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.

Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes

NASA Astrophysics Data System (ADS)

Levi, Adam; Ori, Amos

2015-05-01

Computation of the renormalized stress-energy tensor is the most serious obstacle in studying the dynamical, self-consistent, semiclassical evaporation of a black hole in 4D. The difficulty arises from the delicate regularization procedure for the stress-energy tensor, combined with the fact that in practice the modes of the field need to be computed numerically. We have developed a new method for numerical implementation of the point-splitting regularization in 4D, applicable to the renormalized stress-energy tensor as well as to ⟨ϕ2⟩ren , namely the renormalized ⟨ϕ2⟩. So far we have formulated two variants of this method: t -splitting (aimed for stationary backgrounds) and angular splitting (for spherically symmetric backgrounds). In this paper we introduce our basic approach, and then focus on the t -splitting variant, which is the simplest of the two (deferring the angular-splitting variant to a forthcoming paper). We then use this variant, as a first stage, to calculate ⟨ϕ2⟩ren in Schwarzschild spacetime, for a massless scalar field in the Boulware state. We compare our results to previous ones, obtained by a different method, and find full agreement. We discuss how this approach can be applied (using the angular-splitting variant) to analyze the dynamical self-consistent evaporation of black holes.

Generalized recursion relations for correlators in the gauge-gravity correspondence.

PubMed

Raju, Suvrat

2011-03-04

We show that a generalization of the Britto-Cachazo-Feng-Witten recursion relations gives a new and efficient method of computing correlation functions of the stress tensor or conserved currents in conformal field theories with an (d+1)-dimensional anti-de Sitter space dual, for d≥4, in the limit where the bulk theory is approximated by tree-level Yang-Mills theory or gravity. In supersymmetric theories, additional correlators of operators that live in the same multiplet as a conserved current or stress tensor can be computed by these means.

Conservation laws and stress-energy-momentum tensors for systems with background fields

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

Gratus, Jonathan, E-mail: j.gratus@lancaster.ac.uk; The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD; Obukhov, Yuri N., E-mail: yo@thp.uni-koeln.de

2012-10-15

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics inmore » media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.« less

Use of non-fault fractures in stress tensor reconstruction using the Mohr Circle with the Win-tensor program

NASA Astrophysics Data System (ADS)

Delvaux, Damien

2016-04-01

Paleostress inversion of geological fault-slip data is usually done using the directional part of the applied stress tensor on a slip plane and comparing it with the observed slip lines. However, this method do not fully exploit the brittle data sets as those are composed of shear and tension fractures, in addition to faults. Brittle deformation can be decomposed in two steps. An initial fracture/failure in previously intact rock generate extension/tensile fractures or shear fractures, both without visible opening or displacement. This first step may or not be followed by fracture opening to form tension joints, frictional shearing to form shear faults, or a combination of opening and shearing which produces hybrid fractures. Fractured rock outcrop contain information of the stress conditions that acted during both brittle deformation steps. The purpose here is to investigate how the fracture pattern generated during the initial fracture/failure step might be used in paleostress reconstruction. Each fracture is represented on the Mohr Circle by its resolved normal and shear stress magnitudes. We consider the typical domains on the Mohr circle where the different types de fractures nucleate (tension, hybrid, shear and compression fractures), as well the domain which contain reactivated fractures (faults reactivating an initial fracture plane). In function of the fracture type defined in the field, a "distance" is computed on the Mohr circle between each point and its expected corresponding nucleation/reactivation domain. This "Mohr Distance" is then used as function to minimize during the inversion. We implemented this new function in the Win-Tensor program, and tested it with natural and synthetic data sets from different stress regimes. It can be used alone using only the Mohr Distance on each plane (function F10), or combined with the angular misfit between observed striae and resolved shear directions (composite function F11). When used alone (F10), only the 3 stress axes can be determined and the stress ratio R (sigma 2-3)/sigma1-3) has to be pre-determined. With the combined function (F11), it provide an additional constrain to the classical angular misfit. With data sets composed of a majority of neoformed fractures, stress inversion using the Mohr Distance F10 function provide a good approximation of the 3 stress axes (using only the fracture data) as compared with the results of the F11 composite function (using also the observed slip lines). Tensor program is available at (http://www.damiendelvaux.be/Tensor/tensor-index.html).

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

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

Levashov, V. A.

2016-03-07

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectorsmore » of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ{sub 1} ≥ λ{sub 2} ≥ λ{sub 3} ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ{sub 2}/λ{sub 1}) and (λ{sub 3}/λ{sub 2}) are essentially identical to each other in the liquids state. We also found that λ{sub 2} tends to be equal to the geometric average of λ{sub 1} and λ{sub 3}. In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.« less

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors.

PubMed

Levashov, V A

2016-03-07

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ1 ≥ λ2 ≥ λ3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ2/λ1) and (λ3/λ2) are essentially identical to each other in the liquids state. We also found that λ2 tends to be equal to the geometric average of λ1 and λ3. In our view, correlations between the eigenvalues may represent "the Poisson ratio effect" at the atomic scale.

Quantum electromagnetic stress tensor in an inhomogeneous medium

NASA Astrophysics Data System (ADS)

Parashar, Prachi; Milton, Kimball A.; Li, Yang; Day, Hannah; Guo, Xin; Fulling, Stephen A.; Cavero-Peláez, Inés

2018-06-01

Continuing a program of examining the behavior of the vacuum expectation value of the stress tensor in a background which varies only in a single direction, we here study the electromagnetic stress tensor in a medium with permittivity depending on a single spatial coordinate, specifically, a planar dielectric half-space facing a vacuum region. There are divergences occurring that are regulated by temporal and spatial point splitting, which have a universal character for both transverse electric and transverse magnetic modes. The nature of the divergences depends on the model of dispersion adopted. And there are singularities occurring at the edge between the dielectric and vacuum regions, which also have a universal character, depending on the structure of the discontinuities in the material properties there. Remarks are offered concerning renormalization of such models, and the significance of the stress tensor. The ambiguity in separating "bulk" and "scattering" parts of the stress tensor is discussed.

SORTAN: a Unix program for calculation and graphical presentation of fault slip as induced by stresses

NASA Astrophysics Data System (ADS)

Pascal, Christophe

2004-04-01

Stress inversion programs are nowadays frequently used in tectonic analysis. The purpose of this family of programs is to reconstruct the stress tensor characteristics from fault slip data acquired in the field or derived from earthquake focal mechanisms (i.e. inverse methods). Until now, little attention has been paid to direct methods (i.e. to determine fault slip directions from an inferred stress tensor). During the 1990s, the fast increase in resolution in 3D seismic reflection techniques made it possible to determine the geometry of subsurface faults with a satisfactory accuracy but not to determine precisely their kinematics. This recent improvement allows the use of direct methods. A computer program, namely SORTAN, is introduced. The program is highly portable on Unix platforms, straightforward to install and user-friendly. The computation is based on classical stress-fault slip relationships and allows for fast treatment of a set of faults and graphical presentation of the results (i.e. slip directions). In addition, the SORTAN program permits one to test the sensitivity of the results to input uncertainties. It is a complementary tool to classical stress inversion methods and can be used to check the mechanical consistency and the limits of structural interpretations based upon 3D seismic reflection surveys.

Stress formulation in the all-electron full-potential linearized augmented plane wave method

NASA Astrophysics Data System (ADS)

Nagasako, Naoyuki; Oguchi, Tamio

2012-02-01

Stress formulation in the linearlized augmented plane wave (LAPW) method has been proposed in 2002 [1] as an extension of the force formulation in the LAPW method [2]. However, pressure calculations only for Al and Si were reported in Ref.[1] and even now stress calculations have not yet been fully established in the LAPW method. In order to make it possible to efficiently relax lattice shape and atomic positions simultaneously and to precisely evaluate the elastic constants in the LAPW method, we reformulate stress formula in the LAPW method with the Soler-Williams representation [3]. Validity of the formulation is tested by comparing the pressure obtained as the trace of stress tensor with that estimated from total energies for a wide variety of material systems. Results show that pressure is estimated within the accuracy of less than 0.1 GPa. Calculations of the shear elastic constant show that the shear components of the stress tensor are also precisely computed with the present formulation [4].[4pt] [1] T. Thonhauser et al., Solid State Commun. 124, 275 (2002).[0pt] [2] R. Yu et al., Phys. Rev. B 43, 6411 (1991).[0pt] [3] J. M. Soler and A. R. Williams, Phys. Rev. B 40, 1560 (1989).[0pt] [4] N. Nagasako and T. Oguchi, J. Phys. Soc. Jpn. 80, 024701 (2011).

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.

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.

Assessment of Reynolds stress components and turbulent pressure loss using 4D flow MRI with extended motion encoding.

PubMed

Haraldsson, Henrik; Kefayati, Sarah; Ahn, Sinyeob; Dyverfeldt, Petter; Lantz, Jonas; Karlsson, Matts; Laub, Gerhard; Ebbers, Tino; Saloner, David

2018-04-01

To measure the Reynolds stress tensor using 4D flow MRI, and to evaluate its contribution to computed pressure maps. A method to assess both velocity and Reynolds stress using 4D flow MRI is presented and evaluated. The Reynolds stress is compared by cross-sectional integrals of the Reynolds stress invariants. Pressure maps are computed using the pressure Poisson equation-both including and neglecting the Reynolds stress. Good agreement is seen for Reynolds stress between computational fluid dynamics, simulated MRI, and MRI experiment. The Reynolds stress can significantly influence the computed pressure loss for simulated (eg, -0.52% vs -15.34% error; P < 0.001) and experimental (eg, 306 ± 11 vs 203 ± 6 Pa; P < 0.001) data. A 54% greater pressure loss is seen at the highest experimental flow rate when accounting for Reynolds stress (P < 0.001). 4D flow MRI with extended motion-encoding enables quantification of both the velocity and the Reynolds stress tensor. The additional information provided by this method improves the assessment of pressure gradients across a stenosis in the presence of turbulence. Unlike conventional methods, which are only valid if the flow is laminar, the proposed method is valid for both laminar and disturbed flow, a common presentation in diseased vessels. Magn Reson Med 79:1962-1971, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole.

PubMed

Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten

2017-04-07

We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.

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).

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.

NIED seismic moment tensor catalogue for regional earthquakes around Japan: quality test and application

NASA Astrophysics Data System (ADS)

Kubo, Atsuki; Fukuyama, Eiichi; Kawai, Hiroyuki; Nonomura, Ken'ichi

2002-10-01

We have examined the quality of the National Research Institute for Earth Science and Disaster Prevention (NIED) seismic moment tensor (MT) catalogue obtained using a regional broadband seismic network (FREESIA). First, we examined using synthetic waveforms the robustness of the solutions with regard to data noise as well as to errors in the velocity structure and focal location. Then, to estimate the reliability, robustness and validity of the catalogue, we compared it with the Harvard centroid moment tensor (CMT) catalogue as well as the Japan Meteorological Agency (JMA) focal mechanism catalogue. We found out that the NIED catalogue is consistent with Harvard and JMA catalogues within the uncertainty of 0.1 in moment magnitude, 10 km in depth, and 15° in direction of the stress axes. The NIED MT catalogue succeeded in reducing to 3.5 the lower limit of moment magnitude above which the moment tensor could be reliably estimated. Finally, we estimated the stress tensors in several different regions by using the NIED MT catalogue. This enables us to elucidate the stress/deformation field in and around the Japanese islands to understand the mode of deformation and applied stress. Moreover, we identified a region of abnormal stress in a swarm area from stress tensor estimates.

Reversible and dissipative macroscopic contributions to the stress tensor: active or passive?

PubMed

Brand, H R; Pleiner, H; Svenšek, D

2014-09-01

The issue of dynamic contributions to the macroscopic stress tensor has been of high interest in the field of bio-inspired active systems over the last few years. Of particular interest is a direct coupling ("active term") of the stress tensor with the order parameter, the latter describing orientational order induced by active processes. Here we analyze more generally possible reversible and irreversible dynamic contributions to the stress tensor for various passive and active macroscopic systems. This includes systems with tetrahedral/octupolar order, polar and non-polar (chiral) nematic and smectic liquid crystals, as well as active fluids with a dynamic preferred (polar or non-polar) direction. We show that it cannot a priori be seen, neither from the symmetry properties of the macroscopic variables involved, nor from the structure of the cross-coupling contributions to the stress tensor, whether the system studied is active or passive. Rather, that depends on whether the variables that give rise to those cross-couplings in the stress tensor are driven or not. We demonstrate that several simplified descriptions of active systems in the literature that neglect the necessary counter term to the active term violate linear irreversible thermodynamics and lead to an unphysical contribution to the entropy production.

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.

From orientation to magnitudes in paleostress determinations using fault slip data

NASA Astrophysics Data System (ADS)

Angelier, Jacques

Determinations of reduced stress tensors using fault slip data yield the orientation of principal stress axes and the ratio Φ of the differences between principal stress magnitudes. The use of rupture and friction laws allows determination of the two remaining unknowns, that is, the reconstruction of the complete stress tensor. Taking into account the depth of overburden brings an additional constraint. The method is applied and discussed in the case of the Hoover Dam site (western U.S.A.), where large data sets and rock mechanics information are available. Differences between intact sample and rock mass properties account for apparent disagreements between paleostress levels determined in similar tectonic environments. Pore pressure plays an important role; where information about pore pressure is absent, zero and hydrostatic pore pressure cases should be considered as limits.

On actions for (entangling) surfaces and DCFTs

NASA Astrophysics Data System (ADS)

Armas, Jay; Tarrío, Javier

2018-04-01

The dynamics of surfaces and interfaces describe many physical systems, including fluid membranes, entanglement entropy and the coupling of defects to quantum field theories. Based on the formulation of submanifold calculus developed by Carter, we introduce a new variational principle for (entangling) surfaces. This principle captures all diffeomorphism constraints on surface/interface actions and their associated spacetime stress tensor. The different couplings to the geometric tensors appearing in the surface action are interpreted in terms of response coefficients within elasticity theory. An example of a surface action with edges at the two-derivative level is studied, including both the parity-even and parity-odd sectors. Its conformally invariant counterpart restricts the type of conformal anomalies that can appear in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics, it is shown that classification methods can be used to constrain the stress tensor of (entangling) surfaces at a given order in derivatives. This analysis reveals a purely geometric parity-odd contribution to the Young modulus of a thin elastic membrane. Extending this novel variational principle to BCFTs and DCFTs in curved spacetimes allows to obtain the Ward identities for diffeomorphism and Weyl transformations. In this context, we provide a formal derivation of the contact terms in the stress tensor and of the displacement operator for a broad class of actions.

Triaxial X-Ray Diffraction Method and its Application to Monitor Residual Stress in Surface Layers after High-Feed Milling

NASA Astrophysics Data System (ADS)

Zaušková, Lucia; Czán, Andrej; Šajgalík, Michal; Pobijak, Jozef; Mikloš, Matej

2017-10-01

High-feed milling is a milling method characteristic with shallow depth of cut and high feed rate to maximize the amount of removed metal from a part, generating residual stresses in the surface and subsurface layers of the machined parts. The residual stress has a large influence on the functional properties of the components. The article is focused on the application of triaxial x-ray diffraction method to monitor residual stresses after high feed milling. Significance of triaxial measuring method is the capability of measuring in different angles so it is possible to acquire stress tensor containing normal and shear stress components.

Damped regional-scale stress inversions: Methodology and examples for southern California and the Coalinga aftershock sequence

USGS Publications Warehouse

Hardebeck, J.L.; Michael, A.J.

2006-01-01

We present a new focal mechanism stress inversion technique to produce regional-scale models of stress orientation containing the minimum complexity necessary to fit the data. Current practice is to divide a region into small subareas and to independently fit a stress tensor to the focal mechanisms of each subarea. This procedure may lead to apparent spatial variability that is actually an artifact of overfitting noisy data or nonuniquely fitting data that does not completely constrain the stress tensor. To remove these artifacts while retaining any stress variations that are strongly required by the data, we devise a damped inversion method to simultaneously invert for stress in all subareas while minimizing the difference in stress between adjacent subareas. This method is conceptually similar to other geophysical inverse techniques that incorporate damping, such as seismic tomography. In checkerboard tests, the damped inversion removes the stress rotation artifacts exhibited by an undamped inversion, while resolving sharper true stress rotations than a simple smoothed model or a moving-window inversion. We show an example of a spatially damped stress field for southern California. The methodology can also be used to study temporal stress changes, and an example for the Coalinga, California, aftershock sequence is shown. We recommend use of the damped inversion technique for any study examining spatial or temporal variations in the stress field.

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.

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Complete stress tensor determination by microearthquake analysis

NASA Astrophysics Data System (ADS)

Slunga, R.

2010-12-01

Jones 1984 found that half of the shallow strike-slip EQ in California had at least one M>2 foreshock. By the Gutenberg law this means at least 3-20 M>0 (low b-value 0.4-0.8). deformations within the crust. This was confirmed by observations in Iceland after 1990 when anew seismic network in Iceland operated by IMO started. Like the Parkfield project in California the SIL network in Iceland was established in an area predicted (Einarsson et al 1981, Stefansson and Halldorsson 1988) to be struck by major EQs within decades of years. The area of main interest have a detection threshold of M=0. A physical approach was chosen to the earthquake warning problem (Stefansson et al 1993) and therefore all microearthquakes were analyzed for FPS by the spectral amplitude method (Slunga 1981). As the shear slip is caused by the in situ stress it is logical to investigate what bounds the FPS puts on the stress tensor. McKenzie 1969 assumed that the earthquake takes place in a crust containing only one fracture, the fault plane. He found that in s uch a case only very weak constraints could be put on the stress. This was widely accepted t o be valid also for microearthquakes in the real crust and lead to methods (Angelier 1978, G ephart and Forsythe 1984 etc) to put four constraints on the stress tensor by assuming that the same stress tensor is causing the slip on four or more different fractures. Another and more realistic approach is to assume that the crust have frequent fractures with almost all orientations. In such a case one can rely on Coulomb's failure criterion for isotropic mat erial (gives four constraints) instead of the weaker Bolt's criterion (giving only one const raint). One obvious fifth constraint is to require the vertical stress to equal the lithosta tic pressure. A sixth constraint is achieved by requiring that the deviatoric elastic energy is minimized. The water pressure is also needed for the fourth constraint by Coulomb (CFS=0 ). It can be related to the depth based on the assumptions of a fractured crust, widely vary ing stress field, and a general closeness to instability as found by stress measurements (Jamison and Cook 1976). Wheather this approach is working or not is best answered by applying it to real data. This was provided by the IMO network in Iceland. Along Southern Iceland Seismic Zone (SISZ) more than 200,000 microearthquakes and a few M 5 EQs and 2 M=6.6 EQs have been recorded. The results will be presented it is obvious that the use of the stresses determined from the microearthquake recordings may significa ntly improve earthquake warnings and will make it possible to use the absolute C FS method for more deterministic predictions. Note that the microearthquake meth od only shows the part of the stress field that has caused slip. Volumes with st able stress will not show up. However stress measurements (Brown and Hoek 1978, Slunga 1988) have shown that the crustal stresses in general are close to instabi lity and microearthquake source analysis has shown that a large number of differ ent fractures become unstable within longer time windows. This may explain the e xcellent results given by the Icelandic tests of the absolute stress tensor fiel d as given by the microearthquakes. However I prefer to call this stress apparen t.

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

DOE PAGES

Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy

2016-10-18

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property.more » Furthermore, the Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.« less

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

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

Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property.more » Furthermore, the Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.« less

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.

Spatial distribution of F-net moment tensors for the 2005 West Off Fukuoka Prefecture Earthquake determined by the extended method of the NIED F-net routine

NASA Astrophysics Data System (ADS)

Matsumoto, Takumi; Ito, Yoshihiro; Matsubayashi, Hirotoshi; Sekiguchi, Shoji

2006-01-01

The 2005 West Off Fukuoka Prefecture Earthquake with a Japan Meteorological Agency (JMA) magnitude (MJMA) of 7.0 occurred on March 20, 2005. We determined moment tensor solutions, using a surface wave with an extended method of the NIED F-net routine processing. The horizontal distance to the station is rounded to the nearest interval of 1 km, and the variance reduction approach is applied to a focal depth from 2 km with an interval of 1 km. We obtain the moment tensors of 101 events with (MJMA) exceeding 3.0 and spatial distribution of these moment tensors. The focal mechanism of aftershocks is mainly of the strike-slip type. The alignment of the epicenters in the rupture zone of the main-shock is oriented between N110°E and N130°E, which is close to the strike of the main-shock's moment tensor solutions (N122°E). These moment tensor solutions of intermediatesized aftershocks around the focal region represent basic and important information concerning earthquakes in investigating regional tectonic stress fields, source mechanisms and so on.

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.

Tensorial analysis of Eshelby stresses in 3D supercooled liquids

NASA Astrophysics Data System (ADS)

Lemaître, Anaël

2015-10-01

It was recently proposed that the local rearrangements governing relaxation in supercooled liquids impress on the liquid medium long-ranged (Eshelby) stress fluctuations that accumulate over time. From this viewpoint, events must be characterized by elastic dipoles, which are second order tensors, and Eshelby fields are expected to show up in stress and stress increment correlations, which are fourth order tensor fields. We construct here an analytical framework that permits analyzing such tensorial correlations in isotropic media in view of accessing Eshelby fields. Two spherical bases are introduced, which correspond to Cartesian and spherical coordinates for tensors. We show how they can be used to decompose stress correlations and thus test such properties as isotropy and power-law scalings. Eshelby fields and the predicted stress correlations in an infinite medium are shown to belong to an algebra that can conveniently be described using the spherical tensor bases. Using this formalism, we demonstrate that the inherent stress field of 3D supercooled liquids is power law correlated and carries the signature of Eshelby fields, thus supporting the idea that relaxation events give rise to Eshelby stresses that accumulate over time.

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.

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)

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.

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

Schiappacasse, Enrico D.; Fewster, Christopher J.; Ford, L. H.

2018-01-01

Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we study a specific operator that contributes to the stress-energy tensor of a massless scalar field in Minkowski spacetime, namely, the normal ordered square of the time derivative of the field. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lend additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.

Elliptic Relaxation of a Tensor Representation for the Redistribution Terms in a Reynolds Stress Turbulence Model

NASA Technical Reports Server (NTRS)

Carlson, J. R.; Gatski, T. B.

2002-01-01

A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented. 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. Direct numerical simulation data and Reynolds stress solutions using a full differential approach are compared for the case of fully developed channel flow.

Mesoscopic model for the viscosities of nematic liquid crystals.

PubMed

Chrzanowska, A; Kröger, M; Sellers, S

1999-10-01

Based on the definition of the mesoscopic concept by Blenk et al. [Physica A 174, 119 (1991); J. Noneq. Therm. 16, 67 (1991); Mol. Cryst. Liq. Cryst. 204, 133 (1991)] an approach to calculate the Leslie viscosity coefficients for nematic liquid crystals is presented. The approach rests upon the mesoscopic stress tensor, whose structure is assumed similar to the macroscopic Leslie viscous stress. The proposed form is also the main dissipation part of the mesoscopic Navier-Stokes equation. On the basis of the correspondence between microscopic and mesoscopic scales a mean-field mesoscopic potential is introduced. It allows us to obtain the stress tensor angular velocity of the free rotating molecules with the help of the orientational Fokker-Planck equation. The macroscopic stress tensor is calculated as an average of the mesoscopic counterpart. Appropriate relations among mesoscopic viscosities have been found. The mesoscopic analysis results are shown to be consistent with the diffusional model of Kuzuu-Doi and Osipov-Terentjev with the exception of the shear viscosity alpha(4). In the nematic phase alpha(4) is shown to have two contributions: isotropic and nematic. There exists an indication that the influence of the isotropic part is dominant over the nematic part. The so-called microscopic stress tensor used in the microscopic theories is shown to be the mean-field potential-dependent representation of the mesoscopic stress tensor. In the limiting case of total alignment the Leslie coefficients are estimated for the diffusional and mesoscopic models. They are compared to the results of the affine transformation model of the perfectly ordered systems. This comparison shows disagreement concerning the rotational viscosity, whereas the coefficients characteristic for the symmetric part of the viscous stress tensor remain the same. The difference is caused by the hindered diffusion in the affine model case.

A Review of Tensors and Tensor Signal Processing

NASA Astrophysics Data System (ADS)

Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

Determination of Multiple Near-Surface Residual Stress Components in Laser Peened Aluminum Alloy via the Contour Method

NASA Astrophysics Data System (ADS)

Toparli, M. Burak; Fitzpatrick, Michael E.; Gungor, Salih

2015-09-01

In this study, residual stress fields, including the near-surface residual stresses, were determined for an Al7050-T7451 sample after laser peening. The contour method was applied to measure one component of the residual stress, and the relaxed stresses on the cut surfaces were then measured by X-ray diffraction. This allowed calculation of the three orthogonal stress components using the superposition principle. The near-surface results were validated with results from incremental hole drilling and conventional X-ray diffraction. The results demonstrate that multiple residual stress components can be determined using a combination of the contour method and another technique. If the measured stress components are congruent with the principal stress axes in the sample, then this allows for determination of the complete stress tensor.

Geomechanical simulation of the stress tensor rotation caused by injection of cold water in a deep geothermal reservoir

DOE PAGES

Jeanne, Pierre; Rutqvist, Jonny; Dobson, Patrick F.; ...

2015-11-12

We present a three-dimensional thermohydromechanical numerical study of the evolution and distribution of the stress tensor within the northwest part of The Geysers geothermal reservoir (in California), including a detailed study of the region around one injection well from 2003 to 2012. Initially, after imposing a normal faulting stress regime, we calculated local changes in the stress regime around injection wells. Our results were compared with previously published studies in which the stress state was inferred from inverting the focal plane mechanism of seismic events. Our main finding is that changes in stress tensor orientation are caused by injection-induced progressivemore » cooling of the reservoir, as well as by the seasonal variations in injection rate. Because of the gravity flow and cooling around a liquid zone formed by the injection, the vertical stress reduction is larger and propagates far below the injection well. At the same time, the horizontal stress increases, mostly because of stress redistribution below and above the cooling area. These two phenomena cause the rotation of the stress tensor and the appearance of a strike-slip regime above, inside, and below the cooling area. The cooling and the associated rotation of the stress regime can play a significant role in the observed long-term deepening of the microseismicity below active injection wells.« less

Dense lower crust elevates long-term earthquake rates in the New Madrid seismic zone

USGS Publications Warehouse

Levandowski, William Brower; Boyd, Oliver; Ramirez-Guzman, Leonardo

2016-01-01

Knowledge of the local state of stress is critical in appraising intraplate seismic hazard. Inverting earthquake moment tensors, we demonstrate that principal stress directions in the New Madrid seismic zone (NMSZ) differ significantly from those in the surrounding region. Faults in the NMSZ that are incompatible with slip in the regional stress field are favorably oriented relative to local stress. We jointly analyze seismic velocity, gravity, and topography to develop a 3-D crustal and upper mantle density model, revealing uniquely dense lower crust beneath the NMSZ. Finite element simulations then estimate the stress tensor due to gravitational body forces, which sums with regional stress. The anomalous lower crust both elevates gravity-derived stress at seismogenic depths in the NMSZ and rotates it to interfere more constructively with far-field stress, producing a regionally maximal deviatoric stress coincident with the highest concentration of modern seismicity. Moreover, predicted principal stress directions mirror variations (observed independently in moment tensors) at the NMSZ and across the region.

Polymer Fluid Dynamics: Continuum and Molecular Approaches.

PubMed

Bird, R B; Giacomin, A J

2016-06-07

To solve problems in polymer fluid dynamics, one needs the equations of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (a) One can write a continuum expression for the stress tensor in terms of kinematic tensors, or (b) one can select a molecular model that represents the polymer molecule and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. We restrict the discussion primarily to the simplest stress tensor expressions or constitutive equations containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. Studying the simplest models allows us to discover which types of empiricisms or molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows, which are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.

Stochastic Gravity: Theory and Applications.

PubMed

Hu, Bei Lok; Verdaguer, Enric

2004-01-01

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Triaxial Measurement Method for Analysis of Residual Stress after High Feed Milling by X-Ray Diffraction

NASA Astrophysics Data System (ADS)

Čuma, Matúš; Török, Jozef; Telišková, Monika

2016-12-01

Surface integrity is a broad term which includes various quality factors affecting the functional properties of parts. Residual stress is one of these factors. Machining generates residual stresses in the surface and subsurface layers of the structural elements. X-ray diffractometry is a non-destructive method applicable for the measurement of residual stresses in surface and subsurface layers of components. The article is focused on the non-destructive progressive method of triaxial measurement of residual stress after machining the surface of sample by high feed milling technology. Significance of triaxial measuring is the capability of measuring in different angles so it is possible to acquire stress tensor containing normal and shear stress components acting in the spot of measuring, using a Cartesian coordinate system.

Complex brittle deformation pattern along the Southern Patagonian Andes (Argentina)

NASA Astrophysics Data System (ADS)

Barberón, Vanesa; Sue, Christian; Ronda, Gonzalo; Ghiglione, Matías

2016-04-01

The Southern Patagonian Andes is located in the southern extreme of the Pacific subduction zone, where the Antartic oceanic plate sinks underneath South America. The history of the area begins with compression during Paleozoic, Jurassic extension associated to the rift and opening of the South Atlantic Ocean, then a sag stage in the Lower Cretaceous followed by a foreland phase as a result of plate tectonics (Ghiglione et al., 2016). The kinematic study is concentrated in the Argentinean foothills, between 46°40' and 48° SL. We measured around 800 fault planes and their striaes with the sense of movement in order to characterize the stress field. The software used to make the stress inversion were Tensor (Delvaux, 2011) and Multiple Inverse Method MIM (Yamaji et al., 2011). The stress field map was built with the results of the MIM. We present new data from 48 sites located in the northern sector of the Southern Patagonian Andes. The measurements were made in several rocks from Paleozoic to Lower Cretaceous, even though most were taken in pyroclastic jurassic rocks from El Quemado Complex. Paleostress tensors obtained are mostly strike-slip, although a 25% is normal and there are a few compresional. The pattern of faults found is complex. In some sites the tensor can be locally linked to satellite images and observations from the field or be related to a major thrust front. There is no clear correlation between the age and/or lithology with the tensor since the youngest rocks measured are Lower Cretaceous. Probably there are several generations of family faults connected to different and recent tectonic phases then the paleostress tensors might correspond to the latest tectonic events.

Membrane paradigm of black holes in Chern-Simons modified gravity

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

Zhao, Tian-Yi; Wang, Towe, E-mail: zhaotianyi5566@foxmail.com, E-mail: twang@phy.ecnu.edu.cn

2016-06-01

The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.

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.

Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias

DOE PAGES

Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing

2015-09-30

We report non-destructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 mm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positionsmore » were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.« less

Stress field modeling of the Carpathian Basin based on compiled tectonic maps

NASA Astrophysics Data System (ADS)

Albert, Gáspár; Ungvári, Zsuzsanna; Szentpéteri, Krisztián

2014-05-01

The estimation of the stress field in the Carpathian Basin is tackled by several authors. Their modeling methods usually based on measurements (borehole-, focal mechanism- and geodesic data) and the result is a possible structural pattern of the region. Our method works indirectly: the analysis is aimed to project a possible 2D stress field over the already mapped/known/compiled lineament pattern. This includes a component-wise interpolation of the tensor-field, which is based on the generated irregular point cloud in the puffer zone of the mapped lineaments. The interpolated values appear on contour and tensor maps, and show the relative stress field of the area. In 2006 Horváth et al. compiled the 'Atlas of the present-day geodynamics of the Pannonian basin'. To test our method we processed the lineaments of the 1:1 500 000 scale 'Map of neotectonic (active) structures' published in this atlas. The geodynamic parameters (i.e. normal, reverse, right- and left lateral strike-slip faults, etc.) of the lines on this map were mostly explained in the legend. We classified the linear elements according to these parameters and created a geo-referenced mapping database. This database contains the polyline sections of the map lineaments as vectors (i.e. line sections), and the directions of the stress field as attributes of these vectors. The directions of the dip-parallel-, strike-parallel- and vertical stress-vectors are calculated from the geodynamical parameters of the line section. Since we created relative stress field properties, the eigenvalues of the vectors were maximized to one. Each point in the point cloud inherits the stress property of the line section, from which it was derived. During the modeling we tried several point-cloud generating- and interpolation methods. The analysis of the interpolated tensor fields revealed that the model was able to reproduce a geodynamic synthesis of the Carpathian Basin, which can be correlated with the synthesis of the Atlas published in 2006. The method was primarily aimed to reconstruct paleo-stress fields. References Horváth, F., Bada, G., Windhoffer, G., Csontos, L., Dombrádi, E., Dövényi, P., Fodor, L., Grenerczy, G., Síkhegyi, F., Szafián, P., Székely, B., Timár, G., Tóth, L., Tóth, T. 2006: Atlas of the present-day geodynamics of the Pannonian basin: Euroconform maps with explanatory text. Magyar Geofizika 47, 133-137.

Elastic constants of hcp 4He: Path-integral Monte Carlo results versus experiment

NASA Astrophysics Data System (ADS)

Ardila, Luis Aldemar Peña; Vitiello, Silvio A.; de Koning, Maurice

2011-09-01

The elastic constants of hcp 4He are computed using the path-integral Monte Carlo (PIMC) method. The stiffness coefficients are obtained by imposing different distortions to a periodic cell containing 180 atoms, followed by measurement of the elements of the corresponding stress tensor. For this purpose an appropriate path-integral expression for the stress tensor observable is derived and implemented into the pimc++ package. In addition to allowing the determination of the elastic stiffness constants, this development also opens the way to an explicit atomistic determination of the Peierls stress for dislocation motion using the PIMC technique. A comparison of the results to available experimental data shows an overall good agreement of the density dependence of the elastic constants, with the single exception of C13. Additional calculations for the bcc phase, on the other hand, show good agreement for all elastic constants.

Seismic velocity structure and microearthquake source properties at The Geysers, California, geothermal area

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

O'Connell, D.R.

1986-12-01

The method of progressive hypocenter-velocity inversion has been extended to incorporate S-wave arrival time data and to estimate S-wave velocities in addition to P-wave velocities. S-wave data to progressive inversion does not completely eliminate hypocenter-velocity tradeoffs, but they are substantially reduced. Results of a P and S-wave progressive hypocenter-velocity inversion at The Geysers show that the top of the steam reservoir is clearly defined by a large decrease of V/sub p//V/sub s/ at the condensation zone-production zone contact. The depth interval of maximum steam production coincides with minimum observed V/sub p//V/sub s/, and V/sub p//V/sub s/ increses below the shallowmore » primary production zone suggesting that reservoir rock becomes more fluid saturated. The moment tensor inversion method was applied to three microearthquakes at The Geysers. Estimated principal stress orientations were comparable to those estimated using P-wave firstmotions as constraints. Well constrained principal stress orientations were obtained for one event for which the 17 P-first motions could not distinguish between normal-slip and strike-slip mechanisms. The moment tensor estimates of principal stress orientations were obtained using far fewer stations than required for first-motion focal mechanism solutions. The three focal mechanisms obtained here support the hypothesis that focal mechanisms are a function of depth at The Geysers. Progressive inversion as developed here and the moment tensor inversion method provide a complete approach for determining earthquake locations, P and S-wave velocity structure, and earthquake source mechanisms.« less

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.

Normal stress differences and beyond-Navier-Stokes hydrodynamics

NASA Astrophysics Data System (ADS)

Alam, Meheboob; Saha, Saikat

2017-06-01

A recently proposed beyond-Navier-Stokes order hydrodynamic theory for dry granular fluids is revisited by focussing on the behaviour of the stress tensor and the scaling of related transport coefficients in the dense limit. For the homogeneous shear flow, it is shown that the eigen-directions of the second-moment tensor and those of the shear tensor become co-axial, thus making the first normal stress difference (N1) to zero in the same limit. In contrast, the origin of the second normal stress difference (N2) is tied to the `excess' temperature along the mean-vorticity direction and the imposed shear field, respectively, in the dilute and dense flows. The scaling relations for transport coefficients are suggested based on the present theory.

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.

Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.

NASA Astrophysics Data System (ADS)

Pascal, C.; Jaques Ribeiro, L. M.

2017-12-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal 3D exposures of mineralised quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To further constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of 300 MPa and formation depths of 10 km. As a second step, we measured 600 subhorizontal quartz veins in all the levels of the mine. The inversion of the attitudes of the veins allowed for reconstructing the orientations of the principal axes of stress, the unscaled Mohr circle and the relative pore pressure. After merging these results with the previously obtained absolute pore pressure we reconstructed the six parameters of the paleostress tensor.

Radiation Forces and Torques without Stress (Tensors)

ERIC Educational Resources Information Center

Bohren, Craig F.

2011-01-01

To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…

Experimental Measurement of In Situ Stress

NASA Astrophysics Data System (ADS)

Tibbo, Maria; Milkereit, Bernd; Nasseri, Farzine; Schmitt, Douglas; Young, Paul

2016-04-01

The World Stress Map data is determined by stress indicators including earthquake focal mechanisms, in situ measurement in mining, oil and gas boreholes as well as the borehole cores, and geologic data. Unfortunately, these measurements are not only infrequent but sometimes infeasible, and do not provide nearly enough data points with high accuracy to correctly infer stress fields in deep mines around the world. Improvements in stress measurements of Earth's crust is fundamental to several industries such as oil and gas, mining, nuclear waste management, and enhanced geothermal systems. Quantifying the state of stress and the geophysical properties of different rock types is a major complication in geophysical monitoring of deep mines. Most stress measurement techniques involve either the boreholes or their cores, however these measurements usually only give stress along one axis, not the complete stress tensor. The goal of this project is to investigate a new method of acquiring a complete stress tensor of the in situ stress in the Earth's crust. This project is part of a comprehensive, exploration geophysical study in a deep, highly stressed mine located in Sudbury, Ontario, Canada, and focuses on two boreholes located in this mine. These boreholes are approximately 400 m long with NQ diameters and are located at depths of about 1300 - 1600 m and 1700 - 2000 m. Two borehole logging surveys were performed on both boreholes, October 2013 and July 2015, in order to perform a time-lapse analysis of the geophysical changes in the mine. These multi-parameter surveys include caliper, full waveform sonic, televiewer, chargeability (IP), and resistivity. Laboratory experiments have been performed on borehole core samples of varying geologies from each borehole. These experiments have measured the geophysical properties including elastic modulus, bulk modulus, P- and S-wave velocities, and density. The apparatus' used for this project are geophysical imaging cells capable of hydrostatic stress (σ1 = σ2 = σ3), differential stress (σ1 > σ2 = σ3), and the unique true triaxial stress (σ1 > σ2 > σ3). Velocity surveys can be acquired along all three axes, and therefore the effects of σ1,σ2,σ3 on the velocity-stress curve can be obtained. These geophysical cells are being used to reproduce the borehole P- and S-wave velocities by altering the differential stress, allowing for the unique position of determining the stress tensor. Currently, results have been obtained for differential stress (σ1 > σ2 = σ3), and true triaxial experiments will determine if σ3 is the missing factor to reproducing the borehole velocities. This project is the first to combine time - lapse borehole logging data and experimental laboratory data to infer a complete stress tensor.

