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.

Detection of whole-brain abnormalities in temporal lobe epilepsy using tensor-based morphometry with DARTEL

NASA Astrophysics Data System (ADS)

Li, Wenjing; He, Huiguang; Lu, Jingjing; Lv, Bin; Li, Meng; Jin, Zhengyu

2009-10-01

Tensor-based morphometry (TBM) is an automated technique for detecting the anatomical differences between populations by examining the gradients of the deformation fields used to nonlinearly warp MR images. The purpose of this study was to investigate the whole-brain volume changes between the patients with unilateral temporal lobe epilepsy (TLE) and the controls using TBM with DARTEL, which could achieve more accurate inter-subject registration of brain images. T1-weighted images were acquired from 21 left-TLE patients, 21 right-TLE patients and 21 healthy controls, which were matched in age and gender. The determinants of the gradient of deformation fields at voxel level were obtained to quantify the expansion or contraction for individual images relative to the template, and then logarithmical transformation was applied on it. A whole brain analysis was performed using general lineal model (GLM), and the multiple comparison was corrected by false discovery rate (FDR) with p<0.05. For left-TLE patients, significant volume reductions were found in hippocampus, cingulate gyrus, precentral gyrus, right temporal lobe and cerebellum. These results potentially support the utility of TBM with DARTEL to study the structural changes between groups.

A Novel Small-Specimen Planar Biaxial Testing System With Full In-Plane Deformation Control.

PubMed

Potter, Samuel; Graves, Jordan; Drach, Borys; Leahy, Thomas; Hammel, Chris; Feng, Yuan; Baker, Aaron; Sacks, Michael S

2018-05-01

Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × ∼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.

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.

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.

Kinematic assumptions and their consequences on the structure of field equations in continuum dislocation theory

NASA Astrophysics Data System (ADS)

Silbermann, C. B.; Ihlemann, J.

2016-03-01

Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.

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.

Flexoelectricity as a bulk property

NASA Astrophysics Data System (ADS)

Resta, Raffaele

2010-03-01

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

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.

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.

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

NASA Technical Reports Server (NTRS)

Bergan, Andrew C.; Leone, Frank A., Jr.

2016-01-01

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

Evaluation of an Eulerian multi-material mixture formulation based on a single inverse deformation gradient tensor field

DOE PAGES

Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.; ...

2017-12-31

We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to Lagrangian (Benson 1992) and arbitrary Lagrangian-Eulerian (ALE) methods (Donea et al. 2004), fully Eulerian methods use grids that do not change in time. Consequently, Eulerian methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less

Evaluation of an Eulerian multi-material mixture formulation based on a single inverse deformation gradient tensor field

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

Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.

We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to Lagrangian (Benson 1992) and arbitrary Lagrangian-Eulerian (ALE) methods (Donea et al. 2004), fully Eulerian methods use grids that do not change in time. Consequently, Eulerian methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less

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

PubMed

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

2018-01-15

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

Hybrid High-Order methods for finite deformations of hyperelastic materials

NASA Astrophysics Data System (ADS)

Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

2018-01-01

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.

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.

The exponentiated Hencky energy: anisotropic extension and case studies

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Theoretical study of NMR, infrared and Raman spectra on triple-decker phthalocyanines

NASA Astrophysics Data System (ADS)

Suzuki, Atsushi; Oku, Takeo

2016-02-01

Electronic structures and magnetic properties of multi-decker phthalocyanines were studied by theoretical calculation. Electronic structures, excited processes at multi-states, isotropic chemical shifts of 13C, 14N and 1H-nuclear magnetic resonance (NMR), principle V-tensor in electronic field gradient (EFG) tensor and asymmetry parameters (η), vibration mode in infrared (IR) and Raman spectra of triple-decker phthalocyanines were calculated by density functional theory (DFT) and time-dependent DFT using B3LYP as basis function. Electron density distribution was delocalized on the phthalocyanine rings with electron static potential. Considerable separation of chemical shifts in 13C, 14N and 1H-NMR was originated from nuclear spin interaction between nitrogen and carbon atoms, nuclear quadrupole interaction based on EFG and η of central metal under crystal field. Calculated optical absorption at multi-excited process was derived from overlapping π-orbital on the phthalocyanine rings. The vibration modes in IR and Raman spectra were based on in-plane deformation and stretching vibrations of metal-ligand coordination bond on the deformed structure.

Using tensor-based morphometry to detect structural brain abnormalities in rats with adolescent intermittent alcohol exposure

NASA Astrophysics Data System (ADS)

Paniagua, Beatriz; Ehlers, Cindy; Crews, Fulton; Budin, Francois; Larson, Garrett; Styner, Martin; Oguz, Ipek

2011-03-01

Understanding the effects of adolescent binge drinking that persist into adulthood is a crucial public health issue. Adolescent intermittent ethanol exposure (AIE) is an animal model that can be used to investigate these effects in rodents. In this work, we investigate the application of a particular image analysis technique, tensor-based morphometry, for detecting anatomical differences between AIE and control rats using Diffusion Tensor Imaging (DTI). Deformation field analysis is a popular method for detecting volumetric changes analyzing Jacobian determinants calculated on deformation fields. Recent studies showed that computing deformation field metrics on the full deformation tensor, often referred to as tensor-based morphometry (TBM), increases the sensitivity to anatomical differences. In this paper we conduct a comprehensive TBM study for precisely locating differences between control and AIE rats. Using a DTI RARE sequence designed for minimal geometric distortion, 12-directional images were acquired postmortem for control and AIE rats (n=9). After preprocessing, average images for the two groups were constructed using an unbiased atlas building approach. We non-rigidly register the two atlases using Large Deformation Diffeomorphic Metric Mapping, and analyze the resulting deformation field using TBM. In particular, we evaluate the tensor determinant, geodesic anisotropy, and deformation direction vector (DDV) on the deformation field to detect structural differences. This yields data on the local amount of growth, shrinkage and the directionality of deformation between the groups. We show that TBM can thus be used to measure group morphological differences between rat populations, demonstrating the potential of the proposed framework.

Diffusion tensor analysis with invariant gradients and rotation tangents.

