gradient tensor using highly sensitive SQUID gradiometers. This significantly constrains the solutions of the inverse problem. Furthermore, information on the ratio between induced and remanent magnetization is obtained. Special care has been taken to reduce motion noise while acquiring data in airborne operation. Therefore, the sensors are mounted in a nonmagnetic and aerodynamically shaped bird made of fiberglas with a high drag tail which stabilizes the bird even at low velocities. The system is towed by a helicopter and kept at 30m above ground during data acquisition. Additionally, the system in the bird incorporates an inertial unit for geo-referencing and enhanced motion noise compensation, a radar altimeter for topographic correction and a GPS system for high precision positioning. Advanced data processing techniques using reference magnetometer and inertial unit data result in a very low system noise of less than 60 pT/m peak to peak in airborne operation. To show the performance of the system we present example results from survey areas within the Thuringian basin and along its bordering highlands. The mapped gradient tensor components show a high correlation to existing geologic maps. Furthermore, the measured gradient components indicate that some of the observed magnetic anomalies have a strong remanent magnetization. One example of interpretation of the acquired data of a magnetic anomaly related to a larger gabbro formation is presented.

Robotic Online Path Planning on Point Cloud.

PubMed

Liu, Ming

2016-05-01

This paper deals with the path-planning problem for mobile wheeled- or tracked-robot which drive in 2.5-D environments, where the traversable surface is usually considered as a 2-D-manifold embedded in a 3-D ambient space. Specially, we aim at solving the 2.5-D navigation problem using raw point cloud as input. The proposed method is independent of traditional surface parametrization or reconstruction methods, such as a meshing process, which generally has high-computational complexity. Instead, we utilize the output of 3-D tensor voting framework on the raw point clouds. The computation of tensor voting is accelerated by optimized implementation on graphics computation unit. Based on the tensor voting results, a novel local Riemannian metric is defined using the saliency components, which helps the modeling of the latent traversable surface. Using the proposed metric, we prove that the geodesic in the 3-D tensor space leads to rational path-planning results by experiments. Compared to traditional methods, the results reveal the advantages of the proposed method in terms of smoothing the robot maneuver while considering the minimum travel distance.

Tensor scale-based fuzzy connectedness image segmentation

NASA Astrophysics Data System (ADS)

Saha, Punam K.; Udupa, Jayaram K.

2003-05-01

Tangible solutions to image segmentation are vital in many medical imaging applications. Toward this goal, a framework based on fuzzy connectedness was developed in our laboratory. A fundamental notion called "affinity" - a local fuzzy hanging togetherness relation on voxels - determines the effectiveness of this segmentation framework in real applications. In this paper, we introduce the notion of "tensor scale" - a recently developed local morphometric parameter - in affinity definition and study its effectiveness. Although, our previous notion of "local scale" using the spherical model successfully incorporated local structure size into affinity and resulted in measureable improvements in segmentation results, a major limitation of the previous approach was that it ignored local structural orientation and anisotropy. The current approach of using tensor scale in affinity computation allows an effective utilization of local size, orientation, and ansiotropy in a unified manner. Tensor scale is used for computing both the homogeneity- and object-feature-based components of affinity. Preliminary results of the proposed method on several medical images and computer generated phantoms of realistic shapes are presented. Further extensions of this work are discussed.

Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media

NASA Astrophysics Data System (ADS)

Toptygin, I. N.

2017-12-01

Applying a quantum mechanical treatment to a high-frequency macroscopic electromagnetic field and radiative phenomena in a medium, we construct quantum operators for energy-momentum tensor components in dispersive media and find their eigenvalues, which are different in the Minkowski and Abraham representations. It is shown that the photon momentum in a medium resulting from the quantization of the vector potential differs from that defined from Abraham’s symmetric energy-momentum-tensor but is equal to the momentum defined from the Minkowski tensor. A similar result is obtained by calculating the intrinsic angular momentum (spin) of an electro-magnetic field in the medium. Only the Minkowski tensor leads to the experimentally confirmed spin values that are multiples of ħ, providing the grounds for choosing the Minkowski representation as the proper form for the momentum density of a transverse electromagnetic field in a transparent medium, in both classical and quantum descriptions of the field. The Abraham representation is unsuitable for this purpose and leads to contradictions. The conclusion drawn does not apply to quasistatic and static fields.

Transport tensors in perfectly aligned low-density fluids: Self-diffusion and thermal conductivity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, G. S.; Kumar, B.

2001-06-01

The modified Taxman equation for the kinetic theory of low-density fluids composed of rigid aspherical molecules possessing internal degrees of freedom is generalized to obtain the transport tensors in a fluid of aligned molecules. The theory takes care of the shape of the particles exactly but the solution has been obtained only for the case of perfectly aligned hard spheroids within the framework of the first Sonine polynomial approximation. The expressions for the thermal-conductivity components have been obtained for the first time whereas the self-diffusion components obtained here turn out to be exactly the same as those derived by Kumarmore » and Masters [Mol. Phys. >81, 491 (1994)] through the solution of the Lorentz-Boltzmann equation. All our expressions yield correct results in the hard-sphere limit.« less

An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.

Global Existence Results for Viscoplasticity at Finite Strain

NASA Astrophysics Data System (ADS)

Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe

2018-01-01

We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant plastic rate, and thus depends on the plastic state variable. The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energy-dissipation-balance and energy-dissipation-inequality solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory.

Search for a Scalar Component in the Weak Interaction

NASA Astrophysics Data System (ADS)

Zakoucky, Dalibor; Baczyk, Pavel; Ban, Gilles; Beck, Marcus; Breitenfeldt, Martin; Couratin, Claire; Fabian, Xavier; Finlay, Paul; Flechard, Xavier; Friedag, Peter; Glück, Ferenc; Herlert, Alexander; Knecht, Andreas; Kozlov, Valentin; Lienard, Etienne; Porobic, Tomica; Soti, Gergelj; Tandecki, Michael; Vangorp, Simon; Weinheimer, Christian; Wursten, Elise; Severijns, Nathal

Weak interactions are described by the Standard Model which uses the basic assumption of a pure "V(ector)-A(xial vector)" character for the interaction. However, after more than half a century of model development and experimental testing of its fundamental ingredients, experimental limits for possible admixtures of scalar and/or tensor interactions are still as high as 7%. The WITCH project (Weak Interaction Trap for CHarged particles) at the isotope separator ISOLDE at CERN is trying to probe the structure of the weak interaction in specific low energy β-decays in order to look for possible scalar or tensor components or at least significantly improve the current experimental limits. This worldwide unique experimental setup consisting of a combination of two Penning ion traps and a retardation spectrometer allows to catch, trap and cool the radioactive nuclei provided by the ISOLDE separator, form a cooled and scattering-free radioactive source of β-decaying nuclei and let these nuclei decay at rest. The precise measurement of the shape of the energy spectrum of the recoiling nuclei, the shape of which is very sensitive to the character of the weak interaction, enables searching for a possible admixture of a scalar/tensor component in the dominant vector/axial vector mode. First online measurements with the isotope 35Ar were performed in 2011 and 2012. The current status of the experiment, the data analysis and results as well as extensive simulations will be presented and discussed.

A software to measure phase-velocity dispersion from ambient-noise correlations and its application to the SNSN data

NASA Astrophysics Data System (ADS)

Sadeghisorkhani, Hamzeh; Gudmundsson, Ólafur

2017-04-01

Graphical software for phase-velocity dispersion measurements of surface waves in noise-correlation traces, called GSpecDisp, is presented. It is an interactive environment for the measurements and presentation of the results. It measures phase-velocity dispersion curves in the frequency domain based on matching of the real part of the cross-correlation spectrum with the appropriate Bessel function. The inputs are time-domain cross-correlations in SAC format. It can measure two types of phase-velocity dispersion curves; 1- average phase-velocity of a region, and 2- single-pair phase velocity. The average phase-velocity dispersion curve of a region can be used as a reference curve to automatically select the dispersion curves from each single-pair cross-correlation in that region. It also allows the users to manually refine the selections. Therefore, no prior knowledge is needed for an unknown region. GSpecDisp can measure the phase velocity of Rayleigh and Love waves from all possible components of the noise correlation tensor, including diagonal and off-diagonal components of the tensor. First, we explain how GSpecDisp is applied to measure phase-velocity dispersion curves. Then, we demonstrate measurement results on synthetic and real data from the Swedish National Seismic Network (SNSN). We compare the results with two other methods of phase-velocity dispersion measurements. Finally, we compare phase-velocity dispersion curves of Rayleigh waves obtained from different components of the correlation tensor.

Grid-search Moment Tensor Estimation: Implementation and CTBT-related Application

NASA Astrophysics Data System (ADS)

Stachnik, J. C.; Baker, B. I.; Rozhkov, M.; Friberg, P. A.; Leifer, J. M.

2017-12-01

This abstract presents a review work related to moment tensor estimation for Expert Technical Analysis at the Comprehensive Test Ban Treaty Organization. In this context of event characterization, estimation of key source parameters provide important insights into the nature of failure in the earth. For example, if the recovered source parameters are indicative of a shallow source with large isotropic component then one conclusion is that it is a human-triggered explosive event. However, an important follow-up question in this application is - does an alternative hypothesis like a deeper source with a large double couple component explain the data approximately as well as the best solution? Here we address the issue of both finding a most likely source and assessing its uncertainty. Using the uniform moment tensor discretization of Tape and Tape (2015) we exhaustively interrogate and tabulate the source eigenvalue distribution (i.e., the source characterization), tensor orientation, magnitude, and source depth. The benefit of the grid-search is that we can quantitatively assess the extent to which model parameters are resolved. This provides a valuable opportunity during the assessment phase to focus interpretation on source parameters that are well-resolved. Another benefit of the grid-search is that it proves to be a flexible framework where different pieces of information can be easily incorporated. To this end, this work is particularly interested in fitting teleseismic body waves and regional surface waves as well as incorporating teleseismic first motions when available. Being that the moment tensor search methodology is well-established we primarily focus on the implementation and application. We present a highly scalable strategy for systematically inspecting the entire model parameter space. We then focus on application to regional and teleseismic data recorded during a handful of natural and anthropogenic events, report on the grid-search optimum, and discuss the resolution of interesting and/or important recovered source properties.

Spinors: A Mathematica package for doing spinor calculus in General Relativity

NASA Astrophysics Data System (ADS)

Gómez-Lobo, Alfonso García-Parrado; Martín-García, José M.

2012-10-01

The Spinors software is a Mathematica package which implements 2-component spinor calculus as devised by Penrose for General Relativity in dimension 3+1. The Spinors software is part of the xAct system, which is a collection of Mathematica packages to do tensor analysis by computer. In this paper we give a thorough description of Spinors and present practical examples of use. Program summary Program title: Spinors Catalogue identifier: AEMQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 117039 No. of bytes in distributed program, including test data, etc.: 300404 Distribution format: tar.gz Programming language: Mathematica. Computer: Any computer running Mathematica 7.0 or higher. Operating system: Any operating system compatible with Mathematica 7.0 or higher. RAM: 94Mb in Mathematica 8.0. Classification: 1.5. External routines: Mathematica packages xCore, xPerm and xTensor which are part of the xAct system. These can be obtained at http://www.xact.es. Nature of problem: Manipulation and simplification of spinor expressions in General Relativity. Solution method: Adaptation of the tensor functionality of the xAct system for the specific situation of spinor calculus in four dimensional Lorentzian geometry. Restrictions: The software only works on 4-dimensional Lorentzian space-times with metric of signature (1, -1, -1, -1). There is no direct support for Dirac spinors. Unusual features: Easy rules to transform tensor expressions into spinor ones and back. Seamless integration of abstract index manipulation of spinor expressions with component computations. Running time: Under one second to handle and canonicalize standard spinorial expressions with a few dozen indices. (These expressions arise naturally in the transformation of a spinor expression into a tensor one or vice versa.)

Three-dimensional seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland

USGS Publications Warehouse

Miller, A.D.; Julian, B.R.; Foulger, G.R.

1998-01-01

The volcanic and geothermal areas of Iceland are rich sources of non-double-couple (non-DC) earthquakes. A state-of-the-art digital seismometer network deployed at the Hengill-Grensdalur volcanic complex in 1991 recorded 4000 small earthquakes. We used the best recorded of these to determine 3-D VP and VP/VS structure tomographically and accurate earthquake moment tensors. The VP field is dominated by high seismic wave speed bodies interpreted as solidified intrusions. A widespread negative (-4 per cent) VP/VS anomaly in the upper 4 km correlates with the geothermal field, but is too strong to be caused solely by the effect of temperature upon liquid water or the presence of vapour, and requires in addition mineralogical or lithological differences between the geothermal reservoir and its surroundings. These may be caused by geothermal alteration. Well-constrained moment tensors were obtained for 70 of the best-recorded events by applying linear programming methods to P- and S-wave polarities and amplitude ratios. About 25 per cent of the mechanisms are, within observational error, consistent with DC mechanisms consistent with shear faulting. The other 75 per cent have significantly non-DC mechanisms. Many have substantial explosive components, one has a substantial implosive component, and the deviatoric component of many is strongly non-DC. Many of the non-DC mechanisms are consistent, within observational error, with simultaneous tensile and shear faulting. However, the mechanisms occupy a continuum in source-type parameter space and probably at least one additional source process is occurring. This may be fluid flow into newly formed cracks, causing partial compensation of the volumetric component. Studying non-shear earthquakes such as these has great potential for improving our understanding of geothermal processes and earthquake source processes in general.

Viscoplasticity: A thermodynamic formulation

NASA Technical Reports Server (NTRS)

Freed, A. D.; Chaboche, J. L.

1989-01-01

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity, as it applies to initially isotropic materials. Three fundamental internal state variables are admitted. They are: a tensor valued back stress for kinematic effects, and the scalar valued drag and yield strengths for isotropic effects. All three are considered to phenomenologically evolve according to competitive processes between strain hardening, strain induced dynamic recovery, and time induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is put forth. This theory allows each of the three fundamental internal variables to be composed as a sum of independently evolving constituents.

Development of solution techniques for nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Vos, R. G.; Andrews, J. S.

1974-01-01

Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

Polarized-cathodoluminescence study of uniaxial and biaxial stress in GaAs/Si

NASA Technical Reports Server (NTRS)

Rich, D. H.; Ksendzov, A.; Terhune, R. W.; Grunthaner, F. J.; Wilson, B. A.; Shen, H.; Dutta, M.; Vernon, S. M.; Dixon, T. M.

1991-01-01

The strain-induced splitting of the heavy-hole (hh) and light-hole (lh) valence bands for 4-microns thick GaAs/Si is examined on a microscopic scale using linear polarized-cathodoluminescence imaging and spectroscopy. The energies and intensities of the hh- and lh-exciton luminescence are quantitatively analyzed to determine spatial variations in the stress tensor. The results indicate that regions near and far from the microcracks are primarily subject to uniaxial and biaxial tensile stresses, respectively. The transition region where biaxial stress gradually converts to uniaxial stress is analyzed, and reveals a mixing of lh and hh characters in the strain-split bands.

STATISTICS OF THE VELOCITY GRADIENT TENSOR IN SPACE PLASMA TURBULENT FLOWS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Consolini, Giuseppe; Marcucci, Maria Federica; Pallocchia, Giuseppe

2015-10-10

In the last decade, significant advances have been presented for the theoretical characterization and experimental techniques used to measure and model all of the components of the velocity gradient tensor in the framework of fluid turbulence. Here, we attempt the evaluation of the small-scale velocity gradient tensor for a case study of space plasma turbulence, observed in the Earth's magnetosheath region by the CLUSTER mission. In detail, we investigate the joint statistics P(R, Q) of the velocity gradient geometric invariants R and Q, and find that this P(R, Q) is similar to that of the low end of the inertialmore » range for fluid turbulence, with a pronounced increase in the statistics along the so-called Vieillefosse tail. In the context of hydrodynamics, this result is referred to as the dissipation/dissipation-production due to vortex stretching.« less

The Constantine (Algeria) seismic sequence of 27 October 1985: a new rupture model from aftershock relocation, focal mechanisms, and stress tensors

NASA Astrophysics Data System (ADS)

Ousadou, F.; Dorbath, L.; Dorbath, C.; Bounif, M. A.; Benhallou, H.

2013-04-01

The October 27, 1985 Constantine earthquake of magnitude MS 5.9 (NEIC) although moderate is the strongest earthquake recorded in the eastern Tellian Atlas (northeast Algeria) since the beginning of instrumental seismology. The main shock locations given by different institutions are scattered and up to 10 km away northwest from the NE-SW 30 km long elongated aftershocks cloud localized by a dedicated temporary portable network. The focal mechanism indicates left-lateral strike-slip on an almost vertical fault with a small reverse component on the northwest dipping plane. This paper presents relocations of the main shock and aftershocks using TomoDD. One hundred thirty-eight individual focal mechanisms have been built allowing the determination of the stress tensor at different scales. A rupture model has been suggested, which explains the different observations of aftershock distribution and stress tensor rotation.