Moment tensor clustering: a tool to monitor mining induced seismicity

NASA Astrophysics Data System (ADS)

Cesca, Simone; Dahm, Torsten; Tolga Sen, Ali

2013-04-01

Automated moment tensor inversion routines have been setup in the last decades for the analysis of global and regional seismicity. Recent developments could be used to analyse smaller events and larger datasets. In particular, applications to microseismicity, e.g. in mining environments, have then led to the generation of large moment tensor catalogues. Moment tensor catalogues provide a valuable information about the earthquake source and details of rupturing processes taking place in the seismogenic region. Earthquake focal mechanisms can be used to discuss the local stress field, possible orientations of the fault system or to evaluate the presence of shear and/or tensile cracks. Focal mechanism and moment tensor solutions are typically analysed for selected events, and quick and robust tools for the automated analysis of larger catalogues are needed. We propose here a method to perform cluster analysis for large moment tensor catalogues and identify families of events which characterize the studied microseismicity. Clusters include events with similar focal mechanisms, first requiring the definition of distance between focal mechanisms. Different metrics are here proposed, both for the case of pure double couple, constrained moment tensor and full moment tensor catalogues. Different clustering approaches are implemented and discussed. The method is here applied to synthetic and real datasets from mining environments to demonstrate its potential: the proposed cluserting techniques prove to be able to automatically recognise major clusters. An important application for mining monitoring concerns the early identification of anomalous rupture processes, which is relevant for the hazard assessment. This study is funded by the project MINE, which is part of the R&D-Programme GEOTECHNOLOGIEN. The project MINE is funded by the German Ministry of Education and Research (BMBF), Grant of project BMBF03G0737.

Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration

NASA Astrophysics Data System (ADS)

Becattini, F.; Grossi, E.

2015-08-01

We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with nonvanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second-order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between ρ and p , that is, the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field—both massive and massless—and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these nonideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensors of the scalar field—canonical or improved—are thermodynamically inequivalent.

Analysis of Multi-Layered Materials Under High Velocity Impact Using CTH

DTIC Science & Technology

2008-03-01

of state . The other relationship deals with the deviatoric stress and is taken care of by the constitutive equations which are discussed in the next...models in CTH decompose the total stress tensor into the spherical and deviatoric parts. The spherical part of the stress tensor is the equation of state ...investigate the effects of wave propagation. Waves in rods are considered to create a state of

Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

NASA Astrophysics Data System (ADS)

Babadjian, Jean-François; Mora, Maria Giovanna

2018-04-01

This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic - perfectly plastic materials obeying a Drucker-Prager or Mohr-Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.

In Silico Investigation of Intracranial Blast Mitigation with Relevance to Military Traumatic Brain Injury

DTIC Science & Technology

2010-09-01

how personal protective equipment affects the brain’s response to blasts. In this study we investigated the effect of the Advanced Combat...analyzing stress wave propagation, which is the main dynamic effect loading the brain tissue during a blast event. We consider two key metrics of stress ...Cauchy stress tensor, and sij ¼ σij − 13σkkδij are the compo- nents of the deviatoric stress tensor (24). Fig. 1 shows snapshots of the pressure

Two formalisms, one renormalized stress-energy tensor

NASA Astrophysics Data System (ADS)

Barceló, C.; Carballo, R.; Garay, L. J.

2012-04-01

We explicitly compare the structure of the renormalized stress-energy tensor of a massless scalar field in a (1+1) curved spacetime as obtained by two different strategies: normal-mode construction of the field operator and one-loop effective action. We pay special attention to where and how the information related to the choice of vacuum state in both formalisms is encoded. By establishing a clear translation map between both procedures, we show that these two potentially different renormalized stress-energy tensors are actually equal, when using vacuum-state choices related by this map. One specific aim of the analysis is to facilitate the comparison of results regarding semiclassical effects in gravitational collapse as obtained within these different formalisms.

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.

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.

Distinguishing and quantifying the torquoselectivity in competitive ring-opening reactions using the stress tensor and QTAIM.

PubMed

Guo, Huan; Morales-Bayuelo, Alejandro; Xu, Tianlv; Momen, Roya; Wang, Lingling; Yang, Ping; Kirk, Steven R; Jenkins, Samantha

2016-12-05

Currently the theories to explain and predict the classification of the electronic reorganization due to the torquoselectivity of a ring-opening reaction cannot accommodate the directional character of the reaction pathway; the torquoselectivity is a type of stereoselectivity and therefore is dependent on the pathway. Therefore, in this investigation we introduced new measures from quantum theory of atoms in molecules and the stress tensor to clearly distinguish and quantify the transition states of the inward (TSIC) and outward (TSOC) conrotations of competitive ring-opening reactions of 3-(trifluoromethyl)cyclobut-1-ene and 1-cyano-1-methylcyclobutene. We find the metallicity ξ(r b ) of the ring-opening bond does not occur exactly at the transition state in agreement with transition state theory. The vector-based stress tensor response β σ was used to distinguish the effect of the CN, CH 3 , and CF 3 groups on the TSIC and TSOC paths that was consistent with the ellipticity ε, the total local energy density H(r b ) and the stress tensor stiffness S σ . We determine the directional properties of the TSIC and TSOC ring-opening reactions by constructing a stress tensor UσTS space with trajectories TσTS (s) with length l in real space, longer l correlated with the lowest density functional theory-evaluated total energy barrier and hence will be more thermodynamically favored. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

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

Importance of Force Decomposition for Local Stress Calculations in Biomembrane Molecular Simulations.

PubMed

Vanegas, Juan M; Torres-Sánchez, Alejandro; Arroyo, Marino

2014-02-11

Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.

A tensorial description of particle perception in black-hole physics

NASA Astrophysics Data System (ADS)

Barbado, Luis C.; Barceló, Carlos; Garay, Luis J.; Jannes, G.

2016-09-01

In quantum field theory in curved backgrounds, one typically distinguishes between objective, tensorial quantities such as the renormalized stress-energy tensor (RSET) and subjective, nontensorial quantities such as Bogoliubov coefficients which encode perception effects associated with the specific trajectory of a detector. In this work, we propose a way to treat both objective and subjective notions on an equal tensorial footing. For that purpose, we define a new tensor which we will call the perception renormalized stress-energy tensor (PeRSET). The PeRSET is defined as the subtraction of the RSET corresponding to two different vacuum states. Based on this tensor, we can define perceived energy densities and fluxes. The PeRSET helps us to have a more organized and systematic understanding of various results in the literature regarding quantum field theory in black hole spacetimes. We illustrate the physics encoded in this tensor by working out various examples of special relevance.

Stress field estimation based on focal mechanisms and back projected imaging in the Eastern Llanos Basin (Colombia)

NASA Astrophysics Data System (ADS)

Gómez-Alba, Sebastián; Fajardo-Zarate, Carlos Eduardo; Vargas, Carlos Alberto

2016-11-01

At least 156 earthquakes (Mw 2.8-4.4) were detected in Puerto Gaitán, Colombia (Eastern Llanos Basin) between April 2013 and December 2014. Out of context, this figure is not surprising. However, from its inception in 1993, the Colombian National Seismological Network (CNSN) found no evidence of significant seismic events in this region. In this study, we used CNSN data to model the rupture front and orientation of the highest-energy events. For these earthquakes, we relied on a joint inversion method to estimate focal mechanisms and, in turn, determine the area's fault trends and stress tensor. While the stress tensor defines maximum stress with normal tendency, focal mechanisms generally represent normal faults with NW orientation, an orientation which lines up with the tracking rupture achieved via Back Projection Imaging for the study area. We ought to bear in mind that this anomalous earthquake activity has taken place within oil fields. In short, the present paper argues that, based on the spatiotemporal distribution of seismic events, hydrocarbon operations may induce the study area's seismicity.

A note on stress-driven anisotropic diffusion and its role in active deformable media.

PubMed

Cherubini, Christian; Filippi, Simonetta; Gizzi, Alessio; Ruiz-Baier, Ricardo

2017-10-07

We introduce a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to employ diffusion tensors directly influenced by the coupling with mechanical stress. The proposed generalised reaction-diffusion-mechanics model reveals that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the mathematical model and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-driven diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electric feedback in actively deforming bio-materials such as the cardiac tissue. Copyright © 2017. Published by Elsevier Ltd.

Remarks on turbulent constitutive relations

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Lumley, John L.

1993-01-01

The paper demonstrates that the concept of turbulent constitutive relations can be used to construct general models for various turbulent correlations. Some of the Generalized Cayley-Hamilton formulas for relating tensor products of higher extension to tensor products of lower extension are introduced. The combination of dimensional analysis and invariant theory can lead to 'turbulent constitutive relations' (or general turbulence models) for, in principle, any turbulent correlations. As examples, the constitutive relations for Reynolds stresses and scalar fluxes are derived. The results are consistent with ones from Renormalization Group (RNG) theory and two-scale Direct-Interaction Approximation (DIA) method, but with a more general form.

Energy Flux Positivity and Unitarity in Conformal Field Theories

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

Kulaxizi, Manuela; Parnachev, Andrei

2011-01-07

We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop light like poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-freemore » is equivalent to the condition of positivity of energy flux.« less

Inversion of calcite twin data for paleostress orientations and magnitudes: A new technique tested and calibrated on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

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

2018-01-01

The inversion of calcite twin data is a powerful tool to reconstruct paleostresses sustained by carbonate rocks during their geological history. Following Etchecopar's (1984) pioneering work, this study presents a new technique for the inversion of calcite twin data that reconstructs the 5 parameters of the deviatoric stress tensors from both monophase and polyphase twin datasets. The uncertainties in the parameters of the stress tensors reconstructed by this new technique are evaluated on numerically-generated datasets. The technique not only reliably defines the 5 parameters of the deviatoric stress tensor, but also reliably separates very close superimposed stress tensors (30° of difference in maximum principal stress orientation or switch between σ3 and σ2 axes). The technique is further shown to be robust to sampling bias and to slight variability in the critical resolved shear stress. Due to our still incomplete knowledge of the evolution of the critical resolved shear stress with grain size, our results show that it is recommended to analyze twin data subsets of homogeneous grain size to minimize possible errors, mainly those concerning differential stress values. The methodological uncertainty in principal stress orientations is about ± 10°; it is about ± 0.1 for the stress ratio. For differential stresses, the uncertainty is lower than ± 30%. Applying the technique to vein samples within Mesozoic limestones from the Monte Nero anticline (northern Apennines, Italy) demonstrates its ability to reliably detect and separate tectonically significant paleostress orientations and magnitudes from naturally deformed polyphase samples, hence to fingerprint the regional paleostresses of interest in tectonic studies.

Forces in General Relativity

ERIC Educational Resources Information Center

Ridgely, Charles T.

2010-01-01

Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…

Single-shot full strain tensor determination with microbeam X-ray Laue diffraction and a two-dimensional energy-dispersive detector.

PubMed

Abboud, A; Kirchlechner, C; Keckes, J; Conka Nurdan, T; Send, S; Micha, J S; Ulrich, O; Hartmann, R; Strüder, L; Pietsch, U

2017-06-01

The full strain and stress tensor determination in a triaxially stressed single crystal using X-ray diffraction requires a series of lattice spacing measurements at different crystal orientations. This can be achieved using a tunable X-ray source. This article reports on a novel experimental procedure for single-shot full strain tensor determination using polychromatic synchrotron radiation with an energy range from 5 to 23 keV. Microbeam X-ray Laue diffraction patterns were collected from a copper micro-bending beam along the central axis (centroid of the cross section). Taking advantage of a two-dimensional energy-dispersive X-ray detector (pnCCD), the position and energy of the collected Laue spots were measured for multiple positions on the sample, allowing the measurement of variations in the local microstructure. At the same time, both the deviatoric and hydrostatic components of the elastic strain and stress tensors were calculated.

Synchrotron X-ray microbeam diffraction measurements of full elastic long range internal strain and stress tensors in commercial-purity aluminum processed by multiple passes of equal-channel angular pressing

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

Phan, Thien Q.; Levine, Lyle E.; Lee, I-Fang

Synchrotron X-ray microbeam diffraction was used to measure the full elastic long range internal strain and stress tensors of low dislocation density regions within the submicrometer grain/subgrain structure of equal-channel angular pressed (ECAP) aluminum alloy AA1050 after 1, 2, and 8 passes using route B C. This is the first time that full tensors were measured in plastically deformed metals at this length scale. The maximum (most tensile or least compressive) principal elastic strain directions for the unloaded 1 pass sample for the grain/subgrain interiors align well with the pressing direction, and are more random for the 2 and 8more » pass samples. The measurements reported here indicate that the local stresses and strains become increasingly isotropic (homogenized) with increasing ECAP passes using route BC. The average maximum (in magnitude) LRISs are -0.43 σ a for 1 pass, -0.44 σ a for 2 pass, and 0.14 σ a for the 8 pass sample. Furthermore, these LRISs are larger than those reported previously because those earlier measurements were unable to measure the full stress tensor. Significantly, the measured stresses are inconsistent with the two-component composite model.« less

Synchrotron X-ray microbeam diffraction measurements of full elastic long range internal strain and stress tensors in commercial-purity aluminum processed by multiple passes of equal-channel angular pressing

DOE PAGES

Phan, Thien Q.; Levine, Lyle E.; Lee, I-Fang; ...

2016-04-23

Synchrotron X-ray microbeam diffraction was used to measure the full elastic long range internal strain and stress tensors of low dislocation density regions within the submicrometer grain/subgrain structure of equal-channel angular pressed (ECAP) aluminum alloy AA1050 after 1, 2, and 8 passes using route B C. This is the first time that full tensors were measured in plastically deformed metals at this length scale. The maximum (most tensile or least compressive) principal elastic strain directions for the unloaded 1 pass sample for the grain/subgrain interiors align well with the pressing direction, and are more random for the 2 and 8more » pass samples. The measurements reported here indicate that the local stresses and strains become increasingly isotropic (homogenized) with increasing ECAP passes using route BC. The average maximum (in magnitude) LRISs are -0.43 σ a for 1 pass, -0.44 σ a for 2 pass, and 0.14 σ a for the 8 pass sample. Furthermore, these LRISs are larger than those reported previously because those earlier measurements were unable to measure the full stress tensor. Significantly, the measured stresses are inconsistent with the two-component composite model.« less

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.

Einstein gravity 3-point functions from conformal field theory

NASA Astrophysics Data System (ADS)

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein

2017-12-01

We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈 T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

Determination of stress glut moments of total degree 2 from teleseismic surface wave amplitude spectra

NASA Astrophysics Data System (ADS)

Bukchin, B. G.

1995-08-01

A special case of the seismic source, where the stress glut tensor can be expressed as a product of a uniform moment tensor and a scalar function of spatial coordinates and time, is considered. For such a source, a technique of determining stress glut moments of total degree 2 from surface wave amplitude spectra is described. The results of application of this technique for the estimation of spatio-temporal characteristics of the Georgian earthquake, 29.04.91 are presented.

[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

PubMed

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

Characterizing heterogeneous properties of cerebral aneurysms with unknown stress-free geometry: a precursor to in vivo identification.

PubMed

Zhao, Xuefeng; Raghavan, Madhavan L; Lu, Jia

2011-05-01

Knowledge of elastic properties of cerebral aneurysms is crucial for understanding the biomechanical behavior of the lesion. However, characterizing tissue properties using in vivo motion data presents a tremendous challenge. Aside from the limitation of data accuracy, a pressing issue is that the in vivo motion does not expose the stress-free geometry. This is compounded by the nonlinearity, anisotropy, and heterogeneity of the tissue behavior. This article introduces a method for identifying the heterogeneous properties of aneurysm wall tissue under unknown stress-free configuration. In the proposed approach, an accessible configuration is taken as the reference; the unknown stress-free configuration is represented locally by a metric tensor describing the prestrain from the stress-free configuration to the reference configuration. Material parameters are identified together with the metric tensor pointwisely. The paradigm is tested numerically using a forward-inverse analysis loop. An image-derived sac is considered. The aneurysm tissue is modeled as an eightply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain-energy function containing four material parameters. The parameters are assumed to vary continuously in two assigned patterns to represent two types of material heterogeneity. Nine configurations between the diastolic and systolic pressures are generated by forward quasi-static finite element analyses. These configurations are fed to the inverse analysis to delineate the material parameters and the metric tensor. The recovered and the assigned distributions are in good agreement. A forward verification is conducted by comparing the displacement solutions obtained from the recovered and the assigned material parameters at a different pressure. The nodal displacements are found in excellent agreement.

Focal mechanisms and tidal modulation for tectonic tremors in Taiwan

NASA Astrophysics Data System (ADS)

Ide, S.; Yabe, S.; Tai, H. J.; Chen, K. H.

2015-12-01

Tectonic tremors in Taiwan have been discovered beneath the southern Central Range, but their hosting structure has been unknown. Here we constrain the focal mechanism of underground deformation related to tremors, using moment tensor inversion in the very low frequency band and tidal stress analysis. Three types of seismic data are used for two analysis steps: detection of tremors and the moment tensor inversion. Short-period seismograms from CWBSN are used for tremor detection. Broadband seismograms from BATS and the TAIGER project are used for both steps. About 1000 tremors were detected using an envelope correlation method in the high frequency band (2-8 Hz). Broadband seismograms are stacked relative to the tremor timing, and inverted for a moment tensor in the low frequency band (0.02-0.05 Hz). The best solution was obtained at 32 km depth, as a double-couple consistent with a low-angle thrust fault dipping to the east-southeast, or a high-angle thrust with a south-southwest strike. Almost all tremors occur when tidal shear stress is positive and normal stress is negative (clamping). Since the clamping stress is high for a high-angle thrust fault, the low-angle thrust fault is more likely to be the fault plane. Tremor rate increases non-linearly with increasing shear stress, suggesting a velocity strengthening friction law. The high tidal sensitivity is inconsistent with horizontal slip motion suggested by previous studies, and normal faults that dominates regional shallow earthquakes. Our results favor thrust slip on a low-angle fault dipping to the east-southeast, consistent with the subduction of the Eurasian plate. The tremor region is characterized by a deep thermal anomaly with decrease normal stress. This region has also experienced enough subduction to produce metamorphic fluids. A large amount of fluid and low vertical stress may explain the high tidal sensitivity.

8 January 2013 Mw=5.7 North Aegean Sea Earthquake Sequence

NASA Astrophysics Data System (ADS)

Kürçer, Akın; Yalçın, Hilal; Gülen, Levent; Kalafat, Doǧan

2014-05-01

The deformation of the North Aegean Sea is mainly controlled by the westernmost segments of North Anatolian Fault Zone (NAFZ). On January 8, 2013, a moderate earthquake (Mw= 5.7) occurred in the North Aegean Sea, which may be considered to be a part of westernmost splay of the NAFZ. A series of aftershocks were occurred within four months following the mainschock, which have magnitudes varying from 1.9 to 5.0. In this study, a total of 23 earthquake moment tensor solutions that belong to the 2013 earthquake sequence have been obtained by using KOERI and AFAD seismic data. The most widely used Gephart & Forsyth (1984) and Michael (1987) methods have been used to carry out stress tensor inversions. Based on the earthquake moment tensor solutions, distribution of epicenters and seismotectonic setting, the source of this earthquake sequence is a N75°E trending pure dextral strike-slip fault. The temporal and spatial distribution of earthquakes indicate that the rupture unilaterally propagated from SW to NE. The length of the fault has been calculated as approximately 12 km. using the afterschock distribution and empirical equations, suggested by Wells and Coppersmith (1994). The stress tensor analysis indicate that the dominant faulting type in the region is strike-slip and the direction of the regional compressive stress is WNW-ESE. The 1968 Aghios earthquake (Ms=7.3; Ambraseys and Jackson, 1998) and 2013 North Aegean Sea earthquake sequences clearly show that the regional stress has been transferred from SW to NE in this region. The last historical earthquake, the Bozcaada earthquake (M=7.05) had been occurred in the northeast of the 2013 earthquake sequence in 1672. The elapsed time (342 year) and regional stress transfer point out that the 1672 earthquake segment is probably a seismic gap. According to the empirical equations, the surface rupture length of the 1672 Earthquake segment was about 47 km, with a maximum displacement of 170 cm and average displacement of 107 cm. These values indicate that the 1672 earthquake segment is a potential earthquake hazard for this region.

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.

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.

Correlation Between Fracture Network Properties and Stress Variability in Geological Media

NASA Astrophysics Data System (ADS)

Lei, Qinghua; Gao, Ke

2018-05-01

We quantitatively investigate the stress variability in fractured geological media under tectonic stresses. The fracture systems studied include synthetic fracture networks following power law length scaling and natural fracture patterns based on outcrop mapping. The stress field is derived from a finite-discrete element model, and its variability is analyzed using a set of mathematical formulations that honor the tensorial nature of stress data. We show that local stress perturbation, quantified by the Euclidean distance of a local stress tensor to the mean stress tensor, has a positive, linear correlation with local fracture intensity, defined as the total fracture length per unit area within a local sampling window. We also evaluate the stress dispersion of the entire stress field using the effective variance, that is, a scalar-valued measure of the overall stress variability. The results show that a well-connected fracture system under a critically stressed state exhibits strong local and global stress variabilities.

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.

Mysteries of R ik = 0: A novel paradigm in Einstein's theory of gravitation

NASA Astrophysics Data System (ADS)

Vishwakarma, Ram Gopal

2014-02-01

Despite a century-long effort, a proper energy-stress tensor of the gravitational field, could not have been discovered. Furthermore, it has been discovered recently that the standard formulation of the energy-stress tensor of matter, suffers from various inconsistencies and paradoxes, concluding that the tensor is not consistent with the geometric formulation of gravitation [Astrophys. Space Sci., 2009, 321: 151; Astrophys. Space Sci., 2012, 340: 373]. This perhaps hints that a consistent theory of gravitation should not have any bearing on the energy-stress tensor. It is shown here that the so-called "vacuum" field equations R ik = 0 do not represent an empty spacetime, and the energy, momenta and angular momenta of the gravitational and the matter fields are revealed through the geometry, without including any formulation thereof in the field equations. Though, this novel discovery appears baffling and orthogonal to the usual understanding, is consistent with the observations at all scales, without requiring the hypothetical dark matter, dark energy or inflation. Moreover, the resulting theory circumvents the long-standing problems of the standard cosmology, besides explaining some unexplained puzzles.

FAST TRACK COMMUNICATION The Bel-Robinson tensor for topologically massive gravity

NASA Astrophysics Data System (ADS)

Deser, S.; Franklin, J.

2011-02-01

We construct, and establish the (covariant) conservation of, a 4-index 'super stress tensor' for topologically massive gravity. Separately, we discuss its invalidity in quadratic curvature models and suggest a generalization.

The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results

PubMed Central

Seppecher, P.

2015-01-01

In order to found continuum mechanics, two different postulations have been used. The first, introduced by Lagrange and Piola, starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients. Then, by using the divergence theorem, a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body. This method assumes an a priori notion of internal work, regards stress tensors as dual of virtual displacements and their gradients, deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts. The second method, conceived by Cauchy and based on the celebrated tetrahedron argument, starts by postulating the type of contact interactions which can be exerted on the boundary of every (suitably) regular part of a body. Then it proceeds by proving the existence of stress tensors from a balance-type postulate. In this paper, we review some relevant literature on the subject, discussing how the two postulations can be reconciled in the case of higher gradient theories. Finally, we underline the importance of the concept of contact surface, edge and wedge s-order forces. PMID:26730215

New seismogenic stress fields for southern Italy from a Bayesian approach

NASA Astrophysics Data System (ADS)

Totaro, Cristina; Orecchio, Barbara; Presti, Debora; Scolaro, Silvia; Neri, Giancarlo

2017-04-01

A new database of high-quality waveform inversion focal mechanism has been compiled for southern Italy by integrating the highest quality solutions, available from literature and catalogues, and 146 newly-computed ones. All the selected focal mechanisms are (i) coming from the Italian CMT, Regional CMT and TDMT catalogues (Pondrelli et al., PEPI 2006, PEPI 2011; http://www.ingv.it), or (ii) computed by using the Cut And Paste (CAP) method (Zhao & Helmberger, BSSA 1994; Zhu & Helmberger, BSSA 1996). Specific tests have been carried out in order to evaluate the robustness of the obtained solutions (e.g., by varying both seismic network configuration and Earth structure parameters) and to estimate uncertainties on the focal mechanism parameters. Only the resulting highest-quality solutions have been enclosed in the database, that has then been used for computation of posterior density distributions of stress tensor components by a Bayesian method (Arnold & Townend, GJI 2007). This algorithm furnishes the posterior density function of the principal components of stress tensor (maximum σ1, intermediate σ2, and minimum σ3 compressive stress, respectively) and the stress-magnitude ratio (R). Before stress computation, we applied the k-means clustering algorithm to subdivide the focal mechanism catalog on the basis of earthquake locations. This approach allows identifying the sectors to be investigated without any "a priori" constraint from faulting type distribution. The large amount of data and the application of the Bayesian algorithm allowed us to provide a more accurate local-to-regional scale stress distribution that has shed new light on the kinematics and dynamics of this very complex area, where lithospheric unit configuration and geodynamic engines are still strongly debated. The new high-quality information here furnished will then represent very useful tools and constraints for future geophysical analyses and geodynamic modeling.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

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).

Rotational relaxation time as unifying time scale for polymer and fiber drag reduction

NASA Astrophysics Data System (ADS)

Boelens, A. M. P.; Muthukumar, M.

2016-05-01

Using hybrid direct numerical simulation plus Langevin dynamics, a comparison is performed between polymer and fiber stress tensors in turbulent flow. The stress tensors are found to be similar, suggesting a common drag reducing mechanism in the onset regime for both flexible polymers and rigid fibers. Since fibers do not have an elastic backbone, this must be a viscous effect. Analysis of the viscosity tensor reveals that all terms are negligible, except the off-diagonal shear viscosity associated with rotation. Based on this analysis, we identify the rotational orientation time as the unifying time scale setting a new time criterion for drag reduction by both flexible polymers and rigid fibers.

Rotational relaxation time as unifying time scale for polymer and fiber drag reduction.

PubMed

Boelens, A M P; Muthukumar, M

2016-05-01

Using hybrid direct numerical simulation plus Langevin dynamics, a comparison is performed between polymer and fiber stress tensors in turbulent flow. The stress tensors are found to be similar, suggesting a common drag reducing mechanism in the onset regime for both flexible polymers and rigid fibers. Since fibers do not have an elastic backbone, this must be a viscous effect. Analysis of the viscosity tensor reveals that all terms are negligible, except the off-diagonal shear viscosity associated with rotation. Based on this analysis, we identify the rotational orientation time as the unifying time scale setting a new time criterion for drag reduction by both flexible polymers and rigid fibers.

Vacuum polarization of the quantized massive fields in Friedman-Robertson-Walker spacetime

NASA Astrophysics Data System (ADS)

Matyjasek, Jerzy; Sadurski, Paweł; Telecka, Małgorzata

2014-04-01

The stress-energy tensor of the quantized massive fields in a spatially open, flat, and closed Friedman-Robertson-Walker universe is constructed using the adiabatic regularization (for the scalar field) and the Schwinger-DeWitt approach (for the scalar, spinor, and vector fields). It is shown that the stress-energy tensor calculated in the sixth adiabatic order coincides with the result obtained from the regularized effective action, constructed from the heat kernel coefficient a3. The behavior of the tensor is examined in the power-law cosmological models, and the semiclassical Einstein field equations are solved exactly in a few physically interesting cases, such as the generalized Starobinsky models.

A Note on the Application of the Extended Bernoulli Equation

DTIC Science & Technology

1999-02-01

as OV s ... - Vp „ _ = -±L L + VO , (2) Dt p where DIDt denotes the material derivative (discussed in following section); V is the vector...force potential; V is the vector gradient operator; s (J is the deviatoric-stress tensor arising from any type of elasto-viscoplastic constitutive...behavior; and s ^j is index notation for dsy/dxp denoting the following vector condensation of the deviatoric-stress tensor: ds ds ds

Charged Vaidya solution satisfies weak energy condition

NASA Astrophysics Data System (ADS)

Chatterjee, Soumyabrata; Ganguli, Suman; Virmani, Amitabh

2016-07-01

The external matter stress-tensor supporting charged Vaidya solution appears to violate weak energy condition in certain region of the spacetime. Motivated by this, a new interpretation of charged Vaidya solution was proposed by Ori (Class Quant Grav 8:1559, 1991) in which the energy condition continues to be satisfied. In this construction, one glues an outgoing Vaidya solution to the original ingoing Vaidya solution provided the surface where the external stress-tensor vanishes is spacelike. We revisit this study and extend it to higher-dimensions, to AdS settings, and to higher-derivative f( R) theories. In asymptotically flat space context, we explore in detail the case when the mass function m( v) is proportional to the charge function q( v). When the proportionality constant ν = q(v)/m(v) lies in between zero and one, we show that the surface where the external stress-tensor vanishes is spacelike and lies in between the inner and outer apparent horizons.

Electrostatic forces in the Poisson-Boltzmann systems

NASA Astrophysics Data System (ADS)

Xiao, Li; Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2013-09-01

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

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.

Intrinsic Viscosity of Dendrimers via Equilibrium Molecular Dynamics

NASA Astrophysics Data System (ADS)

Drew, Phil; Adolf, David

2004-03-01

Equilibrium molecular dynamics simulations of dendrimers in dilute solution have been performed using dl-poly. Analysis of the system stress tensor via the Green-Kubo formula produces the viscosity of the dendrimer solution which, when coupled with that of a solvent only system leads to the intrinsic viscosity of the dendrimer solute. Particular attention has been paid to error analysis as the auto-correlation of the stress tensor exhibits a long time tail, potentially leading to large uncertainties in the solution, and hence intrinsic, viscosities. In order to counter this effect and provide reliable statistical averaging, simulations have been run spanning very many times the longest system relaxation. Comparison is made to previous studies, using different techniques, which suggest a peak in the intrinsic viscosity of dendrimers at around generation four. Results are also presented from investigations in to the individual contributions to the system stress tensor from the solvent and the solute.

Design and Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging

DTIC Science & Technology

2011-10-01

the deviatoric part of a tensor in the reference configuration and p = −∂Ψ ∂J is the hydrostatic pressure. Using the chain 4 rule, equation 13 can be...Kirchoff stress tensor S to the current configuration, and a scaling with the inverse of the volume ratio, transforms equation 16 to the Cauchy stress ...a characteristic of most soft tissues. Then, similar to equation 13, the second Piola-Kirchoff stress is given by: S = 2J−2/3DEV [ ∂Ψisoc ( C ) ∂C

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.

Finite element models of earthquake cycles in mature strike-slip fault zones

NASA Astrophysics Data System (ADS)

Lynch, John Charles

The research presented in this dissertation is on the subject of strike-slip earthquakes and the stresses that build and release in the Earth's crust during earthquake cycles. Numerical models of these cycles in a layered elastic/viscoelastic crust are produced using the finite element method. A fault that alternately sticks and slips poses a particularly challenging problem for numerical implementation, and a new contact element dubbed the "Velcro" element was developed to address this problem (Appendix A). Additionally, the finite element code used in this study was bench-marked against analytical solutions for some simplified problems (Chapter 2), and the resolving power was tested for the fault region of the models (Appendix B). With the modeling method thus developed, there are two main questions posed. First, in Chapter 3, the effect of a finite-width shear zone is considered. By defining a viscoelastic shear zone beneath a periodically slipping fault, it is found that shear stress concentrates at the edges of the shear zone and thus causes the stress tensor to rotate into non-Andersonian orientations. Several methods are used to examine the stress patterns, including the plunge angles of the principal stresses and a new method that plots the stress tensor in a manner analogous to seismic focal mechanism diagrams. In Chapter 4, a simple San Andreas-like model is constructed, consisting of two great earthquake producing faults separated by a freely-slipping shorter fault. The model inputs of lower crustal viscosity, fault separation distance, and relative breaking strengths are examined for their effect on fault communication. It is found that with a lower crustal viscosity of 1018 Pa s (in the lower range of estimates for California), the two faults tend to synchronize their earthquake cycles, even in the cases where the faults have asymmetric breaking strengths. These models imply that postseismic stress transfer over hundreds of kilometers may play a significant roll in the variability of earthquake repeat times. Specifically, small perturbations in the model parameters can lead to results similar to such observed phenomena as earthquake clustering and disruptions to so-called "characteristic" earthquake cycles.

Mode-sum regularization of ⟨ϕ2⟩ in the angular-splitting method

NASA Astrophysics Data System (ADS)

Levi, Adam; Ori, Amos

2016-08-01

The computation of the renormalized stress-energy tensor or ⟨ϕ2⟩ren in curved spacetime is a challenging task, at both the conceptual and technical levels. Recently we developed a new approach to compute such renormalized quantities in asymptotically flat curved spacetimes, based on the point-splitting procedure. Our approach requires the spacetime to admit some symmetry. We already implemented this approach to compute ⟨ϕ2⟩ren in a stationary spacetime using t splitting, namely splitting in the time-translation direction. Here we present the angular-splitting version of this approach, aimed for computing renormalized quantities in a general (possibly dynamical) spherically symmetric spacetime. To illustrate how the angular-splitting method works, we use it here to compute ⟨ϕ2⟩ren for a quantum massless scalar field in Schwarzschild background, in various quantum states (Boulware, Unruh, and Hartle-Hawking states). We find excellent agreement with the results obtained from the t -splitting variant and also with other methods. Our main goal in pursuing this new mode-sum approach was to enable the computation of the renormalized stress-energy tensor in a dynamical spherically symmetric background, e.g. an evaporating black hole. The angular-splitting variant presented here is most suitable to this purpose.

Detailed stress tensor measurements in a centrifugal compressor vaneless diffuser

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

Pinarbasi, A.; Johnson, M.W.

1996-04-01

Detailed flow measurements have been made in the vaneless diffuser of a large low-speed centrifugal compressor using hot-wire anemometry. The three time mean velocity components and full stress tensor distributions have been determined on eight measurement plans within the diffuser. High levels of Reynolds stress result in the rapid mixing out of the blade wake. Although high levels of turbulent kinetic energy are found in the passage wake, they are not associated with strong Reynolds stresses and hence the passage wake mixes out only slowly. Low-frequency meandering of the wake position is therefore likely to be responsible for the highmore » kinetic energy levels. The anisotropic nature of the turbulence suggests that Reynolds stress turbulence models are required for CFD modeling of diffuser flows.« less

Full paleostress tensor reconstruction using quartz veins of Panasqueira Mine, central Portugal; part I: Paleopressure determination

NASA Astrophysics Data System (ADS)

Jaques, Luís; Pascal, Christophe

2017-09-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal exposures of mineralized quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. The present contribution focuses specifically on the determination of pore pressure. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of ∼300 MPa and formation depths of ∼10 km. Such formation depths are in good agreement with the regional geological evolution. The obtained pore pressure will be merged with vein inversion results, in order to achieve full paleostress tensor restoration, in a forthcoming companion paper.

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.

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

Brizard, Alain J.; Tronci, Cesare

The variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.

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.

Magnification effect of Kerr metric by configurations of collisionless particles in non-isotropic kinetic equilibria

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Stuchlík, Zdeněk

2018-05-01

A test fluid composed of relativistic collisionless neutral particles in the background of Kerr metric is expected to generate non-isotropic equilibrium configurations in which the corresponding stress-energy tensor exhibits pressure and temperature anisotropies. This arises as a consequence of the constraints placed on single-particle dynamics by Killing tensor symmetries, leading to a peculiar non-Maxwellian functional form of the kinetic distribution function describing the continuum system. Based on this outcome, in this paper the generation of Kerr-like metric by collisionless N -body systems of neutral matter orbiting in the field of a rotating black hole is reported. The result is obtained in the framework of covariant kinetic theory by solving the Einstein equations in terms of an analytical perturbative treatment whereby the gravitational field is decomposed as a prescribed background metric tensor described by the Kerr solution plus a self-field correction. The latter one is generated by the uncharged fluid at equilibrium and satisfies the linearized Einstein equations having the non-isotropic stress-energy tensor as source term. It is shown that the resulting self-metric is again of Kerr type, providing a mechanism of magnification of the background metric tensor and its qualitative features.

Sparse alignment for robust tensor learning.

PubMed

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

Stress before and after the 2002 Denali fault earthquake

USGS Publications Warehouse

Wesson, R.L.; Boyd, O.S.

2007-01-01

Spatially averaged, absolute deviatoric stress tensors along the faults ruptured during the 2002 Denali fault earthquake, both before and after the event, are derived, using a new method, from estimates of the orientations of the principal stresses and the stress change associated with the earthquake. Stresses are estimated in three regions along the Denali fault, one of which also includes the Susitna Glacier fault, and one region along the Totschunda fault. Estimates of the spatially averaged shear stress before the earthquake resolved onto the faults that ruptured during the event range from near 1 MPa to near 4 MPa. Shear stresses estimated along the faults in all these regions after the event are near zero (0 ?? 1 MPa). These results suggest that deviatoric stresses averaged over a few tens of km along strike are low, and that the stress drop during the earthquake was complete or nearly so.

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.

The calculation of the viscosity from the autocorrelation function using molecular and atomic stress tensors

NASA Astrophysics Data System (ADS)

Cui, S. T.

The stress-stress correlation function and the viscosity of a united-atom model of liquid decane are studied by equilibrium molecular dynamics simulation using two different formalisms for the stress tensor: the atomic and the molecular formalisms. The atomic and molecular correlation functions show dramatic difference in short-time behaviour. The integrals of the two correlation functions, however, become identical after a short transient period whichis significantly shorter than the rotational relaxation time of the molecule. Both reach the same plateau value in a time period corresponding to this relaxation time. These results provide a convenient guide for the choice of the upper integral time limit in calculating the viscosity by the Green-Kubo formula.

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

NASA Astrophysics Data System (ADS)

Ye, Qian; Lin, Haoze

2017-07-01

Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.

Mass Function of Galaxy Clusters in Relativistic Inhomogeneous Cosmology

NASA Astrophysics Data System (ADS)

Ostrowski, Jan J.; Buchert, Thomas; Roukema, Boudewijn F.

The current cosmological model (ΛCDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average description of the Universe from first principles of general relativity, since in general, the Einstein tensor built from the averaged metric is not equal to the averaged stress-energy tensor. In this context, the discrepancy between these quantities is called "cosmological backreaction" and has been the subject of scientific debate among cosmologists and relativists for more than 20 years. Here we present one of the methods to tackle this problem, i.e. averaging the scalar parts of the Einstein equations, together with its application, the cosmological mass function of galaxy clusters.

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.

On computing stress in polymer systems involving multi-body potentials from molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Fu, Yao; Song, Jeong-Hoon

2014-08-01

Hardy stress definition has been restricted to pair potentials and embedded-atom method potentials due to the basic assumptions in the derivation of a symmetric microscopic stress tensor. Force decomposition required in the Hardy stress expression becomes obscure for multi-body potentials. In this work, we demonstrate the invariance of the Hardy stress expression for a polymer system modeled with multi-body interatomic potentials including up to four atoms interaction, by applying central force decomposition of the atomic force. The balance of momentum has been demonstrated to be valid theoretically and tested under various numerical simulation conditions. The validity of momentum conservation justifies the extension of Hardy stress expression to multi-body potential systems. Computed Hardy stress has been observed to converge to the virial stress of the system with increasing spatial averaging volume. This work provides a feasible and reliable linkage between the atomistic and continuum scales for multi-body potential systems.