PubMed

Kindlmann, Gordon; Ennis, Daniel B; Whitaker, Ross T; Westin, Carl-Fredrik

2007-11-01

Guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters, we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation. Tensor shape and orientation both have three degrees-of-freedom, spanned by invariant gradients and rotation tangents, respectively. As an initial demonstration of the framework, we create a tunable measure of tensor difference that can selectively respond to shape and orientation. Second, to analyze the spatial gradient in a tensor volume (a third-order tensor), our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries, as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented. Finally, we apply the framework to decompose the fourth-order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance, including a direct approximation for the variance of tensor invariants such as fractional anisotropy.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Local White Matter Geometry from Diffusion Tensor Gradients

PubMed Central

Savadjiev, Peter; Kindlmann, Gordon L.; Bouix, Sylvain; Shenton, Martha E.; Westin, Carl-Fredrik

2009-01-01

We introduce a mathematical framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia. PMID:19896542

Local White Matter Geometry from Diffusion Tensor Gradients

PubMed Central

Savadjiev, Peter; Kindlmann, Gordon L.; Bouix, Sylvain; Shenton, Martha E.; Westin, Carl-Fredrik

2010-01-01

We introduce a mathematical framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia. PMID:20426006

Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence

NASA Astrophysics Data System (ADS)

Danish, Mohammad; Meneveau, Charles

2018-04-01

Knowledge of local flow-topology, the patterns of streamlines around a moving fluid element as described by the velocity-gradient tensor, is useful for developing insights into turbulence processes, such as energy cascade, material element deformation, or scalar mixing. Much has been learned in the recent past about flow topology at the smallest (viscous) scales of turbulence. However, less is known at larger scales, for instance, at the inertial scales of turbulence. In this work, we present a detailed study on the scale dependence of various quantities of interest, such as the population fraction of different types of flow-topologies, the joint probability distribution of the second and third invariants of the velocity gradient tensor, and the geometrical alignment of vorticity with strain-rate eigenvectors. We perform the analysis on a simulation dataset of isotropic turbulence at Reλ=433 . While quantities appear close to scale invariant in the inertial range, we observe a "bump" in several quantities at length scales between the inertial and viscous ranges. For instance, the population fraction of unstable node-saddle-saddle flow topology shows an increase when reducing the scale from the inertial entering the viscous range. A similar bump is observed for the vorticity-strain-rate alignment. In order to document possible dynamical causes for the different trends in the viscous and inertial ranges, we examine the probability fluxes appearing in the Fokker-Plank equation governing the velocity gradient invariants. Specifically, we aim to understand whether the differences observed between the viscous and inertial range statistics are due to effects caused by pressure, subgrid-scale, or viscous stresses or various combinations of these terms. To decompose the flow into small and large scales, we mainly use a spectrally compact non-negative filter with good spatial localization properties (Eyink-Aluie filter). The analysis shows that when going from the inertial range into the viscous range, the subgrid-stress effect decreases more rapidly as a function of scale than the viscous effects increase. To make up for the difference, the pressure Hessian also behaves somewhat differently in the viscous than in the inertial range. The results have implications for models for the velocity gradient tensor showing that the effects of subgrid scales may not be simply modeled via a constant eddy viscosity in the inertial range if one wishes to reproduce the observed trends.

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

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Zhong, Yiyuan; Chen, Chaojian; Tang, Jingtian; Kalscheuer, Thomas; Maurer, Hansruedi; Li, Yang

2018-03-01

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

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

NASA Astrophysics Data System (ADS)

Pumir, Alain; Bodenschatz, Eberhard; Xu, Haitao

2013-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Eigenvector of gravity gradient tensor for estimating fault dips considering fault type

NASA Astrophysics Data System (ADS)

Kusumoto, Shigekazu

2017-12-01

The dips of boundaries in faults and caldera walls play an important role in understanding their formation mechanisms. The fault dip is a particularly important parameter in numerical simulations for hazard map creation as the fault dip affects estimations of the area of disaster occurrence. In this study, I introduce a technique for estimating the fault dip using the eigenvector of the observed or calculated gravity gradient tensor on a profile and investigating its properties through numerical simulations. From numerical simulations, it was found that the maximum eigenvector of the tensor points to the high-density causative body, and the dip of the maximum eigenvector closely follows the dip of the normal fault. It was also found that the minimum eigenvector of the tensor points to the low-density causative body and that the dip of the minimum eigenvector closely follows the dip of the reverse fault. It was shown that the eigenvector of the gravity gradient tensor for estimating fault dips is determined by fault type. As an application of this technique, I estimated the dip of the Kurehayama Fault located in Toyama, Japan, and obtained a result that corresponded to conventional fault dip estimations by geology and geomorphology. Because the gravity gradient tensor is required for this analysis, I present a technique that estimates the gravity gradient tensor from the gravity anomaly on a profile.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

New methods for interpretation of magnetic vector and gradient tensor data I: eigenvector analysis and the normalised source strength

NASA Astrophysics Data System (ADS)

Clark, David A.

2012-09-01

Acquisition of magnetic gradient tensor data is likely to become routine in the near future. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for several elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalised 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 magnetisation direction. In combination the NSS and its vector gradient 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. Inversion based on the vector gradient of the NSS over the Tallawang magnetite deposit obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Besides the geological applications, the algorithms for the dipole model are readily applicable to the detection, location and characterisation (DLC) of magnetic objects, such as naval mines, unexploded ordnance, shipwrecks, archaeological artefacts, and buried drums.

Deformation and Fabric in Compacted Clay Soils

NASA Astrophysics Data System (ADS)

Wensrich, C. M.; Pineda, J.; Luzin, V.; Suwal, L.; Kisi, E. H.; Allameh-Haery, H.

2018-05-01

Hydromechanical anisotropy of clay soils in response to deformation or deposition history is related to the micromechanics of platelike clay particles and their orientations. In this article, we examine the relationship between microstructure, deformation, and moisture content in kaolin clay using a technique based on neutron scattering. This technique allows for the direct characterization of microstructure within representative samples using traditional measures such as orientation density and soil fabric tensor. From this information, evidence for a simple relationship between components of the deviatoric strain tensor and the deviatoric fabric tensor emerge. This relationship may provide a physical basis for future anisotropic constitutive models based on the micromechanics of these materials.