Black holes in vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic andmore » quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.« less

Short-range correlation in high-momentum antisymmetrized molecular dynamics

NASA Astrophysics Data System (ADS)

Myo, Takayuki

2018-03-01

We propose a new variational method for treating short-range repulsion of bare nuclear force for nuclei in antisymmetrized molecular dynamics (AMD). In AMD, the short-range correlation is described in terms of large imaginary centroids of Gaussian wave packets of nucleon pairs in opposite signs, causing high-momentum components in the nucleon pairs. We superpose these AMD basis states and call this method "high-momentum AMD" (HM-AMD), which is capable of describing the strong tensor correlation [T. Myo et al., Prog. Theor. Exp. Phys., 2017, 111D01 (2017)]. In this letter, we extend HM-AMD by including up to two kinds of nucleon pairs in each AMD basis state utilizing the cluster expansion, which produces many-body correlations involving high-momentum components. We investigate how well HM-AMD describes the short-range correlation by showing the results for ^3H using the Argonne V4^' central potential. It is found that HM-AMD reproduces the results of few-body calculations and also the tensor-optimized AMD. This means that HM-AMD is a powerful approach to describe the short-range correlation in nuclei. In HM-AMD, the momentum directions of nucleon pairs isotropically contribute to the short-range correlation, which is different from the tensor correlation.

Structural Assembly of Multidomain Proteins and Protein Complexes Guided by the Overall Rotational Diffusion Tensor

PubMed Central

Ryabov, Yaroslav; Fushman, David

2008-01-01

We present a simple and robust approach that uses the overall rotational diffusion tensor as a structural constraint for domain positioning in multidomain proteins and protein-protein complexes. This method offers the possibility to use NMR relaxation data for detailed structure characterization of such systems provided the structures of individual domains are available. The proposed approach extends the concept of using long-range information contained in the overall rotational diffusion tensor. In contrast to the existing approaches, we use both the principal axes and principal values of protein’s rotational diffusion tensor to determine not only the orientation but also the relative positioning of the individual domains in a protein. This is achieved by finding the domain arrangement in a molecule that provides the best possible agreement with all components of the overall rotational diffusion tensor derived from experimental data. The accuracy of the proposed approach is demonstrated for two protein systems with known domain arrangement and parameters of the overall tumbling: the HIV-1 protease homodimer and Maltose Binding Protein. The accuracy of the method and its sensitivity to domain positioning is also tested using computer-generated data for three protein complexes, for which the experimental diffusion tensors are not available. In addition, the proposed method is applied here to determine, for the first time, the structure of both open and closed conformations of Lys48-linked di-ubiquitin chain, where domain motions render impossible accurate structure determination by other methods. The proposed method opens new avenues for improving structure characterization of proteins in solution. PMID:17550252

The Application of Strain Range Partitioning Method to Torsional Creep-Fatigue Interaction

NASA Technical Reports Server (NTRS)

Zamrik, S. Y.

1975-01-01

The method of strain range partitioning was applied to a series of torsional fatigue tests conducted on tubular 304 stainless steel specimens at 1200 F. Creep strain was superimposed on cycling strain, and the resulting strain range was partitioned into four components; completely reversed plastic shear strain, plastic shear strain followed by creep strain, creep strain followed by plastic strain and completely reversed creep strain. Each strain component was related to the cyclic life of the material. The damaging effects of the individual strain components were expressed by a linear life fraction rule. The plastic shear strain component showed the least detrimental factor when compared to creep strain reversed by plastic strain. In the latter case, a reduction of torsional fatigue life in the order of magnitude of 1.5 was observed.

Seismic moment tensor for anisotropic media: implication for Non-double-couple earthquakes

NASA Astrophysics Data System (ADS)

Cai, X.; Chen, X.; Chen, Y.; Cai, M.

2008-12-01

It is often found that the inversion results of seismic moment tensor from real seismic recorded data show the trace of seismic moment tensor M is not zero, a phenomenon called non-double-couple earthquake sources mechanism. Recently we have derived the analytical expressions of M in transversely isotropic media with the titled axis of symmetry and the results shows even only pure shear-motion of fault can lead to the implosive components determined by several combined anisotropic elastic constants. Many non-double-couple earthquakes from observations often appear in volcanic and geothermal areas (Julian, 1998), where there exist a mount of stress-aligned fluid-saturated parallel vertical micro-cracks identical to transversely isotropic media (Crampin, 2008), this stress-aligned crack will modify the seismic moment tensor. In another word, non-double-couple earthquakes don't mean to have a seismic failure movement perpendicular to the fault plane, while traditional research of seismic moment tensor focus on the case of isotropy, which cannot provide correct interpretation of seismic source mechanism. Reference: Julian, B.R., Miller, A.D. and Foulger, G.R., 1998. Non-double-couple earthquakes,1. Theory, Rev. Geophys., 36, 525¨C549. Crampin,S., Peacock,S., 2008, A review of the current understanding of seismic shear-wave splitting in the Earth's crust and common fallacies in interpretation, wave motion, 45,675-722

Time-Optimized High-Resolution Readout-Segmented Diffusion Tensor Imaging

PubMed Central

Reishofer, Gernot; Koschutnig, Karl; Langkammer, Christian; Porter, David; Jehna, Margit; Enzinger, Christian; Keeling, Stephen; Ebner, Franz

2013-01-01

Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min) generates results comparable to the un-regularized data with three averages (48 min). This significant reduction in scan time renders high resolution (1×1×2.5 mm3) diffusion tensor imaging of the entire brain applicable in a clinical context. PMID:24019951

ON THE SPIN CORRELATIONS OF MUONS AND TAU LEPTONS GENERATED IN THE ANNIHILATION PROCESSES e+e- → μ+μ-, e+e- → τ+τ-

NASA Astrophysics Data System (ADS)

Lyuboshitz, Valery V.; Lyuboshitz, Vladimir L.

2014-12-01

Using the technique of helicity amplitudes, the electromagnetic process e+e- → μ+μ-(τ+τ-) is theoretically studied in the one-photon approximation. The structure of the triplet states of the final (μ+μ-) system is analyzed. It is shown that in the case of unpolarized electron and positron the final muons are also unpolarized, but their spins are strongly correlated. Explicit expressions for the components of the correlation tensor of the (μ+μ-) system are derived. The formula for the angular correlation at the decays of final muons μ+ and μ- is obtained. It is demonstrated that spin correlations of muons in the considered process have the purely quantum character, since one of the Bell-type incoherence inequalities for the correlation tensor components is always violated.

SPIN CORRELATIONS OF THE FINAL LEPTONS IN THE TWO-PHOTON PROCESSES γγ → e+e-, μ+μ-, τ+τ-

NASA Astrophysics Data System (ADS)

Lyuboshitz, Valery V.; Lyuboshitz, Vladimir L.

2014-12-01

The spin structure of the process γγ → e+e- is theoretically investigated. It is shown that, if the primary photons are unpolarized, the final electron and positron are unpolarized as well but their spins are strongly correlated. For the final (e+e-) system, explicit expressions for the components of the correlation tensor are derived, and the relative fractions of singlet and triplet states are found. It is demonstrated that in the process γγ → e+e- one of the Bell-type incoherence inequalities for the correlation tensor components is always violated and, thus, spin correlations of the electron and positron in this process have the strongly pronounced quantum character. Analogous consideration can be wholly applied as well to the two-photon processes γγ → μ+μ- and γγ → τ+τ-, which become possible at considerably higher energies.

Non-equilibrium surface tension of the vapour-liquid interface of active Lennard-Jones particles

NASA Astrophysics Data System (ADS)

Paliwal, Siddharth; Prymidis, Vasileios; Filion, Laura; Dijkstra, Marjolein

2017-08-01

We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid phase coexistence of active Lennard-Jones particles with planar interfaces. We measure the normal and tangential components of the pressure tensor along the direction perpendicular to the interface and verify mechanical equilibrium of the two coexisting phases. In addition, we determine the non-equilibrium interfacial tension by integrating the difference of the normal and tangential components of the pressure tensor and show that the surface tension as a function of strength of particle attractions is well fitted by simple power laws. Finally, we measure the interfacial stiffness using capillary wave theory and the equipartition theorem and find a simple linear relation between surface tension and interfacial stiffness with a proportionality constant characterized by an effective temperature.

Magnetic hyperbolic optical metamaterials

DOE PAGES

Kruk, Sergey S.; Wong, Zi Jing; Pshenay-Severin, Ekaterina; ...

2016-04-13

Strongly anisotropic media where the principal components of electric permittivity or magnetic permeability tensors have opposite signs are termed as hyperbolic media. Such media support propagating electromagnetic waves with extremely large wave vectors exhibiting unique optical properties. However, in all artificial and natural optical materials studied to date, the hyperbolic dispersion originates solely from the electric response. This then restricts material functionality to one polarization of light and inhibits free-space impedance matching. Such restrictions can be overcome in media having components of opposite signs for both electric and magnetic tensors. Here we present the experimental demonstration of the magnetic hyperbolicmore » dispersion in three-dimensional metamaterials. We also measure metamaterial isofrequency contours and reveal the topological phase transition between the elliptic and hyperbolic dispersion. In the hyperbolic regime, we demonstrate the strong enhancement of thermal emission, which becomes directional, coherent and polarized. These findings show the possibilities for realizing efficient impedance-matched hyperbolic media for unpolarized light.« less

Sakata-Taketani spin-0 theory with external field interactions - Lagrangian formalism and causal properties

NASA Technical Reports Server (NTRS)

Guertin, R. F.; Wilson, T. L.

1977-01-01

To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.

Ordered rate constitutive theories for thermoviscoelastic solids with memory in Lagrangian description using Gibbs potential

NASA Astrophysics Data System (ADS)

Surana, K. S.; Reddy, J. N.; Nunez, Daniel

2015-11-01

This paper presents ordered rate constitutive theories of orders m and n, i.e., ( m, n) for finite deformation of homogeneous, isotropic, compressible and incompressible thermoviscoelastic solids with memory in Lagrangian description using entropy inequality in Gibbs potential Ψ as an alternate approach of deriving constitutive theories using entropy inequality in terms of Helmholtz free energy density Φ. Second Piola-Kirchhoff stress σ [0] and Green's strain tensor ɛ [0] are used as conjugate pair. We consider Ψ, heat vector q, entropy density η and rates of upto orders m and n of σ [0] and ɛ [0], i.e., σ [ i]; i = 0, 1, . . . , m and ɛ [ j]; j = 0, 1, . . . , n. We choose Ψ, ɛ [ n], q and η as dependent variables in the constitutive theories with ɛ [ j]; j = 0, 1, . . . , n - 1, σ [ i]; i = 0, 1, . . . , m, temperature gradient g and temperature θ as their argument tensors. Rationale for this choice is explained in the paper. Entropy inequality, decomposition of σ [0] into equilibrium and deviatoric stresses, the conditions resulting from entropy inequality and the theory of generators and invariants are used in the derivations of ordered rate constitutive theories of orders m and n in stress and strain tensors. Constitutive theories for the heat vector q (of up to orders m and n - 1) that are consistent (in terms of the argument tensors) with the constitutive theories for ɛ [ n] (of up to orders m and n) are also derived. Many simplified forms of the rate theories of orders ( m, n) are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing ɛ [ n] and q using the combined generators of the argument tensors about a known configuration {{\\underline{\\varOmega}}} in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one ( m = 1, n = 1) when further simplified result in constitutive theories that resemble currently used theories but are in fact different. The solid continua characterized by these theories have mechanisms of elasticity, dissipation and memory, i.e., relaxation behavior or rheology. Fourier heat conduction law is shown to be an over simplified case of the rate theory of order one ( m = 1, n = 1) for q. The paper establishes when there is equivalence between the constitutive theories derived here using Ψ and those presented in reference Surana et al. (Acta Mech. doi:10.1007/s00707-014-1173-6, 2014) that are derived using Helmholtz free energy density Φ. The fundamental differences between the two constitutive theories in terms of physics and their explicit forms using Φ and Ψ are difficult to distinguish from the ordered theories of orders ( m, n) due to complexity of expressions. However, by choosing lower ordered theories, the difference between the two approaches can be clearly seen.

Near real-time estimation of the seismic source parameters in a compressed domain

NASA Astrophysics Data System (ADS)

Rodriguez, Ismael A. Vera

Seismic events can be characterized by its origin time, location and moment tensor. Fast estimations of these source parameters are important in areas of geophysics like earthquake seismology, and the monitoring of seismic activity produced by volcanoes, mining operations and hydraulic injections in geothermal and oil and gas reservoirs. Most available monitoring systems estimate the source parameters in a sequential procedure: first determining origin time and location (e.g., epicentre, hypocentre or centroid of the stress glut density), and then using this information to initialize the evaluation of the moment tensor. A more efficient estimation of the source parameters requires a concurrent evaluation of the three variables. The main objective of the present thesis is to address the simultaneous estimation of origin time, location and moment tensor of seismic events. The proposed method displays the benefits of being: 1) automatic, 2) continuous and, depending on the scale of application, 3) of providing results in real-time or near real-time. The inversion algorithm is based on theoretical results from sparse representation theory and compressive sensing. The feasibility of implementation is determined through the analysis of synthetic and real data examples. The numerical experiments focus on the microseismic monitoring of hydraulic fractures in oil and gas wells, however, an example using real earthquake data is also presented for validation. The thesis is complemented with a resolvability analysis of the moment tensor. The analysis targets common monitoring geometries employed in hydraulic fracturing in oil wells. Additionally, it is presented an application of sparse representation theory for the denoising of one-component and three-component microseismicity records, and an algorithm for improved automatic time-picking using non-linear inversion constraints.

Diffusion tensor optical coherence tomography

NASA Astrophysics Data System (ADS)

Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.

2018-01-01

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

Tensor integrand reduction via Laurent expansion

DOE PAGES

Hirschi, Valentin; Peraro, Tiziano

2016-06-09

We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reductionmore » tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem95. We find that Ninja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than Ninja. Lastly, we considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.« less

Intermolecular shielding contributions studied by modeling the 13C chemical-shift tensors of organic single crystals with plane waves

PubMed Central

Johnston, Jessica C.; Iuliucci, Robbie J.; Facelli, Julio C.; Fitzgerald, George; Mueller, Karl T.

2009-01-01

In order to predict accurately the chemical shift of NMR-active nuclei in solid phase systems, magnetic shielding calculations must be capable of considering the complete lattice structure. Here we assess the accuracy of the density functional theory gauge-including projector augmented wave method, which uses pseudopotentials to approximate the nodal structure of the core electrons, to determine the magnetic properties of crystals by predicting the full chemical-shift tensors of all 13C nuclides in 14 organic single crystals from which experimental tensors have previously been reported. Plane-wave methods use periodic boundary conditions to incorporate the lattice structure, providing a substantial improvement for modeling the chemical shifts in hydrogen-bonded systems. Principal tensor components can now be predicted to an accuracy that approaches the typical experimental uncertainty. Moreover, methods that include the full solid-phase structure enable geometry optimizations to be performed on the input structures prior to calculation of the shielding. Improvement after optimization is noted here even when neutron diffraction data are used for determining the initial structures. After geometry optimization, the isotropic shift can be predicted to within 1 ppm. PMID:19831448

Dual boundary element formulation for elastoplastic fracture mechanics

NASA Astrophysics Data System (ADS)

Leitao, V.; Aliabadi, M. H.; Rooke, D. P.

1995-01-01

In this paper the extension of the dual boundary element method (DBEM) to the analysis of elastoplastic fracture mechanics (EPFM) problems is presented. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. In order to avoid collocation at crack tips, crack kinks and crack-edge corners, both crack surfaces are discretized with discontinuous quadratic boundary elements. The elasto-plastic behavior is modelled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral and/or triangular cells. This formulation was implemented for two-dimensional domains only, although there is no theoretical or numerical limitation to its application to three-dimensional ones. A center-cracked plate and a slant edge-cracked plate subjected to tensile load are analysed and the results are compared with others available in the literature. J-type integrals are calculated.

Kinetic theory of binary particles with unequal mean velocities and non-equipartition energies

NASA Astrophysics Data System (ADS)

Chen, Yanpei; Mei, Yifeng; Wang, Wei

2017-03-01

The hydrodynamic conservation equations and constitutive relations for a binary granular mixture composed of smooth, nearly elastic spheres with non-equipartition energies and different mean velocities are derived. This research is aimed to build three-dimensional kinetic theory to characterize the behaviors of two species of particles suffering different forces. The standard Enskog method is employed assuming a Maxwell velocity distribution for each species of particles. The collision components of the stress tensor and the other parameters are calculated from the zeroth- and first-order approximation. Our results demonstrate that three factors, namely the differences between two granular masses, temperatures and mean velocities all play important roles in the stress-strain relation of the binary mixture, indicating that the assumption of energy equipartition and the same mean velocity may not be acceptable. The collision frequency and the solid viscosity increase monotonously with each granular temperature. The zeroth-order approximation to the energy dissipation varies greatly with the mean velocities of both species of spheres, reaching its peak value at the maximum of their relative velocity.

Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies.

PubMed

Olives, Juan

2010-03-03

The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the temperature, the chemical potentials and the surface strain tensor (true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A new definition of the surface stress is given and the corresponding surface thermodynamics equations are presented. The mechanical equilibrium equation at the surface is then obtained. It involves the surface stress and is similar to the Cauchy equation for the volume. Its normal component is a generalization of the Laplace equation. At a (body-fluid-fluid) triple contact line, two equations are obtained, which represent: (i) the equilibrium of the forces (surface stresses) for a triple line fixed on the body; (ii) the equilibrium relative to the motion of the line with respect to the body. This last equation leads to a strong modification of Young's classical capillary equation.