Seismotectonics and crustal stress across the northern Arabian plate

NASA Astrophysics Data System (ADS)

yassminh, R.; Gomez, F. G.; Sandvol, E. A.; Ghalib, H. A.; Daoud, M.

2013-12-01

The region encompassing the collision of northern Arabia with Eurasia is a tectonically heterogeneous region of distributed deformation. The northern Arabia plate is bounded to the west by the subducting Sinai plate and the left-lateral Dead Sea transform. This complexity suggests that there are, multiple competing processes that may influence regional tectonics in northern Arabia and adjacent areas. Earthquake mechanisms provide insight into crustal kinematics and stress; however, reliable determination of earthquake source parameters can be challenging in a complex geological region, such as the continental collision zone between the Arabian and Eurasian plates. The goal of this study is to investigate spatial patterns of the crustal stress in the northern Arabian plate and surrounding area. The focal mechanisms used in this study are based on (1) first-motion polarities for earthquakes recorded by Syrian earthquake center during 2000-2011, and (2) regional moment tensors from broadband seismic data, from Turkey and Iraq. First motion focal mechanisms were assigned quality classifications based on the variation of both nodal planes. Regional moment tensor analysis can be significantly influenced by seismic velocity structure; thus, we have divided the study area into regions based on tectonic units. For each region, a specific velocity model is defined using waveform-modeling technique prior to the regional moment tensor inversion. The resulting focal mechanisms, combined with other previously published focal mechanisms for the study area, provide a basis for stress inversion analysis. The resulting deviatoric stress tensors show the spatial distribution of the maximum horizontal stress varies from NW-SE along the Dead Sea Fault to the N-S toward the east. We interpret this to reflect the eastward change from the transform to collision processes in northern Arabia. Along the Dead Sea Fault, transposition of the sigma-1 and sigma-2 to vertical and horizontal, respectively, may relate to influences from the subducted part of the Sinai plate. This change in regional stress is also consistent with extensional strains observed from GPS velocities.

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.

Regional flow simulation in fractured aquifers using stress-dependent parameters.

PubMed

Preisig, Giona; Joel Cornaton, Fabien; Perrochet, Pierre

2012-01-01

A model function relating effective stress to fracture permeability is developed from Hooke's law, implemented in the tensorial form of Darcy's law, and used to evaluate discharge rates and pressure distributions at regional scales. The model takes into account elastic and statistical fracture parameters, and is able to simulate real stress-dependent permeabilities from laboratory to field studies. This modeling approach gains in phenomenology in comparison to the classical ones because the permeability tensors may vary in both strength and principal directions according to effective stresses. Moreover this method allows evaluation of the fracture porosity changes, which are then translated into consolidation of the medium. © 2011, The Author(s). Ground Water © 2011, National Ground Water Association.

Normal-faulting stress state associated with low differential stress in an overriding plate in northeast Japan prior to the 2011 Mw 9.0 Tohoku earthquake

NASA Astrophysics Data System (ADS)

Otsubo, Makoto; Miyakawa, Ayumu; Imanishi, Kazutoshi

2018-03-01

Spatial and temporal variations in inland crustal stress prior to the 2011 Mw 9.0 Tohoku earthquake are investigated using focal mechanism solutions for shallow seismicity in Iwaki City, Japan. The multiple inverse method of stress tensor inversion detected two normal-faulting stress states that dominate in different regions. The stress field around Iwaki City changed from a NNW-SSE-trending triaxial extensional stress (stress regime A) to a NW-SE-trending axial tension (stress regime B) between 2005 and 2008. These stress changes may be the result of accumulated extensional stress associated with co- and post-seismic deformation due to the M7 class earthquakes. In this study we suggest that the stress state around Iwaki City prior to the 2011 Tohoku earthquake may have been extensional with a low differential stress. High pore pressure is required to cause earthquakes under such small differential stresses.

New constraints on micro-seismicity and stress state in the western part of the North Anatolian Fault Zone: Observations from a dense seismic array

NASA Astrophysics Data System (ADS)

Altuncu Poyraz, Selda; Teoman, M. Uğur; Türkelli, Niyazi; Kahraman, Metin; Cambaz, Didem; Mutlu, Ahu; Rost, Sebastian; Houseman, Gregory A.; Thompson, David A.; Cornwell, David; Utkucu, Murat; Gülen, Levent

2015-08-01

With the aim of extensively investigating the crustal structure beneath the western segment of the North Anatolian Fault Zone where it splays into northern and southern branches, a temporary seismic network (dense array for North Anatolia-DANA) consisting of 70 stations was deployed in early May 2012 and operated for 18 months in the Sakarya region during the FaultLab experiment. Out of 2437 events contaminated by explosions, we extracted 1371 well located earthquakes. The enhanced station coverage having a nominal station spacing of 7 km, lead to a minimum magnitude calculation of 0.1. Horizontal and vertical location uncertainties within the array do not exceed 0.8 km and 0.9 km, respectively. We observe considerable seismic activity along both branches of the fault where the depth of the seismogenic zone was mostly confined to 15 km. Using our current earthquake catalog we obtained a b-value of 1. We also mapped the b-value variation with depth and observed a gradual decrease. Furthermore, we determined the source parameters of 41 earthquakes with magnitudes greater than 1.8 using P-wave first motion polarity method. Regional Moment Tensor Inversion method was also applied to earthquakes with magnitudes greater than 3.0. Focal mechanism solutions confirm that Sakarya and its vicinity is stressed by a compressional regime showing a primarily oblique-slip motion character. Stress tensor analysis indicates that the maximum principal stress is aligned in WNW-ESE direction and the tensional axis is aligned in NNE-SSW direction.

The genetic algorithm: A robust method for stress inversion

NASA Astrophysics Data System (ADS)

Thakur, Prithvi; Srivastava, Deepak C.; Gupta, Pravin K.

2017-01-01

The stress inversion of geological or geophysical observations is a nonlinear problem. In most existing methods, it is solved by linearization, under certain assumptions. These linear algorithms not only oversimplify the problem but also are vulnerable to entrapment of the solution in a local optimum. We propose the use of a nonlinear heuristic technique, the genetic algorithm, which searches the global optimum without making any linearizing assumption or simplification. The algorithm mimics the natural evolutionary processes of selection, crossover and mutation and, minimizes a composite misfit function for searching the global optimum, the fittest stress tensor. The validity and efficacy of the algorithm are demonstrated by a series of tests on synthetic and natural fault-slip observations in different tectonic settings and also in situations where the observations are noisy. It is shown that the genetic algorithm is superior to other commonly practised methods, in particular, in those tectonic settings where none of the principal stresses is directed vertically and/or the given data set is noisy.

Simultaneous inversion of seismic velocity and moment tensor using elastic-waveform inversion of microseismic data: Application to the Aneth CO2-EOR field

NASA Astrophysics Data System (ADS)

Chen, Y.; Huang, L.

2017-12-01

Moment tensors are key parameters for characterizing CO2-injection-induced microseismic events. Elastic-waveform inversion has the potential to providing accurate results of moment tensors. Microseismic waveforms contains information of source moment tensors and the wave propagation velocity along the wavepaths. We develop an elastic-waveform inversion method to jointly invert the seismic velocity model and moment tensor. We first use our adaptive moment-tensor joint inversion method to estimate moment tensors of microseismic events. Our adaptive moment-tensor inversion method jointly inverts multiple microseismic events with similar waveforms within a cluster to reduce inversion uncertainty for microseismic data recorded using a single borehole geophone array. We use this inversion result as the initial model for our elastic-waveform inversion to minimize the cross-correlated-based data misfit between observed data and synthetic data. We verify our method using synthetic microseismic data and obtain improved results of both moment tensors and seismic velocity model. We apply our new inversion method to microseismic data acquired at a CO2-enhanced oil recovery field in Aneth, Utah, using a single borehole geophone array. The results demonstrate that our new inversion method significantly reduces the data misfit compared to the conventional ray-theory-based moment-tensor inversion.

Automatic deformable diffusion tensor registration for fiber population analysis.

PubMed

Irfanoglu, M O; Machiraju, R; Sammet, S; Pierpaoli, C; Knopp, M V

2008-01-01

In this work, we propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Images. Our registration method models the distances in between the tensors with Geode-sic-Loxodromes and employs a version of Multi-Dimensional Scaling (MDS) algorithm to unfold the manifold described with this metric. Defining the same shape properties as tensors, the vector images obtained through MDS are fed into a multi-step vector-image registration scheme and the resulting deformation fields are used to reorient the tensor fields. Results on brain DTI indicate that the proposed method is very suitable for deformable fiber-to-fiber correspondence and DTI-atlas construction.

Reynolds stress flow shear and turbulent energy transfer in reversed field pinch configuration

NASA Astrophysics Data System (ADS)

Vianello, Nicola; Spolaore, Monica; Serianni, Gianluigi; Regnoli, Giorgio; Spada, Emanuele; Antoni, Vanni; Bergsåker, Henric; Drake, James R.

2003-10-01

The role of Reynolds Stress tensor on flow generation in turbulent fluids and plasmas is still an open question and the comprehension of its behavior may assist the understanding of improved confinement scenario. It is generally believed that shear flow generation may occur by an interaction of the turbulent Reynolds stress with the shear flow. It is also generally believed that this mechanism may influence the generation of zonal flow shears. The evaluation of the complete Reynolds Stress tensor requires contemporary measurements of its electrostatic and magnetic part: this requirement is more restrictive for Reversed Field Pinch configuration where magnetic fluctuations are larger than in tokamak . A new diagnostic system which combines electrostatic and magnetic probes has been installed in the edge region of Extrap-T2R reversed field pinch. With this new probe the Reynolds stress tensor has been deduced and its radial profile has been reconstructed on a shot to shot basis exploring differen plasma conditions. These profiles have been compared with the naturally occurring velocity flow profile, in particular during Pulsed Poloidal Current Drive experiment, where a strong variation of ExB flow radial profile has been registered. The study of the temporal evolution of Reynolds stress reveals the appearance of strong localized bursts: these are considered in relation with global MHD relaxation phenomena, which naturally occur in the core of an RFP plasma sustaining its configuration.

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.

Einstein Revisited - Gravity in Curved Spacetime Without Event Horizons

NASA Astrophysics Data System (ADS)

Leiter, Darryl

2000-04-01

In terms of covariant derivatives with respect to flat background spacetimes upon which the physical curved spacetime is imposed (1), covariant conservation of energy momentum requires, via the Bianchi Identity, that the Einstein tensor be equated to the matter energy momentum tensor. However the Einstein tensor covariantly splits (2) into two tensor parts: (a) a term proportional to the gravitational stress energy momentum tensor, and (b) an anti-symmetric tensor which obeys a covariant 4-divergence identity called the Freud Identity. Hence covariant conservation of energy momentum requires, via the Freud Identity, that the Freud tensor be equal to a constant times the matter energy momentum tensor. The resultant field equations (3) agree with the Einstein equations to first order, but differ in higher orders (4) such that black holes are replaced by "red holes" i.e., dense objects collapsed inside of their photon orbits with no event horizons. (1) Rosen, N., (1963), Ann. Phys. v22, 1; (2) Rund, H., (1991), Alg. Grps. & Geom. v8, 267; (3) Yilmaz, Hl, (1992), Nuo. Cim. v107B, 946; (4) Roberstson, S., (1999),Ap.J. v515, 365.

Stress Energy tensor in LCFT and the Logarithmic Sugawara construction

NASA Astrophysics Data System (ADS)

Kogan, Ian I.; Nichols, Alexander

2002-01-01

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c = -2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra.

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.

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.

Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector

NASA Astrophysics Data System (ADS)

Garfinkle, David; Glass, E. N.

2013-03-01

Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for finding Killing tensors. In all cases one decomposes both the tensor and the equation it satisfies into pieces along the Killing vector and pieces orthogonal to the Killing vector. Solving the separate equations that result from this decomposition requires less computing than integrating the original equation. In each case, examples are given to illustrate the method.

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.

Killing approximation for vacuum and thermal stress-energy tensor in static space-times

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

Frolov, V.P.; Zel'nikov, A.I.

1987-05-15

The problem of the vacuum polarization of conformal massless fields in static space-times is considered. A tensor T/sub ..mu..//sub ..nu../ constructed from the curvature, the Killing vector, and their covariant derivatives is proposed which can be used to approximate the average value of the stress-energy tensor /sup ren/ in such spaces. It is shown that if (i) its trace T /sub epsilon//sup epsilon/ coincides with the trace anomaly /sup ren/, (ii) it satisfies the conservation law T/sup ..mu..//sup epsilon/ /sub ;//sub epsilon/ = 0, and (iii) it has the correct behavior under the scale transformations, then it is uniquely definedmore » up to a few arbitrary constants. These constants must be chosen to satisfy the boundary conditions. In the case of a static black hole in a vacuum these conditions single out the unique tensor T/sub ..mu..//sub ..nu../ which provides a good approximation for /sup ren/ in the Hartle-Hawking vacuum. The relation between this approach and the Page-Brown-Ottewill approach is discussed.« less

Physical stress, mass, and energy for non-relativistic matter

NASA Astrophysics Data System (ADS)

Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.

2017-06-01

For theories of relativistic matter fields there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for non-relativistic matter theories. We point out that while the physical non-relativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. We also provide computations of these quantities for some simple non-relativistic actions.

Using Perturbation Theory to Reduce Noise in Diffusion Tensor Fields

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Xu, Dongrong; Laine, Andrew F.; Liu, Jun; Peterson, Bradley S.

2009-01-01

We propose the use of Perturbation theory to reduce noise in Diffusion Tensor (DT) fields. Diffusion Tensor Imaging (DTI) encodes the diffusion of water molecules along different spatial directions in a positive-definite, 3 × 3 symmetric tensor. Eigenvectors and eigenvalues of DTs allow the in vivo visualization and quantitative analysis of white matter fiber bundles across the brain. The validity and reliability of these analyses are limited, however, by the low spatial resolution and low Signal-to-Noise Ratio (SNR) in DTI datasets. Our procedures can be applied to improve the validity and reliability of these quantitative analyses by reducing noise in the tensor fields. We model a tensor field as a three-dimensional Markov Random Field and then compute the likelihood and the prior terms of this model using Perturbation theory. The prior term constrains the tensor field to be smooth, whereas the likelihood term constrains the smoothed tensor field to be similar to the original field. Thus, the proposed method generates a smoothed field that is close in structure to the original tensor field. We evaluate the performance of our method both visually and quantitatively using synthetic and real-world datasets. We quantitatively assess the performance of our method by computing the SNR for eigenvalues and the coherence measures for eigenvectors of DTs across tensor fields. In addition, we quantitatively compare the performance of our procedures with the performance of one method that uses a Riemannian distance to compute the similarity between two tensors, and with another method that reduces noise in tensor fields by anisotropically filtering the diffusion weighted images that are used to estimate diffusion tensors. These experiments demonstrate that our method significantly increases the coherence of the eigenvectors and the SNR of the eigenvalues, while simultaneously preserving the fine structure and boundaries between homogeneous regions, in the smoothed tensor field. PMID:19540791

On volume-source representations based on the representation theorem

NASA Astrophysics Data System (ADS)

Ichihara, Mie; Kusakabe, Tetsuya; Kame, Nobuki; Kumagai, Hiroyuki

2016-01-01

We discuss different ways to characterize a moment tensor associated with an actual volume change of ΔV C , which has been represented in terms of either the stress glut or the corresponding stress-free volume change ΔV T . Eshelby's virtual operation provides a conceptual model relating ΔV C to ΔV T and the stress glut, where non-elastic processes such as phase transitions allow ΔV T to be introduced and subsequent elastic deformation of - ΔV T is assumed to produce the stress glut. While it is true that ΔV T correctly represents the moment tensor of an actual volume source with volume change ΔV C , an explanation as to why such an operation relating ΔV C to ΔV T exists has not previously been given. This study presents a comprehensive explanation of the relationship between ΔV C and ΔV T based on the representation theorem. The displacement field is represented using Green's function, which consists of two integrals over the source surface: one for displacement and the other for traction. Both integrals are necessary for representing volumetric sources, whereas the representation of seismic faults includes only the first term, as the second integral over the two adjacent fault surfaces, across which the traction balances, always vanishes. Therefore, in a seismological framework, the contribution from the second term should be included as an additional surface displacement. We show that the seismic moment tensor of a volume source is directly obtained from the actual state of the displacement and stress at the source without considering any virtual non-elastic operations. A purely mathematical procedure based on the representation theorem enables us to specify the additional imaginary displacement necessary for representing a volume source only by the displacement term, which links ΔV C to ΔV T . It also specifies the additional imaginary stress necessary for representing a moment tensor solely by the traction term, which gives the "stress glut." The imaginary displacement-stress approach clarifies the mathematical background to the classical theory.

Generalized Higher Order Orthogonal Iteration for Tensor Learning and Decomposition.

PubMed

Liu, Yuanyuan; Shang, Fanhua; Fan, Wei; Cheng, James; Cheng, Hong

2016-12-01

Low-rank tensor completion (LRTC) has successfully been applied to a wide range of real-world problems. Despite the broad, successful applications, existing LRTC methods may become very slow or even not applicable for large-scale problems. To address this issue, a novel core tensor trace-norm minimization (CTNM) method is proposed for simultaneous tensor learning and decomposition, and has a much lower computational complexity. In our solution, first, the equivalence relation of trace norm of a low-rank tensor and its core tensor is induced. Second, the trace norm of the core tensor is used to replace that of the whole tensor, which leads to two much smaller scale matrix TNM problems. Finally, an efficient alternating direction augmented Lagrangian method is developed to solve our problems. Our CTNM formulation needs only O((R N +NRI)log(√{I N })) observations to reliably recover an N th-order I×I×…×I tensor of n -rank (r,r,…,r) , compared with O(rI N-1 ) observations required by those tensor TNM methods ( I > R ≥ r ). Extensive experimental results show that CTNM is usually more accurate than them, and is orders of magnitude faster.

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

NASA Astrophysics Data System (ADS)

Mukhamediev, Sh. A.

2014-09-01

Rock masses contain ubiquitous multiscale heterogeneities, which (or whose boundaries) serve as the surfaces of discontinuity for some characteristics of the stress state, e.g., for the orientation of principal stress axes. Revealing the regularities that control these discontinuities is a key to understanding the processes taking place at the boundaries of the heterogeneities and for designing the correct procedures for reconstructing and theoretical modeling of tectonic stresses. In the present study, the local laws describing the refraction of the axes of extreme principal stresses T 1 (maximal tension in the deviatoric sense) and T 3 (maximal compression) of the Cauchy stress tensor at the transition over the elementary area n of discontinuity whose orientation is specified by the unit normal n are derived. It is assumed that on the area n of discontinuity, frictional contact takes place. No hypotheses are made on the constitutive equations, and a priori constraints are not posed on the orientation on the stress axes. Two domains, which adjoin area n on the opposite sides and are conventionally marked + and -, are distinguished. In the case of the two-dimensional (2D) stress state, any principal stress axis on passing from domain - to domain + remains in the same quadrant of the plane as the continuation of this axis in domain +. The sign and size of the refraction angle depend on the sign and amplitude of the jump of the normal stress, which is tangential to the surface of discontinuity. In the three-dimensional (3D) case, the refraction of axes T 1 and T 3 should be analyzed simultaneously. For each side, + and -, the projections of the T 1 and T 3 axes on the generally oriented plane n form the shear sectors S + and S -, which are determined unambiguously and to whose angular domains the possible directions p + and p - of the shear stress vectors belong. In order for the extreme stress axes T {1/+}, T {3/+} and T {1/-}, T {3/-} to be statically compatible on the generally oriented plane n, it is required that sectors S + and S - had a nonempty intersection. The direction vectors p + and p - are determined uniquely if, besides axes T {1/-}, T {3/-} and T {1/+}, T {3/+}, also the ratios of differential stresses R + and R - (0 ≤ R ± ≤ 1) are known. This is equivalent to specifying the reduced stress tensors T {/R +} and T {/R -} The necessary condition for tensors T {/R +} and T {/R -} being statically compatible on plane n is the equality p + = p -. In this paper, simple methods are suggested for solving the inverse problem of constructing the set of the orientations of the extreme stress axes from the known direction p of the shear stress vector on plane n and from the data on the shear sector. Based on these methods and using the necessary conditions of local equilibrium on plane n formulated above, all the possible orientations of axes T {1/+}, T {3/+} are determined if the projections of axes T {1/-}, T {3/-} axes on side — are given. The angle between the projections of axes T {1/+}, T {1/-} and/or T {3/+}, T {3/-} on the plane can attain 90°. Besides the general case, also the particular cases of the contact between the degenerate stress states and the special position of plane n relative to the principal stress axes are thoroughly examined. Generalization of the obtained results makes it possible to plot the local diagram of the orientations of axes T {1/+}, T {3/+} for a given sector S -. This diagram is a so-called stress orientation sphere, which is subdivided into three pairs of areas (compression, tension, and compression-extension). The tension and compression zones cannot contain the poles of T {3/+} and T {1/+} axes, respectively. The compression-extension zones can contain the poles of either T {1/+} or T {3/+} axis but not both poles simultaneously. In the particular case when the shear stress vector has a unique direction p - on side -, the areas of compression-extension disappear and the diagram is reduced to a beach-ball plot, which visualizes the focal mechanism solution of an earthquake. If area n is a generally oriented plane and if the orientation of the pairs of the statically compatible axes T {1/-}, T {3/-} and T {1/+}, T {3/+} is specified, then, the stress values on side + are uniquely determined from the known stress values on side -. From the value of differential stress ratio R -, one can calculate the value of R +, and using the values of the principal stresses on side -, determine the total stress tensor T + on side +. The obtained results are supported by the laboratory experiments and drilling data. In particular, these results disclose the drawbacks of some established notions and methods in which the possible refraction of the stress axes is unreasonably ignored or taken into account improperly. For example, it is generally misleading to associate the slip on the preexisting fault with the orientation of any particular trihedron of the principal stress axes. The reconstruction should address the potentially statically compatible principal stress axes, which are differently oriented on opposite sides of the fault plane. The fact that, based on the orientation of the intraplate principal stresses at the base of the lithosphere, one cannot make a conclusion on the active or passive influence of the mantle flows on the lithospheric plate motion is another example. The present relationships linking the stress values on the opposite sides of the fault plane on which the orientations of the principal stress axes are known demonstrate the incorrectness of the existing methods, in which the reduced stress tensors within the material domains are reconstructed without allowance for the dynamic interaction of these domains with their neighbors. In addition, using the obtained results, one can generalize the notion of the zone of dynamical control of a fault onto the case of the existence of discontinuities in this region and analyze the stress transfer across the system of the faults.

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.

Tensor-based Dictionary Learning for Spectral CT Reconstruction

PubMed Central

Zhang, Yanbo; Wang, Ge

2016-01-01

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628

Universality for shape dependence of Casimir effects from Weyl anomaly

NASA Astrophysics Data System (ADS)

Miao, Rong-Xin; Chu, Chong-Sun

2018-03-01

We reveal elegant relations between the shape dependence of the Casimir effects and Weyl anomaly in boundary conformal field theories (BCFT). We show that for any BCFT which has a description in terms of an effective action, the near boundary divergent behavior of the renormalized stress tensor is completely determined by the central charges of the theory. These relations are verified by free BCFTs. We also test them with holographic models of BCFT and find exact agreement. We propose that these relations between Casimir coefficients and central charges hold for any BCFT. With the holographic models, we reproduce not only the precise form of the near boundary divergent behavior of the stress tensor, but also the surface counter term that is needed to make the total energy finite. As they are proportional to the central charges, the near boundary divergence of the stress tensor must be physical and cannot be dropped by further artificial renormalization. Our results thus provide affirmative support on the physical nature of the divergent energy density near the boundary, whose reality has been a long-standing controversy in the literature.

Phase transformations in nanograin materials under high pressure and plastic shear: nanoscale mechanisms.

PubMed

Levitas, Valery I; Javanbakht, Mahdi

2014-01-07

There are two main challenges in the discovery of new high pressure phases (HPPs) and transforming this discovery into technologies: finding conditions to synthesize new HPPs and finding ways to reduce the phase transformation (PT) pressure to an economically reasonable level. Based on the results of pressure-shear experiments in the rotational diamond anvil cell (RDAC), superposition of plastic shear on high pressure is a promising way to resolve these problems. However, physical mechanisms behind these phenomena are not yet understood. Here, we elucidate generic mechanisms of coupled nucleation and evolution of dislocation and HPP structures in the nanograin material under pressure and shear utilizing the developed advanced phase field approach (PFA). Dislocations are generated at the grain boundaries and are densely piled up near them, creating a strong concentrator of the stress tensor. Averaged shear stress is essentially larger in the nanograin material due to grain boundary strengthening. This leads to the increase in the local thermodynamic driving force for PT, which allows one to significantly reduce the applied pressure. For all cases, the applied pressure is 3-20 times lower than the PT pressure and 2-12.5 times smaller than the phase equilibrium pressure. Interaction between nuclei leads sometimes to their coalescence and growth of the HPP away from stress concentrators. Plasticity plays a dual role: in addition to creating stress concentrators, it may relax stresses at other concentrators, thus competing with PT. Some ways to optimize the loading parameters have been found that lead to methods for controlling PT. Since such a local stress tensor with high shear stress component cannot be created without plastic deformations, this may lead to new transformation paths and phases, which are hidden during pressure induced PTs.

Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

Vector and tensor contributions to the curvature perturbation at second order

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

Carrilho, Pedro; Malik, Karim A., E-mail: p.gregoriocarrilho@qmul.ac.uk, E-mail: k.malik@qmul.ac.uk

2016-02-01

We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from different splits of the spatial metric, and compare the expressions. The results are valid at all scales and include all contributions from scalar, vector and tensor perturbations, as well as anisotropic stress, with all our results written purely in terms of gauge invariant quantities. Taking the large-scale approximation, we find that a conserved quantity exists only if, in addition to the non-adiabatic pressure, the transverse traceless part ofmore » the anisotropic stress tensor is also negligible. We also find that the version of the gauge invariant curvature perturbation which is exactly conserved is the one defined with the determinant of the spatial part of the inverse metric.« less

Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

PubMed

Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Real-time object recognition in multidimensional images based on joined extended structural tensor and higher-order tensor decomposition methods

NASA Astrophysics Data System (ADS)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.

New Views on Dark Matter from Emergent Gravity

NASA Astrophysics Data System (ADS)

Sun, Sichun; Zhang, Yun-Long

2018-01-01

We discuss a scenario that apparent dark matter comes from the induced gravity in the (3+1)- dimensional spacetime, which can be embedded into one higher dimensional flat spacetime. The stress tensor of dark energy and dark matter is identified with the Brown-York stress tensor on the hypersurface, and we find an interesting constraint relation between the dark matter and dark energy density parameter and baryonic density parameter. Our approach may show a new understanding for Verlinde's emergent gravity from higher dimensions. We also comment on some phenomenological implications, including gravitational wave solutions and MOND limit.

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.

Crustal stress across the northern Arabian plate and the relationship with the plate boundary forces

NASA Astrophysics Data System (ADS)

Yassminh, Rayan

The region encompassing the collision of northern Arabia with Eurasia is a tectonically heterogeneous region of distributed deformation. The northern Arabia plate is bounded to the west by the subducting Sinai plate and the left-lateral Dead Sea transform. This complexity suggests that there are multiple competing processes that may influence regional tectonics in northern Arabia and adjacent areas. Earthquake mechanisms provide insight into crustal kinematics and stress; however, reliable determination of earthquake source parameters can be challenging in a complex geological region, such as the continental collision zone between the Arabian and Eurasian plates. The goal of this study is to investigate spatial patterns of the crustal stress in the northern Arabian plate and surrounding area. The focal mechanisms used in this study are based on (1) first-motion polarities for earthquakes recorded by Syrian earthquake center during 2000-2011, and (2) regional moment tensors from broadband seismic data, from Turkey and Iraq. First motion focal mechanisms were assigned quality classifications based on the variation of both nodal planes. Regional moment tensor analysis can be significantly influenced by seismic velocity structure; thus, we have divided the study area into regions based on tectonic units. For each region, the velocity model is described using a waveform-modeling technique prior to the regional moment tensor inversion. The resulting focal mechanisms, combined with other previously published focal mechanisms for the study area, provide a basis for stress inversion analysis. The resulting deviatoric stress tensors show the spatial distribution of the maximum horizontal stress varies from NW-SE along the Dead Sea Fault to the N-S toward the east. We interpret this to reflect the eastward change from the transform to collision processes in northern Arabia. Along the Dead Sea Fault, transposition of the sigma-1 and sigma-2 to vertical and horizontal, respectively, may relate to influences from the subducted part of the Sinai plate. This change in regional stress is also consistent with extensional strains observed from GPS velocities.

Spatial and Temporal Variations in the Moment Tensor Solutions of the 2008 Wenchuan Earthquake Aftershocks and Their Tectonic Implications

NASA Astrophysics Data System (ADS)

Lin, X.; Dreger, D.; Ge, H.; Xu, P.; Wu, M.; Chiang, A.; Zhao, G.; Yuan, H.

2018-03-01

Following the mainshock of the 2008 M8 Wenchuan Earthquake, there were more than 300 ML ≥ 4.0 aftershocks that occurred between 12 May 2008 and 8 September 2010. We analyzed the broadband waveforms for these events and found 160 events with sufficient signal-to-noise levels to invert for seismic moment tensors. Considering the length of the activated fault and the distances to the recording stations, four velocity models were employed to account for variability in crustal structure. The moment tensor solutions show considerable variations with a mixture of mainly reverse and strike-slip mechanisms and a small number of normal events and ambiguous events. We analyzed the spatial and temporal distribution of the aftershocks and their mechanism types to characterize the structure and the deformation occurring in the Longmen Shan fold and thrust belt. Our results suggest that the stress is very complex at the Longmen Shan fault zone. The moment tensors have both a spatial segmentation with two major categories of the moment tensor of thrust and strike slip; and a temporal pattern that the majority of the aftershocks gradually migrated to thrust-type events. The variability of aftershock mechanisms is a strong indication of significant tectonic release and stress reorganization that activated numerous small faults in the system.

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

A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise

PubMed Central

Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang

2014-01-01

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method. PMID:24573313

A tensor-based subspace approach for bistatic MIMO radar in spatial colored noise.

PubMed

Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang

2014-02-25

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method.

On computing stress in polymer systems involving multi-body potentials from molecular dynamics simulation

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

Fu, Yao, E-mail: fu5@mailbox.sc.edu, E-mail: jhsong@cec.sc.edu; Song, Jeong-Hoon, E-mail: fu5@mailbox.sc.edu, E-mail: jhsong@cec.sc.edu

2014-08-07

Hardy stress definition has been restricted to pair potentials and embedded-atom method potentials due to the basic assumptions in the derivation of a symmetric microscopic stress tensor. Force decomposition required in the Hardy stress expression becomes obscure for multi-body potentials. In this work, we demonstrate the invariance of the Hardy stress expression for a polymer system modeled with multi-body interatomic potentials including up to four atoms interaction, by applying central force decomposition of the atomic force. The balance of momentum has been demonstrated to be valid theoretically and tested under various numerical simulation conditions. The validity of momentum conservation justifiesmore » the extension of Hardy stress expression to multi-body potential systems. Computed Hardy stress has been observed to converge to the virial stress of the system with increasing spatial averaging volume. This work provides a feasible and reliable linkage between the atomistic and continuum scales for multi-body potential systems.« less

Tensor-based spatiotemporal saliency detection

NASA Astrophysics Data System (ADS)

Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

2018-03-01

This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

Trapping of a micro-bubble by non-paraxial Gaussian beam: computation using the FDTD method.

PubMed

Sung, Seung-Yong; Lee, Yong-Gu

2008-03-03

Optical forces on a micro-bubble were computed using the Finite Difference Time Domain method. Non-paraxial Gaussian beam equation was used to represent the incident laser with high numerical aperture, common in optical tweezers. The electromagnetic field distribution around a micro-bubble was computed using FDTD method and the electromagnetic stress tensor on the surface of a micro-bubble was used to compute the optical forces. By the analysis of the computational results, interesting relations between the radius of the circular trapping ring and the corresponding stability of the trap were found.

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.

What Is Better Than Coulomb Failure Stress? A Ranking of Scalar Static Stress Triggering Mechanisms from 105 Mainshock-Aftershock Pairs

NASA Astrophysics Data System (ADS)

Meade, Brendan J.; DeVries, Phoebe M. R.; Faller, Jeremy; Viegas, Fernanda; Wattenberg, Martin

2017-11-01

Aftershocks may be triggered by the stresses generated by preceding mainshocks. The temporal frequency and maximum size of aftershocks are well described by the empirical Omori and Bath laws, but spatial patterns are more difficult to forecast. Coulomb failure stress is perhaps the most common criterion invoked to explain spatial distributions of aftershocks. Here we consider the spatial relationship between patterns of aftershocks and a comprehensive list of 38 static elastic scalar metrics of stress (including stress tensor invariants, maximum shear stress, and Coulomb failure stress) from 213 coseismic slip distributions worldwide. The rates of true-positive and false-positive classification of regions with and without aftershocks are assessed with receiver operating characteristic analysis. We infer that the stress metrics that are most consistent with observed aftershock locations are maximum shear stress and the magnitude of the second and third invariants of the stress tensor. These metrics are significantly better than random assignment at a significance level of 0.005 in over 80% of the slip distributions. In contrast, the widely used Coulomb failure stress criterion is distinguishable from random assignment in only 51-64% of the slip distributions. These results suggest that a number of alternative scalar metrics are better predictors of aftershock locations than classic Coulomb failure stress change.

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.

A bulk viscosity approach for shock capturing on unstructured grids

NASA Astrophysics Data System (ADS)

Shoeybi, Mohammad; Larsson, Nils Johan; Ham, Frank; Moin, Parviz

2008-11-01

The bulk viscosity approach for shock capturing (Cook and Cabot, JCP, 2005) augments the bulk part of the viscous stress tensor. The intention is to capture shock waves without dissipating turbulent structures. The present work extends and modifies this method for unstructured grids. We propose a method that properly scales the bulk viscosity with the grid spacing normal to the shock for unstructured grid for which the shock is not necessarily aligned with the grid. The magnitude of the strain rate tensor used in the original formulation is replaced with the dilatation, which appears to be more appropriate in the vortical turbulent flow regions (Mani et al., 2008). The original form of the model is found to have an impact on dilatational motions away form the shock wave, which is eliminated by a proposed localization of the bulk viscosity. Finally, to allow for grid adaptation around shock waves, an explicit/implicit time advancement scheme has been developed that adaptively identifies the stiff regions. The full method has been verified with several test cases, including 2D shock-vorticity entropy interaction, homogenous isotropic turbulence, and turbulent flow over a cylinder.

Hybrid immersed interface-immersed boundary methods for AC dielectrophoresis

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

Hossan, Mohammad Robiul; Department of Engineering and Physics, University of Central Oklahoma, Edmond, OK 73034-5209; Dillon, Robert

2014-08-01

Dielectrophoresis, a nonlinear electrokinetic transport mechanism, has become popular in many engineering applications including manipulation, characterization and actuation of biomaterials, particles and biological cells. In this paper, we present a hybrid immersed interface–immersed boundary method to study AC dielectrophoresis where an algorithm is developed to solve the complex Poisson equation using a real variable formulation. An immersed interface method is employed to obtain the AC electric field in a fluid media with suspended particles and an immersed boundary method is used for the fluid equations and particle transport. The convergence of the proposed algorithm as well as validation of themore » hybrid scheme with experimental results is presented. In this paper, the Maxwell stress tensor is used to calculate the dielectrophoretic force acting on particles by considering the physical effect of particles in the computational domain. Thus, this study eliminates the approximations used in point dipole methods for calculating dielectrophoretic force. A comparative study between Maxwell stress tensor and point dipole methods for computing dielectrophoretic forces are presented. The hybrid method is used to investigate the physics of dielectrophoresis in microfluidic devices using an AC electric field. The numerical results show that with proper design and appropriate selection of applied potential and frequency, global electric field minima can be obtained to facilitate multiple particle trapping by exploiting the mechanism of negative dielectrophoresis. Our numerical results also show that electrically neutral particles form a chain parallel to the applied electric field irrespective of their initial orientation when an AC electric field is applied. This proposed hybrid numerical scheme will help to better understand dielectrophoresis and to design and optimize microfluidic devices.« less

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

A Local Fast Marching-Based Diffusion Tensor Image Registration Algorithm by Simultaneously Considering Spatial Deformation and Tensor Orientation

PubMed Central

Xue, Zhong; Li, Hai; Guo, Lei; Wong, Stephen T.C.

2010-01-01

It is a key step to spatially align diffusion tensor images (DTI) to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints. Different from traditional scalar or multi-channel image registration methods, tensor orientation should be considered in DTI registration. Recently, several DTI registration methods have been proposed in the literature, but deformation fields are purely dependent on the tensor features not the whole tensor information. Other methods, such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms, use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration. However, only relatively local tensor information such as voxel-wise tensor-similarity, is utilized. This paper proposes a new DTI image registration algorithm, called local fast marching (FM)-based simultaneous registration. The algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation, and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest. These local fast marching-based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures. Using simulated and real DTI human brain data the experimental results show that the proposed algorithm is more accurate compared with the FA-based registration and is more efficient than its counterpart, the neighborhood tensor similarity-based registration. PMID:20382233

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.

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.

Tensor-based dynamic reconstruction method for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.

2017-03-01

Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order tensor that consists of a low rank tensor and a sparse tensor within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank tensor models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse tensor captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the tensor-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank tensor and the sparse tensor, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image tensor. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.

Tensor Toolbox for MATLAB v. 3.0

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

Kola, Tamara; Bader, Brett W.; Acar Ataman, Evrim NMN

Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features. It also provides algorithms for tensor decomposition and factorization, algorithms for computing tensor eigenvalues, and methods for visualization of results.

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov-Uvarov Method

NASA Astrophysics Data System (ADS)

Akpan, N. Ikot; Hassan, Hassanabadi; Tamunoimi, M. Abbey

2015-12-01

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseudospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.

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

Analytical Summary. Part 1. The Physical Properties of STS under Triaxial Stress

DTIC Science & Technology

1946-06-01

between Octahedral Shear Stress and Octahedral Shear Strain for Zero Mean Hydrostatic Tension. Data for SIS of 115000 (lb)/(in)2 Tensile Strength. Figure (5...the specimen and the twist by the equation a4• S The tensors I + VAr and (I + VAr)-1 have the matrices Ii 0 0 0 00 0 i O and 0 1 0 0 s 1 jO- si The...given in terms of s by the equations = - + V. + ’s + ___ Sis + + =. 2 ’ = - i + i+ 1s2 is 44 e/ l+ 44S2 The rate of strain tensor X has the components

Retrospective Correction of Physiological Noise in DTI Using an Extended Tensor Model and Peripheral Measurements

PubMed Central

Mohammadi, Siawoosh; Hutton, Chloe; Nagy, Zoltan; Josephs, Oliver; Weiskopf, Nikolaus

2013-01-01

Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framework of the extended tensor model two types of regressors, which respectively modeled small (linear) and strong (nonlinear) variations in the diffusion signal, were derived from peripheral measures. We tested the performance of four extended tensor models with different physiological noise regressors on nongated and gated diffusion tensor imaging data, and compared it to an established data-driven robust fitting method. In the brainstem and cerebellum the extended tensor models reduced the noise in the tensor-fit by up to 23% in accordance with previous studies on physiological noise. The extended tensor model addresses both large-amplitude outliers and small-amplitude signal-changes. The framework of the extended tensor model also facilitates further investigation into physiological noise in diffusion tensor imaging. The proposed extended tensor model can be readily combined with other artefact correction methods such as robust fitting and eddy current correction. PMID:22936599

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.