A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal and polyhedral meshes (u)

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

Lipnikov, Konstantin; Shashkov, Mikhail

2011-01-11

We construct a new mimetic tensor artificial viscosity on general polygonal and polyhedral meshes. The tensor artificial viscosity is based on a mimetic discretization of coordinate invariant operators, divergence of a tensor and gradient of a vector. The focus of this paper is on the symmetric form, div ({mu},{var_epsilon}(u)), of the tensor artificial viscosity where {var_epsilon}(u) is the symmetrized gradient of u and {mu}, is a tensor. The mimetic discretizations of this operator is derived for the case of a full tensor coefficient {mu}, that may reflect a shock direction. We demonstrate performance of the new viscosity for the Nohmore » implosion, Sedov explosion and Saltzman piston problems in both Cartesian and axisymmetric coordinate systems.« less

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

NASA Astrophysics Data System (ADS)

Jiang, Li; Liu, Jie; Zhang, Jianzhong; Feng, Zhibing

2017-12-01

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.

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

Statistics of pressure fluctuations in decaying isotropic turbulence.

PubMed

Kalelkar, Chirag

2006-04-01

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

Measurement tensors in diffusion MRI: generalizing the concept of diffusion encoding.

PubMed

Westin, Carl-Fredrik; Szczepankiewicz, Filip; Pasternak, Ofer; Ozarslan, Evren; Topgaard, Daniel; Knutsson, Hans; Nilsson, Markus

2014-01-01

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

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.

Implementation and application of a gradient enhanced crystal plasticity model

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

USGS Publications Warehouse

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

2007-01-01

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

Fluid Registration of Diffusion Tensor Images Using Information Theory

PubMed Central

Chiang, Ming-Chang; Leow, Alex D.; Klunder, Andrea D.; Dutton, Rebecca A.; Barysheva, Marina; Rose, Stephen E.; McMahon, Katie L.; de Zubicaray, Greig I.; Toga, Arthur W.; Thompson, Paul M.

2008-01-01

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or J-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the J-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data. PMID:18390342

Deformation of compound shells under action of internal shock wave loading

NASA Astrophysics Data System (ADS)

Chernobryvko, Marina; Kruszka, Leopold; Avramov, Konstantin

2015-09-01

The compound shells under the action of internal shock wave loading are considered. The compound shell consists of a thin cylindrical shell and two thin parabolic shells at the edges. The boundary conditions in the shells joints satisfy the equality of displacements. The internal shock wave loading is modelled as the surplus pressure surface. This pressure is a function of the shell coordinates and time. The strain rate deformation of compound shell takes place in both the elastic and in plastic stages. In the elastic stage the equations of the structure motions are obtained by the assumed-modes method, which uses the kinetic and potential energies of the cylindrical and two parabolic shells. The dynamic behaviour of compound shells is treated. In local plastic zones the 3-D thermo-elastic-plastic model is used. The deformations are described by nonlinear model. The stress tensor elements are determined using dynamic deformation theory. The deformation properties of materials are influenced by the strain rate behaviour, the influence of temperature parameters, and the elastic-plastic properties of materials. The dynamic yield point of materials and Pisarenko-Lebedev's criterion of destruction are used. The modified adaptive finite differences method of numerical analysis is suggested for those simulations. The accuracy of the numerical simulation is verified on each temporal step of calculation and in the case of large deformation gradients.

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

PubMed

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

2015-05-01

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

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

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

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

2015-05-15

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

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

DOE PAGES

Song, Chenchen; Martinez, Todd J.

2017-08-29

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-10-01

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. The resulting energy conservation in micro-canonical AIMD demonstrates that the implementation provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

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

Song, Chenchen; Martinez, Todd J.

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

Concepts and procedures required for successful reduction of tensor magnetic gradiometer data obtained from an unexploded ordnance detection demonstration at Yuma Proving Grounds, Arizona

USGS Publications Warehouse

Bracken, Robert E.; Brown, Philip J.

2006-01-01

On March 12, 2003, data were gathered at Yuma Proving Grounds, in Arizona, using a Tensor Magnetic Gradiometer System (TMGS). This report shows how these data were processed and explains concepts required for successful TMGS data reduction. Important concepts discussed include extreme attitudinal sensitivity of vector measurements, low attitudinal sensitivity of gradient measurements, leakage of the common-mode field into gradient measurements, consequences of thermal drift, and effects of field curvature. Spatial-data collection procedures and a spin-calibration method are addressed. Discussions of data-reduction procedures include tracking of axial data by mathematically matching transfer functions among the axes, derivation and application of calibration coefficients, calculation of sensor-pair gradients, thermal-drift corrections, and gradient collocation. For presentation, the magnetic tensor at each data station is converted to a scalar quantity, the I2 tensor invariant, which is easily found by calculating the determinant of the tensor. At important processing junctures, the determinants for all stations in the mapped area are shown in shaded relief map-view. Final processed results are compared to a mathematical model to show the validity of the assumptions made during processing and the reasonableness of the ultimate answer obtained.

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

NASA Astrophysics Data System (ADS)

Buxton, Oliver; Ganapathisubramani, Bharathram

2008-11-01

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

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.

Current crustal deformation of the Taiwan orogen reassessed by cGPS strain-rate estimation and focal mechanism stress inversion

NASA Astrophysics Data System (ADS)