Effect of temperature on In_{{\\varvec{x}}} Ga_{1-{{\\varvec{x}}}} As/GaAs quantum dots

NASA Astrophysics Data System (ADS)

Borji, Mahdi Ahmadi; Reyahi, Ali; Rajaei, Esfandiar; Ghahremani, Mohsen

2017-08-01

In this paper, the strain, band-edge, and energy levels of pyramidal In_x Ga_{1-x} As/GaAs quantum dots are investigated by 1-band effective mass approach. It is shown that while temperature has no remarkable effect on the strain tensor, the band gap lowers and the radiation wavelength elongates by increasing temperature. Also, band gap and energy do not linearly decrease by temperature rise. Our results appear to agree with former researches. This can be used in designing laser devices and sensors when applied in different working temperatures. Furthermore, when the device works for a long time, self-heating occurs which changes the characteristics of the output.

IBMISPS (International Brain Mapping & Intraoperative Surgical Planning Symposium)

DTIC Science & Technology

2005-12-01

they received the 2005 Excellence in R, D & E award for their contribution in the feild of prosthetics and brain imaging. Excellence in Educational...specific bipolar magnetic gradient pulses which measure the velocity vector components of motion. Presented here are the development of dynamic MR...movies of quantitative velocity vector components, 30 frames per second. The 3 velocity vector maps with tensor analysis produced maps of the

A trial of reliable estimation of non-double-couple component of microearthquakes

NASA Astrophysics Data System (ADS)

Imanishi, K.; Uchide, T.

2017-12-01

Although most tectonic earthquakes are caused by shear failure, it has been reported that injection-induced seismicity and earthquakes occurring in volcanoes and geothermal areas contain non double couple (non-DC) components (e.g, Dreger et al., 2000). Also in the tectonic earthquakes, small non-DC components are beginning to be detected (e.g, Ross et al., 2015). However, it is generally limited to relatively large earthquakes that the non-DC component can be estimated with sufficient accuracy. In order to gain further understanding of fluid-driven earthquakes and fault zone properties, it is important to estimate full moment tensor of many microearthquakes with high precision. In the last AGU meeting, we proposed a method that iteratively applies the relative moment tensor inversion (RMTI) (Dahm, 1996) to source clusters improving each moment tensor as well as their relative accuracy. This new method overcomes the problem of RMTI that errors in the mechanism of reference events lead to biased solutions for other events, while taking advantage of RMTI that the source mechanisms can be determined without a computation of Green's function. The procedure is briefly summarized as follows: (1) Sample co-located multiple earthquakes with focal mechanisms, as initial solutions, determined by an ordinary method. (2) Apply the RMTI to estimate the source mechanism of each event relative to those of the other events. (3) Repeat the step 2 for the modified source mechanisms until the reduction of total residual converges. In order to confirm whether the method can resolve non-DC components, we conducted numerical tests on synthetic data. Amplitudes were computed assuming non-DC sources, amplifying by factor between 0.2 and 4 as site effects, and adding 10% random noise. As initial solutions in the step 1, we gave DC sources with arbitrary strike, dip and rake angle. In a test with eight sources at 12 stations, for example, all solutions were successively improved by iteration. Non-DC components were successfully resolved in spite of the fact that we gave DC sources as initial solutions. The application of the method to microearthquakes in geothermal area in Japan will be presented.

Algebraic Reynolds stress modeling of turbulence subject to rapid homogeneous and non-homogeneous compression or expansion

NASA Astrophysics Data System (ADS)

Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.

2016-02-01

A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper formulation of the rapid pressure-strain correlation and accounting for the coupling with turbulent density flux, can be an important element in CFD tools for compressible flows.

Different kernel functions due to rainfall response from borehole strainmeter in Taiwan

NASA Astrophysics Data System (ADS)

Yen Chen, Chih; Hu, Jyr Ching; LIu, Chi Ching

2014-05-01

In order to realize reasons inducing earthquakes, project of monitoring of the fault activity using 3-component Gladwin Tensor Strainmeter (GTSM) has been initiated since 2003 in Taiwan, which is one of the most active seismic regions in the world. Observed strain contains several different effects within including barometric, tidal, groundwater, precipitation, tectonics, seismic and other irregular noise. After removing the response of tides and air pressure on strain, we still can find some anomalies highly related to the rainfall in short time in days. The strain response induced by rainfall can be separated into two parts as observation in groundwater, slow response and quick response, respectively. Quick response reflects the strain responding to the load of falling water drops on the ground surface. A kernel function shows the continual response induced by unit precipitation water in time domain. We split the quick response from data removing tidal and barometric response, and then calculate the kernel function by use of deconvolution method. More, an average kernel function was calculated to reduce the noise level. There are five of the sites installed by CGS Taiwan were selected to calculate kernel functions for individual sites. The results show there may be different on rainfall response in different environmental settings. In the case of stations site on gentle terrain, kernel function for each site shows the similar trend, it rises quickly to maximum in 1 to 2 hrs, and then goes down near to zero gently in period of 2-3 days. But in the case of sites settled side by the rivers, there will be 2nd peak of function when collected water in the catchment flows along by the sites related to the hydrograph of creeks. More, landslides will occur in some sites in hazard of landslide with more rainfall stored on, just like DARB in ChiaYi. The curve of kernel function will be controlled by landslides and debris flows.

Characterization of the Mechanical Stress-Strain Performance of Aerospace Alloy Materials Using Frequency-Domain Photoacoustic Ultrasound and Photothermal Methods: An FEM Approach

NASA Astrophysics Data System (ADS)

Huan, Huiting; Mandelis, Andreas; Liu, Lixian

2018-04-01

Determining and keeping track of a material's mechanical performance is very important for safety in the aerospace industry. The mechanical strength of alloy materials is precisely quantified in terms of its stress-strain relation. It has been proven that frequency-domain photothermoacoustic (FD-PTA) techniques are effective methods for characterizing the stress-strain relation of metallic alloys. PTA methodologies include photothermal (PT) diffusion and laser thermoelastic photoacoustic ultrasound (PAUS) generation which must be separately discussed because the relevant frequency ranges and signal detection principles are widely different. In this paper, a detailed theoretical analysis of the connection between thermoelastic parameters and stress/strain tensor is presented with respect to FD-PTA nondestructive testing. Based on the theoretical model, a finite element method (FEM) was further implemented to simulate the PT and PAUS signals at very different frequency ranges as an important analysis tool of experimental data. The change in the stress-strain relation has an impact on both thermal and elastic properties, verified by FEM and results/signals from both PT and PAUS experiments.

High resolution microdiffraction studies using synchrotron radiation

NASA Astrophysics Data System (ADS)

Spolenak, R.; Tamura, N.; Valek, B. C.; MacDowell, A. A.; Celestre, R. S.; Padmore, H. A.; Brown, W. L.; Marieb, T.; Batterman, B. W.; Patel, J. R.

2002-04-01

The advent of third generation synchrotron light sources in combination with x-ray focusing devices such as Kirkpatrick-Baez mirrors make Laue diffraction on a submicron length scale possible. Analysis of Laue images enables us to determine the deviatoric part of the 3D strain tensor to an accuracy of 2×10-4 in strain with a spatial resolution comparable to the grain size in our thin films. In this paper the application of x-ray microdiffraction to the temperature dependence of the mechanical behavior of a sputtered blanket Cu film and of electroplated damascene Cu lines will be presented. Microdiffraction reveals very large variations in the strain of a film or line from grain to grain. When the strain is averaged over a macroscopic region the results are in good agreement with direct macroscopic stress measurements. However, the strain variations are so large that in some cases in which the average stress is tensile there are some grains actually under compression. The full implications of these observations are still being considered, but it is clear that the mechanical properties of thin film materials are now accessible with new visibility.

The Nature of Residual Stress and Its Measurement.

DTIC Science & Technology

1981-07-16

that stress can relax due to microplasticity in the near- surface region (see the chapter by James). As the surface is ini- tially in compression, the...material by boring or electro- polishing and to determine the stress from measurements of strain on the surface opposite to the one where material is...Naval Research, particularly Dr. B. A. MacDcnald. APPENDIX We consider the determination by diffraction of the three-di- mensional stress tensor for a

Combined Near and Far Field High Energy Diffraction Microscopy Dataset for Ti-7Al Tensile Specimen Elastically Loaded In Situ

DOE Data Explorer

Turner, Todd J.; Shade, Paul A; Bernier, Joel V.; Li, Shiu Fai; Schuren, Jay C.; Lind, Jonathan F.; Lienert, Ulrich; Kenesei, Peter; Suter, Robert; Blank, Basil; Almer, Jonathan

2016-01-01

We present both near-field HEDM data that maps out the grain morphology and intragranular crystallographic orientations and far-field HEDM data that provides the grain centroid, grain average crystallographic orientation, and grain average elastic strain tensor for each grain. Finally, we provide a finite element mesh that can be utilized to simulate deformation in the volume of this Ti-7Al specimen.

Hydrogen bond network around the semiquinone of the secondary quinone acceptor Q(B) in bacterial photosynthetic reaction centers.

PubMed

Taguchi, Alexander T; O'Malley, Patrick J; Wraight, Colin A; Dikanov, Sergei A

2015-05-07

By utilizing a combined pulsed EPR and DFT approach, the high-resolution structure of the QB site semiquinone (SQB) was determined. The development of such a technique is crucial toward an understanding of protein-bound semiquinones on the structural level, as (i) membrane protein crystallography typically results in low resolution structures, and (ii) obtaining protein crystals in the semiquinone form is rarely feasible. The SQB hydrogen bond network was investigated with Q- (∼34 GHz) and X-band (∼9.7 GHz) pulsed EPR spectroscopy on fully deuterated reactions centers from Rhodobacter sphaeroides. Simulations in the SQB g-tensor reference frame provided the principal values and directions of the H-bond proton hyperfine tensors. Three protons were detected, one with an anisotropic tensor component, T = 4.6 MHz, assigned to the histidine NδH of His-L190, and two others with similar anisotropic constants T = 3.2 and 3.0 MHz assigned to the peptide NpH of Gly-L225 and Ile-L224, respectively. Despite the strong similarity in the peptide couplings, all hyperfine tensors were resolved in the Q-band ENDOR spectra. The Euler angles describing the series of rotations that bring the hyperfine tensors into the SQB g-tensor reference frame were obtained by least-squares fitting of the spectral simulations to the ENDOR data. These Euler angles show the locations of the hydrogen bonded protons with respect to the semiquinone. Our geometry optimized model of SQB used in previous DFT work is in strong agreement with the angular constraints from the spectral simulations, providing the foundation for future joint pulsed EPR and DFT semiquinone structural determinations in other proteins.

Generalized Rainich conditions, generalized stress-energy conditions, and the Hawking-Ellis classification

NASA Astrophysics Data System (ADS)

Martín–Moruno, Prado; Visser, Matt

2017-11-01

The (generalized) Rainich conditions are algebraic conditions which are polynomial in the (mixed-component) stress-energy tensor. As such they are logically distinct from the usual classical energy conditions (NEC, WEC, SEC, DEC), and logically distinct from the usual Hawking-Ellis (Segré-Plebański) classification of stress-energy tensors (type I, type II, type III, type IV). There will of course be significant inter-connections between these classification schemes, which we explore in the current article. Overall, we shall argue that it is best to view the (generalized) Rainich conditions as a refinement of the classical energy conditions and the usual Hawking-Ellis classification.

Wigner functions for nonparaxial, arbitrarily polarized electromagnetic wave fields in free space.

PubMed

Alonso, Miguel A

2004-11-01

New representations are defined for describing electromagnetic wave fields in free space exactly in terms of rays for any wavelength, level of coherence or polarization, and numerical aperture, as long as there are no evanescent components. These representations correspond to tensors assigned to each ray such that the electric and magnetic energy densities, the Poynting vector, and the polarization properties of the field correspond to simple integrals involving these tensors for the rays that go through the specified point. For partially coherent fields, the ray-based approach provided by the new representations can reduce dramatically the computation times for the physical properties mentioned earlier.

Dilational processes accompanying earthquakes in the Long Valley Caldera

USGS Publications Warehouse

Dreger, Douglas S.; Tkalcic, Hrvoje; Johnston, M.

2000-01-01

Regional distance seismic moment tensor determinations and broadband waveforms of moment magnitude 4.6 to 4.9 earthquakes from a November 1997 Long Valley Caldera swarm, during an inflation episode, display evidence of anomalous seismic radiation characterized by non-double couple (NDC) moment tensors with significant volumetric components. Observed coseismic dilation suggests that hydrothermal or magmatic processes are directly triggering some of the seismicity in the region. Similarity in the NDC solutions implies a common source process, and the anomalous events may have been triggered by net fault-normal stress reduction due to high-pressure fluid injection or pressurization of fluid-saturated faults due to magmatic heating.

Face Hallucination with Linear Regression Model in Semi-Orthogonal Multilinear PCA Method

NASA Astrophysics Data System (ADS)

Asavaskulkiet, Krissada

2018-04-01

In this paper, we propose a new face hallucination technique, face images reconstruction in HSV color space with a semi-orthogonal multilinear principal component analysis method. This novel hallucination technique can perform directly from tensors via tensor-to-vector projection by imposing the orthogonality constraint in only one mode. In our experiments, we use facial images from FERET database to test our hallucination approach which is demonstrated by extensive experiments with high-quality hallucinated color faces. The experimental results assure clearly demonstrated that we can generate photorealistic color face images by using the SO-MPCA subspace with a linear regression model.

Moment tensor inversion with three-dimensional sensor configuration of mining induced seismicity (Kiruna mine, Sweden)

NASA Astrophysics Data System (ADS)

Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian

2018-06-01

Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). A stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double-couple and full moment tensor with high frequency data, is very challenging. Moreover, the application to underground mining system requires accounting for the 3-D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3-D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in the presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to eight events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double-couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip and rake configurations of the double-couple term were obtained. The orientations of the nodal planes of the double-couple component in most cases vary from NNW to NNE with a dip along the ore body or in the opposite direction.

Moment Tensor Inversion with 3D sensor configuration of Mining Induced Seismicity (Kiruna mine, Sweden)

NASA Astrophysics Data System (ADS)

Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian

2018-03-01

Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). Stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double couple and full moment tensor with high frequency data is very challenging. Moreover, the application to underground mining system requires accounting for the 3D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to 8 events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip, rake configurations of the double couple term were obtained. The orientations of the nodal planes of the double-couple component in most cases vary from NNW to NNE with a dip along the ore body or in the opposite direction.

Evolution of stress and strain during 3D folding: application to orthogonal fracture systems in folded turbidites, SW Portugal

NASA Astrophysics Data System (ADS)

Reber, J. E.; Schmalholz, S. M.; Lechmann, S. M.

2009-04-01

We present field data and numerical modeling results which show the evolution of stress and strain patterns during 3D folding resulting in an orthogonal fracture system. The field area is located near Almograve, SW Portugal. The area is part of the Mira Formation which itself is part of the South Portuguese Zone (SPZ). The structural development of the SPZ is characterized by southwest vergent folding and thrust displacement. The metamorphism in the SPZ increases from diagenetic conditions in the southwest to greenschist-facies conditions to the northeast. The Mira Formation is composed of turbiditic layers of Carboniferous age with low sandstone to shale ratio. The data was gathered at three outcrops which show structures similar to chocolate tablet structures in the folded sandstone layers. Chocolate tablet structures are generated under simultaneous extension in two directions and show two fracture systems of the same age which are perpendicular to each other. However, the Mira Formation is located in a convergent area. Also, the outcrops near Almograve show two fracture systems of different age. The fractures orthogonal to the fold axis and the bedding are crosscut by fractures parallel to the fold axis and orthogonal to the bedding. Our hypothesis for the evolution of the observed fracture systems is as follows; the older fractures which are now orthogonal to the fold axis and to the bedding plane were generated during compression while the layers were still approximately horizontal. They are parallel to σ1(i.e. mode 1 fractures). The second and younger fracture family was generated in a phase where there is local extension in the fold limbs. These fractures are orthogonal to the far-field σ1, parallel to the fold axis and perpendicular to the bedding. The shortening direction is constant during the entire folding process. We test our hypothesis with numerical modeling. We use 2D and 3D finite element codes with a mixed formulation for incompressible flow and a viscous rheology. The stress and strain tensor components are calculated at each numerical nodal point. The stress and strain fields are visualized through ellipses and ellipsoids which are calculated using the eigenvalues of the respective tensors. The shortest main axis represents the direction of the smallest stress σ3 and the longest main axis represents the direction of the largest stress σ1. To generate two orthogonal fracture systems in the fold limbs we expect a relatively rapid change of the stress field in the fold limbs during folding. With a relatively slow change of the stress field we would expect to see more than two fracture systems with a wide range of fracture orientation which we did not observe in the field. The preliminary 2D results show, as expected, a sudden flip of the main axes of the stress ellipse which corresponds to a change from limb-parallel compression to extension. For the 3D model we expect similar results and we will investigate the impact of different deformation boundary conditions on the evolution of the 3D stress and strain fields.