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.

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.

TNSPackage: A Fortran2003 library designed for tensor network state methods

NASA Astrophysics Data System (ADS)

Dong, Shao-Jun; Liu, Wen-Yuan; Wang, Chao; Han, Yongjian; Guo, G.-C.; He, Lixin

2018-07-01

Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the operations of tensors, including contraction, permutation, reshaping tensors, SVD and so on. Unfortunately, the most popular computer languages for scientific computation, such as Fortran and C/C++ do not have a standard library for such operations, and therefore make the coding of TNS very tedious. We develop a Fortran2003 package that includes all kinds of basic tensor operations designed for TNS. It is user-friendly and flexible for different forms of TNS, and therefore greatly simplifies the coding work for the TNS methods.

A rederivation of the conformal anomaly for spin-{\\frac{1}{2}}

NASA Astrophysics Data System (ADS)

Godazgar, Hadi; Nicolai, Hermann

2018-05-01

We rederive the conformal anomaly for spin- fermions by a genuine Feynman graph calculation, which has not been available so far. Although our calculation merely confirms a result that has been known for a long time, the derivation is new, and thus furnishes a method to investigate more complicated cases (in particular concerning the significance of the quantum trace of the stress tensor in non-conformal theories) where there remain several outstanding and unresolved issues.

Mechanical behaviour of the human atria.

PubMed

Bellini, Chiara; Di Martino, Elena S; Federico, Salvatore

2013-07-01

This work was aimed at providing a local mechanical characterisation of tissues from the healthy human atria. Thirty-two tissue specimens were harvested from nine adult subjects whose death was not directly related to cardiovascular diseases. Tissues were kept in Tyrode's solution and tested using a planar biaxial device. Results showed that tissues from healthy human atria undergo large deformations under in-plane distributed tensions roughly corresponding to an in vivo pressure of 15 mmHg. The material was modelled as hyperelastic and a Fung-type elastic strain energy potential was chosen. This class of potentials is based on a function of a quadratic form in the components of the Green-Lagrange strain tensor, and it has been previously proved that the fourth-order tensor of this quadratic form is proportional to the linear elasticity tensor of the linearised theory. This has three important consequences: (i) the coefficients in Fung-type potentials have a precise physical meaning; (ii) whenever a microstructural description for the linear elasticity tensor is available, this is automatically inherited by the Fung-type potential; (iii) because of the presence of the linear elasticity tensor in the definition of a Fung-type potential, each of the three normal stresses is coupled with all three normal strains.We propose to include information on the microstructure of the atrium by writing the linear elasticity tensor as the volumetric-fraction-weighed sum of the linear elasticity tensors of the three constituents of the tissue: the ground matrix, the main fibre family and the secondary fibre family. To the best of our knowledge, this is the first time that a Fung-type potential is given a precise structural meaning, based on the directions and the material properties of the fibres. Because of the coupling between normal strains and normal stresses, this structurally-based Fung-type potential allows for discriminating among all testing protocols in planar biaxial stretch.

A Comprehensive Overview of the Duvernay Induced Seismicity near Fox Creek, Alberta

NASA Astrophysics Data System (ADS)

Schultz, R.; Wang, R.; Gu, Y. J.; Haug, K.; Atkinson, G. M.

2016-12-01

In this work we summarize the current state of understanding regarding the induced seismicity related to Duvernay hydraulic fracturing operations in central Alberta, near the town of Fox Creek. Earthquakes in this region cluster into distinct sequences in time, space, and focal mechanism. To corroborate this point, we use cross-correlation detection methods to delineate transient temporal relationships, double-difference relocations to confirm spatial clustering, and moment tensor determinations to show fault motion consistency. The spatiotemporal clustering of sequences is strongly related to nearby hydraulic fracturing operations. In addition, we identify a strong preference for subvertical strike-slip motion with a roughly 45º P-axis orientation, consistent with ambient stress field considerations. The hypocentral geometry in two red traffic light protocol cases, that are robustly constrained by local array data, provide compelling evidence for planar features starting at Duvernay Formation depths and extending into the shallow Precambrian basement. We interpret these features as faults orientated approximately north-south and subvertically, consistent with moment tensor determinations. Finally, we conclude that the primary sequences are best explained as induced events in response to effective stress changes as a result of pore-pressure increase along previously existing faults due to hydraulic fracturing stimulations.

Tensor Fukunaga-Koontz transform for small target detection in infrared images

NASA Astrophysics Data System (ADS)

Liu, Ruiming; Wang, Jingzhuo; Yang, Huizhen; Gong, Chenglong; Zhou, Yuanshen; Liu, Lipeng; Zhang, Zhen; Shen, Shuli

2016-09-01

Infrared small targets detection plays a crucial role in warning and tracking systems. Some novel methods based on pattern recognition technology catch much attention from researchers. However, those classic methods must reshape images into vectors with the high dimensionality. Moreover, vectorizing breaks the natural structure and correlations in the image data. Image representation based on tensor treats images as matrices and can hold the natural structure and correlation information. So tensor algorithms have better classification performance than vector algorithms. Fukunaga-Koontz transform is one of classification algorithms and it is a vector version method with the disadvantage of all vector algorithms. In this paper, we first extended the Fukunaga-Koontz transform into its tensor version, tensor Fukunaga-Koontz transform. Then we designed a method based on tensor Fukunaga-Koontz transform for detecting targets and used it to detect small targets in infrared images. The experimental results, comparison through signal-to-clutter, signal-to-clutter gain and background suppression factor, have validated the advantage of the target detection based on the tensor Fukunaga-Koontz transform over that based on the Fukunaga-Koontz transform.

Obtaining orthotropic elasticity tensor using entries zeroing method.

NASA Astrophysics Data System (ADS)

Gierlach, Bartosz; Danek, Tomasz

2017-04-01

A generally anisotropic elasticity tensor obtained from measurements can be represented by a tensor belonging to one of eight material symmetry classes. Knowledge of symmetry class and orientation is helpful for describing physical properties of a medium. For each non-trivial symmetry class except isotropic this problem is nonlinear. A common method of obtaining effective tensor is a choosing its non-trivial symmetry class and minimizing Frobenius norm between measured and effective tensor in the same coordinate system. Global optimization algorithm has to be used to determine the best rotation of a tensor. In this contribution, we propose a new approach to obtain optimal tensor, with the assumption that it is orthotropic (or at least has a similar shape to the orthotropic one). In orthotropic form tensor 24 out of 36 entries are zeros. The idea is to minimize the sum of squared entries which are supposed to be equal to zero through rotation calculated with optimization algorithm - in this case Particle Swarm Optimization (PSO) algorithm. Quaternions were used to parametrize rotations in 3D space to improve computational efficiency. In order to avoid a choice of local minima we apply PSO several times and only if we obtain similar results for the third time we consider it as a correct value and finish computations. To analyze obtained results Monte-Carlo method was used. After thousands of single runs of PSO optimization, we obtained values of quaternion parts and plot them. Points concentrate in several points of the graph following the regular pattern. It suggests the existence of more complex symmetry in the analyzed tensor. Then thousands of realizations of generally anisotropic tensor were generated - each tensor entry was replaced with a random value drawn from normal distribution having a mean equal to measured tensor entry and standard deviation of the measurement. Each of these tensors was subject of PSO based optimization delivering quaternion for optimal rotation. Computations were parallelized with OpenMP to decrease computational time what enables different tensors to be processed by different threads. As a result the distributions of rotated tensor entries values were obtained. For the entries which were to be zeroed we can observe almost normal distributions having mean equal to zero or sum of two normal distributions having inverse means. Non-zero entries represent different distributions with two or three maxima. Analysis of obtained results shows that described method produces consistent values of quaternions used to rotate tensors. Despite of less complex target function in a process of optimization in comparison to common approach, entries zeroing method provides results which can be applied to obtain an orthotropic tensor with good reliability. Modification of the method can produce also a tool for obtaining effective tensors belonging to another symmetry classes. This research was supported by the Polish National Science Center under contract No. DEC-2013/11/B/ST10/0472.

Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

Inference of segmented color and texture description by tensor voting.

PubMed

Jia, Jiaya; Tang, Chi-Keung

2004-06-01

A robust synthesis method is proposed to automatically infer missing color and texture information from a damaged 2D image by (N)D tensor voting (N > 3). The same approach is generalized to range and 3D data in the presence of occlusion, missing data and noise. Our method translates texture information into an adaptive (N)D tensor, followed by a voting process that infers noniteratively the optimal color values in the (N)D texture space. A two-step method is proposed. First, we perform segmentation based on insufficient geometry, color, and texture information in the input, and extrapolate partitioning boundaries by either 2D or 3D tensor voting to generate a complete segmentation for the input. Missing colors are synthesized using (N)D tensor voting in each segment. Different feature scales in the input are automatically adapted by our tensor scale analysis. Results on a variety of difficult inputs demonstrate the effectiveness of our tensor voting approach.

Stress field modelling from digital geological map data

NASA Astrophysics Data System (ADS)

Albert, Gáspár; Barancsuk, Ádám; Szentpéteri, Krisztián

2016-04-01

To create a model for the lithospheric stress a functional geodatabase is required which contains spatial and geodynamic parameters. A digital structural-geological map is a geodatabase, which usually contains enough attributes to create a stress field model. Such a model is not accurate enough for engineering-geological purposes because simplifications are always present in a map, but in many cases maps are the only sources for a tectonic analysis. The here presented method is designed for field geologist, who are interested to see the possible realization of the stress field over the area, on which they are working. This study presents an application which can produce a map of 3D stress vectors from a kml-file. The core application logic is implemented on top of a spatially aware relational database management system. This allows rapid and geographically accurate analysis of the imported geological features, taking advantage of standardized spatial algorithms and indexing. After pre-processing the map features in a GIS, according to the Type-Property-Orientation naming system, which was described in a previous study (Albert et al. 2014), the first stage of the algorithm generates an irregularly spaced point cloud by emitting a pattern of points within a user-defined buffer zone around each feature. For each point generated, a component-wise approximation of the tensor field at the point's position is computed, derived from the original feature's geodynamic properties. In a second stage a weighted moving average method calculates the stress vectors in a regular grid. Results can be exported as geospatial data for further analysis or cartographic visualization. Computation of the tensor field's components is based on the implementation of the Mohr diagram of a compressional model, which uses a Coulomb fracture criterion. Using a general assumption that the main principal stress must be greater than the stress from the overburden, the differential stress is calculated from the fracture criterion. The calculation includes the gravitational acceleration, the average density of rocks and the experimental 60 degree of the fracture angle from the normal of the fault plane. This way, the stress tensors are calculated as absolute pressure values per square meters on both sides of the faults. If the stress from the overburden is greater than 1 bar (i.e. the faults are buried), a confined compression would be present. Modelling this state of stress may result a confusing pattern of vectors, because in a confined position the horizontal stress vectors may point towards structures primarily associated with extension. To step over this, and to highlight the variability in the stress-field, the model calculates the vectors directly from the differential stress (practically subtracting the minimum principal stress from the critical stress). The result of the modelling is a vector map, which theoretically represents the minimum tectonic pressure in the moment, when the rock body breaks from an initial state. This map - together with the original fault-map - is suitable for determining those areas where unrevealed tectonic, sedimentary and lithological structures are possibly present (e.g. faults, sub-basins and intrusions). With modelling different deformational phases on the same area, change of the stress vectors can be detected which reveals not only the varying directions of the principal stresses, but the tectonic-driven sedimentation patterns too. The decrease of necessary critical stress in the case of a possible reactivation of a fault in subsequent deformation phase can be managed with the down-ranking of the concerning structural elements. Reference: Albert G., Ungvári ZS., Szentpéteri K. 2014: Modeling the present day stress field of the Pannonian Basin from neotectonic maps - In: Beqiraj A, Ionescu C, Christofides G, Uta A, Beqiraj Goga E, Marku S (eds.) Proceedings XX Congress of the Carpathian-Balkan Geological Association. Tirana: p. 2.

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.

Groupwise Registration and Atlas Construction of 4th-Order Tensor Fields Using the ℝ+ Riemannian Metric*

PubMed Central

Barmpoutis, Angelos

2010-01-01

Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge there is no other existing method to achieve this task. First we define a metric on the space of positive-valued functions based on the Riemannian metric of real positive numbers (denoted by ℝ+). Then, we use this metric in a novel functional minimization method for non-rigid 4th-order tensor field registration. We define a cost function that accounts for the 4th-order tensor re-orientation during the registration process and has analytic derivatives with respect to the transformation parameters. Finally, the tensor field atlas is computed as the minimizer of the variance defined using the Riemannian metric. We quantitatively compare the proposed method with other techniques that register scalar-valued or diffusion tensor (rank-2) representations of the DWMRI. PMID:20436782

Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation.

PubMed

Freistühler, Heinrich; Temple, Blake

2014-06-08

CURRENT THEORIES OF DISSIPATION IN THE RELATIVISTIC REGIME SUFFER FROM ONE OF TWO DEFICITS: either their dissipation is not causal or no profiles for strong shock waves exist. This paper proposes a relativistic Navier-Stokes-Fourier-type viscosity and heat conduction tensor such that the resulting second-order system of partial differential equations for the fluid dynamics of pure radiation is symmetric hyperbolic. This system has causal dissipation as well as the property that all shock waves of arbitrary strength have smooth profiles. Entropy production is positive both on gradients near those of solutions to the dissipation-free equations and on gradients of shock profiles. This shows that the new dissipation stress tensor complies to leading order with the principles of thermodynamics. Whether higher order modifications of the ansatz are required to obtain full compatibility with the second law far from the zero-dissipation equilibrium is left to further investigations. The system has exactly three a priori free parameters χ , η , ζ , corresponding physically to heat conductivity, shear viscosity and bulk viscosity. If the bulk viscosity is zero (as is stated in the literature) and the total stress-energy tensor is trace free, the entire viscosity and heat conduction tensor is determined to within a constant factor.

Analysis of spatial correlations in a model two-dimensional liquid through eigenvalues and eigenvectors of atomic-level stress matrices.

PubMed

Levashov, V A; Stepanov, M G

2016-01-01

Considerations of local atomic-level stresses associated with each atom represent a particular approach to address structures of disordered materials at the atomic level. We studied structural correlations in a two-dimensional model liquid using molecular dynamics simulations in the following way. We diagonalized the atomic-level stress tensor of every atom and investigated correlations between the eigenvalues and orientations of the eigenvectors of different atoms as a function of distance between them. It is demonstrated that the suggested approach can be used to characterize structural correlations in disordered materials. In particular, we found that changes in the stress correlation functions on decrease of temperature are the most pronounced for the pairs of atoms with separation distance that corresponds to the first minimum in the pair density function. We also show that the angular dependencies of the stress correlation functions previously reported by Wu et al. [Phys. Rev. E 91, 032301 (2015)10.1103/PhysRevE.91.032301] do not represent the anisotropic Eshelby's stress fields, as it is suggested, but originate in the rotational properties of the stress tensors.

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.

Bridging scales of crustal stress patterns using the new World Stress Map

NASA Astrophysics Data System (ADS)

Heidbach, O.; Rajabi, M.; Cui, X.; Fuchs, K. W.; Mueller, B.; Reinecker, J.; Reiter, K.; Tingay, M. R. P.; Wenzel, F.; Xie, F.; Ziegler, M.; Zoback, M. D.; Zoback, M. L.

2017-12-01

Knowledge of the contemporary crustal stress field is a key parameter for the understanding of geodynamic processes such as global plate tectonics and the earthquake cycle. It is also an essential parameter for our sustainable and safe usage of Earth's resources, which is a major challenge for energy security in the 21st century. Since 1986, the World Stress Map (WSM) project has systematically compiled present-day stress information and provides a unique public domain global database. It is a long-term project based on an international network of partners from academia and industry. All data are public and available on the project website at world-stress-map.org. For the 30th anniversary of the project a new database has been compiled, containing double the amount of data records (n=42,870) including new data records from almost 4,000 deep boreholes. The new compilation focused on areas with previously sparse data coverage in order to resolve the stress pattern on different spatial scales. The significantly higher data density can now be used to resolve stress pattern heterogeneities on regional and local scales, as well as with depth in some regions. We present three results derived from the new WSM compilation: 1.) The global comparison between absolute plate motion and the mean of the orientation of maximum horizontal stress SHmax on a regular grid shows that there is still a correlation for the North and South America plate, but deviations from this general trend are now also clearly resolved. 2.) The variability of the crustal stress pattern changes when zooming in from plate-wide scale down to basin scale at 100 km. We show examples for Eastern Australia, Oklahoma and Central Europe. This regional and local variability of the stress pattern can be used as a proxy to identify and quantify regional and local stress sources by means of geomechanical-numerical models of the 3D stress tensor. 3.) Finally we present briefly the general concept of a multi-stage 3D geomechanical-numerical model workflow based on the WSM data to describe the in situ stress tensor. 3D Geomechanical-numerical modelling of the in situ stress state is essential to derive a continuous description of the stress tensor e.g. in order to estimate the distance to a critical stress state.

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.

SGS Closure Methodology for Surface-layer Rough-wall Turbulence.

NASA Astrophysics Data System (ADS)

Brasseur, James G.; Juneja, Anurag

1998-11-01

As reported in another abstract, necessary under-resolution and anisotropy of integral scales near the surface in LES of rough-wall boundary layers cause errors in the statistical structure of the modeled subgrid-scale (SGS) acceleration using eddy viscosity and similarity closures. The essential difficulty is an overly strong coupling between the modeled SGS stress tensor and predicted resolved velocity u^r. Specific to this problem, we propose a class of SGS closures in which subgrid scale velocities u^s1 between an explicit filter scale Δ and the grid scale δ are estimated from the solution to a separate prognostic equation, and the SGS stress tensor is formed using u^s1 as a surrogate for subgrid velocity u^s. The method is currently under development for pseudo-spectral LES where a filter at scales δ < Δ is explicit. The exact evolution equation for u^s1 contains dynamical interactions between u^r and u^s1 which can be calculated directly, and a term which is modeled to capture energy flux from the s1 scales without altering u^s1 structure. Three levels of closure for SGS stress are possible at different levels of accuracy and computational expense. The cheapest model has been tested with DNS and LES of anisotropic buoyancy-driven turbulence. Preliminary results show major improvement in the structure of the predicted SGS acceleration with much of the spurious coupling between u^r and SGS stress removed. Performance, predictions and cost of the three levels of closure are under analysis.

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.

Traffic speed data imputation method based on tensor completion.

PubMed

Ran, Bin; Tan, Huachun; Feng, Jianshuai; Liu, Ying; Wang, Wuhong

2015-01-01

Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.

Traffic Speed Data Imputation Method Based on Tensor Completion

PubMed Central

Ran, Bin; Feng, Jianshuai; Liu, Ying; Wang, Wuhong

2015-01-01

Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches. PMID:25866501

Conformal and Nearly Conformal Theories at Large N

NASA Astrophysics Data System (ADS)

Tarnoplskiy, Grigory M.

In this thesis we present new results in conformal and nearly conformal field theories in various dimensions. In chapter two, we study different properties of the conformal Quantum Electrodynamics (QED) in continuous dimension d. At first we study conformal QED using large Nf methods, where Nf is the number of massless fermions. We compute its sphere free energy as a function of d, ignoring the terms of order 1/Nf and higher. For finite Nf we use the epsilon-expansion. Next we use a large Nf diagrammatic approach to calculate the leading corrections to CT, the coefficient of the two-point function of the stress-energy tensor, and CJ, the coefficient of the two-point function of the global symmetry current. We present explicit formulae as a function of d and check them versus the expectations in 2 and 4 - epsilon dimensions. In chapter three, we discuss vacuum stability in 1 + 1 dimensional conformal field theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective in/out Lagrangian. The two-form is expressed in terms of a Riemann-Hilbert decomposition for background gauge fields, and is given by its novel "functional'' version in the gravitational case. In chapter four, we explore Tensor models. Such models possess the large N limit dominated by the melon diagrams. The quantum mechanics of a real anti-commuting rank-3 tensor has a large N limit similar to the Sachdev-Ye-Kitaev (SYK) model. We also discuss the quantum mechanics of a complex 3-index anti-commuting tensor and argue that it is equivalent in the large N limit to a version of SYK model with complex fermions. Finally, we discuss models of a commuting tensor in dimension d. We study the spectrum of the large N quantum field theory of bosonic rank-3 tensors using the Schwinger-Dyson equations. We compare some of these results with the 4 - epsilon expansion, finding perfect agreement. We also study the spectra of bosonic theories of rank q - 1 tensors with φq interactions.

On physical property tensors invariant under line groups.

PubMed

Litvin, Daniel B

2014-03-01

The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of an infinite number of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an index n and a physical property tensor of rank m, the form of the tensor for all line group types indexed with n > m is the same, leaving only a finite number of tensor forms to be determined.

A Three-Dimensional Eulerian Code for Simulation of High-Speed Multimaterial Interactions

DTIC Science & Technology

2011-08-01

PDE -based extension. The extension process is done on only the host cells on a particular processor. After extension the parallel communication is...condensation shocks, explosive debris transport, detonation in heterogeneous media and so on. In these flows complex interactions occur between the...A.22] and ijΩ is the spin tensor. The Jaumann derivative is used to ensure objectivity of the stress tensor with respect to rotation

Experimental Validation of a Coupled Fluid-Multibody Dynamics Model for Tanker Trucks

DTIC Science & Technology

2007-11-08

order to accurately predict the dynamic response of tanker trucks, the model must accurately account for the following effects : • Incompressible...computational code which uses a time- accurate explicit solution procedure is used to solve both the solid and fluid equations of motion. Many commercial...position vector, τ is the deviatoric stress tensor, D is the rate of deformation tensor, f r is the body force vector, r is the artificial

Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

PubMed

Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik

2007-01-01

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

Quantum field theory in spaces with closed timelike curves

NASA Astrophysics Data System (ADS)

Boulware, David G.

1992-11-01

Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Irreducible Representations of Oscillatory and Swirling Flows in Active Soft Matter

NASA Astrophysics Data System (ADS)

Ghose, Somdeb; Adhikari, R.

2014-03-01

Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.

Surface energy and surface stress on vicinals by revisiting the Shuttleworth relation

NASA Astrophysics Data System (ADS)

Hecquet, Pascal

2018-04-01

In 1998 [Surf. Sci. 412/413, 639 (1998)], we showed that the step stress on vicinals varies as 1/L, L being the distance between steps, while the inter-step interaction energy primarily follows the law as 1/L2 from the well-known Marchenko-Parshin model. In this paper, we give a better understanding of the interaction term of the step stress. The step stress is calculated with respect to the nominal surface stress. Consequently, we calculate the diagonal surface stresses in both the vicinal system (x, y, z) where z is normal to the vicinal and the projected system (x, b, c) where b is normal to the nominal terrace. Moreover, we calculate the surface stresses by using two methods: the first called the 'Zero' method, from the surface pressure forces and the second called the 'One' method, by homogeneously deforming the vicinal in the parallel direction, x or y, and by calculating the surface energy excess proportional to the deformation. By using the 'One' method on the vicinal Cu(0 1 M), we find that the step deformations, due to the applied deformation, vary as 1/L by the same factor for the tensor directions bb and cb, and by twice the same factor for the parallel direction yy. Due to the vanishing of the surface stress normal to the vicinal, the variation of the step stress in the direction yy is better described by using only the step deformation in the same direction. We revisit the Shuttleworth formula, for while the variation of the step stress in the direction xx is the same between the two methods, the variation in the direction yy is higher by 76% for the 'Zero' method with respect to the 'One' method. In addition to the step energy, we confirm that the variation of the step stress must be taken into account for the understanding of the equilibrium of vicinals when they are not deformed.

Entanglement branching operator

NASA Astrophysics Data System (ADS)

Harada, Kenji

2018-01-01

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

On the magnetic polarizability tensor of US coinage

NASA Astrophysics Data System (ADS)

Davidson, John L.; Abdel-Rehim, Omar A.; Hu, Peipei; Marsh, Liam A.; O'Toole, Michael D.; Peyton, Anthony J.

2018-03-01

The magnetic dipole polarizability tensor of a metallic object gives unique information about the size, shape and electromagnetic properties of the object. In this paper, we present a novel method of coin characterization based on the spectroscopic response of the absolute tensor. The experimental measurements are validated using a combination of tests with a small set of bespoke coin surrogates and simulated data. The method is applied to an uncirculated set of US coins. Measured and simulated spectroscopic tensor responses of the coins show significant differences between different coin denominations. The presented results are encouraging as they strongly demonstrate the ability to characterize coins using an absolute tensor approach.

The Spacetime Between Einstein and Kaluza-Klein: Further Explorations

NASA Astrophysics Data System (ADS)

Vuille, Chris

2017-01-01

Tensor multinomials can be used to create a generalization of Einstein's general relativity that in a mathematical sense falls between Einstein's original theory in four dimensions and the Kaluza-Klein theory in five dimensions. In the extended theory there are only four physical dimensions, but the tensor multinomials are expanded operators that can accommodate other forces of nature. The equivalent Ricci tensor of this geometry yields vacuum general relativity and electromagnetism, as well as a Klein-Gordon-like quantum scalar field. With a generalization of the stress-energy tensor, an exact solution for a plane-symmetric dust can be found where the scalar portion of the field drives early universe inflation, levels off for a period, then causes a later continued universal acceleration, a possible geometric mechanism for the inflaton or dark energy. Some new explorations of the equations, the problems, and possibilities will be presented and discussed.

Very low frequency earthquakes (VLFEs) detected during episodic tremor and slip (ETS) events in Cascadia using a match filter method indicate repeating events

NASA Astrophysics Data System (ADS)

Hutchison, A. A.; Ghosh, A.

2016-12-01

Very low frequency earthquakes (VLFEs) occur in transitional zones of faults, releasing seismic energy in the 0.02-0.05 Hz frequency band over a 90 s duration and typically have magntitudes within the range of Mw 3.0-4.0. VLFEs can occur down-dip of the seismogenic zone, where they can transfer stress up-dip potentially bringing the locked zone closer to a critical failure stress. VLFEs also occur up-dip of the seismogenic zone in a region along the plate interface that can rupture coseismically during large megathrust events, such as the 2011 Tohoku-Oki earthquake [Ide et al., 2011]. VLFEs were first detected in Cascadia during the 2011 episodic tremor and slip (ETS) event, occurring coincidentally with tremor [Ghosh et al., 2015]. However, during the 2014 ETS event, VLFEs were spatially and temporally asynchronous with tremor activity [Hutchison and Ghosh, 2016]. Such contrasting behaviors remind us that the mechanics behind such events remain elusive, yet they are responsible for the largest portion of the moment release during an ETS event. Here, we apply a match filter method using known VLFEs as template events to detect additional VLFEs. Using a grid-search centroid moment tensor inversion method, we invert stacks of the resulting match filter detections to ensure moment tensor solutions are similar to that of the respective template events. Our ability to successfully employ a match filter method to VLFE detection in Cascadia intrinsically indicates that these events can be repeating, implying that the same asperities are likely responsible for generating multiple VLFEs.

Study of the Rock Mass Failure Process and Mechanisms During the Transformation from Open-Pit to Underground Mining Based on Microseismic Monitoring

NASA Astrophysics Data System (ADS)

Zhao, Yong; Yang, Tianhong; Bohnhoff, Marco; Zhang, Penghai; Yu, Qinglei; Zhou, Jingren; Liu, Feiyue

2018-05-01

To quantitatively understand the failure process and failure mechanism of a rock mass during the transformation from open-pit mining to underground mining, the Shirengou Iron Mine was selected as an engineering project case study. The study area was determined using the rock mass basic quality classification method and the kinematic analysis method. Based on the analysis of the variations in apparent stress and apparent volume over time, the rock mass failure process was analyzed. According to the recent research on the temporal and spatial change of microseismic events in location, energy, apparent stress, and displacement, the migration characteristics of rock mass damage were studied. A hybrid moment tensor inversion method was used to determine the rock mass fracture source mechanisms, the fracture orientations, and fracture scales. The fracture area can be divided into three zones: Zone A, Zone B, and Zone C. A statistical analysis of the orientation information of the fracture planes orientations was carried out, and four dominant fracture planes were obtained. Finally, the slip tendency analysis method was employed, and the unstable fracture planes were obtained. The results show: (1) The microseismic monitoring and hybrid moment tensor analysis can effectively analyze the failure process and failure mechanism of rock mass, (2) during the transformation from open-pit to underground mining, the failure type of rock mass is mainly shear failure and the tensile failure is mostly concentrated in the roof of goafs, and (3) the rock mass of the pit bottom and the upper of goaf No. 18 have the possibility of further damage.

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.

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.

A unified tensor level set for image segmentation.

PubMed

Wang, Bin; Gao, Xinbo; Tao, Dacheng; Li, Xuelong

2010-06-01

This paper presents a new region-based unified tensor level set model for image segmentation. This model introduces a three-order tensor to comprehensively depict features of pixels, e.g., gray value and the local geometrical features, such as orientation and gradient, and then, by defining a weighted distance, we generalized the representative region-based level set method from scalar to tensor. The proposed model has four main advantages compared with the traditional representative method as follows. First, involving the Gaussian filter bank, the model is robust against noise, particularly the salt- and pepper-type noise. Second, considering the local geometrical features, e.g., orientation and gradient, the model pays more attention to boundaries and makes the evolving curve stop more easily at the boundary location. Third, due to the unified tensor pixel representation representing the pixels, the model segments images more accurately and naturally. Fourth, based on a weighted distance definition, the model possesses the capacity to cope with data varying from scalar to vector, then to high-order tensor. We apply the proposed method to synthetic, medical, and natural images, and the result suggests that the proposed method is superior to the available representative region-based level set method.

The gravitational wave stress–energy (pseudo)-tensor in modified gravity

NASA Astrophysics Data System (ADS)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

The recent detections of gravitational waves by the advanced LIGO and Virgo detectors open up new tests of modified gravity theories in the strong-field and dynamical, extreme gravity regime. Such tests rely sensitively on the phase evolution of the gravitational waves, which is controlled by the energy–momentum carried by such waves out of the system. We here study four different methods for finding the gravitational wave stress–energy pseudo-tensor in gravity theories with any combination of scalar, vector, or tensor degrees of freedom. These methods rely on the second variation of the action under short-wavelength averaging, the second perturbation of the field equations in the short-wavelength approximation, the construction of an energy complex leading to a Landau–Lifshitz tensor, and the use of Noether’s theorem in field theories about a flat background. We apply these methods in general relativity, Jordan–Fierz–Brans–Dicky theoy, and Einstein-Æther theory to find the gravitational wave stress–energy pseudo-tensor and calculate the rate at which energy and linear momentum is carried away from the system. The stress–energy tensor and the rate of linear momentum loss in Einstein-Æther theory are presented here for the first time. We find that all methods yield the same rate of energy loss, although the stress–energy pseudo-tensor can be functionally different. We also find that the Noether method yields a stress–energy tensor that is not symmetric or gauge-invariant, and symmetrization via the Belinfante procedure does not fix these problems because this procedure relies on Lorentz invariance, which is spontaneously broken in Einstein-Æther theory. The methods and results found here will be useful for the calculation of predictions in modified gravity theories that can then be contrasted with observations.

Vacuum polarization of the electromagnetic field near a rotating black hole

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

Frolov, V.P.; Zel'nikov, A.I.

1985-12-15

The electromagnetic field contribution to the vacuum polarization near a rotating black hole is considered. It is shown that the problem of calculating the renormalized average value of the stress-energy tensor /sup ren/ for the Hartle-Hawking vacuum state at the pole of the event horizon can be reduced to the problem of electro- and magnetostatics in the Kerr spacetime. An explicit expression for /sup ren/ at the pole of the event horizon is obtained and its properties are discussed. It is shown that in the case of a nonrotating black hole the Page-Brown approximation for the electromagnetic stress-energy tensor givesmore » a result which coincides at the event horizon with the exact value of /sup ren/. .AE« less

Stress Energy Tensor in LCFT and LOGARITHMIC Sugawara Construction

NASA Astrophysics Data System (ADS)

Kogan, Ian I.; Nichols, Alexander

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c=-2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra. This is an expanded version of a talk presented by A. Nichols at the conference on Logarithmic Conformal Field Theory and its Applications in Tehran Iran, 2001.

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.

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.

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.

Derivation of the Schwartzchild Metric From the ``Self Censorship'' of the ZPF (Zero Point Energy) in the GEM Theory

NASA Astrophysics Data System (ADS)

Brandenburg, John

2012-10-01

The GEM theory (1) links the EM stress tensor directly to the metric tensor by the principle of ``self censorship'' of the ZPF (2) where the definition of guv = FuwF^wv/ 4 for Planck scale fields makes the stress tensor vanish even when fields are present. The first order form of the metric is recovered as Lorentzian due to alternating regions of strong electric and magnetic fields similar to that seen in models of spacetime in ``Loop Gravity,'' where the model admits perturbations. The GEM ExB drift models of gravity is used The first order perturbations on the fields are considered to be of the order of the fine structure constant alpha. Radiation fields due to a single charged particle of mass M fall off as 1/r and give the values (G=c=1) gtt = 1-2M/r and grr = (1-2M/r). (1) Brandenburg, J.E. (2012)., (2) STAIF II Conference Albuquerque NM 2.Brandenburg, J.E. (2007). IEEE Transactions On Plasma Science, Vol. 35, No. 4., p845.

A practical introduction to tensor networks: Matrix product states and projected entangled pair states

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

Orús, Román, E-mail: roman.orus@uni-mainz.de

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems aremore » also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.« less

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE PAGES

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

2018-03-20

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

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

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

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

Possibilities and limitations of rod-beam theories. [nonlinear distortion tensor and nonlinear stress tensors

NASA Technical Reports Server (NTRS)

Peterson, D.

1979-01-01

Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.

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.

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.

An Assessment of the Seismicity of the Bursa Region from a Temporary Seismic Network

NASA Astrophysics Data System (ADS)

Gok, Elcin; Polat, Orhan

2012-04-01

A temporary earthquake station network of 11 seismological recorders was operated in the Bursa region, south of the Marmara Sea in the northwest of Turkey, which is located at the southern strand of the North Anatolian Fault Zone (NAFZ). We located 384 earthquakes out of a total of 582 recorded events that span the study area between 28.50-30.00°E longitudes and 39.75-40.75°N latitudes. The depth of most events was found to be less than 29 km, and the magnitude interval ranges were between 0.3 ≤ ML ≤ 5.4, with RMS less than or equal to 0.2. Seismic activities were concentrated southeast of Uludag Mountain (UM), in the Kestel-Igdir area and along the Gemlik Fault (GF). In the study, we computed 10 focal mechanisms from temporary and permanents networks. The predominant feature of the computed focal mechanisms is the relatively widespread near horizontal northwest-southeast (NW-SE) T-axis orientation. These fault planes have been used to obtain the orientation and shape factor (R, magnitude stress ratio) of the principal stress tensors (σ1, σ2, σ3). The resulting stress tensors reveal σ1 closer to the vertical (oriented NE-SW) and σ2, σ3 horizontal with R = 0.5. These results confirm that Bursa and its vicinity could be defined by an extensional regime showing a primarily normal to oblique-slip motion character. It differs from what might be expected from the stress tensor inversion for the NAFZ. Different fault patterns related to structural heterogeneity from the north to the south in the study area caused a change in the stress regime from strike-slip to normal faulting.

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2015-04-01

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the naïve scattering algorithm (no memory access optimization). The tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).

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

Tensor sufficient dimension reduction

PubMed Central

Zhong, Wenxuan; Xing, Xin; Suslick, Kenneth

2015-01-01

Tensor is a multiway array. With the rapid development of science and technology in the past decades, large amount of tensor observations are routinely collected, processed, and stored in many scientific researches and commercial activities nowadays. The colorimetric sensor array (CSA) data is such an example. Driven by the need to address data analysis challenges that arise in CSA data, we propose a tensor dimension reduction model, a model assuming the nonlinear dependence between a response and a projection of all the tensor predictors. The tensor dimension reduction models are estimated in a sequential iterative fashion. The proposed method is applied to a CSA data collected for 150 pathogenic bacteria coming from 10 bacterial species and 14 bacteria from one control species. Empirical performance demonstrates that our proposed method can greatly improve the sensitivity and specificity of the CSA technique. PMID:26594304

Analysis of Lithospheric Stresses Using Satellite Gravimetry: Hypotheses and Applications to North Atlantic

NASA Astrophysics Data System (ADS)

Minakov, A.; Medvedev, S.

2017-12-01

Analysis of lithospheric stresses is necessary to gain understanding of the forces that drive plate tectonics and intraplate deformations and the structure and strength of the lithosphere. A major source of lithospheric stresses is believed to be in variations of surface topography and lithospheric density. The traditional approach to stress estimation is based on direct calculations of the Gravitational Potential Energy (GPE), the depth integrated density moment of the lithosphere column. GPE is highly sensitive to density structure which, however, is often poorly constrained. Density structure of the lithosphere may be refined using methods of gravity modeling. However, the resulted density models suffer from non-uniqueness of the inverse problem. An alternative approach is to directly estimate lithospheric stresses (depth integrated) from satellite gravimetry data. Satellite gravity gradient measurements by the ESA GOCE mission ensures a wealth of data for mapping lithospheric stresses if a link between data and stresses or GPE can be established theoretically. The non-uniqueness of interpretation of sources of the gravity signal holds in this case as well. Therefore, the data analysis was tested for the North Atlantic region where reliable additional constraints are supplied by both controlled-source and earthquake seismology. The study involves comparison of three methods of stress modeling: (1) the traditional modeling approach using a thin sheet approximation; (2) the filtered geoid approach; and (3) the direct utilization of the gravity gradient tensor. Whereas the first two approaches (1)-(2) calculate GPE and utilize a computationally expensive finite element mechanical modeling to calculate stresses, the approach (3) uses a much simpler numerical treatment but requires simplifying assumptions that yet to be tested. The modeled orientation of principal stresses and stress magnitudes by each of the three methods are compared with the World Stress Map.

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.

Electrodynamic multiple-scattering method for the simulation of optical trapping atop periodic metamaterials

NASA Astrophysics Data System (ADS)

Yannopapas, Vassilios; Paspalakis, Emmanuel

2018-07-01

We present a new theoretical tool for simulating optical trapping of nanoparticles in the presence of an arbitrary metamaterial design. The method is based on rigorously solving Maxwell's equations for the metamaterial via a hybrid discrete-dipole approximation/multiple-scattering technique and direct calculation of the optical force exerted on the nanoparticle by means of the Maxwell stress tensor. We apply the method to the case of a spherical polystyrene probe trapped within the optical landscape created by illuminating of a plasmonic metamaterial consisting of periodically arranged tapered metallic nanopyramids. The developed technique is ideally suited for general optomechanical calculations involving metamaterial designs and can compete with purely numerical methods such as finite-difference or finite-element schemes.

Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems

PubMed Central

2015-01-01

We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement. PMID:25844072

Vacuum stress energy density and its gravitational implications

NASA Astrophysics Data System (ADS)

Estrada, Ricardo; Fulling, Stephen A.; Kaplan, Lev; Kirsten, Klaus; Liu, Zhonghai; Milton, Kimball A.

2008-04-01

In nongravitational physics the local density of energy is often regarded as merely a bookkeeping device; only total energy has an experimental meaning—and it is only modulo a constant term. But in general relativity the local stress-energy tensor is the source term in Einstein's equation. In closed universes, and those with Kaluza-Klein dimensions, theoretical consistency demands that quantum vacuum energy should exist and have gravitational effects, although there are no boundary materials giving rise to that energy by van der Waals interactions. In the lab there are boundaries, and in general the energy density has a nonintegrable singularity as a boundary is approached (for idealized boundary conditions). As pointed out long ago by Candelas and Deutsch, in this situation there is doubt about the viability of the semiclassical Einstein equation. Our goal is to show that the divergences in the linearized Einstein equation can be renormalized to yield a plausible approximation to the finite theory that presumably exists for realistic boundary conditions. For a scalar field with Dirichlet or Neumann boundary conditions inside a rectangular parallelepiped, we have calculated by the method of images all components of the stress tensor, for all values of the conformal coupling parameter and an exponential ultraviolet cutoff parameter. The qualitative features of contributions from various classes of closed classical paths are noted. Then the Estrada-Kanwal distributional theory of asymptotics, particularly the moment expansion, is used to show that the linearized Einstein equation with the stress-energy near a plane boundary as source converges to a consistent theory when the cutoff is removed. This paper reports work in progress on a project combining researchers in Texas, Louisiana and Oklahoma. It is supported by NSF Grants PHY-0554849 and PHY-0554926.

Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole

NASA Astrophysics Data System (ADS)

Lanir, Assaf; Levi, Adam; Ori, Amos; Sela, Orr

2018-01-01

We derive explicit expressions for the two-point function of a massless scalar field in the interior region of a Reissner-Nordstrom black hole, in both the Unruh and the Hartle-Hawking quantum states. The two-point function is expressed in terms of the standard l m ω modes of the scalar field (those associated with a spherical harmonic Yl m and a temporal mode e-i ω t), which can be conveniently obtained by solving an ordinary differential equation, the radial equation. These explicit expressions are the internal analogs of the well-known results in the external region (originally derived by Christensen and Fulling), in which the two-point function outside the black hole is written in terms of the external l m ω modes of the field. They allow the computation of ⟨Φ2⟩ren and the renormalized stress-energy tensor inside the black hole, after the radial equation has been solved (usually numerically). In the second part of the paper, we provide an explicit expression for the trace of the renormalized stress-energy tensor of a minimally coupled massless scalar field (which is nonconformal), relating it to the d'Alembertian of ⟨Φ2⟩ren . This expression proves itself useful in various calculations of the renormalized stress-energy tensor.

Hawking radiation, covariant boundary conditions, and vacuum states

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

Banerjee, Rabin; Kulkarni, Shailesh

2009-04-15

The basic characteristics of the covariant chiral current and the covariant chiral energy-momentum tensor are obtained from a chiral effective action. These results are used to justify the covariant boundary condition used in recent approaches of computing the Hawking flux from chiral gauge and gravitational anomalies. We also discuss a connection of our results with the conventional calculation of nonchiral currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware) states.

Seismic sensitivity of normal-mode coupling to Lorentz stresses in the Sun

NASA Astrophysics Data System (ADS)

Hanasoge, Shravan M.

2017-09-01

Understanding the governing mechanism of solar magnetism remains an outstanding challenge in astrophysics. Seismology is the most compelling technique to infer the internal properties of the Sun and stars. Waves in the Sun, nominally acoustic, are sensitive to the emergence and cyclical strengthening of magnetic field, evidenced by measured changes in resonant oscillation frequencies that are correlated with the solar cycle. The inference of internal Lorentz stresses from these measurements has the potential to significantly advance our appreciation of the dynamo. Indeed, seismological inverse theory for the Sun is well understood for perturbations in composition, thermal structure and flows but, is not fully developed for magnetism, owing to the complexity of the ideal magnetohydrodynamic (MHD) equation. Invoking first-Born perturbation theory to characterize departures from spherically symmetric hydrostatic models of the Sun and applying the notation of generalized spherical harmonics, we calculate sensitivity functions of seismic measurements to the general time-varying Lorentz stress tensor. We find that eigenstates of isotropic (I.e. acoustic only) background models are dominantly sensitive to isotropic deviations in the stress tensor and much more weakly than anisotropic stresses (and therefore challenging to infer). The apple cannot fall far from the tree.

Stresses in curved nematic membranes.

PubMed

Santiago, J A

2018-05-01

Ordering configurations of a director field on a curved membrane induces stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in Gaussian curvature. These forces are mediated by the Green function of the Laplace-Beltrami operator of the surface. In addition, we find nonisotropic forces that involve derivatives of the Green function and the Gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive with respect to the north pole, indicating that it is an unstable equilibrium point.

Stresses in curved nematic membranes

NASA Astrophysics Data System (ADS)

Santiago, J. A.

2018-05-01

Ordering configurations of a director field on a curved membrane induces stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in Gaussian curvature. These forces are mediated by the Green function of the Laplace-Beltrami operator of the surface. In addition, we find nonisotropic forces that involve derivatives of the Green function and the Gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive with respect to the north pole, indicating that it is an unstable equilibrium point.

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.

Finite-temperature stress calculations in atomic models using moments of position.

PubMed

Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

2018-07-04

Continuum modeling of finite temperature mechanical behavior of atomic systems requires refined description of atomic motions. In this paper, we identify additional kinematical quantities that are relevant for a more accurate continuum description as the system is subjected to step-wise loading. The presented formalism avoids the necessity for atomic trajectory mapping with deformation, provides the definitions of the kinematic variables and their conjugates in real space, and simplifies local work conjugacy. The total work done on an atom under deformation is decomposed into the work corresponding to changing its equilibrium position and work corresponding to changing its second moment about equilibrium position. Correspondingly, we define two kinematic variables: a deformation gradient tensor and a vibration tensor, and derive their stress conjugates, termed here as static and vibration stresses, respectively. The proposed approach is validated using MD simulation in NVT ensembles for fcc aluminum subjected to uniaxial extension. The observed evolution of second moments in the MD simulation with macroscopic deformation is not directly related to the transformation of atomic trajectories through the deformation gradient using generator functions. However, it is noteworthy that deformation leads to a change in the second moment of the trajectories. Correspondingly, the vibration part of the Piola stress becomes particularly significant at high temperature and high tensile strain as the crystal approaches the softening limit. In contrast to the eigenvectors of the deformation gradient, the eigenvectors of the vibration tensor show strong spatial heterogeneity in the vicinity of softening. More importantly, the elliptic distribution of local atomic density transitions to a dumbbell shape, before significant non-affinity in equilibrium positions has occurred.

Finite-temperature stress calculations in atomic models using moments of position

NASA Astrophysics Data System (ADS)

Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

2018-07-01

Continuum modeling of finite temperature mechanical behavior of atomic systems requires refined description of atomic motions. In this paper, we identify additional kinematical quantities that are relevant for a more accurate continuum description as the system is subjected to step-wise loading. The presented formalism avoids the necessity for atomic trajectory mapping with deformation, provides the definitions of the kinematic variables and their conjugates in real space, and simplifies local work conjugacy. The total work done on an atom under deformation is decomposed into the work corresponding to changing its equilibrium position and work corresponding to changing its second moment about equilibrium position. Correspondingly, we define two kinematic variables: a deformation gradient tensor and a vibration tensor, and derive their stress conjugates, termed here as static and vibration stresses, respectively. The proposed approach is validated using MD simulation in NVT ensembles for fcc aluminum subjected to uniaxial extension. The observed evolution of second moments in the MD simulation with macroscopic deformation is not directly related to the transformation of atomic trajectories through the deformation gradient using generator functions. However, it is noteworthy that deformation leads to a change in the second moment of the trajectories. Correspondingly, the vibration part of the Piola stress becomes particularly significant at high temperature and high tensile strain as the crystal approaches the softening limit. In contrast to the eigenvectors of the deformation gradient, the eigenvectors of the vibration tensor show strong spatial heterogeneity in the vicinity of softening. More importantly, the elliptic distribution of local atomic density transitions to a dumbbell shape, before significant non-affinity in equilibrium positions has occurred.

Multiple seismogenic processes for high-frequency earthquakes at Katmai National Park, Alaska: Evidence from stress tensor inversions of fault-plane solutions

USGS Publications Warehouse

Moran, S.C.

2003-01-01

The volcanological significance of seismicity within Katmai National Park has been debated since the first seismograph was installed in 1963, in part because Katmai seismicity consists almost entirely of high-frequency earthquakes that can be caused by a wide range of processes. I investigate this issue by determining 140 well-constrained first-motion fault-plane solutions for shallow (depth < 9 km) earthquakes occuring between 1995 and 2001 and inverting these solutions for the stress tensor in different regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a stress field characterized by horizontally oriented ??1 and ??3 axes, with ??1 rotated slightly (12??) relative to the NUVELIA subduction vector, indicating that these earthquakes are occurring in response to regional tectonic forces. On the other hand, stress tensors for earthquake clusters beneath several Katmai cluster volcanoes have vertically oriented ??1 axes, indicating that these events are occuring in response to local, not regional, processes. At Martin-Mageik, vertically oriented ??1 is most consistent with failure under edifice loading conditions in conjunction with localized pore pressure increases associated with hydrothermal circulation cells. At Trident-Novarupta, it is consistent with a number of possible models, including occurence along fractures formed during the 1912 eruption that now serve as horizontal conduits for migrating fluids and/or volatiles from nearby degassing and cooling magma bodies. At Mount Katmai, it is most consistent with continued seismicity along ring-fracture systems created in the 1912 eruption, perhaps enhanced by circulating hydrothermal fluids and/or seepage from the caldera-filling lake.

Evolution of the stress field in the southern Scotia Arc from the late Mesozoic to the present-day

NASA Astrophysics Data System (ADS)

Maestro, Adolfo; López-Martínez, Jerónimo; Galindo-Zaldívar, Jesús; Bohoyo, Fernando; Mink, Sandra

2014-12-01

The geological evolution of the Scotia Arc, which developed between Antarctica and South America, has facilitated the connection between the Pacific and Atlantic oceans and, has important global implications. To improve the knowledge of the late Mesozoic evolution of the southern Scotia Arc, over 6000 brittle mesostructures were measured over the last 20 years at different outcrops from the northern Antarctic Peninsula and the South Shetland Islands as well as the James Ross and South Orkney archipelagos. This dataset covers a length of more than 1000 km of the arc. Fault data were analysed using the Etchecopar, y-R, Right Dihedra, Stress Inversion and Search Grid Inversion Palaeostress Determination methods. A total of 275 stress tensors were obtained. The results showed that the maximum horizontal stress was in the ENE-WSW and the NW-SE orientations and that the horizontal extension tensors were oriented NE-SW and NW-SE. In addition, seismic activity and focal mechanism solutions were analysed using the Gephart method to establish the present-day stress field and characterise the active tectonics. The results obtained suggest that there is a regional NE-SW compression and a NW-SE extension regime at the present day. The Southern Scotia Arc has a complex geological history due to the different tectonic settings (transform, convergent and divergent) that have affected this sector during its geological evolution from the late Mesozoic until the present day. Six stress fields were obtained from the brittle mesostructure population analysis in the region. The NW-SE and N-S maximum horizontal stresses were related to a combination of Mesozoic oceanic subduction of the former Phoenix Plate under the Pacific margin of the Antarctic Plate, Mesozoic-Cenozoic subduction of the northern Weddell Sea and the Oligocene to the Middle Miocene dextral strike-slip movement between the Scotia and Antarctic plates along the South Scotia Ridge. The NE-SW compression was related to late Miocene to present-day sinistral transcurrent movement along the South Scotia Ridge. Finally, the NW-SE extensional stress field may be related to the development of the following back-arc basins: the Late Cretaceous-Eocene Larsen Basin, the Lower to Middle Miocene Jane Basin and the Pliocene to present-day Bransfield Basin. In addition, the NE-SW and the E-W tensional stress fields were related to the Oligocene opening of the Powell Basin.

Energy Dissipation of Rayleigh Waves due to Absorption Along the Path by the Use of Finite Element Method

DTIC Science & Technology

1979-07-31

3 x 3 t Strain vector a ij,j Space derivative of the stress tensor Fi Force vector per unit volume o Density x CHAPTER III F Total force K Stiffness...matrix 6Vector displacements M Mass matrix B Space operating matrix DO Matrix moduli 2 x 3 DZ Operating matrix in Z direction N Matrix of shape...dissipating medium the deformation of a solid is a function of time, temperature and space . Creep phenomenon is a deformation process in which there is

FDTD simulation of trapping nanowires with linearly polarized and radially polarized optical tweezers.

PubMed

Li, Jing; Wu, Xiaoping

2011-10-10

In this paper a model of the trapping force on nanowires is built by three dimensional finite-difference time-domain (FDTD) and Maxwell stress tensor methods, and the tightly focused laser beam is expressed by spherical vector wave functions (VSWFs). The trapping capacities on nanoscale-diameter nanowires are discussed in terms of a strongly focused linearly polarized beam and radially polarized beam. Simulation results demonstrate that the radially polarized beam has higher trapping efficiency on nanowires with higher refractive indices than linearly polarized beam.

FDTD simulation of trapping nanowires with linearly polarized and radially polarized optical tweezers

PubMed Central

Li, Jing; Wu, Xiaoping

2011-01-01

In this paper a model of the trapping force on nanowires is built by three dimensional finite-difference time-domain (FDTD) and Maxwell stress tensor methods, and the tightly focused laser beam is expressed by spherical vector wave functions (VSWFs). The trapping capacities on nanoscale-diameter nanowires are discussed in terms of a strongly focused linearly polarized beam and radially polarized beam. Simulation results demonstrate that the radially polarized beam has higher trapping efficiency on nanowires with higher refractive indices than linearly polarized beam. PMID:21997083

Motion Detection in Ultrasound Image-Sequences Using Tensor Voting

NASA Astrophysics Data System (ADS)

Inba, Masafumi; Yanagida, Hirotaka; Tamura, Yasutaka

2008-05-01

Motion detection in ultrasound image sequences using tensor voting is described. We have been developing an ultrasound imaging system adopting a combination of coded excitation and synthetic aperture focusing techniques. In our method, frame rate of the system at distance of 150 mm reaches 5000 frame/s. Sparse array and short duration coded ultrasound signals are used for high-speed data acquisition. However, many artifacts appear in the reconstructed image sequences because of the incompleteness of the transmitted code. To reduce the artifacts, we have examined the application of tensor voting to the imaging method which adopts both coded excitation and synthetic aperture techniques. In this study, the basis of applying tensor voting and the motion detection method to ultrasound images is derived. It was confirmed that velocity detection and feature enhancement are possible using tensor voting in the time and space of simulated ultrasound three-dimensional image sequences.

Designing Feature and Data Parallel Stochastic Coordinate Descent Method forMatrix and Tensor Factorization

DTIC Science & Technology

2016-05-11

AFRL-AFOSR-JP-TR-2016-0046 Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization U Kang Korea...maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or   any other aspect...Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA2386

Density functional theory calculations of 95Mo NMR parameters in solid-state compounds.

PubMed

Cuny, Jérôme; Furet, Eric; Gautier, Régis; Le Pollès, Laurent; Pickard, Chris J; d'Espinose de Lacaillerie, Jean-Baptiste

2009-12-21

The application of periodic density functional theory-based methods to the calculation of (95)Mo electric field gradient (EFG) and chemical shift (CS) tensors in solid-state molybdenum compounds is presented. Calculations of EFG tensors are performed using the projector augmented-wave (PAW) method. Comparison of the results with those obtained using the augmented plane wave + local orbitals (APW+lo) method and with available experimental values shows the reliability of the approach for (95)Mo EFG tensor calculation. CS tensors are calculated using the recently developed gauge-including projector augmented-wave (GIPAW) method. This work is the first application of the GIPAW method to a 4d transition-metal nucleus. The effects of ultra-soft pseudo-potential parameters, exchange-correlation functionals and structural parameters are precisely examined. Comparison with experimental results allows the validation of this computational formalism.

BRST Exactness of Stress-Energy Tensors

NASA Astrophysics Data System (ADS)

Miyata, Hideo; Sugimoto, Hiroshi

BRST commutators in the topological conformal field theories obtained by twisting N=2 theories are evaluated explicitly. By our systematic calculations of the multiple integrals which contain screening operators, the BRST exactness of the twisted stress-energy tensors is deduced for classical simple Lie algebras and general level k. We can see that the paths of integrations do not affect the result, and further, the N=2 coset theories are obtained by deleting two simple roots with Kac-label 1 from the extended Dynkin diagram; in other words, by not performing the integrations over the variables corresponding to the two simple roots of Kac-Moody algebras. It is also shown that a series of N=1 theories are generated in the same way by deleting one simple root with Kac-label 2.

Consequences of theory level choice evaluated with new tools from QTAIM and the stress tensor for a dipeptide conformer

NASA Astrophysics Data System (ADS)

Li, Jiahui; Xu, Tianlv; Ping, Yang; van Mourik, Tanja; Früchtl, Herbert; Kirk, Steven R.; Jenkins, Samantha

2018-03-01

QTAIM and the stress tensor were used to provide a detailed analysis of the topology of the molecular graph, BCP and bond-path properties, including the new introduced helicity length H, of a Tyr-Gly dipeptide conformer subjected to a torsion with four levels of theory; MP2, M06-2X, B3LYP-D3 and B3LYP and a modest-sized basis set, 6-31+G(d). Structural effects and bonding properties are quantified and reflect differences in the BSSE and lack of inclusion of dispersion effects in the B3LYP calculations. The helicity length H demonstrated that MP2 produced a unique response to the torsion suggesting future use as a diagnostic tool.

Exact example of backreaction of small scale inhomogeneities in cosmology

NASA Astrophysics Data System (ADS)

Green, Stephen; Wald, Robert

2013-04-01

We construct a one-parameter family of polarized vacuum Gowdy spacetimes on a torus. In the limit as the parameter N goes to infinity, the metric uniformly approaches a smooth ``background metric.'' However, spacetime derivatives of the metric do not approach a limit. As a result, we find that the background metric itself is not a solution of the vacuum Einstein equation. Rather, it is a solution of the Einstein equation with an ``effective stress-energy tensor,'' which is traceless and satisfies the weak energy condition. This is an explicit example of backreaction due to small scale inhomogeneities. We comment on the non-vacuum case, where we have proven in previous work that, provided the matter stress-energy tensor satisfies the weak energy condition, no additional backreaction is possible.

Quantum corrections in thermal states of fermions on anti-de Sitter space-time

NASA Astrophysics Data System (ADS)

Ambruş, Victor E.; Winstanley, Elizabeth

2017-12-01

We study the energy density and pressure of a relativistic thermal gas of massless fermions on four-dimensional Minkowski and anti-de Sitter space-times using relativistic kinetic theory. The corresponding quantum field theory quantities are given by components of the renormalized expectation value of the stress-energy tensor operator acting on a thermal state. On Minkowski space-time, the renormalized vacuum expectation value of the stress-energy tensor is by definition zero, while on anti-de Sitter space-time the vacuum contribution to this expectation value is in general nonzero. We compare the properties of the vacuum and thermal expectation values of the energy density and pressure for massless fermions and discuss the circumstances in which the thermal contribution dominates over the vacuum one.

Rational first integrals of geodesic equations and generalised hidden symmetries

NASA Astrophysics Data System (ADS)

Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro

2016-10-01

We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson-O’Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four-dimensions, by using the Maciejewski-Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing-Yano tensors.

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

Kubo formulas for the shear and bulk viscosity relaxation times and the scalar field theory shear τπ calculation

NASA Astrophysics Data System (ADS)

Czajka, Alina; Jeon, Sangyong

2017-06-01

In this paper we provide a quantum field theoretical study on the shear and bulk relaxation times. First, we find Kubo formulas for the shear and the bulk relaxation times, respectively. They are found by examining response functions of the stress-energy tensor. We use general properties of correlation functions and the gravitational Ward identity to parametrize analytical structures of the Green functions describing both sound and diffusion mode. We find that the hydrodynamic limits of the real parts of the respective energy-momentum tensor correlation functions provide us with the method of computing both the shear and bulk viscosity relaxation times. Next, we calculate the shear viscosity relaxation time using the diagrammatic approach in the Keldysh basis for the massless λ ϕ4 theory. We derive a respective integral equation which enables us to compute η τπ and then we extract the shear relaxation time. The relaxation time is shown to be inversely related to the thermal width as it should be.

Charting the complete elastic properties of inorganic crystalline compounds

PubMed Central

de Jong, Maarten; Chen, Wei; Angsten, Thomas; Jain, Anubhav; Notestine, Randy; Gamst, Anthony; Sluiter, Marcel; Krishna Ande, Chaitanya; van der Zwaag, Sybrand; Plata, Jose J; Toher, Cormac; Curtarolo, Stefano; Ceder, Gerbrand; Persson, Kristin A.; Asta, Mark

2015-01-01

The elastic constant tensor of an inorganic compound provides a complete description of the response of the material to external stresses in the elastic limit. It thus provides fundamental insight into the nature of the bonding in the material, and it is known to correlate with many mechanical properties. Despite the importance of the elastic constant tensor, it has been measured for a very small fraction of all known inorganic compounds, a situation that limits the ability of materials scientists to develop new materials with targeted mechanical responses. To address this deficiency, we present here the largest database of calculated elastic properties for inorganic compounds to date. The database currently contains full elastic information for 1,181 inorganic compounds, and this number is growing steadily. The methods used to develop the database are described, as are results of tests that establish the accuracy of the data. In addition, we document the database format and describe the different ways it can be accessed and analyzed in efforts related to materials discovery and design. PMID:25984348

On the performance of the moment approximation for the numerical computation of fiber stress in turbulent channel flow

NASA Astrophysics Data System (ADS)

Gillissen, J. J. J.; Boersma, B. J.; Mortensen, P. H.; Andersson, H. I.

2007-03-01

Fiber-induced drag reduction can be studied in great detail by means of direct numerical simulation [J. S. Paschkewitz et al., J. Fluid Mech. 518, 281 (2004)]. To account for the effect of the fibers, the Navier-Stokes equations are supplemented by the fiber stress tensor, which depends on the distribution function of fiber orientation angles. We have computed this function in turbulent channel flow, by solving the Fokker-Planck equation numerically. The results are used to validate an approximate method for calculating fiber stress, in which the second moment of the orientation distribution is solved. Since the moment evolution equations contain higher-order moments, a closure relation is required to obtain as many equations as unknowns. We investigate the performance of the eigenvalue-based optimal fitted closure scheme [J. S. Cintra and C. L. Tucker, J. Rheol. 39, 1095 (1995)]. The closure-predicted stress and flow statistics in two-way coupled simulations are within 10% of the "exact" Fokker-Planck solution.

Electromagnetic stress at the boundary: Photon pressure or tension?

PubMed

Wang, Shubo; Ng, Jack; Xiao, Meng; Chan, Che Ting

2016-03-01

It is well known that incident photons carrying momentum ℏk exert a positive photon pressure. But if light is impinging from a negative refractive medium in which ℏk is directed toward the source of radiation, should light exert a photon "tension" instead of a photon pressure? Using an ab initio method that takes the underlying microstructure of a material into account, we find that when an electromagnetic wave propagates from one material into another, the electromagnetic stress at the boundary is, in fact, indeterminate if only the macroscopic parameters are specified. Light can either pull or push the boundary, depending not only on the macroscopic parameters but also on the microscopic lattice structure of the polarizable units that constitute the medium. Within the context of an effective-medium approach, the lattice effect is attributed to electrostriction and magnetostriction, which can be accounted for by the Helmholtz stress tensor if we use the macroscopic fields to calculate the boundary optical stress.

Electromagnetic stress at the boundary: Photon pressure or tension?

PubMed Central

Wang, Shubo; Ng, Jack; Xiao, Meng; Chan, Che Ting

2016-01-01

It is well known that incident photons carrying momentum ℏk exert a positive photon pressure. But if light is impinging from a negative refractive medium in which ℏk is directed toward the source of radiation, should light exert a photon “tension” instead of a photon pressure? Using an ab initio method that takes the underlying microstructure of a material into account, we find that when an electromagnetic wave propagates from one material into another, the electromagnetic stress at the boundary is, in fact, indeterminate if only the macroscopic parameters are specified. Light can either pull or push the boundary, depending not only on the macroscopic parameters but also on the microscopic lattice structure of the polarizable units that constitute the medium. Within the context of an effective-medium approach, the lattice effect is attributed to electrostriction and magnetostriction, which can be accounted for by the Helmholtz stress tensor if we use the macroscopic fields to calculate the boundary optical stress. PMID:27034987

A stress-dependent model for reservoir stimulation in enhanced geothermal systems

NASA Astrophysics Data System (ADS)

Troiano, Antonio; Giulia Di Giuseppe, Maria; Troise, Claudia; De Natale, Giuseppe

2015-04-01

We present a procedure for testing the interpretation of the induced seismicity. The procedure is based on Coulomb stress changes induced by deep fluid injection during well stimulation, providing a way to estimate how the potential for seismic failure in different volumes of a geothermal reservoir might change due to the water injection. Coulomb stress changes appear to be the main cause for the induced seismicity during the water injection. These stress changes do not only result from changes in the pore pressure, but also from the whole change in the stress tensor at any point in the medium, which results from the pressure perturbations. The numerical procedure presented takes into account the permeability increase that is due to the induced stress changes. A conceptual model that links the induced stress tensor and the permeability modifications is considered to estimate the permeability change induced during the water injection. In this way, we can adapt the medium behavior to mechanical changes, in order to better evaluate the effectiveness of the stimulation process for the enhancement of the reservoir permeability, while also refining the reconstruction of the Coulomb stress change patterns. Numerical tests have been developed that consider a physical medium and a geometry of the system comparable with that of Soultz EGS site (Alsace, France). Tests considering a fixed permeability, both isotropic and anisotropic, indicate a general decrease in the pressure changes when an anisotropic permeability was considered, with respect to the isotropic case. A marked elongation of the coulomb stress change patterns in the regional load direction was retrieved. This effect is enforced when a stress-dependent permeability is taken into account. Permeability enhancement progressively enlarges the seismic volume in turns, while decreasing the pressure in the neighborhood of the bottom of the well. The use of stress-dependent permeability also improves the reconstruction of the observed seismicity pattern. In particular, the large maximum of the coulomb stress changes at the point of injection, which was already mitigated by the consideration of anisotropic permeability, appears further decreased in the new data. The improving of the correlation between the coulomb stress changes and the induced seismicity distribution supports the reliability and robustness of the main hypothesis of this study of the relationship between the induced stress tensor variation and the permeability enhancement. The use of stress-dependent permeability constitutes an important step towards the theoretical planning of stimulation procedures, and towards interpretation and mitigation of the induced seismicity.

Plate convergence at the westernmost Philippine Sea Plate

NASA Astrophysics Data System (ADS)

Wu, Wen-Nan; Hsu, Shu-Kun; Lo, Chung-Liang; Chen, How-Wei; Ma, Kuo-Fong

2009-03-01

To understand the convergent characteristics of the westernmost plate boundary between the Philippine Sea Plate (PSP) and Eurasian Plate (EP), we have calculated the stress states of plate motion by focal mechanisms. Cataloged by the Harvard centroid moment tensor solutions (Harvard CMT) and the Broadband Array in Taiwan (BATS) moment tensor, 251 focal mechanisms are used to determine the azimuths of the principal stress axes. We first used all the data to derive the mean stress tensor of the study area. The inversion result shows that the stress regime has a maximum compression along the direction of azimuth N299°. This result is consistent with the general direction of the rigid plate motion between the PSP and EP in the study area. In order to understand the spatial variation of the regional stress pattern, we divided the study area into six sub-areas (blocks A to F) based on the feature of the free-air gravity anomaly. We compare the compressive directions obtained from the stress inversion with the plate motions calculated by the Euler pole and the Global Positioning System (GPS) analysis. As a result, the azimuth of the maximum stress axis, σ1, generally agrees with the directions of the theoretical plate motion and GPS velocity vectors except block C (Lanhsu region) and block F (Ilan plain region). The discrepancy of convergent direction near the Ilan plain region is probably caused by the rifting of the Okinawa Trough. The deviation of the σ1 azimuth in the Lanhsu region could be attributed to a southwestward extrusion of the Luzon Arc (LA) block between 21°N and 22°N whose northern boundary may be associated with the right-lateral NE-SW trending fault (i.e. Huatung Fault, HF) along the Taitung Canyon. Comparing the σ1 stress patterns between block C and block D, great strain energy along HF may not be completely released yet. Alternatively, the upper crust of block C may significantly have decoupled from its lower crust or uppermost mantle.

Fast multipole method using Cartesian tensor in beam dynamic simulation

DOE PAGES

Zhang, He; Huang, He; Li, Rui; ...

2017-03-06

Here, the fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor-based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed.

Probing Earth's State of Stress

NASA Astrophysics Data System (ADS)

Delorey, A. A.; Maceira, M.; Johnson, P. A.; Coblentz, D. D.

2016-12-01

The state of stress in the Earth's crust is a fundamental physical property that controls both engineered and natural systems. Engineered environments including those for hydrocarbon, geothermal energy, and mineral extraction, as well those for storage of wastewater, carbon dioxide, and nuclear fuel are as important as ever to our economy and environment. Yet, it is at spatial scales relevant to these activities where stress is least understood. Additionally, in engineered environments the rate of change in the stress field can be much higher than that of natural systems. In order to use subsurface resources more safely and effectively, we need to understand stress at the relevant temporal and spatial scales. We will present our latest results characterizing the state of stress in the Earth at scales relevant to engineered environments. Two important components of the state of stress are the orientation and magnitude of the stress tensor, and a measure of how close faults are to failure. The stress tensor at any point in a reservoir or repository has contributions from both far-field tectonic stress and local density heterogeneity. We jointly invert seismic (body and surface waves) and gravity data for a self-consistent model of elastic moduli and density and use the model to calculate the contribution of local heterogeneity to the total stress field. We then combine local and plate-scale contributions, using local indicators for calibration and ground-truth. In addition, we will present results from an analysis of the quantity and pattern of microseismicity as an indicator of critically stressed faults. Faults are triggered by transient stresses only when critically stressed (near failure). We show that tidal stresses can trigger earthquakes in both tectonic and reservoir environments and can reveal both stress and poroelastic conditions.

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

DOE PAGES

Lyakh, Dmitry I.

2015-01-05

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typicallymore » appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).« less

Tensor Train Neighborhood Preserving Embedding

NASA Astrophysics Data System (ADS)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

Physics behind the oscillation of pressure tensor autocorrelation function for nanocolloidal dispersions.

PubMed

Wang, Tao; Wang, Xinwei; Luo, Zhongyang; Cen, Kefa

2008-08-01

In this work, extensive equilibrium molecular dynamics simulations are conducted to explore the physics behind the oscillation of pressure tensor autocorrelation function (PTACF) for nanocolloidal dispersions, which leads to strong instability in viscosity calculation. By reducing the particle size and density, we find the intensity of the oscillation decreases while the frequency of the oscillation becomes higher. Careful analysis of the relationship between the oscillation and nanoparticle characteristics reveals that the stress wave scattering/reflection at the particle-liquid interface plays a critical role in PTACF oscillation while the Brownian motion/vibration of solid particles has little effect. Our modeling proves that it is practical to eliminate the PTACF oscillation through suppressing the acoustic mismatch at the solid-liquid interface by designing special nanoparticle materials. It is also found when the particle size is comparable with the wavelength of the stress wave, diffraction of stress wave happens at the interface. Such effect substantially reduces the PTACF oscillation and improves the stability of viscosity calculation.

Quantum field theory in spaces with closed time-like curves

NASA Astrophysics Data System (ADS)

Boulware, D. G.

Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

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.

A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence

NASA Technical Reports Server (NTRS)

Ristorcelli, J. R.

1993-01-01

The turbulent mass flux, or equivalently the fluctuating Favre velocity mean, appears in the first and second moment equations of compressible kappa-epsilon and Reynolds stress closures. Mathematically it is the difference between the unweighted and density-weighted averages of the velocity field and is therefore a measure of the effects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the effects of the mean density gradients, in the same way the anisotropy tensor characterizes the effects of the mean velocity gradients. An evolution equation for the turbulent mass flux is derived. A truncation of this equation produces an algebraic expression for the mass flux. The mass flux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results.

The Reynolds-stress tensor in diffusion flames; An experimental and theoretical investigation

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

Schneider, F.; Janicka, J.

1990-07-01

The authors present measurements and predictions of Reynolds-stress components and mean velocities in a CH{sub 4}-air diffusion flame. A reference beam LDA technique is applied for measuring all Reynolds-stress components. A hologram with dichromated gelatine as recording medium generates strictly coherent reference beams. The theoretical part describes a Reynolds-stress model based on Favre-averaged quantities, paying special attention to modeling the pressure-shear correlation and the dissipation equation in flames. Finally, measurement/prediction comparisons are presented.

Propagation of threading dislocations in heteroepitaxial diamond films with (111) orientation and their role in the formation of intrinsic stress

NASA Astrophysics Data System (ADS)

Gallheber, B.-C.; Klein, O.; Fischer, M.; Schreck, M.

2017-06-01

In the present study, systematic correlations were revealed between the propagation direction of threading dislocations, the off-axis growth conditions, and the stress state of heteroepitaxial diamond on Ir/YSZ/Si(111). Measurements of the strain tensor ɛ ⃡ by X-ray diffraction and the subsequent calculation of the tensor of intrinsic stress σ ⃡ showed stress-free samples as well as symmetric biaxial stress states for on-axis samples. Transmission electron microscopy (TEM) lamellas were prepared for plan-view studies along the [ 1 ¯ 1 ¯ 1 ¯ ] direction and for cross-section investigations along the [11 2 ¯ ] and [1 1 ¯ 0] zone axes. For samples grown on-axis with parameters which avoid the formation of intrinsic stress, the majority of dislocations have line vectors clearly aligned along [111]. A sudden change to conditions that promote stress formation is correlated with an abrupt bending of the dislocations away from [111]. This behaviour is in nice agreement with the predictions of a model that attributes formation of intrinsic stress to an effective climb of dislocations. Further growth experiments under off-axis conditions revealed the generation of stress states with pronounced in-plane anisotropy of several Gigapascal. Their formation is attributed to the combined action of two basic processes, i.e., the step flow driven dislocation tilting and the temperature dependent effective climb of dislocations. Again, our interpretation is supported by the dislocation propagation derived from TEM observations.

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.

Interpolation of orientation distribution functions in diffusion weighted imaging using multi-tensor model.

PubMed

Afzali, Maryam; Fatemizadeh, Emad; Soltanian-Zadeh, Hamid

2015-09-30

Diffusion weighted imaging (DWI) is a non-invasive method for investigating the brain white matter structure and can be used to evaluate fiber bundles. However, due to practical constraints, DWI data acquired in clinics are low resolution. This paper proposes a method for interpolation of orientation distribution functions (ODFs). To this end, fuzzy clustering is applied to segment ODFs based on the principal diffusion directions (PDDs). Next, a cluster is modeled by a tensor so that an ODF is represented by a mixture of tensors. For interpolation, each tensor is rotated separately. The method is applied on the synthetic and real DWI data of control and epileptic subjects. Both experiments illustrate capability of the method in increasing spatial resolution of the data in the ODF field properly. The real dataset show that the method is capable of reliable identification of differences between temporal lobe epilepsy (TLE) patients and normal subjects. The method is compared to existing methods. Comparison studies show that the proposed method generates smaller angular errors relative to the existing methods. Another advantage of the method is that it does not require an iterative algorithm to find the tensors. The proposed method is appropriate for increasing resolution in the ODF field and can be applied to clinical data to improve evaluation of white matter fibers in the brain. Copyright © 2015 Elsevier B.V. All rights reserved.

Accelerated High-Dimensional MR Imaging with Sparse Sampling Using Low-Rank Tensors

PubMed Central

He, Jingfei; Liu, Qiegen; Christodoulou, Anthony G.; Ma, Chao; Lam, Fan

2017-01-01

High-dimensional MR imaging often requires long data acquisition time, thereby limiting its practical applications. This paper presents a low-rank tensor based method for accelerated high-dimensional MR imaging using sparse sampling. This method represents high-dimensional images as low-rank tensors (or partially separable functions) and uses this mathematical structure for sparse sampling of the data space and for image reconstruction from highly undersampled data. More specifically, the proposed method acquires two datasets with complementary sampling patterns, one for subspace estimation and the other for image reconstruction; image reconstruction from highly undersampled data is accomplished by fitting the measured data with a sparsity constraint on the core tensor and a group sparsity constraint on the spatial coefficients jointly using the alternating direction method of multipliers. The usefulness of the proposed method is demonstrated in MRI applications; it may also have applications beyond MRI. PMID:27093543

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

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

Huang, He; Luo, Li -Shi; Li, Rui

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

DOE PAGES

Huang, He; Luo, Li -Shi; Li, Rui; ...

2018-05-17

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

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

Lyakh, Dmitry I.

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typicallymore » appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).« less

Tensor scale: An analytic approach with efficient computation and applications☆

PubMed Central

Xu, Ziyue; Saha, Punam K.; Dasgupta, Soura

2015-01-01

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods. PMID:26236148

New insights on the matter-gravity coupling paradigm.

PubMed

Delsate, Térence; Steinhoff, Jan

2012-07-13

The coupling between matter and gravity in general relativity is given by a proportionality relation between the stress tensor and the geometry. This is an oriented assumption driven by the fact that both the stress tensor and the Einstein tensor are divergenceless. However, general relativity is in essence a nonlinear theory, so there is no obvious reason why the coupling to matter should be linear. On another hand, modified theories of gravity usually affect the vacuum dynamics, yet keep the coupling to matter linear. In this Letter, we address the implications of consistent nonlinear gravity-matter coupling. The Eddington-inspired Born-Infeld theory recently introduced by Bañados and Ferreira provides an enlightening realization of such coupling modifications. We find that this theory coupled to a perfect fluid reduces to general relativity coupled to a nonlinearly modified perfect fluid, leading to an ambiguity between modified coupling and modified equation of state. We discuss observational consequences of this degeneracy and argue that such a completion of general relativity is viable from both an experimental and theoretical point of view through energy conditions, consistency, and singularity-avoidance perspectives. We use these results to discuss the impact of changing the coupling paradigm.