Chen, Sean Kuanhsiang; Wu, Yih-Min; Hsu, Ya-Ju; Chan, Yu-Chang

2017-07-01

We study internal deformation of the Taiwan orogen, a young arc-continental collision belt, which the spatial heterogeneity remains unclear. We aim to ascertain heterogeneity of the orogenic crust in depth when specifying general mechanisms of the Taiwan orogeny. To reach this goal, we used updated data of continuous GPS (cGPS) and earthquake focal mechanisms to reassess geodetic strain-rate and seismic stress fields of Taiwan, respectively. We updated the both data sets from 1990 to 2015 to provide large amount of constraints on surficial and internal deformation of the crust for a better understanding. We estimated strain-rate tensors by calculating gradient tensors of cGPS station velocities in horizontal 0.1°-spacing grids via Delaunay triangulation. We determined stress tensors within a given horizontal and vertical grid cell of 0.1° and 10 km, respectively, by employing the spatial and temporal stress inversion. To minimize effects of the 1999 Mw 7.6 Chi-Chi earthquake on trends of the strain and stress, we modified observational possible bias of the cGPS velocities after the earthquake and removed the first 15-month focal mechanisms within the fault rupture zone. We also calculated the Anderson fault parameter (Aϕ) based on stress ratios and rake angles to quantitatively describe tectonic regimes of Taiwan. By examining directions of seismic compressive axes and styles of faulting, our results indicate that internal deformation of the crust is presently heterogeneous in the horizontal and vertical spaces. Directions of the compressive axes are fan-shaped oriented between N10°W and N110°W in the western and mid-eastern Taiwan at the depths of 0-20 km and near parallel to orientations of geodetic compressional axes. The orientations agreed with predominantly reverse faulting in the western Taiwan at the same depth range, implying a brittle deformation regime against the Peikang Basement High. Orientations of the compressive axes most rotated counter-clockwise at the depths of 20-40 km, coinciding with transition of styles of faulting from reverse to strike-slip faulting along the depths as revealed by variation of the Aϕ values. The features indicate that internal deformation of the upper crust is primarily driven by the same compressional mechanism. It implies that geodetic strains could detect the deformation from surface down to a maximal depth of 20 km in most regimes of Taiwan. We find that heterogeneity in orientations of compressive axes and styles of faulting is strong in two regimes at the northern and southern Central Range, coinciding to areas of the orogenic thinned/thickened crust. Conversely, the heterogeneity is weak in the central Western Foothills at surrounding area of root of the overthickened crust. This observation, coupled with regional seismological observations, may imply that vertical deformation from crustal thickening and thinning and thinning-related dynamics from mantle flows may have joint influence on degree of stress heterogeneity.

STATISTICS OF THE VELOCITY GRADIENT TENSOR IN SPACE PLASMA TURBULENT FLOWS

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

Consolini, Giuseppe; Marcucci, Maria Federica; Pallocchia, Giuseppe

2015-10-10

In the last decade, significant advances have been presented for the theoretical characterization and experimental techniques used to measure and model all of the components of the velocity gradient tensor in the framework of fluid turbulence. Here, we attempt the evaluation of the small-scale velocity gradient tensor for a case study of space plasma turbulence, observed in the Earth's magnetosheath region by the CLUSTER mission. In detail, we investigate the joint statistics P(R, Q) of the velocity gradient geometric invariants R and Q, and find that this P(R, Q) is similar to that of the low end of the inertialmore » range for fluid turbulence, with a pronounced increase in the statistics along the so-called Vieillefosse tail. In the context of hydrodynamics, this result is referred to as the dissipation/dissipation-production due to vortex stretching.« less

Toward an improved determination of Earth's lithospheric magnetic field from satellite observations

NASA Astrophysics Data System (ADS)

Kotsiaros, S.

2016-12-01

An analytical and numerical analysis of the spectral properties of the gradient tensor, initially performed by Rummel and van Gelderen (1992) for the gravity potential, shows that when the tensor elements are grouped into sets of semi-tangential and pure-tangential parts, they produce almost identical signal content as the normal element. Moreover, simple eigenvalue relations can be derived between these sets and the spherical harmonic expansion of the potential. This theoretical development generally applies to any potential field. First, the analysis of Rummel and van Gelderen (1992) is adapted to the magnetic field case and then the elements of the magnetic gradient tensor are estimated by 2 years of Swarm data and grouped into Γ(1) = {[∇B]rθ,[∇B]rφ} resp. Γ(2) = {[∇B]θθ-[∇B]φφ, 2[∇B]θφ}. It is shown that the estimated combinations Γ(1) and Γ(2) produce similar signal content as the theoretical radial gradient [∇B]rr. These results demonstrate the ability of multi-satellite missions such as Swarm, which cannot directly measure the radial gradient, to retrieve similar signal content by means of the horizontal gradients. Finally, lithospheric field models are derived using the gradient combinations Γ(1) and Γ(2) and compared with models derived from traditional vector and gradient data. The model resulting from Γ(1) leads to a very similar, and in particular cases improved, model compared to models retrieved by using approximately three times more data, i.e. a full set of vector, North-South and East-West gradients. ReferencesRummel, R., and M. van Gelderen (1992), Spectral analysis of the full gravity tensor, Geophysical Journal International, 111 (1), 159-169.

Solution of Einsteins Equation for Deformation of a Magnetized Neutron Star

NASA Astrophysics Data System (ADS)

Rizaldy, R.; Sulaksono, A.

2018-04-01

We studied the effect of very large and non-uniform magnetic field existed in the neutron star on the deformation of the neutron star. We used in our analytical calculation, multipole expansion of the tensor metric and the momentum-energy tensor in Legendre polynomial expansion up to the quadrupole order. In this way we obtain the solutions of Einstein’s equation with the correction factors due to the magnetic field are taken into account. We obtain from our numerical calculation that the degree of deformation (ellipticity) is increased when the the mass is decreased.

Predicting viscous-range velocity gradient dynamics in large-eddy simulations of turbulence

NASA Astrophysics Data System (ADS)

Johnson, Perry; Meneveau, Charles

2017-11-01

The details of small-scale turbulence are not directly accessible in large-eddy simulations (LES), posing a modeling challenge because many important micro-physical processes depend strongly on the dynamics of turbulence in the viscous range. Here, we introduce a method for coupling existing stochastic models for the Lagrangian evolution of the velocity gradient tensor with LES to simulate unresolved dynamics. The proposed approach is implemented in LES of turbulent channel flow and detailed comparisons with DNS are carried out. An application to modeling the fate of deformable, small (sub-Kolmogorov) droplets at negligible Stokes number and low volume fraction with one-way coupling is carried out. These results illustrate the ability of the proposed model to predict the influence of small scale turbulence on droplet micro-physics in the context of LES. This research was made possible by a graduate Fellowship from the National Science Foundation and by a Grant from The Gulf of Mexico Research Initiative.

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

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.

Q-space trajectory imaging for multidimensional diffusion MRI of the human brain

PubMed Central

Westin, Carl-Fredrik; Knutsson, Hans; Pasternak, Ofer; Szczepankiewicz, Filip; Özarslan, Evren; van Westen, Danielle; Mattisson, Cecilia; Bogren, Mats; O’Donnell, Lauren; Kubicki, Marek; Topgaard, Daniel; Nilsson, Markus

2016-01-01

This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture. PMID:26923372

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.

New methods for interpretation of magnetic vector and gradient tensor data II: application to the Mount Leyshon anomaly, Queensland, Australia

NASA Astrophysics Data System (ADS)

Clark, David A.