Theory of electromagnetic wave propagation in ferromagnetic Rashba conductor

NASA Astrophysics Data System (ADS)

Shibata, Junya; Takeuchi, Akihito; Kohno, Hiroshi; Tatara, Gen

2018-02-01

We present a comprehensive study of various electromagnetic wave propagation phenomena in a ferromagnetic bulk Rashba conductor from the perspective of quantum mechanical transport. In this system, both the space inversion and time reversal symmetries are broken, as characterized by the Rashba field α and magnetization M, respectively. First, we present a general phenomenological analysis of electromagnetic wave propagation in media with broken space inversion and time reversal symmetries based on the dielectric tensor. The dependence of the dielectric tensor on the wave vector q and M is retained to first order. Then, we calculate the microscopic electromagnetic response of the current and spin of conduction electrons subjected to α and M, based on linear response theory and the Green's function method; the results are used to study the system optical properties. First, it is found that a large α enhances the anisotropic properties of the system and enlarges the frequency range in which the electromagnetic waves have hyperbolic dispersion surfaces and exhibit unusual propagations known as negative refraction and backward waves. Second, we consider the electromagnetic cross-correlation effects (direct and inverse Edelstein effects) on the wave propagation. These effects stem from the lack of space inversion symmetry and yield q-linear off-diagonal components in the dielectric tensor. This induces a Rashba-induced birefringence, in which the polarization vector rotates around the vector (α ×q ) . In the presence of M, which breaks time reversal symmetry, there arises an anomalous Hall effect and the dielectric tensor acquires off-diagonal components linear in M. For α ∥M , these components yield the Faraday effect for the Faraday configuration q ∥M and the Cotton-Mouton effect for the Voigt configuration ( q ⊥M ). When α and M are noncollinear, M- and q-induced optical phenomena are possible, which include nonreciprocal directional dichroism in the Voigt configuration. In these nonreciprocal optical phenomena, a "toroidal moment," α ×M , and a "quadrupole moment," αiMj+Miαj , play central roles. These phenomena are strongly enhanced at the spin-split transition edge in the electron band.

Kinematic assumptions and their consequences on the structure of field equations in continuum dislocation theory

NASA Astrophysics Data System (ADS)

Silbermann, C. B.; Ihlemann, J.

2016-03-01

Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez-Ruiz, F. J.; Blas, F. J., E-mail: felipe@uhu.es; Moreno-Ventas Bravo, A. I.

We determine the interfacial properties of a symmetrical binary mixture of equal-sized spherical Lennard-Jones molecules, σ{sub 11} = σ{sub 22}, with the same dispersive energy between like species, ϵ{sub 11} = ϵ{sub 22}, but different dispersive energies between unlike species low enough to induce phase separation. We use the extensions of the improved version of the inhomogeneous long-range corrections of Janecek [J. Phys. Chem. B 110, 6264 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] and Martínez-Ruiz et al. [J. Chem. Phys. 141, 184701 (2014)], to deal with the interaction energy and microscopic components ofmore » the pressure tensor. We perform Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of the symmetrical mixture with different cut-off distances r{sub c} and in combination with the inhomogeneous long-range corrections. The pressure tensor is obtained using the mechanical (virial) and thermodynamic route. The liquid-liquid interfacial tension is also evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the test-area methodology. This allows to check the validity of the recent extensions presented to deal with the contributions due to long-range corrections for intermolecular energy and pressure tensor in the case of binary mixtures that exhibit liquid-liquid immiscibility. In addition to the pressure tensor and the surface tension, we also obtain density profiles and coexistence densities and compositions as functions of pressure, at a given temperature. According to our results, the main effect of increasing the cut-off distance r{sub c} is to sharpen the liquid-liquid interface and to increase the width of the biphasic coexistence region. Particularly interesting is the presence of a relative minimum in the total density profiles of the symmetrical mixture. This minimum is related with a desorption of the molecules at the interface, a direct consequence of a combination of the weak dispersive interactions between unlike species of the symmetrical binary mixture, and the presence of an interfacial region separating the two immiscible liquid phases in coexistence.« less

Bayesian ISOLA: new tool for automated centroid moment tensor inversion

NASA Astrophysics Data System (ADS)

Vackář, Jiří; Burjánek, Jan; Gallovič, František; Zahradník, Jiří; Clinton, John

2017-04-01

Focal mechanisms are important for understanding seismotectonics of a region, and they serve as a basic input for seismic hazard assessment. Usually, the point source approximation and the moment tensor (MT) are used. We have developed a new, fully automated tool for the centroid moment tensor (CMT) inversion in a Bayesian framework. It includes automated data retrieval, data selection where station components with various instrumental disturbances and high signal-to-noise are rejected, and full-waveform inversion in a space-time grid around a provided hypocenter. The method is innovative in the following aspects: (i) The CMT inversion is fully automated, no user interaction is required, although the details of the process can be visually inspected latter on many figures which are automatically plotted.(ii) The automated process includes detection of disturbances based on MouseTrap code, so disturbed recordings do not affect inversion.(iii) A data covariance matrix calculated from pre-event noise yields an automated weighting of the station recordings according to their noise levels and also serves as an automated frequency filter suppressing noisy frequencies.(iv) Bayesian approach is used, so not only the best solution is obtained, but also the posterior probability density function.(v) A space-time grid search effectively combined with the least-squares inversion of moment tensor components speeds up the inversion and allows to obtain more accurate results compared to stochastic methods. The method has been tested on synthetic and observed data. It has been tested by comparison with manually processed moment tensors of all events greater than M≥3 in the Swiss catalogue over 16 years using data available at the Swiss data center (http://arclink.ethz.ch). The quality of the results of the presented automated process is comparable with careful manual processing of data. The software package programmed in Python has been designed to be as versatile as possible in order to be applicable in various networks ranging from local to regional. The method can be applied either to the everyday network data flow, or to process large previously existing earthquake catalogues and data sets.

Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence

NASA Astrophysics Data System (ADS)

Danish, Mohammad; Meneveau, Charles

2018-04-01

Knowledge of local flow-topology, the patterns of streamlines around a moving fluid element as described by the velocity-gradient tensor, is useful for developing insights into turbulence processes, such as energy cascade, material element deformation, or scalar mixing. Much has been learned in the recent past about flow topology at the smallest (viscous) scales of turbulence. However, less is known at larger scales, for instance, at the inertial scales of turbulence. In this work, we present a detailed study on the scale dependence of various quantities of interest, such as the population fraction of different types of flow-topologies, the joint probability distribution of the second and third invariants of the velocity gradient tensor, and the geometrical alignment of vorticity with strain-rate eigenvectors. We perform the analysis on a simulation dataset of isotropic turbulence at Reλ=433 . While quantities appear close to scale invariant in the inertial range, we observe a "bump" in several quantities at length scales between the inertial and viscous ranges. For instance, the population fraction of unstable node-saddle-saddle flow topology shows an increase when reducing the scale from the inertial entering the viscous range. A similar bump is observed for the vorticity-strain-rate alignment. In order to document possible dynamical causes for the different trends in the viscous and inertial ranges, we examine the probability fluxes appearing in the Fokker-Plank equation governing the velocity gradient invariants. Specifically, we aim to understand whether the differences observed between the viscous and inertial range statistics are due to effects caused by pressure, subgrid-scale, or viscous stresses or various combinations of these terms. To decompose the flow into small and large scales, we mainly use a spectrally compact non-negative filter with good spatial localization properties (Eyink-Aluie filter). The analysis shows that when going from the inertial range into the viscous range, the subgrid-stress effect decreases more rapidly as a function of scale than the viscous effects increase. To make up for the difference, the pressure Hessian also behaves somewhat differently in the viscous than in the inertial range. The results have implications for models for the velocity gradient tensor showing that the effects of subgrid scales may not be simply modeled via a constant eddy viscosity in the inertial range if one wishes to reproduce the observed trends.

The method of planes pressure tensor for a spherical subvolume

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heyes, D. M., E-mail: d.heyes@imperial.ac.uk; Smith, E. R., E-mail: edward.smith05@imperial.ac.uk; Dini, D., E-mail: d.dini@imperial.ac.uk

2014-02-07

Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emergemore » naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.« less

High pressure phase transformations revisited

NASA Astrophysics Data System (ADS)

Levitas, Valery I.

2018-04-01

High pressure phase transformations play an important role in the search for new materials and material synthesis, as well as in geophysics. However, they are poorly characterized, and phase transformation pressure and pressure hysteresis vary drastically in experiments of different researchers, with different pressure transmitting media, and with different material suppliers. Here we review the current state, challenges in studying phase transformations under high pressure, and the possible ways in overcoming the challenges. This field is critically compared with fields of phase transformations under normal pressure in steels and shape memory alloys, as well as plastic deformation of materials. The main reason for the above mentioned discrepancy is the lack of understanding that there is a fundamental difference between pressure-induced transformations under hydrostatic conditions, stress-induced transformations under nonhydrostatic conditions below yield, and strain-induced transformations during plastic flow. Each of these types of transformations has different mechanisms and requires a completely different thermodynamic and kinetic description and experimental characterization. In comparison with other fields the following challenges are indicated for high pressure phase transformation: (a) initial and evolving microstructure is not included in characterization of transformations; (b) continuum theory is poorly developed; (c) heterogeneous stress and strain fields in experiments are not determined, which leads to confusing material transformational properties with a system behavior. Some ways to advance the field of high pressure phase transformations are suggested. The key points are: (a) to take into account plastic deformations and microstructure evolution during transformations; (b) to formulate phase transformation criteria and kinetic equations in terms of stress and plastic strain tensors (instead of pressure alone); (c) to develop multiscale continuum theories, and (d) to couple experimental, theoretical, and computational studies of the behavior of a tested sample to extract information about fields of stress and strain tensors and concentration of high pressure phase, transformation criteria and kinetics. The ideal characterization should contain complete information which is required for simulation of the same experiments.

High pressure phase transformations revisited.

PubMed

Levitas, Valery I

2018-04-25

High pressure phase transformations play an important role in the search for new materials and material synthesis, as well as in geophysics. However, they are poorly characterized, and phase transformation pressure and pressure hysteresis vary drastically in experiments of different researchers, with different pressure transmitting media, and with different material suppliers. Here we review the current state, challenges in studying phase transformations under high pressure, and the possible ways in overcoming the challenges. This field is critically compared with fields of phase transformations under normal pressure in steels and shape memory alloys, as well as plastic deformation of materials. The main reason for the above mentioned discrepancy is the lack of understanding that there is a fundamental difference between pressure-induced transformations under hydrostatic conditions, stress-induced transformations under nonhydrostatic conditions below yield, and strain-induced transformations during plastic flow. Each of these types of transformations has different mechanisms and requires a completely different thermodynamic and kinetic description and experimental characterization. In comparison with other fields the following challenges are indicated for high pressure phase transformation: (a) initial and evolving microstructure is not included in characterization of transformations; (b) continuum theory is poorly developed; (c) heterogeneous stress and strain fields in experiments are not determined, which leads to confusing material transformational properties with a system behavior. Some ways to advance the field of high pressure phase transformations are suggested. The key points are: (a) to take into account plastic deformations and microstructure evolution during transformations; (b) to formulate phase transformation criteria and kinetic equations in terms of stress and plastic strain tensors (instead of pressure alone); (c) to develop multiscale continuum theories, and (d) to couple experimental, theoretical, and computational studies of the behavior of a tested sample to extract information about fields of stress and strain tensors and concentration of high pressure phase, transformation criteria and kinetics. The ideal characterization should contain complete information which is required for simulation of the same experiments.

CT-derived Biomechanical Metrics Improve Agreement Between Spirometry and Emphysema

PubMed Central

Bhatt, Surya P.; Bodduluri, Sandeep; Newell, John D.; Hoffman, Eric A.; Sieren, Jessica C.; Han, Meilan K.; Dransfield, Mark T.; Reinhardt, Joseph M.

2016-01-01

Rationale and Objectives Many COPD patients have marked discordance between FEV1 and degree of emphysema on CT. Biomechanical differences between these patients have not been studied. We aimed to identify reasons for the discordance between CT and spirometry in some patients with COPD. Materials and Methods Subjects with GOLD stage I–IV from a large multicenter study (COPDGene) were arranged by percentiles of %predicted FEV1 and emphysema on CT. Three categories were created using differences in percentiles: Catspir with predominant airflow obstruction/minimal emphysema, CatCT with predominant emphysema/minimal airflow obstruction, and Catmatched with matched FEV1 and emphysema. Image registration was used to derive Jacobian determinants, a measure of lung elasticity, anisotropy and strain tensors, to assess biomechanical differences between groups. Regression models were created with the above categories as outcome variable, adjusting for demographics, scanner type, quantitative CT-derived emphysema, gas trapping, and airway thickness (Model 1), and after adding biomechanical CT metrics (Model 2). Results Jacobian determinants, anisotropy and strain tensors were strongly associated with FEV1. With Catmatched as control, Model 2 predicted Catspir and CatCT better than Model 1 (Akaike Information Criterion, AIC 255.8 vs. 320.8). In addition to demographics, the strongest independent predictors of FEV1 were Jacobian mean (β= 1.60,95%CI = 1.16 to 1.98; p<0.001), coefficient of variation (CV) of Jacobian (β= 1.45,95%CI = 0.86 to 2.03; p<0.001) and CV strain (β= 1.82,95%CI = 0.68 to 2.95; p = 0.001). CVs of Jacobian and strain are both potential markers of biomechanical lung heterogeneity. Conclusions CT-derived measures of lung mechanics improve the link between quantitative CT and spirometry, offering the potential for new insights into the linkage between regional parenchymal destruction and global decrement in lung function in COPD patients. PMID:27055745

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

NASA Technical Reports Server (NTRS)

Leone, Frank A., Jr.

2015-01-01

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Induced Seismicity at the UK "Hot Dry Rock" Test Site for Geothermal Energy Production

NASA Astrophysics Data System (ADS)

Li, Xun; Main, Ian; Jupe, Andrew

2018-03-01

In enhanced geothermal systems (EGS), fluid is injected at high pressure in order to stimulate fracturing and/or fluid flow through otherwise relatively impermeable underlying hot rocks to generate power and/or heat. The stimulation induces micro-earthquakes whose precise triggering mechanism and relationship to new and pre-existing fracture networks are still the subject of some debate. Here we analyse the dataset for induced micro-earthquakes at the UK "hot dry rock" experimental geothermal site (Rosemanowes, Cornwall). We quantify the evolution of several metrics used to characterise induced seismicity, including the seismic strain partition factor and the "seismogenic index". The results show a low strain partition factor of 0.01% and a low seismogenenic index indicating that aseismic processes dominate. We also analyse the spatio-temporal distribution of hypocentres, using simple models for the evolution of hydraulic diffusivity by (a) isotropic and (b) anisotropic pore-pressure relaxation. The principal axes of the diffusivity or permeability tensor inferred from the spatial distribution of earthquake foci are aligned parallel to the present-day stress field, although the maximum permeability is vertical, whereas the maximum principal stress is horizontal. Our results are consistent with a triggering mechanism that involves (a) seismic shear slip along optimally-oriented pre-existing fractures, (b) a large component of aseismic slip with creep (c) activation of tensile fractures as hydraulic conduits created by both the present-day stress field and by the induced shear slip, both exploiting pre-existing joint sets exposed in borehole data.

Three-dimensional modelling and geothermal process simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burns, K.L.

1990-01-01

The subsurface geological model or 3-D GIS is constructed from three kinds of objects, which are a lithotope (in boundary representation), a number of fault systems, and volumetric textures (vector fields). The chief task of the model is to yield an estimate of the conductance tensors (fluid permeability and thermal conductivity) throughout an array of voxels. This is input as material properties to a FEHM numerical physical process model. The main task of the FEHM process model is to distinguish regions of convective from regions of conductive heat flow, and to estimate the fluid phase, pressure and flow paths. Themore » temperature, geochemical, and seismic data provide the physical constraints on the process. The conductance tensors in the Franciscan Complex are to be derived by the addition of two components. The isotropic component is a stochastic spatial variable due to disruption of lithologies in melange. The deviatoric component is deterministic, due to smoothness and continuity in the textural vector fields. This decomposition probably also applies to the engineering hydrogeological properties of shallow terrestrial fluvial systems. However there are differences in quantity. The isotropic component is much more variable in the Franciscan, to the point where volumetric averages are misleading, and it may be necessary to select that component from several, discrete possible states. The deviatoric component is interpolated using a textural vector field. The Franciscan field is much more complicated, and contains internal singularities. 27 refs., 10 figs.« less

PBO Borehole Strainmeters and Pore Pressure Sensors: Recording Hydrological Strain Signals

NASA Astrophysics Data System (ADS)

Gottlieb, M. H.; Hodgkinson, K. M.; Mencin, D.; Henderson, D. B.; Johnson, W.; Van Boskirk, E.; Pyatt, C.; Mattioli, G. S.

2017-12-01

UNAVCO operates a network of 75 borehole strainmeters along the west coast of the United States and Vancouver Island, Canada as part of the Plate Boundary Observatory (PBO), the geodetic component of the NSF-funded Earthscope program. Borehole strainmeters are designed to detect variations in the strain field at the nanostrain level and can easily detect transient strains caused by aseismic creep events, Episodic Tremor and Slip (ETS) events and seismically induced co- and post-seimic signals. In 2016, one strainmeter was installed in an Oklahoma oil field to characterize in-situ deformation during CO2 injection. Twenty-three strainmeter sites also have pore pressure sensors to measure fluctuations in groundwater pressure. Both the strainmeter network and the pore pressure sensors provide unique data against which those using water-level measurements, GPS time-series or InSAR data can compare possible subsidence signals caused by groundwater withdrawal or fluid re-injection. Operating for 12 years, the PBO strainmeter and pore pressure network provides a long-term, continuous, 1-sps record of deformation. PBO deploys GTSM21 tensor strainmeters from GTSM Technologies, which consist of four horizontal strain gauges stacked vertically, at different orientations, within a single 2 m-long instrument. The strainmeters are typically installed at depths of 200 to 250 m and grouted into the bottom of 15 cm diameter boreholes. The pore pressure sensors are Digiquartz Depth Sensors from Paros Scientific. These sensors are installed in 2" PVC, sampling groundwater through a screened section 15 m above the co-located strainmeter. These sensors are also recording at 1-sps with a resolution in the hundredths of hPa. High-rate local barometric pressure data and low-rate rainfall data also available at all locations. PBO Strainmeter and pore pressure data are available in SEED, SAC-ASCII and time-stamped ASCII format from the IRIS Data Managements Center. Strainmeter data are available at 2-hour latency while the pore pressure data are available in real-time. Links for data access, instrument and borehole information and station histories are available from UNAVCO's Borehole Data web page (https://www.unavco.org/data/strain-seismic/bsm-data/bsm-data.html ).