Why fibers are better turbulent drag reducing agents than polymers

NASA Astrophysics Data System (ADS)

Boelens, Arnout; Muthukumar, Murugappan

2016-11-01

It is typically found in literature that fibers are not as effective as drag reducing agents as polymers. However, for low concentrations, when adding charged polymers to either distilled or salt water, it is found that polymers showing rod-like behavior are better drag reducing agents than polymers showing coil-like behavior. In this study, using hybrid Direct Numerical Simulation with Langevin dynamics, a comparison is performed between polymer and fiber stress tensors in turbulent flow. The stress tensors are found to be similar, suggesting a common drag reducing mechanism in the onset regime. Since fibers do not have an elastic backbone, this must be a viscous effect. Analysis of the viscosity tensor reveals that all terms are negligible, except the off-diagonal shear viscosity associated with rotation. Based on this analysis, we are able to explain why charged polymers showing rod-like behavior are better drag reducing agents than polymers showing coil-like behavior. Additionally, we identify the rotational orientation time as the unifying time scale setting a new time criterion for drag reduction by both flexible polymers and rigid fibers. This research was supported by NSF Grant No. DMR-1404940 and AFOSR Grant No. FA9550-14-1-0164.

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).

Simultaneous Tensor Decomposition and Completion Using Factor Priors.

PubMed

Chen, Yi-Lei; Hsu, Chiou-Ting Candy; Liao, Hong-Yuan Mark

2013-08-27

Tensor completion, which is a high-order extension of matrix completion, has generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called Simultaneous Tensor Decomposition and Completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data, and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.

Development of the Tensoral Computer Language

NASA Technical Reports Server (NTRS)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

A fictitious domain finite element method for simulations of fluid-structure interactions: The Navier-Stokes equations coupled with a moving solid

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel

2015-05-01

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an optimal approximation of the normal stress tensor at the interface. The dynamics of the solid is governed by the Newton's laws and the interface between the fluid and the structure is materialized by a level-set which cuts the elements of the mesh. An algorithm is proposed in order to treat the time evolution of the geometry and numerical results are presented on a classical benchmark of the motion of a disk falling in a channel.

Investigation of Thermal Stress Convection in Nonisothermal Gases Under Microgravity Conditions

NASA Technical Reports Server (NTRS)

Mackowski, Daniel W.; Knight, Roy W.

1996-01-01

Microgravity conditions offer an environment in which convection in a nonisothermal gas could be driven primarily by thermal stress. A direct examination of thermal stress flows would be invaluable in assessing the accuracy of the Burnett terms in the fluid stress tensor. We present a preliminary numerical investigation of the competing effects of thermal stress, thermal creep at the side walls, and buoyancy on gas convection in nonuniformly heated containers under normal and reduced gravity levels. Conditions in which thermal stress convection becomes dominant are identified, and issues regarding the experimental measurement of the flows are discussed.

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.

Application of Deep Learning and Supervised Learning Methods to Recognize Nonlinear Hidden Pattern in Water Stress Levels from Spatiotemporal Datasets across Rural and Urban US Counties

NASA Astrophysics Data System (ADS)

Eisenhart, T.; Josset, L.; Rising, J. A.; Devineni, N.; Lall, U.

2017-12-01

In the wake of recent water crises, the need to understand and predict the risk of water stress in urban and rural areas has grown. This understanding has the potential to improve decision making in public resource management, policy making, risk management and investment decisions. Assuming an underlying relationship between urban and rural water stress and observable features, we apply Deep Learning and Supervised Learning models to uncover hidden nonlinear patterns from spatiotemporal datasets. Results of interest includes prediction accuracy on extreme categories (i.e. urban areas highly prone to water stress) and not solely the average risk for urban or rural area, which adds complexity to the tuning of model parameters. We first label urban water stressed counties using annual water quality violations and compile a comprehensive spatiotemporal dataset that captures the yearly evolution of climatic, demographic and economic factors of more than 3,000 US counties over the 1980-2010 period. As county-level data reporting is not done on a yearly basis, we test multiple imputation methods to get around the issue of missing data. Using Python libraries, TensorFlow and scikit-learn, we apply and compare the ability of, amongst other methods, Recurrent Neural Networks (testing both LSTM and GRU cells), Convolutional Neural Networks and Support Vector Machines to predict urban water stress. We evaluate the performance of those models over multiple time spans and combine methods to diminish the risk of overfitting and increase prediction power on test sets. This methodology seeks to identify hidden nonlinear patterns to assess the predominant data features that influence urban and rural water stress. Results from this application at the national scale will assess the performance of deep learning models to predict water stress risk areas across all US counties and will highlight a predominant Machine Learning method for modeling water stress risk using spatiotemporal data.

A dynamic regularized gradient model of the subgrid-scale stress tensor for large-eddy simulation

NASA Astrophysics Data System (ADS)

Vollant, A.; Balarac, G.; Corre, C.

2016-02-01

Large-eddy simulation (LES) solves only the large scales part of turbulent flows by using a scales separation based on a filtering operation. The solution of the filtered Navier-Stokes equations requires then to model the subgrid-scale (SGS) stress tensor to take into account the effect of scales smaller than the filter size. In this work, a new model is proposed for the SGS stress model. The model formulation is based on a regularization procedure of the gradient model to correct its unstable behavior. The model is developed based on a priori tests to improve the accuracy of the modeling for both structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce enough global SGS dissipation, respectively. LES is then performed for a posteriori validation. This work is an extension to the SGS stress tensor of the regularization procedure proposed by Balarac et al. ["A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations," Phys. Fluids 25(7), 075107 (2013)] to model the SGS scalar flux. A set of dynamic regularized gradient (DRG) models is thus made available for both the momentum and the scalar equations. The second objective of this work is to compare this new set of DRG models with direct numerical simulations (DNS), filtered DNS in the case of classic flows simulated with a pseudo-spectral solver and with the standard set of models based on the dynamic Smagorinsky model. Various flow configurations are considered: decaying homogeneous isotropic turbulence, turbulent plane jet, and turbulent channel flows. These tests demonstrate the stable behavior provided by the regularization procedure, along with substantial improvement for velocity and scalar statistics predictions.

Model for quantum effects in stellar collapse

NASA Astrophysics Data System (ADS)

Arderucio-Costa, Bruno; Unruh, William G.

2018-01-01

We present a simple model for stellar collapse and evaluate the quantum mechanical stress-energy tensor to argue that quantum effects do not play an important role for the collapse of astrophysical objects.

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.

Stress Fields Along Okinawa Trough and Ryukyu Arc Inferred From Regional Broadband Moment Tensors

NASA Astrophysics Data System (ADS)

Kubo, A.; Fukuyama, E.

2001-12-01

Most shallow earthquakes along Okinawa trough and Ryukyu arc are relatively small (M<5.5). Focal mechanism estimations for such events were difficult due to insufficient dataset. However, this situation is improved by regional broadband network (FREESIA). Lower limit of magnitude of the earthquakes determined becomes 1.5 smaller in M{}w than that of Harvard moment tensors. As a result, we could examine the stress field in more detail than Fournier et al.(2001, JGR, 106, 13751-) did based on surface geology and teleseismic moment tensors. In the NE Okinawa trough, extension axes are oblique to the trough strike, while in SW Okinawa trough, they are perpendicular to the trough. Fault type in SW is normal fault and gradually changes to mixture of normal and strike slip toward NE. In the Ryukyu arc, extension axes are parallel to the arc. Although this feature is not clear in the NW Ryukyu arc, arc parallel extension may be a major property of entire arc. Dominant fault type is normal fault and several strike slips with the same extensional component are included. The volcanic train is located at the edge of arc parallel extension field faced A simple explanation of the arc parallel extension is the response to the opening motion of the Okinawa trough. Another possible mechanism is forearc movement due to oblique subduction which is enhanced in SW. We consider that the Okinawa trough and the Ryukyu arc are independent stress provinces.

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

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-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

Optical trapping forces of a focused azimuthally polarized Bessel-Gaussian beam on a double-layered sphere

NASA Astrophysics Data System (ADS)

Wu, F. P.; Zhang, B.; Liu, Z. L.; Tang, Y.; Zhang, N.

2017-12-01

We calculate the trapping forces exerted by a highly focused Bessel-Gaussian beam on a double-layered sphere by means of vector diffraction integral, T-matrix method and Maxwell stress tensor integral. The Bessel-Gaussian beam is azimuthally polarized. Numerical results predicate that the double-layered sphere with air core can be stably trapped in three-dimensions. The trapping forces and efficiencies are dependent on the refraction index and size of the inner core. The trapping efficiency can be optimized by choosing the refraction indices of the inner core and outer layer. Our computational method can be easily modified for other laser beams and particles with arbitrary geometries and multilayers.

Determining transport coefficients for a microscopic simulation of a hadron gas

NASA Astrophysics Data System (ADS)

Pratt, Scott; Baez, Alexander; Kim, Jane

2017-02-01

Quark-gluon plasmas produced in relativistic heavy-ion collisions quickly expand and cool, entering a phase consisting of multiple interacting hadronic resonances just below the QCD deconfinement temperature, T ˜155 MeV. Numerical microscopic simulations have emerged as the principal method for modeling the behavior of the hadronic stage of heavy-ion collisions, but the transport properties that characterize these simulations are not well understood. Methods are presented here for extracting the shear viscosity and two transport parameters that emerge in Israel-Stewart hydrodynamics. The analysis is based on studying how the stress-energy tensor responds to velocity gradients. Results are consistent with Kubo relations if viscous relaxation times are twice the collision time.

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

PubMed

Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

2015-09-01

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

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.

Relating Residual Stress and Substructural Evolution During Tensile Deformation of an Aluminum-Manganese Alloy

NASA Astrophysics Data System (ADS)

Lodh, Arijit; Tak, Tawqeer Nasir; Prakash, Aditya; Guruprasad, P. J.; Hutchinson, Christopher; Samajdar, Indradev

2017-11-01

Interrupted tensile tests were coupled with ex situ measurements of residual stress and microtexture. The residual stress quantification involved measurements of six independent Laue spots and conversion of the interplanar spacings to the residual stress tensor. A clear orientation-dependent residual stress evolution emerged from the experiments and the numerical simulations. For the orientations undergoing negligible changes in ρ GND (density of geometrically necessary dislocation), the residual stress developments appeared to be governed by the elastic stiffness of the grain clusters. For the others, the evolution of the residual stress and ρ GND exhibited a clear orientation-dependent scaling.

An enhanced structure tensor method for sea ice ridge detection from GF-3 SAR imagery

NASA Astrophysics Data System (ADS)

Zhu, T.; Li, F.; Zhang, Y.; Zhang, S.; Spreen, G.; Dierking, W.; Heygster, G.

2017-12-01

In SAR imagery, ridges or leads are shown as the curvilinear features. The proposed ridge detection method is facilitated by their curvilinear shapes. The bright curvilinear features are recognized as the ridges while the dark curvilinear features are classified as the leads. In dual-polarization HH or HV channel of C-band SAR imagery, the bright curvilinear feature may be false alarm because the frost flowers of young leads may show as bright pixels associated with changes in the surface salinity under calm surface conditions. Wind roughened leads also trigger the backscatter increasing that can be misclassified as ridges [1]. Thus the width limitation is considered in this proposed structure tensor method [2], since only shape feature based method is not enough for detecting ridges. The ridge detection algorithm is based on the hypothesis that the bright pixels are ridges with curvilinear shapes and the ridge width is less 30 meters. Benefited from GF-3 with high spatial resolution of 3 meters, we provide an enhanced structure tensor method for detecting the significant ridge. The preprocessing procedures including the calibration and incidence angle normalization are also investigated. The bright pixels will have strong response to the bandpass filtering. The ridge training samples are delineated from the SAR imagery in the Log-Gabor filters to construct structure tensor. From the tensor, the dominant orientation of the pixel representing the ridge is determined by the dominant eigenvector. For the post-processing of structure tensor, the elongated kernel is desired to enhance the ridge curvilinear shape. Since ridge presents along a certain direction, the ratio of the dominant eigenvector will be used to measure the intensity of local anisotropy. The convolution filter has been utilized in the constructed structure tensor is used to model spatial contextual information. Ridge detection results from GF-3 show the proposed method performs better compared to the direct threshold method.

Diffusion Tensor Image Registration Using Hybrid Connectivity and Tensor Features

PubMed Central

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-01-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. PMID:24293159

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.

Stress regimes in the northwest of Iran from stress inversion of earthquake focal mechanisms

NASA Astrophysics Data System (ADS)

Afra, Mahsa; Moradi, Ali; Pakzad, Mehrdad

2017-11-01

Northwestern Iran is one of the seismically active regions with a high seismic risk in the world. This area is a part of the complex tectonic system due to the interaction between Arabia, Anatolia and Eurasia. The purpose of this study is to deduce the stress regimes in the northwestern Iran and surrounding regions from stress inversion of earthquake focal mechanisms. We compile 92 focal mechanisms data from the Global CMT catalogue and other sources and also determine the focal mechanisms of 14 earthquakes applying the moment tensor inversion. We divide the studied region into 9 zones using similarity of the horizontal GPS velocities and existing focal mechanisms. We implement two stress inversion methods, Multiple Inverse Method and Iterative Joint Inversion Method, which provide comparable results in terms of orientations of maximum horizontal stress axes SHmax. The similar results of the two methods should make us more confident about the interpretations. We consider zones of exclusion surrounding all the earthquakes according to independent focal mechanisms hypothesis. The hypothesis says that the inversion should involve events that are far enough from each other in order that any previous event doesn't affect the stress field near the earthquake under consideration. Accordingly we deal with the matter by considering zones of exclusion around all the events. The result of exclusion is only significant for eastern Anatolia. The stress regime in this region changes from oblique to strike slip faulting because of the exclusion. In eastern Anatolia, the direction of maximum horizontal stress is nearly north-south. The direction alters to east-west in Talesh region. Errors of σ1 are lower in all zones comparing with errors of σ2 and σ3 and there is a trade-off between data resolution and covariance of the model. The results substantiate the strike-slip and thrust faulting stress regimes in the northwest of Iran.

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%.

Stress-stress correlator in ϕ 4 theory: poles or a cut?

NASA Astrophysics Data System (ADS)

Moore, Guy D.

2018-05-01

We explore the analytical properties of the traceless stress tensor 2-point function at zero momentum and small frequency (relevant for shear viscosity and hydrodynamic response) in hot, weakly coupled λ ϕ 4 theory. We show that, rather than one or a small number of poles, the correlator has a cut along the negative imaginary frequency axis. We briefly discuss this result's relevance for constructing 2'nd order hydrodynamic models of hot relativistic field theories.

Simultaneous tensor decomposition and completion using factor priors.

PubMed

Chen, Yi-Lei; Hsu, Chiou-Ting; Liao, Hong-Yuan Mark

2014-03-01

The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.

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.

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.

Estimation of Uncertainties of Full Moment Tensors

DTIC Science & Technology

2017-10-06

Nevada Test Site (tab. 1 of Ford et al., 2009). Figure 1 shows the three regions and the stations used within the moment tensor inversions . For the...and additional bandpass filtering, were applied during the moment tensor inversions . We use high-frequency P waves for the Uturuncu and NTS events...reliable when we align the P waves on the observed P arrival time. 3.2 Methods Seismic moment tensor inversion requires specifying a misfit function

A fictitious domain approach for the Stokes problem based on the extended finite element method

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel; Lozinski, Alexei

2014-01-01

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries do not match. A mixed finite element method is used for fluid flow. The interface between the fluid and the structure is localized by a level-set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf-sup condition between the spaces for velocity and the Lagrange multiplier. Convergence analysis is given and several numerical tests are performed to illustrate the capabilities of the method.

Eulerian adaptive finite-difference method for high-velocity impact and penetration problems

NASA Astrophysics Data System (ADS)

Barton, P. T.; Deiterding, R.; Meiron, D.; Pullin, D.

2013-05-01

Owing to the complex processes involved, faithful prediction of high-velocity impact events demands a simulation method delivering efficient calculations based on comprehensively formulated constitutive models. Such an approach is presented herein, employing a weighted essentially non-oscillatory (WENO) method within an adaptive mesh refinement (AMR) framework for the numerical solution of hyperbolic partial differential equations. Applied widely in computational fluid dynamics, these methods are well suited to the involved locally non-smooth finite deformations, circumventing any requirement for artificial viscosity functions for shock capturing. Application of the methods is facilitated through using a model of solid dynamics based upon hyper-elastic theory comprising kinematic evolution equations for the elastic distortion tensor. The model for finite inelastic deformations is phenomenologically equivalent to Maxwell's model of tangential stress relaxation. Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest. Sharp interface resolution is achieved by employing level-set functions to track boundary motion, along with a ghost material method to capture the necessary internal boundary conditions for material interactions and stress-free surfaces. The approach is demonstrated for the simulation of high velocity impacts of steel projectiles on aluminium target plates in two and three dimensions.

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.

Stress inversion using borehole images and geometry evolution of the fractures in the Rittershoffen EGS project (Alsace, France).

NASA Astrophysics Data System (ADS)

Azzola, Jérôme; Valley, Benoît; Schmittbuhl, Jean; Genter, Albert; Hehn, Régis

2017-04-01

In the Upper Rhine Graben, several deep geothermal projects based on the Enhanced Geothermal System (EGS) exploit local geothermal reservoirs. The principle underlying this technology consists of increasing the hydraulic performances of the reservoir by stimulating natural fractures using different methods, in order to extract hot water with commercially flow rates. In this domain, the knowledge of the in-situ stress state is of central importance to predict the response of the rock mass to stimulations. Here we characterized the stress tensor from Ultrasonic Borehole Imager (UBI) in the open hole section of the EGS doublet located in Rittershoffen, France (in the Upper Rhine Graben). Interestingly extensive logging programs were leaded at different key moments of the development of the injection well using hydraulic, thermal and chemical stimulation (Baujard et al., 2017)1. The time lapse UBI dataset consists of images of the injection well before, shortly and lastly after the stimulation. The geometry of the induced fractures in compression (breakouts) picked on the UBI images are used to determine the orientation of the in-situ stress tensor. The magnitude of the principal stresses is deduced from the drilling data. The magnitude of the maximum horizontal principal stress is evaluated using an inversion method with three failure criteria (Mohr-Coulomb, Mogi-Coulomb and modified Hoek-Brown criterion) and under the assumption of a vertical or a deviated well. Moreover, the characteristic of the dataset enables the analysis of the evolution of the borehole fracturing, as the deepening or widening of the induced fractures. The correlation of the UBI image allows firstly to determine the tool trajectory and to adapt the post and pre-stimulation images. It secondly leads to the estimation of a complete displacement field which characterizes the deformation induced by the stimulations. Even if the variable image quality deeply conditions the comparison, the considered dataset enabled a consistent evaluation of the in-situ stress field taking place in the underground of the EGS plant, as showed by the comparison to results obtained in the vicinity. Moreover, the study of the evolution of fracturing shows the influence of the stimulation process on the fractures geometry. 1(Baujard, C., Genter, A., Dalmais, E., Maurer, V., Hehn, R., Rosillette, R., Vidal, J., Schmittbuhl, J., 2017). Hydrothermal Characterization of wells GRT-1 and GRT-2 in Rittershoffen, France: Implications on the understanding of natural flow systems in the Rhine Graben, Geothermics, 65, 255-268.

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.

Determination of earthquake source parameters from waveform data for studies of global and regional seismicity

NASA Astrophysics Data System (ADS)

Dziewonski, A. M.; Chou, T.-A.; Woodhouse, J. H.

1981-04-01

It is possible to use the waveform data not only to derive the source mechanism of an earthquake but also to establish the hypocentral coordinates of the `best point source' (the centroid of the stress glut density) at a given frequency. Thus two classical problems of seismology are combined into a single procedure. Given an estimate of the origin time, epicentral coordinates and depth, an initial moment tensor is derived using one of the variations of the method described in detail by Gilbert and Dziewonski (1975). This set of parameters represents the starting values for an iterative procedure in which perturbations to the elements of the moment tensor are found simultaneously with changes in the hypocentral parameters. In general, the method is stable, and convergence rapid. Although the approach is a general one, we present it here in the context of the analysis of long-period body wave data recorded by the instruments of the SRO and ASRO digital network. It appears that the upper magnitude limit of earthquakes that can be processed using this particular approach is between 7.5 and 8.0; the lower limit is, at this time, approximately 5.5, but it could be extended by broadening the passband of the analysis to include energy with periods shorter that 45 s. As there are hundreds of earthquakes each year with magnitudes exceeding 5.5, the seismic source mechanism can now be studied in detail not only for major events but also, for example, for aftershock series. We have investigated the foreshock and several aftershocks of the Sumba earthquake of August 19, 1977; the results show temporal variation of the stress regime in the fault area of the main shock. An area some 150 km to the northwest of the epicenter of the main event became seismically active 49 days later. The sense of the strike-slip mechanism of these events is consistent with the relaxation of the compressive stress in the plate north of the Java trench. Another geophysically interesting result of our analysis is that for 5 out of 11 earthquakes of intermediate and great depth the intermediate principal value of the moment tensor is significant, while for the remaining 6 it is essentially zero, which means that their mechanisms are consistent with a simple double-couple representation. There is clear distinction between these two groups of earthquakes.

Boundary Element Method in a Self-Gravitating Elastic Half-Space and Its Application to Deformation Induced by Magma Chambers

NASA Astrophysics Data System (ADS)

Fang, M.; Hager, B. H.

2014-12-01

In geophysical applications the boundary element method (BEM) often carries the essential physics in addition to being an efficient numerical scheme. For use of the BEM in a self-gravitating uniform half-space, we made extra effort and succeeded in deriving the fundamental solution analytically in closed-form. A problem that goes deep into the heart of the classic BEM is encountered when we try to apply the new fundamental solution in BEM for deformation field induced by a magma chamber or a fluid-filled reservoir. The central issue of the BEM is the singular integral arising from determination of the boundary values. A widely employed technique is to rescale the singular boundary point into a small finite volume and then shrink it to extract the limits. This operation boils down to the calculation of the so-called C-matrix. Authors in the past take the liberty of either adding or subtracting a small volume. By subtracting a small volume, the C-matrix is (1/2)I on a smooth surface, where I is the identity matrix; by adding a small volume, we arrive at the same C-matrix in the form of I - (1/2)I. This evenness is a result of the spherical symmetry of Kelvin's fundamental solution employed. When the spherical symmetry is broken by gravity, the C-matrix is polarized. And we face the choice between right and wrong, for adding and subtracting a small volume yield different C-matrices. Close examination reveals that both derivations, addition and subtraction of a small volume, are ad hoc. To resolve the issue we revisit the Somigliana identity with a new derivation and careful step-by-step anatomy. The result proves that even though both adding and subtracting a small volume appear to twist the original boundary, only addition essentially modifies the original boundary and consequently modifies the physics of the original problem in a subtle way. The correct procedure is subtraction. We complete a new BEM theory by introducing in full analytical form what we call the singular stress tensor for the fundamental solution. We partition the stress tensor of the fundamental solution into a singular part and a regular part. In this way all singular integrals systematically shift into the easy singular stress tensor. Applications of this new BEM to deformation and gravitational perturbation induced by magma chambers of finite volume will be presented.

A Simple Method for Calculating Clebsch-Gordan Coefficients

ERIC Educational Resources Information Center

Klink, W. H.; Wickramasekara, S.

2010-01-01

This paper presents a simple method for calculating Clebsch-Gordan coefficients for the tensor product of two unitary irreducible representations (UIRs) of the rotation group. The method also works for multiplicity-free irreducible representations appearing in the tensor product of any number of UIRs of the rotation group. The generalization to…

The incompressible Rindler fluid versus the Schwarzschild-AdS fluid

NASA Astrophysics Data System (ADS)

Matsuo, Yoshinori; Natsuume, Makoto; Ohta, Masahiro; Okamura, Takashi

2013-02-01

We study the proposal by Bredberg et al. [J. High Energy Phys. 1103, 141 (2011)], where the fluid is defined by the Brown-York tensor on a timelike surface at r = rc in black hole backgrounds. We consider both Rindler space and the Schwarzschild-AdS (SAdS) black hole. The former describes an incompressible fluid, whereas the latter describes the vanishing bulk viscosity at arbitrary rc. Although the near-horizon limit of the SAdS black hole is Rindler space, these two results do not contradict each other. We also find an interesting "coincidence" with the black hole membrane paradigm that gives a negative bulk viscosity. In order to show these results, we rewrite the hydrodynamic stress tensor via metric perturbations using the conservation equation. The resulting expressions are suitable to compare with the Brown-York tensor.

Controlling sign problems in spin models using tensor renormalization

NASA Astrophysics Data System (ADS)

Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan

2014-01-01

We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid

NASA Astrophysics Data System (ADS)

Gao, Tong; Betterton, Meredith D.; Jhang, An-Sheng; Shelley, Michael J.

2017-09-01

We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile "extensor" particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a Doi-Onsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rodlike particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau-deGennes Q -tensor theories for active nematic fluids, as well as by more complex Doi-Onsager theories for polar microtubule-motor-protein systems. We apply the quasiequilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a nonstandard Q -tensor theory. We demonstrate through simulation that this B Q -tensor theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the B Q -tensor model to study the dynamics of extensor suspensions in circular and biconcave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment we find unusual dynamics with activity-controlled defect production and absorption at the boundaries of the domain. In biconcave domains, a Fredericks-like transition occurs as the width of the neck connecting the two disks is varied.

Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme. Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.

Approximate arbitrary κ-state solutions of Dirac equation with Schiöberg and Manning-Rosen potentials within the coulomb-like Yukawa-like and generalized tensor interactions

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Hassanabadi, Hassan; Obong, Hillary Patrick; Mehraban, H.; Yazarloo, Bentol Hoda

2015-07-01

The effects of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT) and generalized tensor (GLT) interactions are investigated in the Dirac theory with Schiöberg and Manning-Rosen potentials within the framework of spin and pseudospin symmetries using the Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions have been approximately obtained in the case of spin and pseudospin symmetries. We have also reported some numerical results and figures to show the effects these tensor interactions.

Relaxation approximation in the theory of shear turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert

1995-01-01

Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.

Hidden symmetries in Sasaki-Einstein geometries

NASA Astrophysics Data System (ADS)

Slesar, V.; Visinescu, M.; Vîlcu, G. E.

2017-07-01

We describe a method for constructing Killing-Yano tensors on Sasaki spaces using their geometrical properties, without the need of solving intricate generalized Killing equations. We obtain the Killing-Yano tensors on toric Sasaki-Einstein spaces using the fact that the metric cones of these spaces are Calabi-Yau manifolds which in turn are described in terms of toric data. We extend the search of Killing-Yano tensors on mixed 3-Sasakian manifolds. We illustrate the method by explicit construction of Killing forms on some spaces of current interest.

Low-Rank Tensor Subspace Learning for RGB-D Action Recognition.

PubMed

Jia, Chengcheng; Fu, Yun

2016-07-09

Since RGB-D action data inherently equip with extra depth information compared with RGB data, recently many works employ RGB-D data in a third-order tensor representation containing spatio-temporal structure to find a subspace for action recognition. However, there are two main challenges of these methods. First, the dimension of subspace is usually fixed manually. Second, preserving local information by finding intraclass and inter-class neighbors from a manifold is highly timeconsuming. In this paper, we learn a tensor subspace, whose dimension is learned automatically by low-rank learning, for RGB-D action recognition. Particularly, the tensor samples are factorized to obtain three Projection Matrices (PMs) by Tucker Decomposition, where all the PMs are performed by nuclear norm in a close-form to obtain the tensor ranks which are used as tensor subspace dimension. Additionally, we extract the discriminant and local information from a manifold using a graph constraint. This graph preserves the local knowledge inherently, which is faster than the previous way by calculating both the intra-class and inter-class neighbors of each sample. We evaluate the proposed method on four widely used RGB-D action datasets including MSRDailyActivity3D, MSRActionPairs, MSRActionPairs skeleton and UTKinect-Action3D datasets, and the experimental results show higher accuracy and efficiency of the proposed method.

Complete set of invariants of a 4th order tensor: the 12 tasks of HARDI from ternary quartics.

PubMed

Papadopoulo, Théo; Ghosh, Aurobrata; Deriche, Rachid

2014-01-01

Invariants play a crucial role in Diffusion MRI. In DTI (2nd order tensors), invariant scalars (FA, MD) have been successfully used in clinical applications. But DTI has limitations and HARDI models (e.g. 4th order tensors) have been proposed instead. These, however, lack invariant features and computing them systematically is challenging. We present a simple and systematic method to compute a functionally complete set of invariants of a non-negative 3D 4th order tensor with respect to SO3. Intuitively, this transforms the tensor's non-unique ternary quartic (TQ) decomposition (from Hilbert's theorem) to a unique canonical representation independent of orientation - the invariants. The method consists of two steps. In the first, we reduce the 18 degrees-of-freedom (DOF) of a TQ representation by 3-DOFs via an orthogonal transformation. This transformation is designed to enhance a rotation-invariant property of choice of the 3D 4th order tensor. In the second, we further reduce 3-DOFs via a 3D rotation transformation of coordinates to arrive at a canonical set of invariants to SO3 of the tensor. The resulting invariants are, by construction, (i) functionally complete, (ii) functionally irreducible (if desired), (iii) computationally efficient and (iv) reversible (mappable to the TQ coefficients or shape); which is the novelty of our contribution in comparison to prior work. Results from synthetic and real data experiments validate the method and indicate its importance.

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

NASA Astrophysics Data System (ADS)

Caputa, Pawel; Kundu, Nilay; Miyaji, Masamichi; Takayanagi, Tadashi; Watanabe, Kento

2017-11-01

We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

General equilibrium second-order hydrodynamic coefficients for free quantum fields

NASA Astrophysics Data System (ADS)

Buzzegoli, M.; Grossi, E.; Becattini, F.

2017-10-01

We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called "Kubo formulae". We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term.

Brownian thermal noise in functional optical surfaces

NASA Astrophysics Data System (ADS)

Kroker, S.; Dickmann, J.; Rojas Hurtado, C. B.; Heinert, D.; Nawrodt, R.; Levin, Y.; Vyatchanin, S. P.

2017-07-01

We present a formalism to compute Brownian thermal noise in functional optical surfaces such as grating reflectors, photonic crystal slabs, or complex metamaterials. Such computations are based on a specific readout variable, typically a surface integral of a dielectric interface displacement weighed by a form factor. This paper shows how to relate this form factor to Maxwell's stress tensor computed on all interfaces of the moving surface. As an example, we examine Brownian thermal noise in monolithic T-shaped grating reflectors. The previous computations by Heinert et al. [Phys. Rev. D 88, 042001 (2013), 10.1103/PhysRevD.88.042001] utilizing a simplified readout form factor produced estimates of thermal noise that are tens of percent higher than those of the exact analysis in the present paper. The relation between the form factor and Maxwell's stress tensor implies a close correlation between the optical properties of functional optical surfaces and thermal noise.

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

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data.

PubMed

Carmichael, Owen; Sakhanenko, Lyudmila

2015-05-15

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way.

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data

PubMed Central

Carmichael, Owen; Sakhanenko, Lyudmila

2015-01-01

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way. PMID:25937674

Maxwell–Dirac stress–energy tensor in terms of Fierz bilinear currents

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

Inglis, Shaun, E-mail: sminglis@utas.edu.au; Jarvis, Peter, E-mail: Peter.Jarvis@utas.edu.au

We analyse the stress–energy tensor for the self-coupled Maxwell–Dirac system in the bilinear current formalism, using two independent approaches. The first method used is that attributed to Belinfante: starting from the spinor form of the action, the well-known canonical stress–energy tensor is augmented, by extending the Noether symmetry current to include contributions from the Lorentz group, to a manifestly symmetric form. This form admits a transcription to bilinear current form. The second method used is the variational derivation based on the covariant coupling to general relativity. The starting point here at the outset is the transcription of the action using,more » as independent field variables, both the bilinear currents, together with a gauge invariant vector field (a proxy for the electromagnetic vector potential). A central feature of the two constructions is that they both involve the mapping of the Dirac contribution to the stress–energy from the spinor fields to the equivalent set of bilinear tensor currents, through the use of appropriate Fierz identities. Although this mapping is done at quite different stages, nonetheless we find that the two forms of the bilinear stress–energy tensor agree. Finally, as an application, we consider the reduction of the obtained stress–energy tensor in bilinear form, under the assumption of spherical symmetry. -- Highlights: •Maxwell–Dirac stress–energy tensor derived in manifestly gauge invariant bilinear form. •Dirac spinor Belinfante tensor transcribed to bilinear fields via Fierz mapping. •Variational stress–energy obtained via bilinearized action, in contrast to Belinfante case. •Independent derivations via the Belinfante and variational methods agree, as required. •Spherical symmetry reduction given as a working example for wider applications.« less

Assessing the Uncertainties on Seismic Source Parameters: Towards Realistic Estimates of Moment Tensor Determinations

NASA Astrophysics Data System (ADS)

Magnoni, F.; Scognamiglio, L.; Tinti, E.; Casarotti, E.

2014-12-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Moment tensor catalogues are ordinarily used by geoscientists, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their own analysis. The 2012 May 20 Emilia mainshock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. An uncertainty of ~0.5 units in magnitude leads to a controversial knowledge of the real size of the event. The possible uncertainty associated to this estimate could be critical for the inference of other seismological parameters, suggesting caution for seismic hazard assessment, coulomb stress transfer determination and other analyses where self-consistency is important. In this work, we focus on the variability of the moment tensor solution, highlighting the effect of four different velocity models, different types and ranges of filtering, and two different methodologies. Using a larger dataset, to better quantify the source parameter uncertainty, we also analyze the variability of the moment tensor solutions depending on the number, the epicentral distance and the azimuth of used stations. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, cannot be considered an absolute value and requires to come out with the related uncertainties and in a reproducible framework characterized by disclosed assumptions and explicit processing workflows.

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

Theory, Solution Methods, and Implementation of the HERMES Model

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

Reaugh, John E.; White, Bradley W.; Curtis, John P.

The HERMES (high explosive response to mechanical stimulus) model was developed over the past decade to enable computer simulation of the mechanical and subsequent energetic response of explosives and propellants to mechanical insults such as impacts, perforations, drops, and falls. The model is embedded in computer simulation programs that solve the non-linear, large deformation equations of compressible solid and fluid flow in space and time. It is implemented as a user-defined model, which returns the updated stress tensor and composition that result from the simulation supplied strain tensor change. Although it is multi-phase, in that gas and solid species aremore » present, it is single-velocity, in that the gas does not flow through the porous solid. More than 70 time-dependent variables are made available for additional analyses and plotting. The model encompasses a broad range of possible responses: mechanical damage with no energetic response, and a continuous spectrum of degrees of violence including delayed and prompt detonation. This paper describes the basic workings of the model.« less

Scale-invariant curvature fluctuations from an extended semiclassical gravity

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

Pinamonti, Nicola, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it; INFN Sezione di Genova, Via Dodecaneso 33, 16146 Genova; Siemssen, Daniel, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it

2015-02-15

We present an extension of the semiclassical Einstein equations which couple n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.

Tensor network method for reversible classical computation

NASA Astrophysics Data System (ADS)

Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.

2018-03-01

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

Turbulent Kinetic Energy (TKE) Budgets Using 5-beam Doppler Profilers

NASA Astrophysics Data System (ADS)

Guerra, M. A.; Thomson, J. M.

2016-12-01

Field observations of turbulence parameters are important for the development of hydrodynamic models, understanding contaminant mixing, and predicting sediment transport. The turbulent kinetic energy (TKE) budget quantifies where turbulence is being produced, dissipated or transported at a specific site. The Nortek Signature 5-beam AD2CP was used to measure velocities at high sampling rates (up to 8 Hz) at Admiralty Inlet and Rich Passage in Puget Sound, WA, USA. Raw along-beam velocity data is quality controlled and is used to estimate TKE spectra, spatial structure functions, and Reynolds stress tensors. Exceptionally low Doppler noise in the data enables clear observations of the inertial sub-range of isotropic turbulence in both the frequency TKE spectra and the spatial structure functions. From these, TKE dissipation rates are estimated following Kolmogorov's theory of turbulence. The TKE production rates are estimated using Reynolds stress tensors together with the vertical shear in the mean flow. The Reynolds stress tensors are estimated following the methodology of Dewey and Stinger (2007), which is significantly improved by inclusion of the 5th beam (as opposed to the conventional 4). These turbulence parameters are used to study the TKE budget along the water column at the two sites. Ebb and flood production and dissipation rates are compared through the water column at both sites. At Admiralty Inlet, dissipation exceeds production during ebb while the opposite occurs during flood because the proximity to a lateral headland. At Rich Passage, production exceeds dissipation through the water column for all tidal conditions due to a vertical sill in the vicinity of the measurement site.

Forward modeling and inversion of tensor CSAMT in 3D anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Tao; Wang, Kun-Peng; Tan, Han-Dong

2017-12-01

Tensor controlled-source audio-frequency magnetotellurics (CSAMT) can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional (3D) staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic, the isotropic inversion will introduce errors to the interpretation.

The Topology of Three-Dimensional Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

MRI diffusion tensor reconstruction with PROPELLER data acquisition.

PubMed

Cheryauka, Arvidas B; Lee, James N; Samsonov, Alexei A; Defrise, Michel; Gullberg, Grant T

2004-02-01

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.

Tensor completion for estimating missing values in visual data.

PubMed

Liu, Ji; Musialski, Przemyslaw; Wonka, Peter; Ye, Jieping

2013-01-01

In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependent relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between FaLRTC an- HaLRTC the former is more efficient to obtain a low accuracy solution and the latter is preferred if a high-accuracy solution is desired.

Federated Tensor Factorization for Computational Phenotyping

PubMed Central

Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian

2017-01-01

Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165

Graphical tensor product reduction scheme for the Lie algebras so(5) = sp(2) , su(3) , and g(2)

NASA Astrophysics Data System (ADS)

Vlasii, N. D.; von Rütte, F.; Wiese, U.-J.

2016-08-01

We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2) , su(3) , and g(2) . This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a ;landscape; of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic ;girdle; method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request.

Analysis of seismicity and stress before and after the Mw 8.1 Pisagua, Chile, 2014 earthquake

NASA Astrophysics Data System (ADS)

Grigoli, F.; Cesca, S.; Dahm, T.; Hainzl, S.

2014-12-01

On April 1st, 2014 at 23:46:50 UTC, a powerful earthquake of magnitude Mw 8.1 occurred offshore the Northern Chile in the region of the North Chilean seismic gap. The epicenter of the earthquake was approximately 50 km offshore the Chilean coast, near the town of Pisagua. Two days after the main event a Mw 7.6 aftershock struck approximately the same area. In order to identify spatio-temporal changes of source parameters and stress before and after the mainshock, we analyzed in detail the local seismicity above magnitude Mw 3.0 within the time period 01/01/2013-30/04/2014 and estimated long term trends in b-values and earthquake productivity. We used data from the IPOC (Integrated Plate boundary Observatory Chile) regional seismic network, consisting of 20 "in land" broadband station deployed and managed by the GFZ-Potsdam. The recorded earthquake catalog shows an intense foreshock activity consisting of more than 1000 M3+ events in the source region. Full waveform techniques are used to derive both locations and focal mechanisms of about 435 seismic events. The location process has been performed by using a waveform stacking method (Grigoli et al 2013, 2014) with a layered velocity model based on CRUST 2.0 (see the attached figure for the location results of one of these events). Moment tensor inversion has been performed by using the KIWI tool software (Cesca et al. 2010), which is based on a two-step inversion approach. The first step consists in the inversion of the amplitude spectra to retrieve the best fitting focal planes, while the second inversion step is carried out in time domain to solve the focal mechanism polarity and to obtain the centroid location and time. Both location and moment tensor inversion resulted in agreement with the geodynamical settings of the region. Mapping the b-value reveals a spatiotemporal anomaly of low b-values characterizing the frequency-magnitude distribution of the foreshocks in the source area of the mainshock. Finally, clustering analysis of the retrieved focal mechanism and a stress tensor inversion has been performed in order to analyze the spatio-temporal evolution of the stress, before and after the mainshock. This work has been funded by the German BMBF "Geothecnologien" project MINE (BMBF03G0737A) and by Hazard and Risk Team (HART) and PBO-Chile of GFZ.

Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

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

Miskovic, Olivera; Olea, Rodrigo; Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso

2009-06-15

It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter gravity action in four dimensions recovers the standard regularization given by the holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows one to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as T{sub j}{sup i}={+-}(l{sup 2}/8{pi}G)C{sub j}{sup i}, which has been observed in recent literature in solitonicmore » solutions and hydrodynamic models. A general procedure to generate the counterterm series for anti-de Sitter gravity in any even dimension from the corresponding Euler term is also briefly discussed.« less

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.

Stress pattern of the Shanxi rift system, North China, inferred from the inversion of new focal mechanisms

NASA Astrophysics Data System (ADS)

Li, Bin; Atakan, Kuvvet; Sørensen, Mathilde Bøttger; Havskov, Jens

2015-05-01

Earthquake focal mechanisms of the Shanxi rift system, North China, are investigated for the time period 1965-April 2014. A total of 143 focal mechanisms of ML ≥ 3.0 earthquakes were compiled. Among them, 105 solutions are newly determined in this study by combining the P-wave first motions and full waveform inversion, and 38 solutions are from available published data. Stress tensor inversion was then performed based on the new database. The results show that most solutions in the Shanxi rift system exhibit normal or strike-slip faulting, and the regional stress field is transtensional and dominated by NNW-SSE extension. This correlates well with results from GPS data, geological field observations and levelling measurements across the faults. Heterogeneity exists in the regional stress field, as indicated by individual stress tensor inversions conducted for five subzones. While the minimum stress axis (σ3) appears to be consistent and stable, the orientations, especially the plunges, of the maximum and intermediate stresses (σ1 and σ2) vary significantly along the strike of the different subzones. Based on our results and combining multidisciplinary observations from geological surveys, GPS and cross-fault monitoring, a kinematic model is proposed for the Shanxi rift system, in which the rift is situated between two opposite rotating crustal blocks, exhibiting a transtensional stress regimes. This model illustrates the present-day stress field and its correlation to the regional tectonics, as well as the current crustal deformation of the Shanxi rift system. Results obtained in this study, may help to understand the geodynamics, neotectonic activity, active seismicity and potential seismic hazard in this region.

Symmetric Positive 4th Order Tensors & Their Estimation from Diffusion Weighted MRI⋆

PubMed Central

Barmpoutis, Angelos; Jian, Bing; Vemuri, Baba C.; Shepherd, Timothy M.

2009-01-01

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite (PSD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the PSD property. There have been several published articles in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positive semi-definite constraint, which is a fundamental constraint since negative values of the diffusivity coefficients are not meaningful. In our methods, we parameterize the 4th order tensors as a sum of squares of quadratic forms by using the so called Gram matrix method from linear algebra and its relation to the Hilbert’s theorem on ternary quartics. This parametric representation is then used in a nonlinear-least squares formulation to estimate the PSD tensors of order 4 from the data. We define a metric for the higher-order tensors and employ it for regularization across the lattice. Finally, performance of this model is depicted on synthetic data as well as real DW-MRI from an isolated rat hippocampus. PMID:17633709

The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

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

Guba, O.; Taylor, M. A.; Ullrich, P. A.

2014-11-27

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution-dependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, formore » regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

The spectral element method on variable resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE PAGES

Guba, O.; Taylor, M. A.; Ullrich, P. A.; ...

2014-06-25

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable resolution grids using the shallow water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution dependent coefficient. For the spectral element method with variable resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity ismore » constructed so that for regions of uniform resolution it matches the traditional constant coefficient hyperviscsosity. With the tensor hyperviscosity the large scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications where long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

A Hydraulic Stress Measurement System for Deep Borehole Investigations

NASA Astrophysics Data System (ADS)

Ask, Maria; Ask, Daniel; Cornet, Francois; Nilsson, Tommy

2017-04-01

Luleå University of Technology (LTU) is developing and building a wire-line system for hydraulic rock stress measurements, with funding from the Swedish Research Council and Luleå University of Technology. In this project, LTU is collaborating with University of Strasbourg and Geosigma AB. The stress state influences drilling and drillability, as well as rock mass stability and permeability. Therefore, knowledge about the state of in-situ stress (stress magnitudes, and orientations) and its spatial variation with depth is essential for many underground rock engineering projects, for example for underground storage of hazardous material (e.g. nuclear waste, carbon dioxide), deep geothermal exploration, and underground infrastructure (e.g. tunneling, hydropower dams). The system is designed to conduct hydraulic stress testing in slim boreholes. There are three types of test methods: (1) hydraulic fracturing, (2) sleeve fracturing and (3) hydraulic testing of pre-existing fractures. These are robust methods for determining in situ stresses from boreholes. Integration of the three methods allows determination of the three-dimensional stress tensor and its spatial variation with depth in a scientific unambiguously way. The stress system is composed of a downhole and a surface unit. The downhole unit consists of hydraulic fracturing equipment (straddle packers and downhole imaging tool) and their associated data acquisition systems. The testing system is state of the art in several aspects including: (1) Large depth range (3 km), (2) Ability to test three borehole dimensions (N=76 mm, H=96 mm, and P=122 mm), (3) Resistivity imager maps the orientation of tested fracture; (4) Highly stiff and resistive to corrosion downhole testing equipment; and (5) Very detailed control on the injection flow rate and cumulative volume is obtained by a hydraulic injection pump with variable piston rate, and a highly sensitive flow-meter. At EGU General Assembly 2017, we would like to present this new and unique stress measurement system and some initial test results from a 1200 m long borehole in crystalline rock.

A generalized electro-elastic theory of polymer networks

NASA Astrophysics Data System (ADS)

Cohen, Noy

2018-01-01

A rigorous multi-scale analysis of the electromechanical coupling in dielectric polymers is conducted. The body couples stemming from a misalignment between the electric field and the electric-dipole density vector are studied and the conservation laws for polymer networks are derived. Using variational principles, expressions for the polarization and the stress are determined. Interestingly, it is found that the stress tensor resulting from coupled loadings in which the electric field is misaligned with the principal stretch directions is not symmetric and the asymmetry arises from the body couples. Next, the electro-mechanical response of a chain is analyzed. The deformations of the individual polymer chains are related to the macroscopic deformation via two highly non-linear constraints - the first pertaining to the compatibility of the local deformations with the imposed macroscopic one and the second stems from the symmetric part of the stress at equilibrium. In accord with the proposed framework, an amended three-chains model is introduced. The predictions of this model are found to be in excellent agreement with experimental findings. Lastly, the behavior of a polymer subjected to a simple shear and an electric field is studied. The offset between the electric field and the principal directions gives rise to body couples, a polarization that is not aligned with the electric field, and an asymmetric stress tensor.

Micro-scale investigation on the quasi-static behavior of granular material

NASA Astrophysics Data System (ADS)

Li, Xia

Granular material exhibits complex responses when subjected to various external loading. Fundamental mechanisms have not been well established so far, including that about the critical state, one of the most important concepts in the modern soil mechanics. With the recognition that granular material is discrete in nature, the basic understanding can only be obtained from the particle scale. The complexity in granular material behavior lies in the fact that the macroscopic behavior of granular material is determined by not only the interactions operating at contacts, but also how the particles become arranged in space to form an internal structure. This research is aimed to microscopically investigate the influence of the internal structure and the fundamental mechanism about the critical state. In view of the extensive laboratory test data already available in the literature, a numerical simulation method, DEM, is employed as the tool to conduct particle-scale investigations. The contact model for two in-contact circular disks is derived theoretically from the elasticity theory, and the result is a linear contact model with constant stiffness and lateral sliding. Based on the contact model, a systematic series of numerical tests has been implemented, and the results can successfully reproduce the main characteristics in the behavior of natural granular material, under various loading conditions. The macro-micro relationship is the link between the investigations at the two worlds. The key point is to describe the internal structure with the two dual cell systems, a particle cell system and a void cell system. Based on these two systems, the stress and strain in a uniform field are equivalently expressed in terms of the contact forces/relative displacements, and the micro-geometrical variables. With the microstructural definition of the stress tensor, the stress state of granular material is studied microscopically. The stress-fabric-force relation is derived, based on the variables describing the statistics of the contact forces and the contact vectors. By studying the evolution of the micro-quantities during shearing, how the internal structure affects the macro stress state under different loading condition is revealed. With the assumption that the influence of the local variance in stress is ignorable, the response of granular material can be investigated based on the void cell system. Starting from the behavior of a single void cell, the evolutions of the internal structure and its influence on the response of granular material are explained. The stress ratio and the dilatancy behavior of granular material are investigated. The influences of the void ratio, the mean normal stress and the drainage condition are discussed. The fundamental mechanism of the critical state is studied in the framework of thermodynamics with properly considering the influence of the internal structure. The normalized stress ratio tensor at critical state is associated with the critical void cell anisotropy, corresponding to the maximal energy dissipation. The (e, p) relationship at critical state is associated with the critical combination of the void cell size and the contact interactions, corresponding to the minimal free energy. The investigation on the influence of the internal structure anisotropy on the granular material behavior and the critical state is carried out. The results show that at small strain levels, the behavior of granular material is mainly affected by the initial fabric. As shearing continuous, the internal structure of granular material is gradually changed. The granular material approaches the critical state, which is irrespective with the initial internal structure. The critical state of granular material is not unique. With different loading modes, the critical state of granular material, including both the critical stress ratio and the critical (e, p) relations, are found to be different. A fabric tensor is defined based on the characteristics of the void cells. The laboratory method to quantify the fabric anisotropy is proposed by deviatoric shearing. 3D numerical simulations have been carried out to investigate the influence of the loading mode, which is found to be an important factor in the large strain behavior of granular material. With the obtained microscopic understanding, the influence of contact model on granular material behavior is investigated. A method to quantify the fabric anisotropy is proposed. And a simple discussion on the state variable used in the elasto-plastic constitutive model is given.

Software Tool for Computing Maximum Von Mises Stress

NASA Technical Reports Server (NTRS)

Chen, Long Y.; Knutson, Kurt; Martin, Eric

2007-01-01

The maximum Van Mises stress and stress direction are of interest far analyzing launch accelerations such as with the Mass Acceleration Curves developed by JPL. Maximum launch stresses can be combined with appropriate load cases at consistent locations with resulting stress tensors. Maximum Van Mises stress is also of interest for understanding maximum operational loading such as traverse events. - For example, planetary traversing simulations may prescribe bounding acceleration values during traverse for a rover such as Mars Science Lab (MSL) in (X,Y,Z) of the rover. - Such accelerations can be really in any directions for many parts such as a mast or head mounted components which can be in numerous configurations and orientations when traversing a planet surface.

A new unified theory of electromagnetic and gravitational interactions

NASA Astrophysics Data System (ADS)

Li, Li-Xin

2016-12-01

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ∇a F ab - ξ R b a A a = -4π J b with ξ = -2, where F ab is the antisymmetric electromagnetic field tensor defined by the potential vector A a , R ab is the Ricci curvature tensor of the hypersurface, and J a is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term ξ R b a A a , whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.

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

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.

In situ seismic anisotropy around deep earthquakes in Japan subduction slabs using Japan Meteorological Agency moment tensors

NASA Astrophysics Data System (ADS)

Li, J.; Zheng, Y.; Thomsen, L.

2017-12-01

Knowing the in situ seismic anisotropy around deep earthquakes in slabs is important in understanding deep-earthquake mechanism as it may provide critically needed information about the rock fabric where deep earthquakes occur. It has been recognized for about 50 years that many deep earthquakes are not double-couple (DC) events. Previously we showed that in situ anisotropy around deep earthquakes could explain such observed non-DC events. Traditionally, the shear wave splitting method has been used to infer such anisotropy around deep earthquakes but this is challenging because it will need many crossing ray paths for the method to localize the anisotropic region (Long 2013). In this abstract, we adopt the same procedure to obtain anisotropy in the Pacific slab under Japan using moment tensors provided by the Japan Meteorological Agency using the F-net data. We directly probe the in situ anisotropy within the subducting slabs using the radiation patterns (represented by the moment tensors) of deep earthquakes (with depth greater than 60 km). By assuming a group of shear dislocation events embedded in a common tilted transversely isotropic (TTI) medium, we used the moment tensors as our input data to invert for the anisotropy in Mariana-Japan-Kuril subducting zone. The TTI medium is characterized by the P and S wave velocities along the symmetry axis (described by two free angles) and three Thomsen parameters. We divided the deep earthquake events into 9 groups by their spatial proximity using the k-means clustering method (Hartigan and Wong 1979). These 9 groups include 2 intermediate-depth groups (depth from 60 km to 300 km) and 7 deep-focus groups (depth greater than 300 km). Our inversion results show that the inverted TTI symmetry axes are perpendicular to the slab interface for two intermediate-depth groups (consistent with dehydration metamorphic reactions) and parallel to the slab interface for 7 deep-focus group. The shear wave anisotropy is best resolved by our inversion algorithm with a typical value of around 28% (ranging from 25% to 41%). Our inverted anisotropy provides direct information of stress and rock fabric inside the subducting slab and may help explain the mechanisms of deep earthquakes.

In flight estimations of Cassini spacecraft inertia tensor and thruster magnitude

NASA Technical Reports Server (NTRS)

Feldman, Antonette; Lee, Allan Y.

2006-01-01

This paper describes two methods used by the Cassini Attitude Control team to determine these key parameters and how flight telemetry was used to estimate them. The method for estimating the spacecraft inertia tensor exploits the conservation of angular momentum during spacecraft slews under reaction wheel control.

g-Tensor determination from single-crystal ESR data

NASA Astrophysics Data System (ADS)

Byrn, Marianne P.; Strouse, Charles E.

A general method is presented for extraction of the g tensor from single-crystal electron spin resonance data. This method does not depend on knowledge of crystal morphology or on the presence of crystallographic symmetry. The g values are obtained from rotations around three arbitrarily chosen but accurately known axes.

Optical forces near micro-fabricated devices

NASA Astrophysics Data System (ADS)

Mejia Prada, Camilo Andres

In this dissertation, I study optical forces near micro-fabricated devices for multi- particle manipulation. I consider particles of different sizes and compositions. In particular, I focus my study on both dielectric and gold particles as well as Giant Unilamellar Vesicles. First, I consider optical forces near a PhC and establish the feasibility of a technique which we term Light-Assisted Templated Self-assembly (LATS). In contrast to previous work on Fabry-Perot enhancement of trapping forces above a flat substrate, I exploit the guided resonance modes of a PhC to provide resonant enhancement of optical forces. Then, I explore optical forces near a Dual Beam Optical Trap (DBOT). I present a method to extract the bending modulus of the membrane from the area strain data. This method incorporates three-dimensional ray-tracing to calculate the applied stress in the DBOT within the ray optics approximation. I compare the optical force calculated using the ray optics approximation and Maxwell Stress Tensor method to ensure the approximation's accuracy. Next, we apply this method to 3 populations of GUVs to extract the bending modulus of membranes comprised of saturated and monounsaturated lipids in both gel and liquid phases.

Detection, localization and classification of multiple dipole-like magnetic sources using magnetic gradient tensor data

NASA Astrophysics Data System (ADS)

Gang, Yin; Yingtang, Zhang; Hongbo, Fan; Zhining, Li; Guoquan, Ren

2016-05-01

We have developed a method for automatic detection, localization and classification (DLC) of multiple dipole sources using magnetic gradient tensor data. First, we define modified tilt angles to estimate the approximate horizontal locations of the multiple dipole-like magnetic sources simultaneously and detect the number of magnetic sources using a fixed threshold. Secondly, based on the isotropy of the normalized source strength (NSS) response of a dipole, we obtain accurate horizontal locations of the dipoles. Then the vertical locations are calculated using magnitude magnetic transforms of magnetic gradient tensor data. Finally, we invert for the magnetic moments of the sources using the measured magnetic gradient tensor data and forward model. Synthetic and field data sets demonstrate effectiveness and practicality of the proposed method.

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

DOE PAGES

Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

2015-04-30

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton andmore » quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.« less

Decentralized Dimensionality Reduction for Distributed Tensor Data Across Sensor Networks.

PubMed

Liang, Junli; Yu, Guoyang; Chen, Badong; Zhao, Minghua

2016-11-01

This paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each tensor mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any tensor data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks.

White matter degeneration in schizophrenia: a comparative diffusion tensor analysis

NASA Astrophysics Data System (ADS)

Ingalhalikar, Madhura A.; Andreasen, Nancy C.; Kim, Jinsuh; Alexander, Andrew L.; Magnotta, Vincent A.

2010-03-01

Schizophrenia is a serious and disabling mental disorder. Diffusion tensor imaging (DTI) studies performed on schizophrenia have demonstrated white matter degeneration either due to loss of myelination or deterioration of fiber tracts although the areas where the changes occur are variable across studies. Most of the population based studies analyze the changes in schizophrenia using scalar indices computed from the diffusion tensor such as fractional anisotropy (FA) and relative anisotropy (RA). The scalar measures may not capture the complete information from the diffusion tensor. In this paper we have applied the RADTI method on a group of 9 controls and 9 patients with schizophrenia. The RADTI method converts the tensors to log-Euclidean space where a linear regression model is applied and hypothesis testing is performed between the control and patient groups. Results show that there is a significant difference in the anisotropy between patients and controls especially in the parts of forceps minor, superior corona radiata, anterior limb of internal capsule and genu of corpus callosum. To check if the tensor analysis gives a better idea of the changes in anisotropy, we compared the results with voxelwise FA analysis as well as voxelwise geodesic anisotropy (GA) analysis.

Tractography from HARDI using an Intrinsic Unscented Kalman Filter

PubMed Central

Cheng, Guang; Salehian, Hesamoddin; Forder, John R.; Vemuri, Baba C.

2014-01-01

A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multi-tensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along. This UKF and its variants reported later in literature however are not intrinsic to the space of diffusion tensors. Lack of this key property can possibly lead to inaccuracies in the multi-tensor estimation as well as in the tractography. In this paper, we propose a novel intrinsic unscented Kalman filter (IUKF) in the space of diffusion tensors which are symmetric positive definite matrices, that can be used for simultaneous recursive estimation of multi-tensors and propagation of directional information for use in fiber tractography from diffusion weighted MR data. In addition to being more accurate, IUKF retains all the advantages of UKF mentioned above. We demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup-challenge (MICCAI 2009) and diffusion weighted MR scans acquired from human brains and rat spinal cords. PMID:25203986

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

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

Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ''Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbationsmore » that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.« less

Seamless Warping of Diffusion Tensor Fields

PubMed Central

Hao, Xuejun; Bansal, Ravi; Plessen, Kerstin J.; Peterson, Bradley S.

2008-01-01

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create “seams” or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT datasets seamlessly from one imaging space to another. Once the bijection has been achieved and tensors have been correctly relocated to the template space, we can appropriately reorient tensors in the template space using a warping method based on Procrustean estimation. PMID:18334425

Conformal Yano-Killing Tensors for Space-times with Cosmological Constant

NASA Astrophysics Data System (ADS)

Czajka, P.; Jezierski, J.

We present a new method for constructing conformal Yano-Killing tensors in five-di\\-men\\-sio\\-nal Anti-de Sitter space-time. The found tensors are represented in two different coordinate systems. We also discuss, in terms of CYK tensors, global charges which are well defined for asymptotically (five-dimensional) Anti-de Sitter space-time. Additionally in Appendix we present our own derivation of conformal Killing one-forms in four-dimensional Anti-de Sitter space-time as an application of the Theorem presented in the paper.

Renormalization group contraction of tensor networks in three dimensions

NASA Astrophysics Data System (ADS)

García-Sáez, Artur; Latorre, José I.

2013-02-01

We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three-dimensional quantum system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE

PubMed Central

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S.

2017-01-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order-k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k}. We derive general inequalities between the lp-norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm (p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations. PMID:28286347

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

PubMed

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S

2017-05-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.

Casimir effect in presence of spontaneous Lorentz symmetry breaking

NASA Astrophysics Data System (ADS)

Escobar, C. A.

2018-01-01

The Casimir effect is one of the most remarkable consequences of the nonzero vacuum energy predicted by quantum field theory. In this contribution we study the Lorentz-violation effects of the minimal standard-model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method, we compute the relevant Green’s function which satisfies given boundary conditions. The standard point-splitting technique allow us to express the vacuum expectation value of the stress-energy tensor in terms of this Green’s function. Finally, we study the Casimir energy and the Casimir force paying particular attention to the quantum effects as approaching the plates.

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.

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.

Triple-material stress-strain resistivity gage

DOEpatents

Stout, R.B.

1987-05-19

A triple material piezoresistive gage provides multi-component elastic stress or strain measurements. Thin foils of three piezoresistive materials, e.g., ytterbium, manganin, and constantan, are configured in a nested serpentine rectilinear grind or other grind arrangement and embedded in a medium, preferably normal to the direction of shock wave propagation. The output of the gage is a resistivity change history for each material of gage. Each resistivity change is independent of the others so that three diagonal components of the elastic stress or strain tensor can be calculated form the resistivity measurements. 4 figs.

Triple-material stress-strain resistivity gage

DOEpatents

Stout, R.B.

1988-05-17

A triple material piezoresistive gage provides multi-component elastic stress measurements is disclosed. Thin foils of three piezoresistive materials, e.g. ytterbium, manganin, and constantan, are configured in a nested serpentine rectilinear grid or other grid arrangement and embedded in a medium, preferably normal to the direction of shock wave propagation. The output of the gage is a resistivity change history for each material of the gage. Each resistivity change is independent of the others so that three diagonal components of the elastic stress or strain tensor can be calculated from the resistivity measurements. 4 figs.

Triple-material stress-strain resistivity gage

DOEpatents

Stout, Ray B.

1988-01-01

A triple material piezoresistive gage provides multi-component elastic stress or measurements. Thin foils of three piezoresistive materials, e.g. ytterbium, manganin, and constantan, are configured in a nested serpentine rectilinear grid or other grid arrangement and embedded in a medium, preferably normal to the direction of shock wave propagation. The output of the gage is a resistivity change history for each material of the gage. Each resistivity change is independent of the others so that three diagonal components of the elastic stress or strain tensor can be calculated from the resistivity measurements.

Effect of microstructural damage on ply stresses in laminated composites

NASA Technical Reports Server (NTRS)

Allen, D. H.; Nottorf, E. W.; Harris, C. E.

1988-01-01

The mechanisms involved in damage and failure of laminated orthotropic composites are investigated theoretically. The continuum model developed accounts for both matrix cracks and interply delamination using second-order tensor-valued internal-state variables based on the locally averaged microcrack dynamics. The derivation of the model is given in detail, and numerical results for sample problems are presented in extensive graphs and tables. The model is shown to be effective in predicting stresses at the ply level, and significant damage-induced decreases in laminate stress states are found.

Frictional sliding inclusions

NASA Astrophysics Data System (ADS)

Huang, Jin H.; Furuhashi, R.; Mura, T.

1993-02-01

S OLUTIONS ARE presented in closed form by using an averaging method for inclusions sliding along an interface due to uniform eigenstrains precribed in the inclusions. The associated stress fields are also analytically determined. A parameter s is introduced to indicate the relative magnitude of sliding compared with the extreme cases of perfect bonding and perfect sliding. When the parameter s becomes zero, the present solution coincides with Eshelby's solution which is the perfectly bonded case. In contrast, when the parameter s is unity, the solution agrees with Volterra's solution (M URA and F URUHASHI, 1984, J. appl. Mech.51, 308] for the perfect sliding case. Because of non-uniform elastic fields caused by sliding along the interface, the well-known Eshelby tensor is modified for the sliding inclusions. Moreover, based on the Mori-Tanaka theory (M ORI and T ANAKA, 1973, Acta Metall.21, 571), an overall stress-strain relation is established to characterize the sliding effect on the overall elastic moduli.

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.

Supervised Variational Relevance Learning, An Analytic Geometric Feature Selection with Applications to Omic Datasets.

PubMed

Boareto, Marcelo; Cesar, Jonatas; Leite, Vitor B P; Caticha, Nestor

2015-01-01

We introduce Supervised Variational Relevance Learning (Suvrel), a variational method to determine metric tensors to define distance based similarity in pattern classification, inspired in relevance learning. The variational method is applied to a cost function that penalizes large intraclass distances and favors small interclass distances. We find analytically the metric tensor that minimizes the cost function. Preprocessing the patterns by doing linear transformations using the metric tensor yields a dataset which can be more efficiently classified. We test our methods using publicly available datasets, for some standard classifiers. Among these datasets, two were tested by the MAQC-II project and, even without the use of further preprocessing, our results improve on their performance.

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.

A Block Coordinate Descent Method for Multi-Convex Optimization with Applications to Nonnegative Tensor Factorization and Completion

DTIC Science & Technology

2012-08-01

model appears in cosmic microwave background analysis [10] which solves min A,Y λ 2 trace ( (ABY − X)>C−1(ABY − X) ) + r(Y), subject to A ∈ D (1.5...and “×n” represent outer product and tensor-matrix multiplication, respectively. (The necessary background of tensor is reviewed in Sec. 3) Most

Stationary black holes with stringy hair

NASA Astrophysics Data System (ADS)

Boos, Jens; Frolov, Valeri P.

2018-01-01

We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes, we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single string tends to zero. In a properly taken limit, the stress-energy tensor of the string distribution is finite. We call such matter stringy matter. We present a solution of the Einstein equations for an electrically charged static black hole with the stringy matter, with and without a cosmological constant. This solution is a warped product of two metrics. One of them is a deformed 2-sphere, whose Gaussian curvature is determined by the energy density of the stringy matter. We discuss the embedding of a corresponding distorted sphere into a three-dimensional Euclidean space and formulate consistency conditions. We also found a relation between the square of the Weyl tensor invariant of the four-dimensional spacetime of the stringy black holes and the energy density of the stringy matter. In the second part of the paper, we discuss test stationary strings in the Kerr geometry and in its Kerr-NUT-(anti-)de Sitter generalizations. Explicit solutions for strings that are regular at the event horizon are obtained. Using these solutions, the stress-energy tensor of the stringy matter in these geometries is calculated. Extraction of the angular momentum from rotating black holes by such strings is also discussed.

Modeling the Proterozoic Basement's Effective Stress Field, Assessing Fault Reactivation Potential Related to Increased Fluid Pressures, and Improved 3D Structural Interpretation of Faulting within Wellington and Anson-Bates Fields, Sumner County, Kansas

NASA Astrophysics Data System (ADS)

Keast, R. T.; Lacroix, B.; Raef, A. E.; Adam, C.; Bidgoli, T. S.; Leclere, H.; Daniel, G.

2017-12-01

South-central Kansas has experienced an increase in seismic activity within the Proterozoic basement. Since 2013, United States Geological Survey (USGS) seismograph stations have recorded 3414 earthquakes. Fluid pressure increases associated with recent high-rate wastewater injection into the dolomitic Arbuckle disposal zone is the hypothesized cause of reactivation of the faulted study region's Proterozoic basement. Although the magnitude of the pressure change required for reactivation of these faults is likely low given failure equilibrium conditions in the midcontinent, heterogeneities in the basement could allow for a range of fluid pressure changes associated with injection. This research aims to quantify the fluid pressure changes responsible for fault reactivation of the Proterozoic basement. To address this issue, we use 103 focal mechanisms and 3,414 seismic events, from the USGS catalog, within an area encompassing 4,000 km2. Three major fault populations have been identified using the dense seismicity and focal mechanism datasets. Win-Tensor paleostress reconstruction software was used to identify effective stress ratios, R = (σ'1/σ'3), and stress tensors for twelve 22 km by 17 km grid squares covering the study area. One fault population strikes parallel with the Nemaha Ridge basement structure ( 030˚). Another reoccurring fault population is oriented 310˚, closely parallel to the Central Kansas Uplift, a subtle anticlinal structure subjected to repeated movement during the Paleozoic. The third population of faults is parallel to the regional maximum compressive stress oriented 265˚ as determined by previous researchers using borehole image logs and shear wave anisotropy. A 3D stress modeling Matlab script was used to analyze fault reactivation potential based on results obtained from Win-Tensor to better understand fault orientations and their susceptibility to reactivation related to pore fluid pressure increases. In addition, the orientations of these normal and strike-slip fault populations suggest the development of a transtensional basin, not yet identified.

A geometric exploration of stress in deformed liquid foams

NASA Astrophysics Data System (ADS)

Evans, Myfanwy E.; Schröder-Turk, Gerd E.; Kraynik, Andrew M.

2017-03-01

We explore an alternate way of looking at the rheological response of a yield stress fluid: using discrete geometry to probe the heterogeneous distribution of stress in soap froth. We present quasi-static, uniaxial, isochoric compression and extension of three-dimensional random monodisperse soap froth in periodic boundary conditions and examine the stress and geometry that result. The stress and shape anisotropy of individual cells is quantified by Q, a scalar measure derived from the interface tensor that gauges each cell’s contribution to the global stress. Cumulatively, the spatial distribution of highly deformed cells allows us to examine how stress is internally distributed. The topology of highly deformed cells, how they arrange relative to one another in space, gives insight into the heterogeneous distribution of stress.

An integrated workflow for stress and flow modelling using outcrop-derived discrete fracture networks

NASA Astrophysics Data System (ADS)

Bisdom, K.; Nick, H. M.; Bertotti, G.

2017-06-01

Fluid flow in naturally fractured reservoirs is often controlled by subseismic-scale fracture networks. Although the fracture network can be partly sampled in the direct vicinity of wells, the inter-well scale network is poorly constrained in fractured reservoir models. Outcrop analogues can provide data for populating domains of the reservoir model where no direct measurements are available. However, extracting relevant statistics from large outcrops representative of inter-well scale fracture networks remains challenging. Recent advances in outcrop imaging provide high-resolution datasets that can cover areas of several hundred by several hundred meters, i.e. the domain between adjacent wells, but even then, data from the high-resolution models is often upscaled to reservoir flow grids, resulting in loss of accuracy. We present a workflow that uses photorealistic georeferenced outcrop models to construct geomechanical and fluid flow models containing thousands of discrete fractures covering sufficiently large areas, that does not require upscaling to model permeability. This workflow seamlessly integrates geomechanical Finite Element models with flow models that take into account stress-sensitive fracture permeability and matrix flow to determine the full permeability tensor. The applicability of this workflow is illustrated using an outcropping carbonate pavement in the Potiguar basin in Brazil, from which 1082 fractures are digitised. The permeability tensor for a range of matrix permeabilities shows that conventional upscaling to effective grid properties leads to potential underestimation of the true permeability and the orientation of principal permeabilities. The presented workflow yields the full permeability tensor model of discrete fracture networks with stress-induced apertures, instead of relying on effective properties as most conventional flow models do.

A curious explanation of some cosmological phenomena

NASA Astrophysics Data System (ADS)

Gopal Vishwakarma, Ram

2013-05-01

Although observational cosmology has shown tremendous growth over the last decade, deep mysteries continue to haunt our theoretical understanding of the ingredients of the concordance cosmological model, which are mainly ‘dark’. More than 95% of the content of the energy-stress tensor has to be in the form of the inflaton field, dark matter and dark energy, which do not have any non-gravitational or laboratory evidence and remain unidentified. Moreover, the dark energy poses a serious confrontation between fundamental physics and cosmology. This makes a strong case to discover alternative theories that do not require the dark sectors of the standard approach to explain the observations. In the present situation, it would be important to gain insight about the requirements of the ‘would-be’ final theory from all possible means. In this context, this paper highlights some, hitherto unnoticed, interesting coincidences that may prove useful to develop insight about the ‘holy grail’ of gravitation. It appears that the requirement of the speculative dark sectors by the energy-stress tensor is indicative of a possible way out of the present crisis appearing in the standard cosmology, in terms of a theory wherein the energy-stress tensor does not play a direct role in the dynamics. It is shown that various cosmological observations can be explained satisfactorily in the framework of one such theory—the Milne model, without requiring the dark sectors of the standard approach. Moreover, the model evades the horizon, flatness and the cosmological constant problems afflicting the standard cosmology. Although Milne's theory is an incomplete, phenomenological theory, and cannot be the final theory of gravitation, nevertheless, it would be worthwhile to study these coincidences, which may help us develop insight about the would-be final theory.

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.

Improvement of Accuracy for Background Noise Estimation Method Based on TPE-AE

NASA Astrophysics Data System (ADS)

Itai, Akitoshi; Yasukawa, Hiroshi

This paper proposes a method of a background noise estimation based on the tensor product expansion with a median and a Monte carlo simulation. We have shown that a tensor product expansion with absolute error method is effective to estimate a background noise, however, a background noise might not be estimated by using conventional method properly. In this paper, it is shown that the estimate accuracy can be improved by using proposed methods.

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

Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei

Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution thatmore » can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.« less

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.

Video denoising using low rank tensor decomposition

NASA Astrophysics Data System (ADS)

Gui, Lihua; Cui, Gaochao; Zhao, Qibin; Wang, Dongsheng; Cichocki, Andrzej; Cao, Jianting

2017-03-01

Reducing noise in a video sequence is of vital important in many real-world applications. One popular method is block matching collaborative filtering. However, the main drawback of this method is that noise standard deviation for the whole video sequence is known in advance. In this paper, we present a tensor based denoising framework that considers 3D patches instead of 2D patches. By collecting the similar 3D patches non-locally, we employ the low-rank tensor decomposition for collaborative filtering. Since we specify the non-informative prior over the noise precision parameter, the noise variance can be inferred automatically from observed video data. Therefore, our method is more practical, which does not require knowing the noise variance. The experimental on video denoising demonstrates the effectiveness of our proposed method.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r(4)) scaling.

PubMed

Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David

2013-08-07

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

NASA Astrophysics Data System (ADS)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

2018-05-01

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

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.

Local nematic susceptibility in stressed BaFe2As2 from NMR electric field gradient measurements

NASA Astrophysics Data System (ADS)

Kissikov, T.; Sarkar, R.; Lawson, M.; Bush, B. T.; Timmons, E. I.; Tanatar, M. A.; Prozorov, R.; Bud'ko, S. L.; Canfield, P. C.; Fernandes, R. M.; Goh, W. F.; Pickett, W. E.; Curro, N. J.

2017-12-01

The electric field gradient (EFG) tensor at the 75As site couples to the orbital occupations of the As p orbitals and is a sensitive probe of local nematicity in BaFe2As2 . We use nuclear magnetic resonance to measure the nuclear quadrupolar splittings and find that the EFG asymmetry responds linearly to the presence of a strain field in the paramagnetic phase. We extract the nematic susceptibility from the slope of this linear response as a function of temperature and find that it diverges near the structural transition, in agreement with other measures of the bulk nematic susceptibility. Our work establishes an alternative method to extract the nematic susceptibility which, in contrast to transport methods, can be extended inside the superconducting state.

Some Recent Developments in Turbulence Closure Modeling

NASA Astrophysics Data System (ADS)

Durbin, Paul A.

2018-01-01

Turbulence closure models are central to a good deal of applied computational fluid dynamical analysis. Closure modeling endures as a productive area of research. This review covers recent developments in elliptic relaxation and elliptic blending models, unified rotation and curvature corrections, transition prediction, hybrid simulation, and data-driven methods. The focus is on closure models in which transport equations are solved for scalar variables, such as the turbulent kinetic energy, a timescale, or a measure of anisotropy. Algebraic constitutive representations are reviewed for their role in relating scalar closures to the Reynolds stress tensor. Seamless and nonzonal methods, which invoke a single closure model, are reviewed, especially detached eddy simulation (DES) and adaptive DES. Other topics surveyed include data-driven modeling and intermittency and laminar fluctuation models for transition prediction. The review concludes with an outlook.

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.

On the equivalence among stress tensors in a gauge-fluid system

NASA Astrophysics Data System (ADS)

Mitra, Arpan Krishna; Banerjee, Rabin; Ghosh, Subir

2017-12-01

In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space-time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.

Features of Relaxation of a Stress Tensor in the Microscopic Volume of Nematic Phase under the Action of a Strong Electric Field

NASA Astrophysics Data System (ADS)

Zakharov, A. V.

2018-02-01

A numerical study of new regimes of reorientation of director field n̂, velocity v, and components of stress tensor σ ij ( ij = x, y, z) of nematic liquid crystal (LC) encapsulated in a rectangular channel under the action of a strong electric field E directed at angle α ( {˜{π }/{2}} ) to the horizontal surfaces bounding the LC channel is proposed. The numerical calculations performed in the framework of nonlinear generalization of the classical Eriksen-Leslie theory have shown that at certain relations between the torques and momenta affecting the unit LC volume and E ≫ E th, transition periodic structures can emerge during reorientation of n̂, if the corresponding distortion mode has the fastest response, and, thus, suppress all other modes. Rotating domains originating within this process decrease the energy dissipation rate and create more favorable regimes of the director field reorientation, as compared with the uniform rotational displacement.

Effective Tolman temperature induced by trace anomaly

NASA Astrophysics Data System (ADS)

Eune, Myungseok; Gim, Yongwan; Kim, Wontae

2017-04-01

Despite the finiteness of stress tensor for a scalar field on the four-dimensional Schwarzschild black hole in the Israel-Hartle-Hawking vacuum, the Tolman temperature in thermal equilibrium is certainly divergent on the horizon due to the infinite blue-shift of the Hawking temperature. The origin of this conflict is due to the fact that the conventional Tolman temperature was based on the assumption of a traceless stress tensor, which is, however, incompatible with the presence of the trace anomaly responsible for the Hawking radiation. Here, we present an effective Tolman temperature which is compatible with the presence of the trace anomaly by using the modified Stefan-Boltzmann law. Eventually, the effective Tolman temperature turns out to be finite everywhere outside the horizon, and so an infinite blue-shift of the Hawking temperature at the event horizon does not appear any more. In particular, it is vanishing on the horizon, so that the equivalence principle is exactly recovered at the horizon.

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.

Scalar field coupling to Einstein tensor in regular black hole spacetime

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wu, Chen

2018-02-01

In this paper, we study the perturbation property of a scalar field coupling to Einstein's tensor in the background of the regular black hole spacetimes. Our calculations show that the the coupling constant η imprints in the wave equation of a scalar perturbation. We calculated the quasinormal modes of scalar field coupling to Einstein's tensor in the regular black hole spacetimes by the 3rd order WKB method.

Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.

PubMed

de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos

2011-01-01

In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.

Identification of the full anisotropic flow resistivity tensor for multiple glass wool and melamine foam samples.