2013-04-01

Acquisition of magnetic gradient tensor data is anticipated to become routine in the near future. In the meantime, modern ultrahigh resolution conventional magnetic data can be used, with certain important caveats, to calculate magnetic vector components and gradient tensor elements from total magnetic intensity (TMI) or TMI gradient surveys. An accompanying paper presented new methods for inverting gradient tensor data to obtain source parameters for several elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalised 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, independent of magnetisation direction. Source locations can be inverted directly from the NSS and its vector gradient. Some of these new methods have been applied to analysis of the magnetic signature of the Early Permian Mount Leyshon gold-mineralised system, Queensland. The Mount Leyshon magnetic anomaly is a prominent TMI low that is produced by rock units with strong reversed remanence acquired during the Late Palaeozoic Reverse Superchron. The inferred magnetic moment for the source zone of the Mount Leyshon magnetic anomaly is ~1010Am2. Its direction is consistent with petrophysical measurements. Given estimated magnetisation from samples and geological information, this suggests a volume of ~1.5km×1.5km×2km (vertical). The inferred depth of the centre of magnetisation is ~900m below surface, suggesting that the depth extent of the magnetic zone is ~1800m. Some of the deeper, undrilled portion of the magnetic zone could be a mafic intrusion similar to the nearby coeval Fenian Diorite, representing part of the parent magma chamber beneath the Mount Leyshon Intrusive Complex.

Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence

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

Johnson, Perry L., E-mail: pjohns86@jhu.edu; Meneveau, Charles

2015-08-15

One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixingmore » properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume deformations. The results serve to characterize the fundamental statistical and geometric structure of turbulence at small scales including cumulative, time integrated effects. These are important for deformable particles such as droplets and polymers advected by turbulence.« less

Extended mimetic gravity: Hamiltonian analysis and gradient instabilities

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Kobayashi, Tsutomu

2017-11-01

We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on "seed" scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is plagued with gradient instabilities, except for a special case where the scalar perturbations are presumably strongly coupled, or otherwise there appear ghost instabilities.

Intrinsic Decomposition of The Stretch Tensor for Fibrous Media

NASA Astrophysics Data System (ADS)

Kellermann, David C.

2010-05-01

This paper presents a novel mechanism for the description of fibre reorientation based on the decomposition of the stretch tensor according to a given material's intrinsic constitutive properties. This approach avoids the necessity for fibre directors, structural tensors or specialised model such as the ideal fibre reinforced model, which are commonly applied to the analysis of fibre kinematics in the finite deformation of fibrous media for biomechanical problems. The proposed approach uses Intrinsic-Field Tensors (IFTs) that build upon the linear orthotropic theory presented in a previous paper entitled Strongly orthotropic continuum mechanics and finite element treatment. The intrinsic decomposition of the stretch tensor therein provides superior capacity to represent the intermediary kinematics driven by finite orthotropic ratios, where the benefits are predominantly expressed in cases of large deformation as is typical in the biomechanical studies. Satisfaction of requirements such as Material Frame-Indifference (MFI) and Euclidean objectivity are demonstrated here—these factors being necessary for the proposed IFTs to be valid tensorial quantities. The resultant tensors, initially for the simplest case of linear elasticity, are able to describe the same fibre reorientation as would the contemporary approaches such as with use of structural tensors and the like, while additionally being capable of showing results intermediary to classical isotropy and the infinitely orthotropic representations. This intermediary case is previously unreported.

Quantifying polymer deformation in viscoelastic turbulence: the geometric decomposition and a Riemannian approach to scalar measures

NASA Astrophysics Data System (ADS)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer; Gayme, Dennice

2017-11-01

We develop a new framework to quantify the fluctuating behaviour of the conformation tensor in viscoelastic turbulent flows. This framework addresses two shortcomings of the classical approach based on Reynolds decomposition: the fluctuating part of the conformation tensor is not guaranteed to be positive definite and it does not consistently represent polymer expansions and contractions about the mean. Our approach employs a geometric decomposition that yields a positive-definite fluctuating conformation tensor with a clear physical interpretation as a deformation to the mean conformation. We propose three scalar measures of this fluctuating conformation tensor, which respect the non-Euclidean Riemannian geometry of the manifold of positive-definite tensors: fluctuating polymer volume, geodesic distance from the mean, and an anisotropy measure. We use these scalar quantities to investigate drag-reduced viscoelastic turbulent channel flow. Our approach establishes a systematic method to study viscoelastic turbulence. It also uncovers interesting phenomena that are not apparent using traditional analysis tools, including a logarithmic decrease in anisotropy of the mean conformation tensor away from the wall and polymer fluctuations peaking beyond the buffer layer. This work has been partially funded by the following NSF Grants: CBET-1652244, OCE-1633124, CBET-1511937.

b matrix errors in echo planar diffusion tensor imaging

PubMed Central

Boujraf, Saïd; Luypaert, Robert; Osteaux, Michel

2001-01-01

Diffusion‐weighted magnetic resonance imaging (DW‐MRI) is a recognized tool for early detection of infarction of the human brain. DW‐MRI uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive parameters that reflect the translational mobility of the water molecules in tissues. If diffusion‐weighted images with different values of b matrix are acquired during one individual investigation, it is possible to calculate apparent diffusion coefficient maps that are the elements of the diffusion tensor. The diffusion tensor elements represent the apparent diffusion coefficient of protons of water molecules in each pixel in the corresponding sample. The relation between signal intensity in the diffusion‐weighted images, diffusion tensor, and b matrix is derived from the Bloch equations. Our goal is to establish the magnitude of the error made in the calculation of the elements of the diffusion tensor when the imaging gradients are ignored. PACS number(s): 87.57. –s, 87.61.–c PMID:11602015

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2014-12-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees and orders, are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the higher-order partial derivatives of the magnetic field in local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (version 0.0) and the main magnetic field model of IGRF11. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the potential field.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

NASA Astrophysics Data System (ADS)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

2018-05-01

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Pressure gradients fail to predict diffusio-osmosis

NASA Astrophysics Data System (ADS)

Liu, Yawei; Ganti, Raman; Frenkel, Daan

2018-05-01

We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for computing such flows and compare them with a reference calculation based on direct, non-equilibrium molecular dynamics simulations. As alternatives, we consider schemes that compute diffusio-osmotic flow from the gradient of the chemical potentials of the constituent species and from the gradient of the component of the pressure tensor parallel to the interface. We find that the approach based on treating chemical potential gradients as external forces acting on various species agrees with the direct simulations, thereby supporting the approach of Marbach et al (2017 J. Chem. Phys. 146 194701). In contrast, an approach based on computing the gradients of the microscopic pressure tensor does not reproduce the direct non-equilibrium results.