A Generalized Orthotropic Elasto-Plastic Material Model for Impact Analysis

NASA Astrophysics Data System (ADS)

Hoffarth, Canio

Composite materials are now beginning to provide uses hitherto reserved for metals in structural systems such as airframes and engine containment systems, wraps for repair and rehabilitation, and ballistic/blast mitigation systems. These structural systems are often subjected to impact loads and there is a pressing need for accurate prediction of deformation, damage and failure. There are numerous material models that have been developed to analyze the dynamic impact response of polymer matrix composites. However, there are key features that are missing in those models that prevent them from providing accurate predictive capabilities. In this dissertation, a general purpose orthotropic elasto-plastic computational constitutive material model has been developed to predict the response of composites subjected to high velocity impacts. The constitutive model is divided into three components - deformation model, damage model and failure model, with failure to be added at a later date. The deformation model generalizes the Tsai-Wu failure criteria and extends it using a strain-hardening-based orthotropic yield function with a non-associative flow rule. A strain equivalent formulation is utilized in the damage model that permits plastic and damage calculations to be uncoupled and capture the nonlinear unloading and local softening of the stress-strain response. A diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, in composites it has been found that loading in one direction can lead to damage in multiple coordinate directions. To account for this phenomena, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. The overall framework is driven by experimental tabulated temperature and rate-dependent stress-strain data as well as data that characterizes the damage matrix and failure. The developed theory has been implemented in a commercial explicit finite element analysis code, LS-DYNARTM, as MAT213. Several verification and validation tests using a commonly available carbon-fiber composite, Toyobo's T800/F3900, have been carried and the results show that the theory and implementation are efficient, robust and accurate.

Symmetry analysis of strain, electric and magnetic fields in the Bi2Se3-class of topological insulators

NASA Astrophysics Data System (ADS)

Rosdahl Brems, Mathias; Paaske, Jens; Lunde, Anders Mathias; Willatzen, Morten

2018-05-01

Based on group theoretical arguments we derive the most general Hamiltonian for the Bi2Se3-class of materials including terms to third order in the wave vector, first order in electric and magnetic fields, first order in strain and first order in both strain and wave vector. We determine analytically the effects of strain on the electronic structure of Bi2Se3. For the most experimentally relevant surface termination we analytically derive the surface state (SS) spectrum, revealing an anisotropic Dirac cone with elliptical constant energy contours giving rise to a direction-dependent group velocity. The spin-momentum locking of strained Bi2Se3 is shown to be modified. Hence, strain control can be used to manipulate the spin degree of freedom via the spin–orbit coupling. We show that for a thin film of Bi2Se3 the SS band gap induced by coupling between the opposite surfaces changes opposite to the bulk band gap under strain. Tuning the SS band gap by strain, gives new possibilities for the experimental investigation of the thickness dependent gap and optimization of optical properties relevant for, e.g., photodetector and energy harvesting applications. We finally derive analytical expressions for the effective mass tensor of the Bi2Se3 class of materials as a function of strain and electric field.

Moment tensor and location of seismic events in the 2017 DPRK test

NASA Astrophysics Data System (ADS)

Wei, S.; Shi, Q.; Chen, Q. F.; Wang, T.

2017-12-01

The main seismic event in the 2017 DPRK test was followed by a secondary event about eight minutes later. We conducted waveform analysis on the regional broadband waveform data to better constrain the moment tensor and location of these two events, to further understand their relations. In the first place, we applied the generalized Cut-And-Paste (gCAP) method to the regional data to invert the full moment tensor solutions of the two events. Our long period (0.02-0.08 Hz for Pnl, 0.02-0.055 Hz for surface waves) inversions show that the main event was composed of large positive ISO component ( 90% of the total moment) and has a moment magnitude of 5.4. In contrast, the second event shows large negative ISO component ( 50% of the total moment) with a moment magnitude of 4.5. Although there are trade-offs between the CLVD and the ISO component for the second event, chiefly caused by the coda waves from the first event, the result is more robust if we force a small CVLD component in the inversion. We also relocated the epicenter of the second event using P-wave first arrival picks, relative to the location of the first event, which has been accurately determined from the high-resolution geodetic data. The calibration from the first event allows us to precisely locate the second event, which shows an almost identical location to the first event. After a polarity correction, their high-frequency ( 0.25 - 0.9 Hz) regional surface waves also display high similarity, supporting the similar location but opposite ISO polarity of the two events. Our results suggest that the second event was likely to be caused by the collapsing after the main event, in agreement with the surface displacement derived from geodetic observation and modeling results.

Quantifying white matter tract diffusion parameters in the presence of increased extra-fiber cellularity and vasogenic edema

PubMed Central

Chiang, Chia-Wen; Wang, Yong; Sun, Peng; Lin, Tsen-Hsuan; Trinkaus, Kathryn; Cross, Anne H.; Song, Sheng-Kwei

2014-01-01

The effect of extra-fiber structural and pathological components confounding diffusion tensor imaging (DTI) computation was quantitatively investigated using data generated by both Monte-Carlo simulations and tissue phantoms. Increased extent of vasogenic edema, by addition of various amount of gel to fixed normal mouse trigeminal nerves or by increasing non-restricted isotropic diffusion tensor components in Monte-Carlo simulations, significantly decreased fractional anisotropy (FA), increased radial diffusivity, while less significantly increased axial diffusivity derived by DTI. Increased cellularity, mimicked by graded increase of the restricted isotropic diffusion tensor component in Monte-Carlo simulations, significantly decreased FA and axial diffusivity with limited impact on radial diffusivity derived by DTI. The MC simulation and tissue phantom data were also analyzed by the recently developed diffusion basis spectrum imaging (DBSI) to simultaneously distinguish and quantify the axon/myelin integrity and extra-fiber diffusion components. Results showed that increased cellularity or vasogenic edema did not affect the DBSI-derived fiber FA, axial or radial diffusivity. Importantly, the extent of extra-fiber cellularity and edema estimated by DBSI correlated with experimentally added gel and Monte-Carlo simulations. We also examined the feasibility of applying 25-direction diffusion encoding scheme for DBSI analysis on coherent white matter tracts. Results from both phantom experiments and simulations suggested that the 25-direction diffusion scheme provided comparable DBSI estimation of both fiber diffusion parameters and extra-fiber cellularity/edema extent as those by 99-direction scheme. An in vivo 25-direction DBSI analysis was performed on experimental autoimmune encephalomyelitis (EAE, an animal model of human multiple sclerosis) optic nerve as an example to examine the validity of derived DBSI parameters with post-imaging immunohistochemistry verification. Results support that in vivo DBSI using 25-direction diffusion scheme correctly reflect the underlying axonal injury, demyelination, and inflammation of optic nerves in EAE mice. PMID:25017446

Old torsion Balance Observations - too old for modern Exploration?

NASA Astrophysics Data System (ADS)

Götze, H.-J.

2003-04-01

Gravity gradiometry is a new gravity measurement technology that could fundamentally change the game of subsurface modelling and enhance geological interpretations: at fully inertial stabilized platforms they provide observed components of the E&{uml;o}tv&{uml;o}s tensor for 3D interpretations in mining and oil exploration and other fields of pure and applied geophysics. Although gravity gradiometry was among the first geophysical methods used successfully in applied Geophysics (E&{uml;o}tv&{uml;o}s torsion balance), the technology fell from favour in the 1930s. From this time measurements, done by torsion balances (Drehwaagen), are presented here which were observed to detect salt domes in the Northwest German basin. The data were digitized from old copies, then reprocessed and recalculated to draw Bouguer anomaly maps. However, the second derivatives of the gravity potential provide also independent data which can be used to constrain forward modelling. 3D modelling of Vxz, Vyz and other components of the E&{uml;o}tv&{uml;o}s tensor provide better insight into the geometry of the salt dome structure than modelling of the Bouguer gravity field. In addition to this first example results from gravity data processing by applying curvature techniques and again 3D forward modelling of second derivatives of the potential of density domains in the uppermost crust in the area of the Dead Sea Transform (Jordan) is presented here. The 3D modelling is conducted by the program package IGMAS which supply possibilities to calculate potential, gravity, its components and the Eötvös tensor components. Based on results so far one can conclude that the knowledge of the "second derivatives of the potential" could fundamentally change the role of gravity field measurements in the process of underground investigations not only for resource exploration but for investigations along large faults systems.

Application of modern tensor calculus to engineered domain structures. 1. Calculation of tensorial covariants.

PubMed

Kopský, Vojtech

2006-03-01

This article is a roadmap to a systematic calculation and tabulation of tensorial covariants for the point groups of material physics. The following are the essential steps in the described approach to tensor calculus. (i) An exact specification of the considered point groups by their embellished Hermann-Mauguin and Schoenflies symbols. (ii) Introduction of oriented Laue classes of magnetic point groups. (iii) An exact specification of matrix ireps (irreducible representations). (iv) Introduction of so-called typical (standard) bases and variables -- typical invariants, relative invariants or components of the typical covariants. (v) Introduction of Clebsch-Gordan products of the typical variables. (vi) Calculation of tensorial covariants of ascending ranks with consecutive use of tables of Clebsch-Gordan products. (vii) Opechowski's magic relations between tensorial decompositions. These steps are illustrated for groups of the tetragonal oriented Laue class D(4z) -- 4(z)2(x)2(xy) of magnetic point groups and for tensors up to fourth rank.

MULTISCALE TENSOR ANISOTROPIC FILTERING OF FLUORESCENCE MICROSCOPY FOR DENOISING MICROVASCULATURE.

PubMed

Prasath, V B S; Pelapur, R; Glinskii, O V; Glinsky, V V; Huxley, V H; Palaniappan, K

2015-04-01

Fluorescence microscopy images are contaminated by noise and improving image quality without blurring vascular structures by filtering is an important step in automatic image analysis. The application of interest here is to automatically extract the structural components of the microvascular system with accuracy from images acquired by fluorescence microscopy. A robust denoising process is necessary in order to extract accurate vascular morphology information. For this purpose, we propose a multiscale tensor with anisotropic diffusion model which progressively and adaptively updates the amount of smoothing while preserving vessel boundaries accurately. Based on a coherency enhancing flow with planar confidence measure and fused 3D structure information, our method integrates multiple scales for microvasculature preservation and noise removal membrane structures. Experimental results on simulated synthetic images and epifluorescence images show the advantage of our improvement over other related diffusion filters. We further show that the proposed multiscale integration approach improves denoising accuracy of different tensor diffusion methods to obtain better microvasculature segmentation.

Current crustal deformation of the Taiwan orogen reassessed by cGPS strain-rate estimation and focal mechanism stress inversion

NASA Astrophysics Data System (ADS)

Chen, Sean Kuanhsiang; Wu, Yih-Min; Hsu, Ya-Ju; Chan, Yu-Chang

2017-07-01

We study internal deformation of the Taiwan orogen, a young arc-continental collision belt, which the spatial heterogeneity remains unclear. We aim to ascertain heterogeneity of the orogenic crust in depth when specifying general mechanisms of the Taiwan orogeny. To reach this goal, we used updated data of continuous GPS (cGPS) and earthquake focal mechanisms to reassess geodetic strain-rate and seismic stress fields of Taiwan, respectively. We updated the both data sets from 1990 to 2015 to provide large amount of constraints on surficial and internal deformation of the crust for a better understanding. We estimated strain-rate tensors by calculating gradient tensors of cGPS station velocities in horizontal 0.1°-spacing grids via Delaunay triangulation. We determined stress tensors within a given horizontal and vertical grid cell of 0.1° and 10 km, respectively, by employing the spatial and temporal stress inversion. To minimize effects of the 1999 Mw 7.6 Chi-Chi earthquake on trends of the strain and stress, we modified observational possible bias of the cGPS velocities after the earthquake and removed the first 15-month focal mechanisms within the fault rupture zone. We also calculated the Anderson fault parameter (Aϕ) based on stress ratios and rake angles to quantitatively describe tectonic regimes of Taiwan. By examining directions of seismic compressive axes and styles of faulting, our results indicate that internal deformation of the crust is presently heterogeneous in the horizontal and vertical spaces. Directions of the compressive axes are fan-shaped oriented between N10°W and N110°W in the western and mid-eastern Taiwan at the depths of 0-20 km and near parallel to orientations of geodetic compressional axes. The orientations agreed with predominantly reverse faulting in the western Taiwan at the same depth range, implying a brittle deformation regime against the Peikang Basement High. Orientations of the compressive axes most rotated counter-clockwise at the depths of 20-40 km, coinciding with transition of styles of faulting from reverse to strike-slip faulting along the depths as revealed by variation of the Aϕ values. The features indicate that internal deformation of the upper crust is primarily driven by the same compressional mechanism. It implies that geodetic strains could detect the deformation from surface down to a maximal depth of 20 km in most regimes of Taiwan. We find that heterogeneity in orientations of compressive axes and styles of faulting is strong in two regimes at the northern and southern Central Range, coinciding to areas of the orogenic thinned/thickened crust. Conversely, the heterogeneity is weak in the central Western Foothills at surrounding area of root of the overthickened crust. This observation, coupled with regional seismological observations, may imply that vertical deformation from crustal thickening and thinning and thinning-related dynamics from mantle flows may have joint influence on degree of stress heterogeneity.

A finite deformation viscoelastic-viscoplastic constitutive model for self-healing materials

NASA Astrophysics Data System (ADS)

Shahsavari, H.; Naghdabadi, R.; Baghani, M.; Sohrabpour, S.

2016-12-01

In this paper, employing the Hencky strain, viscoelastic-viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic-viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing variables and employing the strain equivalence hypothesis, the strain tensor is determined in the effective configuration. Satisfying the Clausius-Duhem inequality, the evolution equations are introduced for the viscoelastic and viscoplastic strains. The damage and healing variables also evolve according to two different prescribed functions. To employ the proposed model in different loading conditions, the model is discretized in the semi-implicit form. Material parameters of the model are identified employing experimental tests on asphalt mixes available in the literature. Finally, capability of the model is demonstrated comparing the model predictions in the creep-recovery and repeated creep-recovery with the experimental results available in the literature and a good agreement between predicted and test results is revealed.

Stochastic Theory for the Clustering of Rapidly Settling, Low-Inertia Particle Pairs in Isotropic Turbulence - II

NASA Astrophysics Data System (ADS)

Rani, Sarma; Gupta, Vijay; Koch, Donald

2017-11-01

A stochastic theory is developed to predict the Radial Distribution Function (RDF) of monodisperse, rapidly settling, low-inertia particle pairs in isotropic turbulence. In the second version of the theory (T2), the dimensionless strain-rate and rotation-rate tensors ``seen'' by the primary particle are assumed to be Gaussian distributed, where the strain-rate and rotation-rate tensors are non-dimensionlized using the instantaneous dissipation rate and enstrophy, respectively. Accordingly, closure is again derived for the drift flux driving particle clustering, in the asympotic limits of Stokes number St =τp /τη << 1 , and settling paramater Sv = gτp /uη >> 1 . Only the drift flux differs for T1 and T2, while the diffusive flux remains the same. The RDFs for rapidly settling pairs again show an inverse power dependency on pair separation r with an exponent, c1, that is proportional to St2 . However, in contrast to T1, the c1 values predicted by T2 show good qualitative and resonable quantitative agreement with the c1 values obtained from DNS of settling particles in isotropic turbulence. Further, the T2-predicted c1 values are smaller than those obtained from DNS of non-settling particles in isotropic turbulence. Funding from the CBET Division of the National Science Foundation is gratefully acknowledged.

Tensor integrand reduction via Laurent expansion

NASA Astrophysics Data System (ADS)

Hirschi, Valentin; Peraro, Tiziano

2016-06-01

We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C ++ library N inja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface N inja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the N inja library and interfaced it to M adL oop, which is part of the public M adG raph5_ aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely C utT ools, S amurai, IREGI, PJF ry++ and G olem95. We find that N inja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than N inja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that N inja's performance scales well with both the rank and multiplicity of the considered process.