PubMed

Van der Kelen, Christophe; Göransson, Peter

2013-12-01

The flow resistivity tensor, which is the inverse of the viscous permeability tensor, is one of the most important material properties for the acoustic performance of porous materials used in acoustic treatments. Due to the manufacturing processes involved, these porous materials are most often geometrically anisotropic on a microscopic scale, and for demanding applications, there is a need for improved characterization methods. This paper discusses recent refinements of a method for the identification of the anisotropic flow resistivity tensor. The inverse estimation is verified for three fictitious materials with different degrees of anisotropy. Measurements are performed on nine glass wool samples and seven melamine foam samples, and the anisotropic flow resistivity tensors obtained are validated by comparison to measurements performed on uni-directional cylindrical samples, extracted from the same, previously measured cubic samples. The variability of flow resistivity in the batch of material from which the glass wool is extracted is discussed. The results for the melamine foam suggest that there is a relation between the direction of highest flow resistivity, and the rise direction of the material.

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.

Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-05-31

We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

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

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

PubMed

Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo

2017-10-12

Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.

Thermodynamics of viscoelastic rate-type fluids with stress diffusion

NASA Astrophysics Data System (ADS)

Málek, Josef; Průša, Vít; Skřivan, Tomáš; Süli, Endre

2018-02-01

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.

Accurate calculation of the geometric measure of entanglement for multipartite quantum states

NASA Astrophysics Data System (ADS)

Teng, Peiyuan

2017-07-01

This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction. Numerical examples are benchmarked and compared. Furthermore, we search for highly entangled qubit states to show the applicability of this method.

Nonlinear deformation of composites with consideration of the effect of couple-stresses

NASA Astrophysics Data System (ADS)

Lagzdiņš, A.; Teters, G.; Zilaucs, A.

1998-09-01

Nonlinear deformation of spatially reinforced composites under active loading (without unloading) is considered. All the theoretical constructions are based on the experimental data on unidirectional and ±π/4 cross-ply epoxy plastics reinforced with glass fibers. Based on the elastic properties of the fibers and EDT-10 epoxy binder, the linear elastic characteristics of a transversely isotropic unidirectionally reinforced fiberglass plastic are found, whereas the nonlinear characteristics are obtained from experiments. For calculating the deformation properties of the ±π/4 cross-ply plastic, a refined version of the Voigt method is applied taking into account also the couple-stresses arising in the composite due to relative rotation of the reinforcement fibers. In addition, a fourth-rank damage tensor is introduced in order to account for the impact of fracture caused by the couple-stresses. The unknown constants are found from the experimental uniaxial tension curve for the cross-ply composite. The comparison between the computed curves and experimental data for other loading paths shows that the description of the nonlinear behavior of composites can be improved by considering the effect of couple-stresses generated by rotations of the reinforcing fibers.

Estimating Stresses, Fault Friction and Fluid Pressure from Topography and Coseismic Slip Models

NASA Astrophysics Data System (ADS)

Styron, R. H.; Hetland, E. A.

2014-12-01

Stress is a first-order control on the deformation state of the earth. However, stress is notoriously hard to measure, and researchers typically only estimate the directions and relative magnitudes of principal stresses, with little quantification of the uncertainties or absolute magnitude. To improve upon this, we have developed methods to constrain the full stress tensor field in a region surrounding a fault, including tectonic, topographic, and lithostatic components, as well as static friction and pore fluid pressure on the fault. Our methods are based on elastic halfspace techniques for estimating topographic stresses from a DEM, and we use a Bayesian approach to estimate accumulated tectonic stress, fluid pressure, and friction from fault geometry and slip rake, assuming Mohr-Coulomb fault mechanics. The nature of the tectonic stress inversion is such that either the stress maximum or minimum is better constrained, depending on the topography and fault deformation style. Our results from the 2008 Wenchuan event yield shear stresses from topography up to 20 MPa (normal-sinistral shear sense) and topographic normal stresses up to 80 MPa on the faults; tectonic stress had to be large enough to overcome topography to produce the observed reverse-dextral slip. Maximum tectonic stress is constrained to be >0.3 * lithostatic stress (depth-increasing), with a most likely value around 0.8, trending 90-110°E. Minimum tectonic stress is about half of maximum. Static fault friction is constrained at 0.1-0.4, and fluid pressure at 0-0.6 * total pressure on the fault. Additionally, the patterns of topographic stress and slip suggest that topographic normal stress may limit fault slip once failure has occurred. Preliminary results from the 2013 Balochistan earthquake are similar, but yield stronger constraints on the upper limits of maximum tectonic stress, as well as tight constraints on the magnitude of minimum tectonic stress and stress orientation. Work in progress on the Wasatch fault suggests that maximum tectonic stress may also be able to be constrained, and that some of the shallow rupture segmentation may be due in part to localized topographic loading. Future directions of this work include regions where high relief influences fault kinematics (such as Tibet).

Tensor-based tracking of the aorta in phase-contrast MR images

NASA Astrophysics Data System (ADS)

Azad, Yoo-Jin; Malsam, Anton; Ley, Sebastian; Rengier, Fabian; Dillmann, Rüdiger; Unterhinninghofen, Roland

2014-03-01

The velocity-encoded magnetic resonance imaging (PC-MRI) is a valuable technique to measure the blood flow velocity in terms of time-resolved 3D vector fields. For diagnosis, presurgical planning and therapy control monitoring the patient's hemodynamic situation is crucial. Hence, an accurate and robust segmentation of the diseased vessel is the basis for further methods like the computation of the blood pressure. In the literature, there exist some approaches to transfer the methods of processing DT-MR images to PC-MR data, but the potential of this approach is not fully exploited yet. In this paper, we present a method to extract the centerline of the aorta in PC-MR images by applying methods from the DT-MRI. On account of this, in the first step the velocity vector fields are converted into tensor fields. In the next step tensor-based features are derived and by applying a modified tensorline algorithm the tracking of the vessel course is accomplished. The method only uses features derived from the tensor imaging without the use of additional morphology information. For evaluation purposes we applied our method to 4 volunteer as well as 26 clinical patient datasets with good results. In 29 of 30 cases our algorithm accomplished to extract the vessel centerline.

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.

Fast Fourier transform discrete dislocation dynamics

NASA Astrophysics Data System (ADS)

Graham, J. T.; Rollett, A. D.; LeSar, R.

2016-12-01

Discrete dislocation dynamics simulations have been generally limited to modeling systems described by isotropic elasticity. Effects of anisotropy on dislocation interactions, which can be quite large, have generally been ignored because of the computational expense involved when including anisotropic elasticity. We present a different formalism of dislocation dynamics in which the dislocations are represented by the deformation tensor, which is a direct measure of the slip in the lattice caused by the dislocations and can be considered as an eigenstrain. The stresses arising from the dislocations are calculated with a fast Fourier transform (FFT) method, from which the forces are determined and the equations of motion are solved. Use of the FFTs means that the stress field is only available at the grid points, which requires some adjustments/regularizations to be made to the representation of the dislocations and the calculation of the force on individual segments, as is discussed hereinafter. A notable advantage of this approach is that there is no computational penalty for including anisotropic elasticity. We review the method and apply it in a simple dislocation dynamics calculation.

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.

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.

Constraining primordial vector mode from B-mode polarization

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

Saga, Shohei; Ichiki, Kiyotomo; Shiraishi, Maresuke, E-mail: saga.shohei@nagoya-u.jp, E-mail: maresuke.shiraishi@pd.infn.it, E-mail: ichiki@a.phys.nagoya-u.ac.jp

The B-mode polarization spectrum of the Cosmic Microwave Background (CMB) may be the smoking gun of not only the primordial tensor mode but also of the primordial vector mode. If there exist nonzero vector-mode metric perturbations in the early Universe, they are known to be supported by anisotropic stress fluctuations of free-streaming particles such as neutrinos, and to create characteristic signatures on both the CMB temperature, E-mode, and B-mode polarization anisotropies. We place constraints on the properties of the primordial vector mode characterized by the vector-to-scalar ratio r{sub v} and the spectral index n{sub v} of the vector-shear power spectrum,more » from the Planck and BICEP2 B-mode data. We find that, for scale-invariant initial spectra, the ΛCDM model including the vector mode fits the data better than the model including the tensor mode. The difference in χ{sup 2} between the vector and tensor models is Δχ{sup 2} = 3.294, because, on large scales the vector mode generates smaller temperature fluctuations than the tensor mode, which is preferred for the data. In contrast, the tensor mode can fit the data set equally well if we allow a significantly blue-tilted spectrum. We find that the best-fitting tensor mode has a large blue tilt and leads to an indistinct reionization bump on larger angular scales. The slightly red-tilted vector mode supported by the current data set can also create O(10{sup -22})-Gauss magnetic fields at cosmological recombination. Our constraints should motivate research that considers models of the early Universe that involve the vector mode.« less

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan

2018-03-01

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan

2018-07-01

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.

Rheological Predictions of Network Systems Swollen with Entangled Solvent

DTIC Science & Technology

2014-04-01

represent binary entanglements and the crosses represent cross-links. Both of which are fixed in space for Green– Kubo calculations or moved affinely for...Two types of calculations can be performed, equilibrium (or Green– Kubo ) calculations in which the rate of deformation tensor21,22 is set to zero and the...autocorrelation function of stress at equilibrium is followed; or flow calculations in which a specific flow field is applied and the stress as a

Modeling Slip System Strength Evolution in Ti 7Al Informed by In situ Grain Stress Measurements (Postprint)

DTIC Science & Technology

2017-02-17

time for the tomography and diffraction sweeps was approximately 42 min. In a typical quasi -static in-situ experiment, loading is halted and the...data is used to extract individual grain- average stress tensors in a large aggregate of Ti-7Al grains (z500) over a time series of prescribed states...for public release: distribution unlimited. © 2017 ELSEVIER LTD (STINFO COPY) AIR FORCE RESEARCH LABORATORY MATERIALS AND MANUFACTURING

Evaluation of mechanical deformation and distributive magnetic loads with different mechanical constraints in two parallel conducting bars

NASA Astrophysics Data System (ADS)

Lee, Ho-Young; Lee, Se-Hee

2017-08-01

Mechanical deformation, bending deformation, and distributive magnetic loads were evaluated numerically and experimentally for conducting materials excited with high current. Until now, many research works have extensively studied the area of magnetic force and mechanical deformation by using coupled approaches such as multiphysics solvers. In coupled analysis for magnetoelastic problems, some articles and commercial software have presented the resultant mechanical deformation and stress on the body. To evaluate the mechanical deformation, the Lorentz force density method (LZ) and the Maxwell stress tensor method (MX) have been widely used for conducting materials. However, it is difficult to find any experimental verification regarding mechanical deformation or bending deformation due to magnetic force density. Therefore, we compared our numerical results to those from experiments with two parallel conducting bars to verify our numerical setup for bending deformation. Before showing this, the basic and interesting coupled simulation was conducted to test the mechanical deformations by the LZ (body force density) and the MX (surface force density) methods. This resulted in MX gave the same total force as LZ, but the local force distribution in MX introduced an incorrect mechanical deformation in the simulation of a solid conductor.

A seismological overview of the induced earthquakes in the Duvernay play near Fox Creek, Alberta

NASA Astrophysics Data System (ADS)

Schultz, Ryan; Wang, Ruijia; Gu, Yu Jeffrey; Haug, Kristine; Atkinson, Gail

2017-01-01

This paper summarizes the current state of understanding regarding the induced seismicity in connection with hydraulic fracturing operations targeting the Duvernay Formation in central Alberta, near the town of Fox Creek. We demonstrate that earthquakes in this region cluster into distinct sequences in time, space, and focal mechanism using (i) cross-correlation detection methods to delineate transient temporal relationships, (ii) double-difference relocations to confirm spatial clustering, and (iii) moment tensor solutions to assess fault motion consistency. The spatiotemporal clustering of the earthquake sequences is strongly related to the nearby hydraulic fracturing operations. In addition, we identify a preference for strike-slip motions on subvertical faults with an approximate 45° P axis orientation, consistent with expectation from the ambient stress field. The hypocentral geometries for two of the largest-magnitude (M 4) sequences that are robustly constrained by local array data provide compelling evidence for planar features starting at Duvernay Formation depths and extending into the shallow Precambrian basement. We interpret these lineaments as subvertical faults orientated approximately north-south, consistent with the regional moment tensor solutions. Finally, we conclude that the sequences were triggered by pore pressure increases in response to hydraulic fracturing stimulations along previously existing faults.

Close-range photogrammetry in underground mining ground control

NASA Astrophysics Data System (ADS)

Benton, Donovan J.; Chambers, Amy J.; Raffaldi, Michael J.; Finley, Seth A.; Powers, Mark J.

2016-09-01

Monitoring underground mine deformation and support conditions has traditionally involved visual inspection and geotechnical instrumentation. Monitoring displacements with conventional instrumentation can be expensive and time-consuming, and the number of locations that can be effectively monitored is generally limited. Moreover, conventional methods typically produce vector rather than tensor descriptions of geometry changes. Tensor descriptions can provide greater insight into hazardous ground movements, particularly in recently excavated openings and in older workings that have been negatively impacted by high stress concentrations, time-dependent deformation, or corrosion of ground support elements. To address these issues, researchers with the National Institute for Occupational Safety and Health, Spokane Mining Research Division are developing and evaluating photogrammetric systems for ground control monitoring applications in underground mines. This research has demonstrated that photogrammetric systems can produce millimeter-level measurements that are comparable to conventional displacement-measuring instruments. This paper provides an overview of the beneficial use of close-range photogrammetry for the following three ground control applications in underground mines: monitoring the deformation of surface support, monitoring rock mass movement, and monitoring the corrosion of surface support. Preliminary field analyses, case studies, limitations, and best practices for these applications are also discussed.

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.

Visualization of 3-D tensor fields

NASA Technical Reports Server (NTRS)

Hesselink, L.

1996-01-01

Second-order tensor fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in tensor fields makes them more complex and abstract than scalar and vector fields. Visualization is a good technique for scientists to gain new insights from them. Visualizing a 3-D continuous tensor field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional tensor fields. It was shown that degenerate points, defined as points where eigenvalues are equal to each other, are the basic singularities underlying the topology of tensor fields. Moreover, it was shown that eigenvectors never cross each other except at degenerate points. Since we live in a three-dimensional world, it is important for us to understand the underlying physics of this world. In this report, we describe a new method for locating degenerate points along with the conditions for classifying them in three-dimensional space. Finally, we discuss some topological features of three-dimensional tensor fields, and interpret topological patterns in terms of physical properties.

Tectonic stress orientations and magnitudes, and friction of faults, deduced from earthquake focal mechanism inversions over the Korean Peninsula

NASA Astrophysics Data System (ADS)

Soh, Inho; Chang, Chandong; Lee, Junhyung; Hong, Tae-Kyung; Park, Eui-Seob

2018-05-01

We characterize the present-day stress state in and around the Korean Peninsula using formal inversions of earthquake focal mechanisms. Two different methods are used to select preferred fault planes in the double-couple focal mechanism solutions: one that minimizes average misfit angle and the other choosing faults with higher instability. We invert selected sets of fault planes for estimating the principal stresses at regularly spaced grid points, using a circular-area data-binning method, where the bin radius is optimized to yield the best possible stress inversion results based on the World Stress Map quality ranking scheme. The inversions using the two methods yield well constrained and fairly comparable results, which indicate that the prevailing stress regime is strike-slip, and the maximum horizontal principal stress (SHmax) is oriented ENE-WSW throughout the study region. Although the orientation of the stresses is consistent across the peninsula, the relative stress magnitude parameter (R-value) varies significantly, from 0.22 in the northwest to 0.89 in the southeast. Based on our knowledge of the R-values and stress regime, and using a value for vertical stress (Sv) estimated from the overburden weight of rock, together with a value for the maximum differential stress (based on the Coulomb friction of faults optimally oriented for slip), we estimate the magnitudes of the two horizontal principal stresses. The horizontal stress magnitudes increase from west to east such that SHmax/Sv ratio rises from 1.5 to 2.4, and the Shmin/Sv ratio from 0.6 to 0.8. The variation in the magnitudes of the tectonic stresses appears to be related to differences in the rigidity of crustal rocks. Using the complete stress tensors, including both orientations and magnitudes, we assess the possible ranges of frictional coefficients for different types of faults. We show that normal and reverse faults have lower frictional coefficients than strike-slip faults, suggesting that the former types of faults can be activated under a strike-slip stress regime. Our observations of the seismicity, with normal faulting concentrated offshore to the northwest and reverse faulting focused offshore to the east, are compatible with the results of our estimates of stress magnitudes.

Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation

NASA Astrophysics Data System (ADS)

Khoromskaia, Venera; Khoromskij, Boris N.

2014-12-01

Our recent method for low-rank tensor representation of sums of the arbitrarily positioned electrostatic potentials discretized on a 3D Cartesian grid reduces the 3D tensor summation to operations involving only 1D vectors however retaining the linear complexity scaling in the number of potentials. Here, we introduce and study a novel tensor approach for fast and accurate assembled summation of a large number of lattice-allocated potentials represented on 3D N × N × N grid with the computational requirements only weakly dependent on the number of summed potentials. It is based on the assembled low-rank canonical tensor representations of the collected potentials using pointwise sums of shifted canonical vectors representing the single generating function, say the Newton kernel. For a sum of electrostatic potentials over L × L × L lattice embedded in a box the required storage scales linearly in the 1D grid-size, O(N) , while the numerical cost is estimated by O(NL) . For periodic boundary conditions, the storage demand remains proportional to the 1D grid-size of a unit cell, n = N / L, while the numerical cost reduces to O(N) , that outperforms the FFT-based Ewald-type summation algorithms of complexity O(N3 log N) . The complexity in the grid parameter N can be reduced even to the logarithmic scale O(log N) by using data-sparse representation of canonical N-vectors via the quantics tensor approximation. For justification, we prove an upper bound on the quantics ranks for the canonical vectors in the overall lattice sum. The presented approach is beneficial in applications which require further functional calculus with the lattice potential, say, scalar product with a function, integration or differentiation, which can be performed easily in tensor arithmetics on large 3D grids with 1D cost. Numerical tests illustrate the performance of the tensor summation method and confirm the estimated bounds on the tensor ranks.

gamAID: Greedy CP tensor decomposition for supervised EHR-based disease trajectory differentiation.

PubMed

Henderson, Jette; Ho, Joyce; Ghosh, Joydeep

2017-07-01

We propose gamAID, an exploratory, supervised nonnegative tensor factorization method that iteratively extracts phenotypes from tensors constructed from medical count data. Using data from diabetic patients who later on get diagnosed with chronic kidney disorder (CKD) as well as diabetic patients who do not receive a CKD diagnosis, we demonstrate the potential of gamAID to discover phenotypes that characterize patients who are at risk for developing a disease.

An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs

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

Kolda, Tamara G.; Mayo, Jackson R.

2014-12-11

Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang [J. Math. Anal. Appl., 350 (2009), pp. 416--422]. Given mth-order, n-dimensional real-valued symmetric tensorsmore » $${\\mathscr{A}}$$ and $$\\boldsymbol{\\mathscr{B}}$$, the goal is to find $$\\lambda \\in \\mathbb{R}$$ and $$\\mathbf{x} \\in \\mathbb{R}^{n}, \\mathbf{x} \

Efficient evaluation of the material response of tissues reinforced by statistically oriented fibres

NASA Astrophysics Data System (ADS)

Hashlamoun, Kotaybah; Grillo, Alfio; Federico, Salvatore

2016-10-01

For several classes of soft biological tissues, modelling complexity is in part due to the arrangement of the collagen fibres. In general, the arrangement of the fibres can be described by defining, at each point in the tissue, the structure tensor (i.e. the tensor product of the unit vector of the local fibre arrangement by itself) and a probability distribution of orientation. In this approach, assuming that the fibres do not interact with each other, the overall contribution of the collagen fibres to a given mechanical property of the tissue can be estimated by means of an averaging integral of the constitutive function describing the mechanical property at study over the set of all possible directions in space. Except for the particular case of fibre constitutive functions that are polynomial in the transversely isotropic invariants of the deformation, the averaging integral cannot be evaluated directly, in a single calculation because, in general, the integrand depends both on deformation and on fibre orientation in a non-separable way. The problem is thus, in a sense, analogous to that of solving the integral of a function of two variables, which cannot be split up into the product of two functions, each depending only on one of the variables. Although numerical schemes can be used to evaluate the integral at each deformation increment, this is computationally expensive. With the purpose of containing computational costs, this work proposes approximation methods that are based on the direct integrability of polynomial functions and that do not require the step-by-step evaluation of the averaging integrals. Three different methods are proposed: (a) a Taylor expansion of the fibre constitutive function in the transversely isotropic invariants of the deformation; (b) a Taylor expansion of the fibre constitutive function in the structure tensor; (c) for the case of a fibre constitutive function having a polynomial argument, an approximation in which the directional average of the constitutive function is replaced by the constitutive function evaluated at the directional average of the argument. Each of the proposed methods approximates the averaged constitutive function in such a way that it is multiplicatively decomposed into the product of a function of the deformation only and a function of the structure tensors only. In order to assess the accuracy of these methods, we evaluate the constitutive functions of the elastic potential and the Cauchy stress, for a biaxial test, under different conditions, i.e. different fibre distributions and different ratios of the nominal strains in the two directions. The results are then compared against those obtained for an averaging method available in the literature, as well as against the integration made at each increment of deformation.

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

PubMed

Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J

2002-01-01

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

Tidal disruption of solid bodies

NASA Technical Reports Server (NTRS)

Dobrovolskis, Anthony R.

1990-01-01

The problem of stress, strain, and breakup in solid satellites and stray bodies subject to tidal perturbations is presently addressed in view of three novel considerations. After presenting a new analytic solution for the stress tensor in a homogeneous and compressible elastic sphere, where the inclusion of compressibility alters stresses by several percent, realistic failure criteria are noted to demonstrate the general failure of such ductile bodies as iron meteoroids by plastic shear, while brittle ice bodies fail by either tensile or shear fracture. A reexamination of crack propagation after initial failure allows the diverse breakup criteria to be reconciled.

A Framework for Load Balancing of Tensor Contraction Expressions via Dynamic Task Partitioning

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

Lai, Pai-Wei; Stock, Kevin; Rajbhandari, Samyam

In this paper, we introduce the Dynamic Load-balanced Tensor Contractions (DLTC), a domain-specific library for efficient task parallel execution of tensor contraction expressions, a class of computation encountered in quantum chemistry and physics. Our framework decomposes each contraction into smaller unit of tasks, represented by an abstraction referred to as iterators. We exploit an extra level of parallelism by having tasks across independent contractions executed concurrently through a dynamic load balancing run- time. We demonstrate the improved performance, scalability, and flexibility for the computation of tensor contraction expressions on parallel computers using examples from coupled cluster methods.

Plasmonic graded nano-disks as nano-optical conveyor belt.

PubMed

Kang, Zhiwen; Lu, Haifei; Chen, Jiajie; Chen, Kun; Xu, Fang; Ho, Ho-Pui

2014-08-11

We propose a plasmonic system consisting of nano-disks (NDs) with graded diameters for the realization of nano-optical conveyor belt. The system contains a couple of NDs with individual elements coded with different resonant wavelengths. By sequentially switching the wavelength and polarization of the excitation source, optically trapped target nano-particle can be transferred from one ND to another. The feasibility of such function is verified based on the three-dimensional finite-difference time-domain technique and the Maxwell stress tensor method. Our design may provide an alternative way to construct nano-optical conveyor belt with which target molecules can be delivered between trapping sites, thus enabling many on-chip optofluidic applications.

Estimation of full moment tensors, including uncertainties, for earthquakes, volcanic events, and nuclear explosions

NASA Astrophysics Data System (ADS)

Alvizuri, Celso; Silwal, Vipul; Krischer, Lion; Tape, Carl

2017-04-01

A seismic moment tensor is a 3 × 3 symmetric matrix that provides a compact representation of seismic events within Earth's crust. We develop an algorithm to estimate moment tensors and their uncertainties from observed seismic data. For a given event, the algorithm performs a grid search over the six-dimensional space of moment tensors by generating synthetic waveforms at each grid point and then evaluating a misfit function between the observed and synthetic waveforms. 'The' moment tensor M for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M, we first convert the misfit function to a probability function. The uncertainty, or rather the confidence, is then given by the 'confidence curve' P(V ), where P(V ) is the probability that the true moment tensor for the event lies within the neighborhood of M that has fractional volume V . The area under the confidence curve provides a single, abbreviated 'confidence parameter' for M. We apply the method to data from events in different regions and tectonic settings: small (Mw < 2.5) events at Uturuncu volcano in Bolivia, moderate (Mw > 4) earthquakes in the southern Alaska subduction zone, and natural and man-made events at the Nevada Test Site. Moment tensor uncertainties allow us to better discriminate among moment tensor source types and to assign physical processes to the events.

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.

Strength Analysis of Glass-Fiber-Reinforced Plastic during Buckling,

DTIC Science & Technology

An algorithm is developed for calculating and analyzing the stress tensor by the experimental function of deflections during the buckling of glass ... fiber -reinforced plastic shells loaded with a hydrostatic load. Malmeyster’s theory of strength is used to qualitatively establish the possible points of shell failure. (Author-PL)

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.

Performance of tensor decomposition-based modal identification under nonstationary vibration

NASA Astrophysics Data System (ADS)

Friesen, P.; Sadhu, A.

2017-03-01

Health monitoring of civil engineering structures is of paramount importance when they are subjected to natural hazards or extreme climatic events like earthquake, strong wind gusts or man-made excitations. Most of the traditional modal identification methods are reliant on stationarity assumption of the vibration response and posed difficulty while analyzing nonstationary vibration (e.g. earthquake or human-induced vibration). Recently tensor decomposition based methods are emerged as powerful and yet generic blind (i.e. without requiring a knowledge of input characteristics) signal decomposition tool for structural modal identification. In this paper, a tensor decomposition based system identification method is further explored to estimate modal parameters using nonstationary vibration generated due to either earthquake or pedestrian induced excitation in a structure. The effects of lag parameters and sensor densities on tensor decomposition are studied with respect to the extent of nonstationarity of the responses characterized by the stationary duration and peak ground acceleration of the earthquake. A suite of more than 1400 earthquakes is used to investigate the performance of the proposed method under a wide variety of ground motions utilizing both complete and partial measurements of a high-rise building model. Apart from the earthquake, human-induced nonstationary vibration of a real-life pedestrian bridge is also used to verify the accuracy of the proposed method.

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.

Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation

PubMed Central

Freistühler, Heinrich; Temple, Blake

2014-01-01

Current theories of dissipation in the relativistic regime suffer from one of two deficits: either their dissipation is not causal or no profiles for strong shock waves exist. This paper proposes a relativistic Navier–Stokes–Fourier-type viscosity and heat conduction tensor such that the resulting second-order system of partial differential equations for the fluid dynamics of pure radiation is symmetric hyperbolic. This system has causal dissipation as well as the property that all shock waves of arbitrary strength have smooth profiles. Entropy production is positive both on gradients near those of solutions to the dissipation-free equations and on gradients of shock profiles. This shows that the new dissipation stress tensor complies to leading order with the principles of thermodynamics. Whether higher order modifications of the ansatz are required to obtain full compatibility with the second law far from the zero-dissipation equilibrium is left to further investigations. The system has exactly three a priori free parameters χ,η,ζ, corresponding physically to heat conductivity, shear viscosity and bulk viscosity. If the bulk viscosity is zero (as is stated in the literature) and the total stress–energy tensor is trace free, the entire viscosity and heat conduction tensor is determined to within a constant factor. PMID:24910526

An Improved Method for Seismic Event Depth and Moment Tensor Determination: CTBT Related Application

NASA Astrophysics Data System (ADS)

Stachnik, J.; Rozhkov, M.; Baker, B.

2016-12-01

According to the Protocol to CTBT, International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event. Determination of seismic event source mechanism and its depth is a part of these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. We show preliminary results using the latter approach from an improved software design and applied on a moderately powered computer. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis/AXISEM full waveform synthetics added to a pre-computed GF archive. Along with traditional post processing analysis of waveform misfits through several objective functions and variance reduction, we follow a probabilistic approach to assess the robustness of moment tensor solution. In a course of this project full moment tensor and depth estimates are determined for DPRK 2009, 2013 and 2016 events and shallow earthquakes using a new implementation of waveform fitting of teleseismic P waves. A full grid search over the entire moment tensor space is used to appropriately sample all possible solutions. A recent method by Tape & Tape (2012) to discretize the complete moment tensor space from a geometric perspective is used. Moment tensors for DPRK events show isotropic percentages greater than 50%. Depth estimates for the DPRK events range from 1.0-1.4 km. Probabilistic uncertainty estimates on the moment tensor parameters provide robustness to solution.

Mean template for tensor-based morphometry using deformation tensors.

PubMed

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

Correlators in tensor models from character calculus

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2017-11-01

We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.

Ward identities and combinatorics of rainbow tensor models

NASA Astrophysics Data System (ADS)

Itoyama, H.; Mironov, A.; Morozov, A.

2017-06-01

We discuss the notion of renormalization group (RG) completion of non-Gaussian Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in application to the matrix and tensor models. With the example of the simplest non-trivial RGB tensor theory (Aristotelian rainbow), we introduce a few methods, which allow one to connect calculations in the tensor models to those in the matrix models. As a byproduct, we obtain some new factorization formulas and sum rules for the Gaussian correlators in the Hermitian and complex matrix theories, square and rectangular. These sum rules describe correlators as solutions to finite linear systems, which are much simpler than the bilinear Hirota equations and the infinite Virasoro recursion. Search for such relations can be a way to solving the tensor models, where an explicit integrability is still obscure.

A General Sparse Tensor Framework for Electronic Structure Theory

DOE PAGES

Manzer, Samuel; Epifanovsky, Evgeny; Krylov, Anna I.; ...

2017-01-24

Linear-scaling algorithms must be developed in order to extend the domain of applicability of electronic structure theory to molecules of any desired size. But, the increasing complexity of modern linear-scaling methods makes code development and maintenance a significant challenge. A major contributor to this difficulty is the lack of robust software abstractions for handling block-sparse tensor operations. We therefore report the development of a highly efficient symbolic block-sparse tensor library in order to provide access to high-level software constructs to treat such problems. Our implementation supports arbitrary multi-dimensional sparsity in all input and output tensors. We then avoid cumbersome machine-generatedmore » code by implementing all functionality as a high-level symbolic C++ language library and demonstrate that our implementation attains very high performance for linear-scaling sparse tensor contractions.« less

Description of plastic deformation of structural materials in triaxial loading

NASA Astrophysics Data System (ADS)

Lagzdins, A.; Zilaucs, A.

2008-03-01

A model of nonassociated plasticity is put forward for initially isotropic materials deforming with residual changes in volume under the action of triaxial normal stresses. The model is based on novel plastic loading and plastic potential functions, which define closed, convex, every where smooth surfaces in the 6D space of symmetric second-rank stress tensors. By way of example, the plastic deformation of a cylindrical concrete specimen wrapped with a CFRP tape and loaded in axial compression is described.

Future Directions of Nonlinear Dynamics in PhysicaL and Biological Systems,

DTIC Science & Technology

1992-01-01

ACKNOWLEDGEMENT This work has been supported in part by the Air Force Office of Scientific Research through Grant No. AFOSR-89-0510 and by NWSC, Crane ...Biological Systemr Edied by PL. Cbhsius et a., Plenu= Press, New York, 1993 121 with the stress tensor (TMm,) having components TMrm ` SYM nNtnN + I...transparent. This also implies that Nt= N, - N where N = N1=1 is the usual boson number operator. It is worth stressing that the notion of q-hermiticity

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

Sun Dongsheng; Wang Hongcai; Ma Yinsheng

In-situ stress change near the fault before and after a great earthquake is a key issue in the geosciences field. In this work, based on the 2008 Great Wenchuan earthquake fault slip dislocation model, the co-seismic stress tensor change due to the Wenchuan earthquake and the distribution functions around the Longmen Shan fault are given. Our calculated results are almost consistent with the before and after great Wenchuan earthquake in-situ measuring results. The quantitative assessment results provide a reference for the study of the mechanism of earthquakes.

Efficient 3-D finite element failure analysis of compression loaded angle-ply plates with holes

NASA Technical Reports Server (NTRS)

Burns, S. W.; Herakovich, C. T.; Williams, J. G.

1987-01-01

Finite element stress analysis and the tensor polynomial failure criterion predict that failure always initiates at the interface between layers on the hole edge for notched angle-ply laminates loaded in compression. The angular location of initial failure is a function of the fiber orientation in the laminate. The dominant stress components initiating failure are shear. It is shown that approximate symmetry can be used to reduce the computer resources required for the case of unaxial loading.

Stress-dependence of kinetic transitions at atomistic defects

NASA Astrophysics Data System (ADS)

Ball, S. L.; Alexander, K. C.; Schuh, C. A.

2018-01-01

The full second-rank activation volume tensors associated with vacancy migration in FCC copper and HCP titanium as well as transition events in the Σ5 (2 1 0) grain boundary in copper are calculated and analyzed. The full tensorial results quantitatively illustrate how the conventional use of an activation volume scalar in atomistic studies of the kinetic processes of complex defects can miss important stress dependencies, in that neither hydrostatic pressure nor deviatoric stress dependencies can be considered alone as dominating the response. The results speak to the importance of anisotropies in the stress-dependence of atomistic kinetics, including crystal structure anisotropy, elastic anisotropy, and defect structure or migration-path anisotropies.

Using Tensor Completion Method to Achieving Better Coverage of Traffic State Estimation from Sparse Floating Car Data

PubMed Central

Ran, Bin; Song, Li; Cheng, Yang; Tan, Huachun

2016-01-01

Traffic state estimation from the floating car system is a challenging problem. The low penetration rate and random distribution make available floating car samples usually cover part space and time points of the road networks. To obtain a wide range of traffic state from the floating car system, many methods have been proposed to estimate the traffic state for the uncovered links. However, these methods cannot provide traffic state of the entire road networks. In this paper, the traffic state estimation is transformed to solve a missing data imputation problem, and the tensor completion framework is proposed to estimate missing traffic state. A tensor is constructed to model traffic state in which observed entries are directly derived from floating car system and unobserved traffic states are modeled as missing entries of constructed tensor. The constructed traffic state tensor can represent spatial and temporal correlations of traffic data and encode the multi-way properties of traffic state. The advantage of the proposed approach is that it can fully mine and utilize the multi-dimensional inherent correlations of traffic state. We tested the proposed approach on a well calibrated simulation network. Experimental results demonstrated that the proposed approach yield reliable traffic state estimation from very sparse floating car data, particularly when dealing with the floating car penetration rate is below 1%. PMID:27448326

Using Tensor Completion Method to Achieving Better Coverage of Traffic State Estimation from Sparse Floating Car Data.

PubMed

Ran, Bin; Song, Li; Zhang, Jian; Cheng, Yang; Tan, Huachun

2016-01-01

Traffic state estimation from the floating car system is a challenging problem. The low penetration rate and random distribution make available floating car samples usually cover part space and time points of the road networks. To obtain a wide range of traffic state from the floating car system, many methods have been proposed to estimate the traffic state for the uncovered links. However, these methods cannot provide traffic state of the entire road networks. In this paper, the traffic state estimation is transformed to solve a missing data imputation problem, and the tensor completion framework is proposed to estimate missing traffic state. A tensor is constructed to model traffic state in which observed entries are directly derived from floating car system and unobserved traffic states are modeled as missing entries of constructed tensor. The constructed traffic state tensor can represent spatial and temporal correlations of traffic data and encode the multi-way properties of traffic state. The advantage of the proposed approach is that it can fully mine and utilize the multi-dimensional inherent correlations of traffic state. We tested the proposed approach on a well calibrated simulation network. Experimental results demonstrated that the proposed approach yield reliable traffic state estimation from very sparse floating car data, particularly when dealing with the floating car penetration rate is below 1%.

Theoretical aspects of fracture mechanics

NASA Astrophysics Data System (ADS)

Atkinson, C.; Craster, R. V.

1995-03-01

In this review we try to cover various topics in fracture mechanics in which mathematical analysis can be used both to aid numerical methods and cast light on key features of the stress field. The dominant singular near crack tip stress field can often be parametrized in terms of three parameters K(sub I), K(sub II) and K(sub III) designating three fracture modes each having an angular variation entirely specified for the stress tensor and displacement vector. These results and contact zone models for removing the interpenetration anomaly are described. Generalizations of the above results to viscoelastic media are described. For homogeneous media with constant Poisson's ratio the angular variation of singular crack tip stresses and displacements are shown to be the same for all time and the same inverse square root singularity as occurs in the elastic medium case is found (this being true for a time varying Poisson ratio too). Only the stress intensity factor varies through time dependence of loads and relaxation properties of the medium. For cracks against bimaterial interfaces both the stress singularity and angular form evolve with time as a function of the time dependent properties of the bimaterial. Similar behavior is identified for sharp notches in viscoelastic plates. The near crack tip behavior in material with non-linear stress strain laws is also identified and stress singularities classified in terms of the hardening exponent for power law hardening materials. Again for interface cracks the near crack tip behavior requires careful analysis and it is shown that more than one singular term may be present in the near crack tip stress field. A variety of theory and applications is presented for inhomogeneous elastic media, coupled thermoelasticity etc. Methods based on reciprocal theorems and dual functions which can also aid in getting awkward singular stress behavior from numerical solutions are also reviewed. Finally theoretical calculations of fiber reinforced and particulate composite toughening mechanisms are briefly reviewed.

Automatic 3D Moment tensor inversions for southern California earthquakes

NASA Astrophysics Data System (ADS)

Liu, Q.; Tape, C.; Friberg, P.; Tromp, J.

2008-12-01

We present a new source mechanism (moment-tensor and depth) catalog for about 150 recent southern California earthquakes with Mw ≥ 3.5. We carefully select the initial solutions from a few available earthquake catalogs as well as our own preliminary 3D moment tensor inversion results. We pick useful data windows by assessing the quality of fits between the data and synthetics using an automatic windowing package FLEXWIN (Maggi et al 2008). We compute the source Fréchet derivatives of moment-tensor elements and depth for a recent 3D southern California velocity model inverted based upon finite-frequency event kernels calculated by the adjoint methods and a nonlinear conjugate gradient technique with subspace preconditioning (Tape et al 2008). We then invert for the source mechanisms and event depths based upon the techniques introduced by Liu et al 2005. We assess the quality of this new catalog, as well as the other existing ones, by computing the 3D synthetics for the updated 3D southern California model. We also plan to implement the moment-tensor inversion methods to automatically determine the source mechanisms for earthquakes with Mw ≥ 3.5 in southern California.

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

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.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

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

Stevens, Andrew J.; Pu, Yunchen; Sun, Yannan

We introduce new dictionary learning methods for tensor-variate data of any order. We represent each data item as a sum of Kruskal decomposed dictionary atoms within the framework of beta-process factor analysis (BPFA). Our model is nonparametric and can infer the tensor-rank of each dictionary atom. This Kruskal-Factor Analysis (KFA) is a natural generalization of BPFA. We also extend KFA to a deep convolutional setting and develop online learning methods. We test our approach on image processing and classification tasks achieving state of the art results for 2D & 3D inpainting and Caltech 101. The experiments also show that atom-rankmore » impacts both overcompleteness and sparsity.« less