Detection of ferromagnetic target based on mobile magnetic gradient tensor system

NASA Astrophysics Data System (ADS)

Gang, Y. I. N.; Yingtang, Zhang; Zhining, Li; Hongbo, Fan; Guoquan, Ren

2016-03-01

Attitude change of mobile magnetic gradient tensor system critically affects the precision of gradient measurements, thereby increasing ambiguity in target detection. This paper presents a rotational invariant-based method for locating and identifying ferromagnetic targets. Firstly, unit magnetic moment vector was derived based on the geometrical invariant, such that the intermediate eigenvector of the magnetic gradient tensor is perpendicular to the magnetic moment vector and the source-sensor displacement vector. Secondly, unit source-sensor displacement vector was derived based on the characteristic that the angle between magnetic moment vector and source-sensor displacement is a rotational invariant. By introducing a displacement vector between two measurement points, the magnetic moment vector and the source-sensor displacement vector were theoretically derived. To resolve the problem of measurement noises existing in the realistic detection applications, linear equations were formulated using invariants corresponding to several distinct measurement points and least square solution of magnetic moment vector and source-sensor displacement vector were obtained. Results of simulation and principal verification experiment showed the correctness of the analytical method, along with the practicability of the least square method.

Dilation and Hypertrophy: A Cell-Based Continuum Mechanics Approach Towards Ventricular Growth and Remodeling

NASA Astrophysics Data System (ADS)

Ulerich, J.; Göktepe, S.; Kuhl, E.

This manuscript presents a continuum approach towards cardiac growth and remodeling that is capable to predict chronic maladaptation of the heart in response to changes in mechanical loading. It is based on the multiplicative decomposition of the deformation gradient into and elastic and a growth part. Motivated by morphological changes in cardiomyocyte geometry, we introduce an anisotropic growth tensor that can capture both hypertrophic wall thickening and ventricular dilation within one generic concept. In agreement with clinical observations, we propose wall thickening to be a stress-driven phenomenon whereas dilation is introduced as a strain-driven process. The features of the proposed approach are illustrated in terms of the adaptation of thin heart slices and in terms overload-induced dilation in a generic bi-ventricular heart model.

Hidden symmetries for ellipsoid-solitonic deformations of Kerr-Sen black holes and quantum anomalies

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2013-02-01

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and we study hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.

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

NASA Astrophysics Data System (ADS)

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

2007-10-01

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

Nanoscale diffractive probing of strain dynamics in ultrafast transmission electron microscopy

PubMed Central

Feist, Armin; Rubiano da Silva, Nara; Liang, Wenxi; Ropers, Claus; Schäfer, Sascha

2018-01-01

The control of optically driven high-frequency strain waves in nanostructured systems is an essential ingredient for the further development of nanophononics. However, broadly applicable experimental means to quantitatively map such structural distortion on their intrinsic ultrafast time and nanometer length scales are still lacking. Here, we introduce ultrafast convergent beam electron diffraction with a nanoscale probe beam for the quantitative retrieval of the time-dependent local deformation gradient tensor. We demonstrate its capabilities by investigating the ultrafast acoustic deformations close to the edge of a single-crystalline graphite membrane. Tracking the structural distortion with a 28-nm/700-fs spatio-temporal resolution, we observe an acoustic membrane breathing mode with spatially modulated amplitude, governed by the optical near field structure at the membrane edge. Furthermore, an in-plane polarized acoustic shock wave is launched at the membrane edge, which triggers secondary acoustic shear waves with a pronounced spatio-temporal dependency. The experimental findings are compared to numerical acoustic wave simulations in the continuous medium limit, highlighting the importance of microscopic dissipation mechanisms and ballistic transport channels. PMID:29464187

Nanoscale diffractive probing of strain dynamics in ultrafast transmission electron microscopy.

PubMed

Feist, Armin; Rubiano da Silva, Nara; Liang, Wenxi; Ropers, Claus; Schäfer, Sascha

2018-01-01

The control of optically driven high-frequency strain waves in nanostructured systems is an essential ingredient for the further development of nanophononics. However, broadly applicable experimental means to quantitatively map such structural distortion on their intrinsic ultrafast time and nanometer length scales are still lacking. Here, we introduce ultrafast convergent beam electron diffraction with a nanoscale probe beam for the quantitative retrieval of the time-dependent local deformation gradient tensor. We demonstrate its capabilities by investigating the ultrafast acoustic deformations close to the edge of a single-crystalline graphite membrane. Tracking the structural distortion with a 28-nm/700-fs spatio-temporal resolution, we observe an acoustic membrane breathing mode with spatially modulated amplitude, governed by the optical near field structure at the membrane edge. Furthermore, an in-plane polarized acoustic shock wave is launched at the membrane edge, which triggers secondary acoustic shear waves with a pronounced spatio-temporal dependency. The experimental findings are compared to numerical acoustic wave simulations in the continuous medium limit, highlighting the importance of microscopic dissipation mechanisms and ballistic transport channels.

A fluid-structure interaction model of soft robotics using an active strain approach

NASA Astrophysics Data System (ADS)

Hess, Andrew; Lin, Zhaowu; Gao, Tong

2017-11-01

Soft robotic swimmers exhibit rich dynamics that stem from the non-linear interplay of the fluid and immersed soft elastic body. Due to the difficulty of handling the nonlinear two-way coupling of hydrodynamic flow and deforming elastic body, studies of flexible swimmers often employ either one-way coupling strategies with imposed motions of the solid body or some simplified elasticity models. To explore the nonlinear dynamics of soft robots powered by smart soft materials, we develop a computational model to deal with the two-way fluid/elastic structure interactions using the fictitious domain method. To mimic the dynamic response of the functional soft material under external actuations, we assume the solid phase to be neo-Hookean, and employ an active strain approach to incorporate actuation, which is based on the multiplicative decomposition of the deformation gradient tensor. We demonstrate the capability of our algorithm by performing a series of numerical explorations that manipulate an elastic structure with finite thickness, starting from simple rectangular or circular plates to soft robot prototypes such as stingrays and jellyfish.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

NASA Astrophysics Data System (ADS)

Sun, Yong; Meng, Zhaohai; Li, Fengting

2018-03-01

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

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.