The Effects of Racket Inertia Tensor on Elbow Loadings and Racket Behavior for Central and Eccentric Impacts

PubMed Central

Nesbit, Steven M.; Elzinga, Michael; Herchenroder, Catherine; Serrano, Monika

2006-01-01

This paper discusses the inertia tensors of tennis rackets and their influence on the elbow swing torques in a forehand motion, the loadings transmitted to the elbow from central and eccentric impacts, and the racket acceleration responses from central and eccentric impacts. Inertia tensors of various rackets with similar mass and mass center location were determined by an inertia pendulum and were found to vary considerably in all three orthogonal directions. Tennis swing mechanics and impact analyses were performed using a computer model comprised of a full-body model of a human, a parametric model of the racket, and an impact function. The swing mechanics analysis of a forehand motion determined that inertia values had a moderate linear effect on the pronation-supination elbow torques required to twist the racket, and a minor effect on the flexion-extension and valgus-varus torques. The impact analysis found that mass center inertia values had a considerable effect on the transmitted torques for both longitudinal and latitudinal eccentric impacts and significantly affected all elbow torque components. Racket acceleration responses to central and eccentric impacts were measured experimentally and found to be notably sensitive to impact location and mass center inertia values. Key Points Tennis biomechanics. Racket inertia tensor. Impact analysis. Full-body computer model. PMID:24260004

Tensor manifold-based extreme learning machine for 2.5-D face recognition

NASA Astrophysics Data System (ADS)

Chong, Lee Ying; Ong, Thian Song; Teoh, Andrew Beng Jin

2018-01-01

We explore the use of the Gabor regional covariance matrix (GRCM), a flexible matrix-based descriptor that embeds the Gabor features in the covariance matrix, as a 2.5-D facial descriptor and an effective means of feature fusion for 2.5-D face recognition problems. Despite its promise, matching is not a trivial problem for GRCM since it is a special instance of a symmetric positive definite (SPD) matrix that resides in non-Euclidean space as a tensor manifold. This implies that GRCM is incompatible with the existing vector-based classifiers and distance matchers. Therefore, we bridge the gap of the GRCM and extreme learning machine (ELM), a vector-based classifier for the 2.5-D face recognition problem. We put forward a tensor manifold-compliant ELM and its two variants by embedding the SPD matrix randomly into reproducing kernel Hilbert space (RKHS) via tensor kernel functions. To preserve the pair-wise distance of the embedded data, we orthogonalize the random-embedded SPD matrix. Hence, classification can be done using a simple ridge regressor, an integrated component of ELM, on the random orthogonal RKHS. Experimental results show that our proposed method is able to improve the recognition performance and further enhance the computational efficiency.

A New Approach for Very Large Broadband Geophysical Monitoring of rock Deformations Into Deep Boreholes: The "High-Pulse Poroelasticity Protocol" (HPPP)

NASA Astrophysics Data System (ADS)

Guglielmi, Y.; Cappa, F.; Virieux, J.; Rutqvist, J.; Tsang, C.

2007-12-01

We present a new approach, called the "High-Pulse Poroelasticity Protocol" (HPPP), for a very large broadband geophysical monitoring of rock deformations into deep boreholes (from 200 m to 1 km depth). The HPPP consists in developing an innovative probe that allows the hydromechanical loading of rocks with synchronous fluid pressure - 3D deformations (translational components along and in the orthogonal plan of the borehole axis, and rotational components along the longitudinal axis) - seismic wave measurements over a broadband of frequencies (from static to dynamic [1-1,000 Hz]). In this protocol, the rock is subjected to a controlled source corresponding to a fast (few seconds) hydraulic pressure pulse (pressure wave) localized into a short injection chamber (from 1 to 3 m) which is isolated between two inflatable packers in a borehole. In the chamber, measurements are done with fibre-optic and acoustic sensors that makes possible to use a wide range of frequencies (1-1,000 Hz) and high accuracy (10-7) sampling of fluid pressure and 3D deformations. When the pressure wave is applied, several poroelastic effects are measured: (i) a static poroelastic response that is linked to the fluid diffusion in phase with mechanical deformation of the porous rock; (ii) a low-frequency slow Biot wave (P2 wave) associated with the motion out of phase of solid and fluid phases; (iii) a high-frequency pressure wave that is generated and converted to seismic waves (P1 and S waves) at the borehole wall. This new approach aims at determining the infinitesimal shear and axial components of the strain tensor within the rock crossed by a borehole. The HPPP also allows studying the relationships between elastic waves propagation and rock hydromechanical properties and state at an intermediate scale (mesoscopic scale), between the laboratory and crustal scales, in a volume of one to a few tens of meters around the borehole. This new approach was designed from previous pulse testing done in a fault zone with a first prototype of the HPPP probe capable of simultaneously measuring changes (with a high frequency [120 Hz] and high accuracy) in fluid pressure (± 1 kPa) and displacement normal to the fault (± 10-7 m). This prototype consisted of a fibre-optic fluid pressure and a fibre-optic normal displacement sensor fixed to the borehole walls by two anchors located on both sides of the fault which was isolated with two packers to create a 0.4 m injection chamber. Results indicated that fiber-optic measurements allow good capturing of all the high-frequency changes during the hydraulic pulse. The method appears useful for accurately measuring time discrepancies between pressure and deformation signals as small as a few milliseconds. Moreover, high-frequency measurement of the fault "pressure-deformation" poroelastic response allows highlighting of a loop-shaped evolution that is not observed in conventional laboratory or in situ experiments. Consequently, the HPPP approach will provide new data with axial and shear components of the strain tensor which will give us additional information for determination of the rock seismic and hydromechanical properties at various depths in the crust. Moreover, the HPPP will be adapted to study seismic and mechanical instability of fault zones under controlled hydraulic loading and localized in a point source.

Second order tensor finite element

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.

1990-01-01

The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

Compressional residual stress in Bastogne boudins revealed by synchrotron X-ray microdiffraction

DOE PAGES

Chen, Kai; Kunz, Martin; Li, Yao; ...

2016-06-22

Lattice distortions in crystals can be mapped at the micron scale using synchrotron X-ray Laue microdiffraction (μXRD). From lattice distortions the shape and orientation of the elastic strain tensor can be derived and interpreted in terms of residual stress. We apply the new method to vein quartz from the original boudinage locality at Bastogne, Belgium. Furthermore, a long-standing debate surrounds the kinematics of the Bastogne boudins. The μXRD measurements reveal a shortening residual elastic strain, perpendicular to the vein wall, corroborating the model that the Bastogne boudins formed by layer-parallel shortening and not by layer-parallel extension, as is in themore » geological community generally inferred by the process of boudinage.« less

Unsupervised Discovery of Demixed, Low-Dimensional Neural Dynamics across Multiple Timescales through Tensor Component Analysis.

PubMed

Williams, Alex H; Kim, Tony Hyun; Wang, Forea; Vyas, Saurabh; Ryu, Stephen I; Shenoy, Krishna V; Schnitzer, Mark; Kolda, Tamara G; Ganguli, Surya

2018-06-27

Perceptions, thoughts, and actions unfold over millisecond timescales, while learned behaviors can require many days to mature. While recent experimental advances enable large-scale and long-term neural recordings with high temporal fidelity, it remains a formidable challenge to extract unbiased and interpretable descriptions of how rapid single-trial circuit dynamics change slowly over many trials to mediate learning. We demonstrate a simple tensor component analysis (TCA) can meet this challenge by extracting three interconnected, low-dimensional descriptions of neural data: neuron factors, reflecting cell assemblies; temporal factors, reflecting rapid circuit dynamics mediating perceptions, thoughts, and actions within each trial; and trial factors, describing both long-term learning and trial-to-trial changes in cognitive state. We demonstrate the broad applicability of TCA by revealing insights into diverse datasets derived from artificial neural networks, large-scale calcium imaging of rodent prefrontal cortex during maze navigation, and multielectrode recordings of macaque motor cortex during brain machine interface learning. Copyright © 2018 Elsevier Inc. All rights reserved.

White matter microstructure and cognitive decline in metabolic syndrome: a review of diffusion tensor imaging.

PubMed

Alfaro, Freddy J; Gavrieli, Anna; Saade-Lemus, Patricia; Lioutas, Vasileios-Arsenios; Upadhyay, Jagriti; Novak, Vera

2018-01-01

Metabolic syndrome is a cluster of cardiovascular risk factors defined by the presence of abdominal obesity, glucose intolerance, hypertension and/or dyslipidemia. It is a major public health epidemic worldwide, and a known risk factor for the development of cognitive dysfunction and dementia. Several studies have demonstrated a positive association between the presence of metabolic syndrome and worse cognitive outcomes, however, evidence of brain structure pathology is limited. Diffusion tensor imaging has offered new opportunities to detect microstructural white matter changes in metabolic syndrome, and a possibility to detect associations between functional and structural abnormalities. This review analyzes the impact of metabolic syndrome on white matter microstructural integrity, brain structure abnormalities and their relationship to cognitive function. Each of the metabolic syndrome components exerts a specific signature of white matter microstructural abnormalities. Metabolic syndrome and its components exert both additive/synergistic, as well as, independent effects on brain microstructure thus accelerating brain aging and cognitive decline. Copyright © 2017 Elsevier Inc. All rights reserved.

A magnetic and electronic circular dichroism study of azurin, plastocyanin, cucumber basic protein, and nitrite reductase based on time-dependent density functional theory calculations.

PubMed

Zhekova, Hristina R; Seth, Michael; Ziegler, Tom

2010-06-03

The excitation, circular dichroism, magnetic circular dichroism (MCD) and electron paramagnetic resonance (EPR) spectra of small models of four blue copper proteins are simulated on the TDDFT/BP86 level. X-Ray diffraction geometries are used for the modeling of the blue copper sites in azurin, plastocyanin, cucumber basic protein, and nitrite reductase. Comparison with experimental data reveals that the calculations reproduce most of the qualitative trends of the observed experimental spectra with some discrepancies in the orbital decompositions and the values of the excitation energies, the g( parallel) components of the g tensor, and the components of the A tensor. These discrepancies are discussed relative to deficiencies in the time-dependent density functional theory (TDDFT) methodology, as opposed to previous studies which address them as a result of insufficient model size or poor performance of the BP86 functional. In addition, attempts are made to elucidate the correlation between the MCD and EPR signals.

Anisotropy of the Reynolds stress tensor in the wakes of wind turbine arrays in Cartesian arrangements with counter-rotating rotors

NASA Astrophysics Data System (ADS)

Hamilton, Nicholas; Cal, Raúl Bayoán

2015-01-01

A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean mechanical energy equation indicate correlation between the degree of anisotropy and the regions of the wind turbine wakes where turbulence kinetic energy is produced. The flux of kinetic energy into the momentum-deficit area of the wake from above the canopy is associated with prolate characteristic spheroids. Flux upward into the wake from below the rotor area is associated with oblate characteristic spheroids. Turbulence in the region of the flow directly following the nacelle of the wind turbines demonstrates greater isotropy than regions following the rotor blades. The power and power coefficients for wind turbines indicate that flow structures on the order of magnitude of the spanwise turbine spacing that increase turbine efficiency depending on particular array configuration.

Full Piezoelectric Multilayer-Stacked Hybrid Actuation/Transduction Systems

NASA Technical Reports Server (NTRS)

Su, Ji; Jiang, Xiaoning; Zu, Tian-Bing

2011-01-01

The Stacked HYBATS (Hybrid Actuation/Transduction system) demonstrates significantly enhanced electromechanical performance by using the cooperative contributions of the electromechanical responses of multilayer, stacked negative strain components and positive strain components. Both experimental and theoretical studies indicate that, for Stacked HYBATS, the displacement is over three times that of a same-sized conventional flextensional actuator/transducer. The coupled resonance mode between positive strain and negative strain components of Stacked HYBATS is much stronger than the resonance of a single element actuation only when the effective lengths of the two kinds of elements match each other. Compared with the previously invented hybrid actuation system (HYBAS), the multilayer Stacked HYBATS can be designed to provide high mechanical load capability, low voltage driving, and a highly effective piezoelectric constant. The negative strain component will contract, and the positive strain component will expand in the length directions when an electric field is applied on the device. The interaction between the two elements makes an enhanced motion along the Z direction for Stacked-HYBATS. In order to dominate the dynamic length of Stacked-HYBATS by the negative strain component, the area of the cross-section for the negative strain component will be much larger than the total cross-section areas of the two positive strain components. The transverse strain is negative and longitudinal strain positive in inorganic materials, such as ceramics/single crystals. Different piezoelectric multilayer stack configurations can make a piezoelectric ceramic/single-crystal multilayer stack exhibit negative strain or positive strain at a certain direction without increasing the applied voltage. The difference of this innovation from the HYBAS is that all the elements can be made from one-of-a-kind materials. Stacked HYBATS can provide an extremely effective piezoelectric constant at both resonance and off resonance frequencies. The effective piezoelectric constant can be alternated by varying the size of each component, the degree of the pre-curvature of the positive strain components, the thickness of each layer in the multilayer stacks, and the piezoelectric constant of the material used. Because all of the elements are piezoelectric components, Stacked HYBATS can serve as projector and receiver for underwater detection. The performance of this innovation can be enhanced by improving the piezoelectric properties.

Stress as an order parameter for the glass transition

NASA Astrophysics Data System (ADS)

Visscher, P. B.; Logan, W. T.

1990-09-01

The stress tensor has been considered as a possible order parameter for the liquid-glass transition, and its autocorrelation matrix (elements of which are the integrands in the Green-Kubo formulas for bulk and shear viscosity) have been measured in simulations. However, only the k=0 spatial Fourier component has apparently been previously measured. We have measured four Fourier components of all matrix elements of the stress-stress correlation function, and we find that some of those with nonzero wave vector are significantly more persistent (slower decaying) than the k=0 component.

A Generalization of the Einstein-Maxwell Equations

NASA Astrophysics Data System (ADS)

Cotton, Fredrick

2016-03-01

The proposed modifications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor and (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two auxiliary fields which describe the particle structure. The additional curvature terms couple both to particle solutions and to electromagnetic and gravitational wave solutions. http://sites.google.com/site/fwcotton/em-30.pdf

Relativistic symmetries in the Rosen—Morse potential and tensor interaction using the Nikiforov—Uvarov method

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-04-01

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen—Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ (κ± 1)r-2. In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov—Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.

Solving a mixture of many random linear equations by tensor decomposition and alternating minimization.

DOT National Transportation Integrated Search

2016-09-01

We consider the problem of solving mixed random linear equations with k components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample...

Homogenized moment tensor and the effect of near-field heterogeneities on nonisotropic radiation in nuclear explosion

NASA Astrophysics Data System (ADS)

Burgos, Gaël.; Capdeville, Yann; Guillot, Laurent

2016-06-01

We investigate the effect of small-scale heterogeneities close to a seismic explosive source, at intermediate periods (20-50 s), with an emphasis on the resulting nonisotropic far-field radiation. First, using a direct numerical approach, we show that small-scale elastic heterogeneities located in the near-field of an explosive source, generate unexpected phases (i.e., long period S waves). We then demonstrate that the nonperiodic homogenization theory applied to 2-D and 3-D elastic models, with various pattern of small-scale heterogeneities near the source, leads to accurate waveforms at a reduced computational cost compared to direct modeling. Further, it gives an interpretation of how nearby small-scale features interact with the source at low frequencies, through an explicit correction to the seismic moment tensor. In 2-D simulations, we find a deviatoric contribution to the moment tensor, as high as 21% for near-source heterogeneities showing a 25% contrast of elastic values (relative to a homogeneous background medium). In 3-D this nonisotropic contribution reaches 27%. Second, we analyze intermediate-periods regional seismic waveforms associated with some underground nuclear explosions conducted at the Nevada National Security Site and invert for the full moment tensor, in order to quantify the relative contribution of the isotropic and deviatoric components of the tensor. The average value of the deviatoric part is about 35%. We conclude that the interactions between an explosive source and small-scale local heterogeneities of moderate amplitude may lead to a deviatoric contribution to the seismic moment, close to what is observed using regional data from nuclear test explosions.

Effective metrics and a fully covariant description of constitutive tensors in electrodynamics

NASA Astrophysics Data System (ADS)

Schuster, Sebastian; Visser, Matt

2017-12-01

Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-) material would provide an analogue space-time model or—vice versa—characterizing which given metric could be modeled with a (meta-) material. While the consistency conditions themselves are by now well known and studied, the form the metric takes once they are satisfied is not. This question is mostly easily answered by keeping the formalisms of the two research fields here in contact as close to each other as possible. While fully covariant formulations of the electrodynamics of media have been around for a long while, they are usually abandoned for (3 +1 )- or six-dimensional formalisms. Here we use the fully unified and fully covariant approach. This enables us even to generalize the consistency conditions for the existence of an effective metric to arbitrary background metrics beyond flat space-time electrodynamics. We also show how the familiar matrices for permittivity ɛ , permeability μ-1, and magnetoelectric effects ζ can be seen as the three independent pieces of the Bel decomposition for the constitutive tensor Za b c d, i.e., the components of an orthogonal decomposition with respect to a given observer with four-velocity Va. Finally, we use the Moore-Penrose pseudoinverse and the closely related pseudodeterminant to then gain the desired reconstruction of the effective metric in terms of the permittivity tensor ɛa b, the permeability tensor [μ-1]a b, and the magnetoelectric tensor ζa b, as an explicit function geff(ɛ ,μ-1,ζ ).

Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities.

PubMed

Frelat, Romain; Lindegren, Martin; Denker, Tim Spaanheden; Floeter, Jens; Fock, Heino O; Sguotti, Camilla; Stäbler, Moritz; Otto, Saskia A; Möllmann, Christian

2017-01-01

Understanding spatio-temporal dynamics of biotic communities containing large numbers of species is crucial to guide ecosystem management and conservation efforts. However, traditional approaches usually focus on studying community dynamics either in space or in time, often failing to fully account for interlinked spatio-temporal changes. In this study, we demonstrate and promote the use of tensor decomposition for disentangling spatio-temporal community dynamics in long-term monitoring data. Tensor decomposition builds on traditional multivariate statistics (e.g. Principal Component Analysis) but extends it to multiple dimensions. This extension allows for the synchronized study of multiple ecological variables measured repeatedly in time and space. We applied this comprehensive approach to explore the spatio-temporal dynamics of 65 demersal fish species in the North Sea, a marine ecosystem strongly altered by human activities and climate change. Our case study demonstrates how tensor decomposition can successfully (i) characterize the main spatio-temporal patterns and trends in species abundances, (ii) identify sub-communities of species that share similar spatial distribution and temporal dynamics, and (iii) reveal external drivers of change. Our results revealed a strong spatial structure in fish assemblages persistent over time and linked to differences in depth, primary production and seasonality. Furthermore, we simultaneously characterized important temporal distribution changes related to the low frequency temperature variability inherent in the Atlantic Multidecadal Oscillation. Finally, we identified six major sub-communities composed of species sharing similar spatial distribution patterns and temporal dynamics. Our case study demonstrates the application and benefits of using tensor decomposition for studying complex community data sets usually derived from large-scale monitoring programs.

An anisotropic elastoplastic constitutive formulation generalised for orthotropic materials

NASA Astrophysics Data System (ADS)

Mohd Nor, M. K.; Ma'at, N.; Ho, C. S.

2018-03-01

This paper presents a finite strain constitutive model to predict a complex elastoplastic deformation behaviour that involves very high pressures and shockwaves in orthotropic materials using an anisotropic Hill's yield criterion by means of the evolving structural tensors. The yield surface of this hyperelastic-plastic constitutive model is aligned uniquely within the principal stress space due to the combination of Mandel stress tensor and a new generalised orthotropic pressure. The formulation is developed in the isoclinic configuration and allows for a unique treatment for elastic and plastic orthotropy. An isotropic hardening is adopted to define the evolution of plastic orthotropy. The important feature of the proposed hyperelastic-plastic constitutive model is the introduction of anisotropic effect in the Mie-Gruneisen equation of state (EOS). The formulation is further combined with Grady spall failure model to predict spall failure in the materials. The proposed constitutive model is implemented as a new material model in the Lawrence Livermore National Laboratory (LLNL)-DYNA3D code of UTHM's version, named Material Type 92 (Mat92). The combination of the proposed stress tensor decomposition and the Mie-Gruneisen EOS requires some modifications in the code to reflect the formulation of the generalised orthotropic pressure. The validation approach is also presented in this paper for guidance purpose. The \\varvec{ψ} tensor used to define the alignment of the adopted yield surface is first validated. This is continued with an internal validation related to elastic isotropic, elastic orthotropic and elastic-plastic orthotropic of the proposed formulation before a comparison against range of plate impact test data at 234, 450 and {895 ms}^{-1} impact velocities is performed. A good agreement is obtained in each test.

Domain Processes in Ferroelectric Ceramics

DTIC Science & Technology

1994-04-14

elastic strain tensor and eikl is the Levi - Civita density. Eqs (11) and (12) has three nontrivial solutions: Xr3 = 0 (13) Xr"= -1 { [ 2sj2Q 12 -Sl I...ABSTRACT (aA~iMUM 200 wardt) This report Outlines the progres achieved during a two year effort sponsored by the AFOSR on the theoretical study of domain...INTRODUCTION This is the final progress report for this two year program sponsored by the Air Force Office of Scientific Research on "Domain Processes in

Micro-mechanics of fiber reinforced bounded and unbounded solids: effective local and non-local thermo-elastic properties, stress concentration factors, and edge effect

DTIC Science & Technology

2005-07-01

second order tensors of local eigenstresses and eigenstrains (transformation fields) which may arise by thermal expansion, plastic deformation, phase...with properties different from those of the homogeneous matrix) can be related to specified eigenstrain *( )e x by replacing the inhomogeneities...homogeneous matrix material only. rλ and mλ could be isotropic or anisotropic if the eigenstrain field *( )e x is uniform in Iv . So the strain at

Lithospheric Stress Tensor from Gravity and Lithospheric Structure Models

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi; Tenzer, Robert

2017-07-01

In this study we investigate the lithospheric stresses computed from the gravity and lithospheric structure models. The functional relation between the lithospheric stress tensor and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of stresses inside the lithosphere, while assuming the horizontal shear stress components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the stress spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear stress tensor components globally at the Moho interface. The results reveal that most of the lithospheric stresses are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest stresses within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced stresses (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading stresses along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated stress spectrum (between the degrees from 13 to 180).

X-ray μ-Laue diffraction analysis of Cu through-silicon vias: A two-dimensional and three-dimensional study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez, Dario Ferreira; Weleguela, Monica Larissa Djomeni; Audoit, Guillaume

2014-10-28

Here, white X-ray μ-beam Laue diffraction is developed and applied to investigate elastic strain distributions in three-dimensional (3D) materials, more specifically, for the study of strain in Cu 10 μm diameter–80 μm deep through-silicon vias (TSVs). Two different approaches have been applied: (i) two-dimensional μ-Laue scanning and (ii) μ-beam Laue tomography. 2D μ-Laue scans provided the maps of the deviatoric strain tensor integrated along the via length over an array of TSVs in a 100 μm thick sample prepared by Focused Ion Beam. The μ-beam Laue tomography analysis enabled to obtain the 3D grain and elemental distribution of both Cu and Si. Themore » position, size (about 3 μm), shape, and orientation of Cu grains were obtained. Radial profiles of the equivalent deviatoric strain around the TSVs have been derived through both approaches. The results from both methods are compared and discussed.« less

Constitutive relations describing creep deformation for multi-axial time-dependent stress states

NASA Astrophysics Data System (ADS)

McCartney, L. N.

1981-02-01

A THEORY of primary and secondary creep deformation in metals is presented, which is based upon the concept of tensor internal state variables and the principles of continuum mechanics and thermodynamics. The theory is able to account for both multi-axial and time-dependent stress and strain states. The wellknown concepts of elastic, anelastic and plastic strains follow naturally from the theory. Homogeneous stress states are considered in detail and a simplified theory is derived by linearizing with respect to the internal state variables. It is demonstrated that the model can be developed in such a way that multi-axial constant-stress creep data can be presented as a single relationship between an equivalent stress and an equivalent strain. It is shown how the theory may be used to describe the multi-axial deformation of metals which are subjected to constant stress states. The multi-axial strain response to a general cyclic stress state is calculated. For uni-axial stress states, square-wave loading and a thermal fatigue stress cycle are analysed.

Evaluation of elastic strain energy of spheroidal inclusions with uniform volumetric and shear eigenstrains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boehm, H.J.; Fischer, F.D.; Reisner, G.

The calculation of the elastic strain energy due to a uniform eigenstrain in an inclusion continues to be of high concern for various problems in material science such as nucleation conditions or transformation conditions for the inclusion. It is the main goal of this note to show that very easily programmable equations can be formulated for a general uniform eigenstrain tensor consisting of three different normal and three different shear strains. Although the authors appreciate the recently published results very much, they do not see any necessity to demonstrate in detail specific results since the following derivation presents a consistentmore » way to calculate the specific strain energy in very few steps. Specifically, a modified notation helps to split the usually lengthy expression into a group of easily expressible terms multiplied by the mixed product terms of the normal eigenstrains and the squares of the shear eigenstrains. Since all entities are expressed with respect to a coordinate frame attached to the inclusion any coordinate transformation can be avoided.« less

Nonlinear guided wave propagation in prestressed plates.

PubMed

Pau, Annamaria; Lanza di Scalea, Francesco

2015-03-01

The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress.

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

Identifying isotropic events using a regional moment tensor inversion

DOE PAGES

Ford, Sean R.; Dreger, Douglas S.; Walter, William R.

2009-01-17

We calculate the deviatoric and isotropic source components for 17 explosions at the Nevada Test Site, as well as 12 earthquakes and 3 collapses in the surrounding region of the western United States, using a regional time domain full waveform inversion for the complete moment tensor. The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination between explosions, earthquakes, and collapses. Confidence regions of the model parameters are estimated from the data misfit by assuming normally distributed parameter values. Wemore » investigate the sensitivity of the resolved parameters of an explosion to imperfect Earth models, inaccurate event depths, and data with low signal-to-noise ratio (SNR) assuming a reasonable azimuthal distribution of stations. In the band of interest (0.02–0.10 Hz) the source-type calculated from complete moment tensor inversion is insensitive to velocity model perturbations that cause less than a half-cycle shift (<5 s) in arrival time error if shifting of the waveforms is allowed. The explosion source-type is insensitive to an incorrect depth assumption (for a true depth of 1 km), and the goodness of fit of the inversion result cannot be used to resolve the true depth of the explosion. Noise degrades the explosive character of the result, and a good fit and accurate result are obtained when the signal-to-noise ratio is greater than 5. We assess the depth and frequency dependence upon the resolved explosive moment. As the depth decreases from 1 km to 200 m, the isotropic moment is no longer accurately resolved and is in error between 50 and 200%. Furthermore, even at the most shallow depth the resultant moment tensor is dominated by the explosive component when the data have a good SNR.« less

Response of turbulence subjected to a straining-relaxation-destraining cycle

NASA Astrophysics Data System (ADS)

Chen, Jun; Meneveau, Charles; Katz, Joseph

2004-11-01

The response of turbulence subjected to planar straining and de-straining is studied experimentally, and the impact of the applied distortions on the energy transfer across different length scales is quantified. The data are obtained using Planar Particle Image Velocimetry (PIV) in a water tank, in which high Reynolds number turbulence with very low mean velocity is generated by an array of spinning grids. Planar straining and de-straining mean flows are produced by pushing and pulling a rectangular piston towards, and away from, the bottom wall of the tank. The data are processed to yield the time evolution of Reynolds stresses, anisotropy tensors, turbulence kinetic energy production, and mean subgrid dissipation rate at various scales. During straining, the production rises rapidly. After the relaxation period the small-scale SGS stresses recover isotropy, but the Reynolds stresses at large scales still display significant anisotropy. When destraining is applied, a strong negative production (back-scattering) is observed, by which turbulence fluctuations return kinetic energy to the mean flow. Reversed energy transfer is also revealed in the vorticity fluctuations history. The experiment allows to disentangle in detail the causes for this global backscatter phenomenon in terms of non-equilibrium conditions of the Reynolds stresses, and to follow the trends as function of scale.

Numerical simulation of a compressible homogeneous, turbulent shear flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Feiereisen, W. J.; Reynolds, W. C.; Ferziger, J. H.

1981-01-01

A direct, low Reynolds number, numerical simulation was performed on a homogeneous turbulent shear flow. The full compressible Navier-Stokes equations were used in a simulation on the ILLIAC IV computer with a 64,000 mesh. The flow fields generated by the code are used as an experimental data base, to examine the behavior of the Reynols stresses in this simple, compressible flow. The variation of the structure of the stresses and their dynamic equations as the character of the flow changed is emphasized. The structure of the tress tensor is more heavily dependent on the shear number and less on the fluctuating Mach number. The pressure-strain correlation tensor in the dynamic uations is directly calculated in this simulation. These correlations are decomposed into several parts, as contrasted with the traditional incompressible decomposition into two parts. The performance of existing models for the conventional terms is examined, and a model is proposed for the 'mean fluctuating' part.

Proposal for a biometrics of the cortical surface: a statistical method for relative surface distance metrics

NASA Astrophysics Data System (ADS)

Bookstein, Fred L.

1995-08-01

Recent advances in computational geometry have greatly extended the range of neuroanatomical questions that can be approached by rigorous quantitative methods. One of the major current challenges in this area is to describe the variability of human cortical surface form and its implications for individual differences in neurophysiological functioning. Existing techniques for representation of stochastically invaginated surfaces do not conduce to the necessary parametric statistical summaries. In this paper, following a hint from David Van Essen and Heather Drury, I sketch a statistical method customized for the constraints of this complex data type. Cortical surface form is represented by its Riemannian metric tensor and averaged according to parameters of a smooth averaged surface. Sulci are represented by integral trajectories of the smaller principal strains of this metric, and their statistics follow the statistics of that relative metric. The diagrams visualizing this tensor analysis look like alligator leather but summarize all aspects of cortical surface form in between the principal sulci, the reliable ones; no flattening is required.

Hyperviscosity for unstructured ALE meshes

NASA Astrophysics Data System (ADS)

Cook, Andrew W.; Ulitsky, Mark S.; Miller, Douglas S.

2013-01-01

An artificial viscosity, originally designed for Eulerian schemes, is adapted for use in arbitrary Lagrangian-Eulerian simulations. Changes to the Eulerian model (dubbed 'hyperviscosity') are discussed, which enable it to work within a Lagrangian framework. New features include a velocity-weighted grid scale and a generalised filtering procedure, applicable to either structured or unstructured grids. The model employs an artificial shear viscosity for treating small-scale vorticity and an artificial bulk viscosity for shock capturing. The model is based on the Navier-Stokes form of the viscous stress tensor, including the diagonal rate-of-expansion tensor. A second-order version of the model is presented, in which Laplacian operators act on the velocity divergence and the grid-weighted strain-rate magnitude to ensure that the velocity field remains smooth at the grid scale. Unlike sound-speed-based artificial viscosities, the hyperviscosity model is compatible with the low Mach number limit. The new model outperforms a commonly used Lagrangian artificial viscosity on a variety of test problems.

The ascending reticular activating system from pontine reticular formation to the thalamus in the human brain.

PubMed

Yeo, Sang Seok; Chang, Pyung Hun; Jang, Sung Ho

2013-01-01

Action of the ascending reticular activating system (ARAS) on the cerebral cortex is responsible for achievement of consciousness. In this study, we attempted to reconstruct the lower single component of the ARAS from the reticular formation (RF) to the thalamus in the normal human brain using diffusion tensor imaging (DTI). Twenty six normal healthy subjects were recruited for this study. A 1.5-T scanner was used for scanning of diffusion tensor images, and the lower single component of the ARAS was reconstructed using FMRIB software. We utilized two ROIs for reconstruction of the lower single component of the ARAS: the seed ROI - the RF of the pons at the level of the trigeminal nerve entry zone, the target ROI - the intralaminar nuclei of the thalamus at the level of the commissural plane. The reconstructed ARAS originated from the pontine RF, ascended through the mesencephalic tegmentum just posterior to the red nucleus, and then terminated on the intralaminar nuclei of the thalamus. No significant differences in fractional anisotropy, mean diffusivity, and tract number were observed between hemispheres (p > 0.05). We reconstructed the lower single component of the ARAS from the RF to the thalamus in the human brain using DTI. The results of this study might be of value for the diagnosis and prognosis of patients with impaired consciousness.

Rotation Dynamics Do Not Determine the Unexpected Isotropy of Methyl Radical EPR Spectra.

PubMed

Benetis, Nikolas P; Dmitriev, Yurij; Mocci, Francesca; Laaksonen, Aatto

2015-09-03

A simple first-principles electronic structure computation, further qc (quantum chemistry) computation, of the methyl radical gives three equal hf (hyperfine) couplings for the three protons with the unpaired electron. The corresponding dipolar tensors were notably rhombic and had different orientations and regular magnitude components, as they should, but what the overall A-tensor was seen by the electron spin is a different story! The final g = (2.002993, 2.002993, 2.002231) tensor and the hf coupling results obtained in vacuum, at the B3LYP/EPRIII level of theory clearly indicate that in particular the above A = (-65.19, -65.19, 62.54) MHz tensor was axial to a first approximation without considering any rotational dynamics for the CH3. This approximation was not applicable, however, for the trifluoromethyl CF3 radical, a heavier and nonplanar rotor with very anisotropic hf coupling, used here for comparison. Finally, a derivation is presented explaining why there is actually no need for the CH3 radicals to consider additional rotational dynamics in order for the electron to obtain an axially symmetric hf (hyperfine) tensor by considering the simultaneous dipolar couplings of the three protons. An additional consequence is an almost isotropic A-tensor for the electron spin of the CH3 radical. To the best of our knowledge, this point has not been discussed in the literature before. The unexpected isotropy of the EPR parameters of CH3 was solely attributed to the rotational dynamics and was not clearly separated from the overall symmetry of the species. The present theoretical results allowed a first explanation of the "forbidden" satellite lines in the CH3 EPR spectrum. The satellites are a fingerprint of the radical rotation, helping thus in distinguishing the CH3 reorientation from quantum rotation at very low temperatures.

Strain effects on the anisotropic thermal transport in crystalline polyethylene

NASA Astrophysics Data System (ADS)

He, Jixiong; Kim, Kyunghoon; Wang, Yangchao; Liu, Jun

2018-01-01

Thermal transport in the axial direction of polymers has been extensively studied, while the strain effect on the thermal conductivity, especially in the radial direction, remains unknown. In this work, we calculated the thermal conductivity in the radial direction of a crystalline polyethylene model and simulated the uniaxial strain effect on the thermal conductivity tensor by molecular dynamics simulations. We found a strong size effect of the thermal transport in the radial direction and estimated that the phonon mean free path can be much larger than the prediction from the classic kinetic theory. We also found that the thermal conductivity in the axial direction increases dramatically with strain, while the thermal conductivity in the radial direction decreases with uniaxial strain. We attribute the reduction of thermal conductivity in the radial direction to the decreases in inter-chain van der Waals forces with strains. The facts that the chains in the crystalline polyethylene became stiffer and more ordered along the chain direction could be the reasons for the increasing thermal conductivity in the axial direction during stretching. Besides, we observed longer phonon lifetime in acoustic branches and higher group velocity in optical branches after uniaxial stretching. Our work provides fundamental understandings on the phonon transport in crystalline polymers, the structure-property relationship in crystalline polymers, and the strain effect in highly anisotropic materials.

Second moment closure analysis of the backstep flow database

NASA Technical Reports Server (NTRS)

Parneix, S.; Laurence, D.; Durbin, P.