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.

Advanced solid elements for sheet metal forming simulation

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

A finite deformation viscoelastic-viscoplastic constitutive model for self-healing materials

NASA Astrophysics Data System (ADS)

Shahsavari, H.; Naghdabadi, R.; Baghani, M.; Sohrabpour, S.

2016-12-01

In this paper, employing the Hencky strain, viscoelastic-viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic-viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing variables and employing the strain equivalence hypothesis, the strain tensor is determined in the effective configuration. Satisfying the Clausius-Duhem inequality, the evolution equations are introduced for the viscoelastic and viscoplastic strains. The damage and healing variables also evolve according to two different prescribed functions. To employ the proposed model in different loading conditions, the model is discretized in the semi-implicit form. Material parameters of the model are identified employing experimental tests on asphalt mixes available in the literature. Finally, capability of the model is demonstrated comparing the model predictions in the creep-recovery and repeated creep-recovery with the experimental results available in the literature and a good agreement between predicted and test results is revealed.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

PubMed

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

Analysis and correction of gradient nonlinearity bias in ADC measurements

PubMed Central

Malyarenko, Dariya I.; Ross, Brian D.; Chenevert, Thomas L.

2013-01-01

Purpose Gradient nonlinearity of MRI systems leads to spatially-dependent b-values and consequently high non-uniformity errors (10–20%) in ADC measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. Methods All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Results Spatial dependence of nonlinearity correction terms accounts for the bulk (75–95%) of ADC bias for FA = 0.3–0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. Conclusions The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. PMID:23794533

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

DOE PAGES

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

2015-05-18

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

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

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2015-07-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16-90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

How Artificial Should the Treatment of a Plasma's Viscosity Be?

NASA Astrophysics Data System (ADS)

Whitney, K. G.; Velikovich, A. L.; Thornhill, J. W.; Davis, J.

1999-11-01

Electron viscosity dominates over ion viscosity and is important in describing the generation of shock fronts in highly ionizable plasmas. The sizes of shock front jumps in electron and ion temperature are determined from the magnitudes of the heat flow vector and pressure tensor, which, in turn, acquire non-negligible nonlinear contributions from the temperature and density gradients when these gradients are large. Thus, a consistent treatment of steep gradient formation in plasmas must come from investigations that include the effects of these nonlinear contributions to heat and momentum transport. Coefficients for each of five nonlinear contributions to the pressure tensor for an (r,z) Z-pinch geometry are presented and discussed in this talk. Hydrodynamic code calculations generally are not designed to provide a testbed for directly evaluating the kinetic energy dissipation that occurs at shock fronts; therefore, the strength of these nonlinear pressure tensor terms will be estimated by post-processing a Z-pinch hydrodynamics calculation and a steady-state planar shock wave calculation.

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)

Triangular prismatic solid-shell element with generalised deformation description

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories

NASA Astrophysics Data System (ADS)

Dong, Xi

2016-06-01

We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy Sn is described by two coefficients: fb(n ) for traceless extrinsic curvature deformations and fc(n ) for Weyl tensor deformations. We provide the first calculation of the coefficient fb(n ) in interacting theories by relating it to the stress tensor one-point function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture fb(n )=fc(n ), motivated by surprising evidence from a variety of free field theories and studies of conical defects, fails holographically.

Validation of buoyancy driven spectral tensor model using HATS data

NASA Astrophysics Data System (ADS)

Chougule, A.; Mann, J.; Kelly, M.; Larsen, G. C.

2016-09-01

We present a homogeneous spectral tensor model for wind velocity and temperature fluctuations, driven by mean vertical shear and mean temperature gradient. Results from the model, including one-dimensional velocity and temperature spectra and the associated co-spectra, are shown in this paper. The model also reproduces two-point statistics, such as coherence and phases, via cross-spectra between two points separated in space. Model results are compared with observations from the Horizontal Array Turbulence Study (HATS) field program (Horst et al. 2004). The spectral velocity tensor in the model is described via five parameters: the dissipation rate (ɛ), length scale of energy-containing eddies (L), a turbulence anisotropy parameter (Γ), gradient Richardson number (Ri) representing the atmospheric stability and the rate of destruction of temperature variance (ηθ).

Active Tensor Magnetic Gradiometer System

DTIC Science & Technology

2007-11-01

Modify Forward Computer Models .............................................................................................2 Modify TMGS Simulator...active magnetic gradient measurement system are based upon the existing tensor magnetic gradiometer system ( TMGS ) developed under project MM-1328...Magnetic Gradiometer System ( TMGS ) for UXO Detection, Imaging, and Discrimination.” The TMGS developed under MM-1328 was successfully tested at the

View-Dependent Streamline Deformation and Exploration

PubMed Central

Tong, Xin; Edwards, John; Chen, Chun-Ming; Shen, Han-Wei; Johnson, Chris R.; Wong, Pak Chung

2016-01-01

Occlusion presents a major challenge in visualizing 3D flow and tensor fields using streamlines. Displaying too many streamlines creates a dense visualization filled with occluded structures, but displaying too few streams risks losing important features. We propose a new streamline exploration approach by visually manipulating the cluttered streamlines by pulling visible layers apart and revealing the hidden structures underneath. This paper presents a customized view-dependent deformation algorithm and an interactive visualization tool to minimize visual clutter in 3D vector and tensor fields. The algorithm is able to maintain the overall integrity of the fields and expose previously hidden structures. Our system supports both mouse and direct-touch interactions to manipulate the viewing perspectives and visualize the streamlines in depth. By using a lens metaphor of different shapes to select the transition zone of the targeted area interactively, the users can move their focus and examine the vector or tensor field freely. PMID:26600061

View-Dependent Streamline Deformation and Exploration

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

Tong, Xin; Edwards, John; Chen, Chun-Ming

Occlusion presents a major challenge in visualizing 3D flow and tensor fields using streamlines. Displaying too many streamlines creates a dense visualization filled with occluded structures, but displaying too few streams risks losing important features. We propose a new streamline exploration approach by visually manipulating the cluttered streamlines by pulling visible layers apart and revealing the hidden structures underneath. This paper presents a customized view-dependent deformation algorithm and an interactive visualization tool to minimize visual cluttering for visualizing 3D vector and tensor fields. The algorithm is able to maintain the overall integrity of the fields and expose previously hidden structures.more » Our system supports both mouse and direct-touch interactions to manipulate the viewing perspectives and visualize the streamlines in depth. By using a lens metaphor of different shapes to select the transition zone of the targeted area interactively, the users can move their focus and examine the vector or tensor field freely.« less

View-Dependent Streamline Deformation and Exploration.