1996-01-01

A Second Moment Closure computation (SMC) is compared in detail with the Direct Numerical Simulation (DNS) data of Le and Moin for the backstep flow at Re = 5,000 in an attempt to understand why the intensity of the backflow and, consequently, the friction coefficient in the recirculation bubble are severely underestimated. The data show that this recirculation bubble is far from being laminar except in the very near wall layer. A novel 'differential a priori' procedure was used, in which the full transport equation for one isolated component of the Reynolds stress tensor was solved using DNS data as input. Conclusions are then different from what would have been deduced by comparing a full simulation to a DNS. One cause of discrepancy was traced back to insufficient transfer of energy to the normal stress by pressure strain, but was not cured. A significant finding, confirmed by the DNS data in the core region of a channel flow, is that the coefficient that controls destruction of dissipation, C epsilon(sub 2), should be decreased by a factor of 2 when production is vanishing. This is also the case in the recirculation bubble, and a new formulation has cured 25% of the backflow discrepancy.

Effect of doping on the intersubband absorption in Si- and Ge-doped GaN/AlN heterostructures

NASA Astrophysics Data System (ADS)

Ajay, A.; Lim, C. B.; Browne, D. A.; Polaczyński, J.; Bellet-Amalric, E.; Bleuse, J.; den Hertog, M. I.; Monroy, E.

2017-10-01

In this paper, we study band-to-band and intersubband (ISB) characteristics of Si- and Ge-doped GaN/AlN heterostructures (planar and nanowires) structurally designed to absorb in the short-wavelength infrared region, particularly at 1.55 μm. Regarding the band-to-band properties, we discuss the variation of the screening of the internal electric field by free carriers, as a function of the doping density and well/nanodisk size. We observe that nanowire heterostructures consistently present longer photoluminescence decay times than their planar counterparts, which supports the existence of an in-plane piezoelectric field associated to the shear component of the strain tensor in the nanowire geometry. Regarding the ISB characteristics, we report absorption covering 1.45-1.75 μm using Ge-doped quantum wells, with comparable performance to Si-doped planar heterostructures. We also report similar ISB absorption in Si- and Ge-doped nanowire heterostructures indicating that the choice of dopant is not an intrinsic barrier for observing ISB phenomena. The spectral shift of the ISB absorption as a function of the doping concentration due to many body effects confirms that Si and Ge efficiently dope GaN/AlN nanowire heterostructures.

Solid-state EPR strategies for the structural characterization of paramagnetic NO adducts of frustrated Lewis pairs (FLPs)

NASA Astrophysics Data System (ADS)

de Oliveira, Marcos; Wiegand, Thomas; Elmer, Lisa-Maria; Sajid, Muhammad; Kehr, Gerald; Erker, Gerhard; Magon, Claudio José; Eckert, Hellmut

2015-03-01

Anisotropic interactions present in three new nitroxide radicals prepared by N,N addition of NO to various borane-phosphane frustrated Lewis pairs (FLPs) have been characterized by continuous-wave (cw) and pulsed X-band EPR spectroscopies in solid FLP-hydroxylamine matrices at 100 K. Anisotropic g-tensor values and 11B, 14N, and 31P hyperfine coupling tensor components have been extracted from continuous-wave lineshape analyses, electron spin echo envelope modulation (ESEEM), and hyperfine sublevel correlation spectroscopy (HYSCORE) experiments with the help of computer simulation techniques. Suitable fitting constraints are developed on the basis of density functional theory (DFT) calculations. These calculations reveal that different from the situation in standard nitroxide radicals (TEMPO), the g-tensors are non-coincident with any of the nuclear hyperfine interaction tensors. The determination of these interaction parameters turns out to be successful, as the cw- and pulse EPR experiments are highly complementary in informational content. While the continuous-wave lineshape is largely influenced by the anisotropic hyperfine coupling to 14N and 31P, the ESEEM and HYSCORE spectra contain important information about the 11B hyperfine coupling and nuclear electric quadrupolar interaction. The set of cw- and pulsed EPR experiments, with fitting constraints developed by DFT calculations, defines an efficient strategy for the structural analysis of paramagnetic FLP adducts.

Solid-state EPR strategies for the structural characterization of paramagnetic NO adducts of frustrated Lewis pairs (FLPs)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oliveira, Marcos de; Magon, Claudio José; Wiegand, Thomas

2015-03-28

Anisotropic interactions present in three new nitroxide radicals prepared by N,N addition of NO to various borane-phosphane frustrated Lewis pairs (FLPs) have been characterized by continuous-wave (cw) and pulsed X-band EPR spectroscopies in solid FLP-hydroxylamine matrices at 100 K. Anisotropic g-tensor values and {sup 11}B, {sup 14}N, and {sup 31}P hyperfine coupling tensor components have been extracted from continuous-wave lineshape analyses, electron spin echo envelope modulation (ESEEM), and hyperfine sublevel correlation spectroscopy (HYSCORE) experiments with the help of computer simulation techniques. Suitable fitting constraints are developed on the basis of density functional theory (DFT) calculations. These calculations reveal that differentmore » from the situation in standard nitroxide radicals (TEMPO), the g-tensors are non-coincident with any of the nuclear hyperfine interaction tensors. The determination of these interaction parameters turns out to be successful, as the cw- and pulse EPR experiments are highly complementary in informational content. While the continuous-wave lineshape is largely influenced by the anisotropic hyperfine coupling to {sup 14}N and {sup 31}P, the ESEEM and HYSCORE spectra contain important information about the {sup 11}B hyperfine coupling and nuclear electric quadrupolar interaction. The set of cw- and pulsed EPR experiments, with fitting constraints developed by DFT calculations, defines an efficient strategy for the structural analysis of paramagnetic FLP adducts.« less

Complete Moment Tensor Determination of Induced Seismicity in Unconventional and Conventional Oil/Gas Fields

NASA Astrophysics Data System (ADS)

Gu, C.; Li, J.; Toksoz, M. N.

2013-12-01

Induced seismicity occurs both in conventional oil/gas fields due to production and water injection and in unconventional oil/gas fields due to hydraulic fracturing. Source mechanisms of these induced earthquakes are of great importance for understanding their causes and the physics of the seismic processes in reservoirs. Previous research on the analysis of induced seismic events in conventional oil/gas fields assumed a double couple (DC) source mechanism. However, recent studies have shown a non-negligible percentage of a non-double-couple (non-DC) component of source moment tensor in hydraulic fracturing events (Šílený et al., 2009; Warpinski and Du, 2010; Song and Toksöz, 2011). In this study, we determine the full moment tensor of the induced seismicity data in a conventional oil/gas field and for hydrofrac events in an unconventional oil/gas field. Song and Toksöz (2011) developed a full waveform based complete moment tensor inversion method to investigate a non-DC source mechanism. We apply this approach to the induced seismicity data from a conventional gas field in Oman. In addition, this approach is also applied to hydrofrac microseismicity data monitored by downhole geophones in four wells in US. We compare the source mechanisms of induced seismicity in the two different types of gas fields and explain the differences in terms of physical processes.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

The self-similarly expanding Eshelby ellipsoidal inclusion: II. The Dynamic Eshelby Tensor for the expanding sphere

NASA Astrophysics Data System (ADS)

Ni, Luqun; Markenscoff, Xanthippi

2016-11-01

The field solution of a self-similarly (subsonically) expanding Eshelby ellipsoidal inclusion obtained in Part I is evaluated for the case of the expanding spherical inclusion under general uniform eigenstrain ɛij* in self-similar motion R = υt, starting from zero dimension. The particle velocity in the interior domain vanishes and the displacement gradient is constant exhibiting the Eshelby property in the self-similar dynamic case. All components of the interior and exterior Dynamic Eshelby Tensor are obtained for the sphere, with the interior ones depending on the wave speeds and the expansion speed of the inclusion, while the exterior ones depend, in addition, on the variable of self-similarity r / t and the direction of the field point. By a limiting procedure the static Eshelby tensor both interior and exterior is retrieved, thus making the static inclusion a special limit of the dynamic self-similarly expanding one. The jump of the particle velocity across the moving inclusion boundary is obtained, and it depends only on the wave and expansion speeds and the direction of the normal.

Critical phenomena at the complex tensor ordering phase transition

NASA Astrophysics Data System (ADS)

Boettcher, Igor; Herbut, Igor F.

2018-02-01

We investigate the critical properties of the phase transition towards complex tensor order that has been proposed to occur in spin-orbit-coupled superconductors. For this purpose, we formulate the bosonic field theory for fluctuations of the complex irreducible second-rank tensor order parameter close to the transition. We then determine the scale dependence of the couplings of the theory by means of the perturbative renormalization group (RG). For the isotropic system, we generically detect a fluctuation-induced first-order phase transition. The initial values for the running couplings are determined by the underlying microscopic model for the tensorial order. As an example, we study three-dimensional Luttinger semimetals with electrons at a quadratic band-touching point. Whereas the strong-coupling transition of the model receives substantial fluctuation corrections, the weak-coupling transition at low temperatures is rendered only weakly first order due to the presence of a fixed point in the vicinity of the RG trajectory. If the number of fluctuating complex components of the order parameter is reduced by cubic anisotropy, the theory maps onto the field theory for frustrated magnetism.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, Jong-Kyu; Logan, Nikolas C.

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly formore » each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.« less

Spatially Resolved Measurement of the Stress Tensor in Thin Membranes Using Bending Waves

NASA Astrophysics Data System (ADS)

Waitz, Reimar; Lutz, Carolin; Nößner, Stephan; Hertkorn, Michael; Scheer, Elke

2015-04-01

The mode shape of bending waves in thin silicon and silicon-carbide membranes is measured as a function of space and time, using a phase-shift interferometer with stroboscopic light. The mode shapes hold information about all the relevant mechanical parameters of the samples, including the spatial distribution of static prestress. We present a simple algorithm to obtain a map of the lateral tensor components of the prestress, with a spatial resolution much better than the wavelength of the bending waves. The method is not limited to measuring the stress of bending waves. It is applicable in almost any situation, where the fields determining the state of the system can be measured as a function of space and time.

Definition of Contravariant Velocity Components

NASA Technical Reports Server (NTRS)

Hung, Ching-moa; Kwak, Dochan (Technical Monitor)

2002-01-01

In this paper we have reviewed the basics of tensor analysis in an attempt to clarify some misconceptions regarding contravariant and covariant vector components as used in fluid dynamics. We have indicated that contravariant components are components of a given vector expressed as a unique combination of the covariant base vector system and, vice versa, that the covariant components are components of a vector expressed with the contravariant base vector system. Mathematically, expressing a vector with a combination of base vector is a decomposition process for a specific base vector system. Hence, the contravariant velocity components are decomposed components of velocity vector along the directions of coordinate lines, with respect to the covariant base vector system. However, the contravariant (and covariant) components are not physical quantities. Their magnitudes and dimensions are controlled by their corresponding covariant (and contravariant) base vectors.

The terrestrial gravitational wave environment from known sources

NASA Technical Reports Server (NTRS)

Webbink, Ronald F.

1993-01-01

The objective of this project was to produce a gravitational wave spectral line list of all known binary stars producing expected strain amplitudes at Earth in excess of h = 10 (exp -21), or gravitational wave fluxes in excess of F = 10 (exp -12) erg cm(exp -2) s(exp -1). These strain and flux limits lie above the anticipated detection thresholds for space-borne laser interferometers capable of detecting gravitational radiation in the 10 micron Hz to 1 Hz frequency range. The source list was intended to provide frequency (including each harmonic), amplitude and phase (for each polarization and harmonic), and celestial coordinates for each system, lacking only the orientation of the principal polarization axis with respect to the pole of the coordinate system, and the sign of the source phase and frequency (or, equivalently, of the sense of rotation of the strain tensor with time) from providing a complete source description. Such a spectral line list would lay essential groundwork for high-sensitivity, low-frequency searches for gravitational radiation.

Elastic field of a spherical inclusion with non-uniform eigenfields in second strain gradient elasticity

NASA Astrophysics Data System (ADS)

Delfani, M. R.; Latifi Shahandashti, M.

2017-09-01

In this paper, within the complete form of Mindlin's second strain gradient theory, the elastic field of an isolated spherical inclusion embedded in an infinitely extended homogeneous isotropic medium due to a non-uniform distribution of eigenfields is determined. These eigenfields, in addition to eigenstrain, comprise eigen double and eigen triple strains. After the derivation of a closed-form expression for Green's function associated with the problem, two different cases of non-uniform distribution of the eigenfields are considered as follows: (i) radial distribution, i.e. the distributions of the eigenfields are functions of only the radial distance of points from the centre of inclusion, and (ii) polynomial distribution, i.e. the distributions of the eigenfields are polynomial functions in the Cartesian coordinates of points. While the obtained solution for the elastic field of the latter case takes the form of an infinite series, the solution to the former case is represented in a closed form. Moreover, Eshelby's tensors associated with the two mentioned cases are obtained.

Induced seismicity at the UK `hot dry rock' test site for geothermal energy production

NASA Astrophysics Data System (ADS)

Li, Xun; Main, Ian; Jupe, Andrew

2018-07-01

In enhanced geothermal systems (EGS), fluid is injected at high pressure in order to stimulate fracturing and/or fluid flow through otherwise relatively impermeable underlying hot rocks to generate power and/or heat. The stimulation induces microearthquakes whose precise triggering mechanism and relationship to new and pre-existing fracture networks are still the subject of some debate. Here, we analyse the data set for induced microearthquakes at the UK `hot dry rock' experimental geothermal site (Rosemanowes, Cornwall). We quantify the evolution of several metrics used to characterise induced seismicity, including the seismic strain partition factor and the `seismogenic index'. The results show a low strain partition factor of 0.01 per cent and a low seismogenic index indicating that aseismic processes dominate. We also analyse the spatio-temporal distribution of hypocentres, using simple models for the evolution of hydraulic diffusivity by (1) isotropic and (2) anisotropic pore-pressure relaxation. The principal axes of the diffusivity or permeability tensor inferred from the spatial distribution of earthquake foci are aligned parallel to the present-day stress field, although the maximum permeability is vertical, whereas the maximum principal stress is horizontal. Our results are consistent with a triggering mechanism that involves (1) seismic shear slip along optimally oriented pre-existing fractures, (2) a large component of aseismic slip with creep and (3) activation of tensile fractures as hydraulic conduits created by both the present-day stress field and by the induced shear slip, both exploiting pre-existing joint sets exposed in borehole data.

Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities

PubMed Central

Lindegren, Martin; Denker, Tim Spaanheden; Floeter, Jens; Fock, Heino O.; Sguotti, Camilla; Stäbler, Moritz; Otto, Saskia A.; Möllmann, Christian

2017-01-01

Understanding spatio-temporal dynamics of biotic communities containing large numbers of species is crucial to guide ecosystem management and conservation efforts. However, traditional approaches usually focus on studying community dynamics either in space or in time, often failing to fully account for interlinked spatio-temporal changes. In this study, we demonstrate and promote the use of tensor decomposition for disentangling spatio-temporal community dynamics in long-term monitoring data. Tensor decomposition builds on traditional multivariate statistics (e.g. Principal Component Analysis) but extends it to multiple dimensions. This extension allows for the synchronized study of multiple ecological variables measured repeatedly in time and space. We applied this comprehensive approach to explore the spatio-temporal dynamics of 65 demersal fish species in the North Sea, a marine ecosystem strongly altered by human activities and climate change. Our case study demonstrates how tensor decomposition can successfully (i) characterize the main spatio-temporal patterns and trends in species abundances, (ii) identify sub-communities of species that share similar spatial distribution and temporal dynamics, and (iii) reveal external drivers of change. Our results revealed a strong spatial structure in fish assemblages persistent over time and linked to differences in depth, primary production and seasonality. Furthermore, we simultaneously characterized important temporal distribution changes related to the low frequency temperature variability inherent in the Atlantic Multidecadal Oscillation. Finally, we identified six major sub-communities composed of species sharing similar spatial distribution patterns and temporal dynamics. Our case study demonstrates the application and benefits of using tensor decomposition for studying complex community data sets usually derived from large-scale monitoring programs. PMID:29136658

Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding.

PubMed

Hanni, Matti; Lantto, Perttu; Runeberg, Nino; Jokisaari, Jukka; Vaara, Juha

2004-09-22

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order Møller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.

A new formulation of the dispersion tensor in homogeneous porous media

NASA Astrophysics Data System (ADS)

Valdés-Parada, Francisco J.; Lasseux, Didier; Bellet, Fabien

2016-04-01

Dispersion is the result of two mass transport processes, namely molecular diffusion, which is a pure mixing effect and hydrodynamic dispersion, which combines mixing and spreading. The identification of each contribution is crucial and is often misinterpreted. Traditionally, under a volume averaging framework, a single closure problem is solved and the resulting fields are substituted into diffusive and dispersive filters. However the diffusive filter (that leads to the effective diffusivity) allows passing information from convection, which leads to an incorrect definition of the effective medium coefficients composing the total dispersion tensor. In this work, we revisit the definitions of the effective diffusivity and hydrodynamic dispersion tensors using the method of volume averaging. Our analysis shows that, in the context of laminar flow with or without inertial effects, two closure problems need to be computed in order to correctly define the corresponding effective medium coefficients. The first closure problem is associated to momentum transport and needs to be solved for a prescribed Reynolds number and flow orientation. The second closure problem is related to mass transport and it is solved first with a zero Péclet number and second with the required Péclet number and flow orientation. All the closure problems are written using closure variables only as required by the upscaling method. The total dispersion tensor is shown to depend on the microstructure, macroscopic flow angles, the cell (or pore) Péclet number and the cell (or pore) Reynolds number. It is non-symmetric in the general case. The condition for quasi-symmetry is highlighted. The functionality of the longitudinal and transverse components of this tensor with the flow angle is investigated for a 2D model porous structure obtaining consistent results with previous studies.