PubMed

Tong, Xin; Edwards, John; Chen, Chun-Ming; Shen, Han-Wei; Johnson, Chris R; Wong, Pak Chung

2016-07-01

Occlusion presents a major challenge in visualizing 3D flow and tensor fields using streamlines. Displaying too many streamlines creates a dense visualization filled with occluded structures, but displaying too few streams risks losing important features. We propose a new streamline exploration approach by visually manipulating the cluttered streamlines by pulling visible layers apart and revealing the hidden structures underneath. This paper presents a customized view-dependent deformation algorithm and an interactive visualization tool to minimize visual clutter in 3D vector and tensor fields. The algorithm is able to maintain the overall integrity of the fields and expose previously hidden structures. Our system supports both mouse and direct-touch interactions to manipulate the viewing perspectives and visualize the streamlines in depth. By using a lens metaphor of different shapes to select the transition zone of the targeted area interactively, the users can move their focus and examine the vector or tensor field freely.

Anisotropic rheology of a polycrystalline aggregate and convection in planetary mantles

NASA Astrophysics Data System (ADS)

Pouilloux, L. S.; Labrosse, S.; Kaminski, E.

2011-12-01

Observations of seismic anisotropy in the Earth mantle is often related to the crystal preferred orientation of polycrystalline aggregates. In this case, the physical properties depends on the direction and require the use of tensors to be fully described. In particular, the viscosity must be defined as a fourth order tensor whereas the thermal conductivity is a 2nd order tensor. However, the dynamical implications of such physical properties have received little attention until now. In this work, we present the mathematical formulation for an anisotropic medium and the relationship with dislocation creep deformation. We explore extensively the problem of the onset of Rayleigh-Bénard convection with such anisotropic properties. We finally presents some numerical results on the time-dependent problem using an orthotropic law for an ice polycrystal. Geophysical implications of this work related to the dynamics of planetary mantles are discussed, especially the potential of anisotropic rheology to localize deformation.

A tensor analysis to evaluate the effect of high-pull headgear on Class II malocclusions.

PubMed

Ngan, P; Scheick, J; Florman, M

1993-03-01

The inaccuracies inherent in cephalometric analysis of treatment effects are well known. The objective of this article is to present a more reliable research tool in the analysis of cephalometric data. Bookstein introduced a dilation function by means of a homogeneous deformation tensor as a method of describing changes in cephalometric data. His article gave an analytic description of the deformation tensor that permits the rapid and highly accurate calculation of it on a desktop computer. The first part of this article describes the underlying ideas and mathematics. The second part uses the tensor analysis to analyze the cephalometric results of a group of patients treated with high-pull activator (HPA) to demonstrate the application of this research tool. Eight patients with Class II skeletal open bite malocclusions in the mixed dentition were treated with HPA. A control sample consisting of eight untreated children with Class II who were obtained from The Ohio State University Growth Study was used as a comparison group. Lateral cephalograms taken before and at the completion of treatment were traced, digitized, and analyzed with the conventional method and tensor analysis. The results showed that HPA had little or no effect on maxillary skeletal structures. However, reduction in growth rate was found with the skeletal triangle S-N-A, indicating a posterior tipping and torquing of the maxillary incisors. The treatment also induced additional deformation on the mandible in a downward and slightly forward direction. Together with the results from the conventional cephalometric analysis, HPA seemed to provide the vertical and rotational control of the maxilla during orthopedic Class II treatment by inhibiting the downward and forward eruptive path of the upper posterior teeth. The newly designed computer software permits rapid analysis of cephalometric data with the tensor analysis on a desktop computer. This tool may be useful in analyzing growth changes for research data.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Small swimmers and sinkers structure the microenvironment by deforming ambient chemical gradients

NASA Astrophysics Data System (ADS)

Inman, B.; Franks, P. J. S.; Torres, C.

2016-02-01

Chemical gradients in the microscale environment determine the rates of fundamental planktonic processes such as signaling and sensing, grazing, predation, mating, infection, nutrient uptake, and primary production. We show that bodies swimming or sinking at low Reynolds number can deform and intensify ambient scalar gradients on the order of 10-1000 times. Over time, this restructuring of the microenvironment in the wake of a moving particle results in elevated diffusive fluxes of ecologically relevant tracers. We use diffusive Stokes flow to model the time evolution of planes of tracer particles that represent a gradient being deformed by a sinking sphere. Ultimately, the degree of gradient intensification and the corresponding diffusive flux enhancement depend on how far a moving body deforms a plane of tracer before it punches through. We derive a scaling for this distance, Ldef, as a function of the Péclet number and describe its importance in the microscale planktonic environment. We then test the modeled gradient deformation, diffusive flux enhancement, and Ldef using an experimental tank apparatus in which the marine copepod, Calanus pacificus, is induced to swim through a layer of tracer dye. We show that the gradient deformation due to the copepod swimming can enhance the apparent tracer diffusivity by 500% over 10 minutes, drawing the tracer out into centimeters-long tendrils. These swimming-induced gradient deformations may be an important source of structure in the microscale environment of the plankton.

Integration of Full Tensor Gravity and Z-Axis Tipper Electromagnetic Passive Low Frequency EM Instruments for Simultaneous Data Acquisition - Final Technical Report

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

Wieberg, Scott

Ground gravity is a common and useful tool for geothermal exploration. Gravity surveys map density changes in the subsurface that may be caused by tectonic deformation such as faulting, fracturing, plutonism, volcanism, hydrothermal alteration, etc. Full Tensor Gravity Gradient (FTG) data has been used for over a decade in both petroleum and mining exploration to map changes in density associated with geologic structure. Measuring the gravity gradient, rather than the gravity field, provides significantly higher resolution data. Modeling studies have shown FTG data to be a viable tool for geothermal exploration, but no FTG data had been acquired for geothermalmore » applications to date. Electromagnetic methods have been used for geothermal exploration for some time. The Z-Axis Tipper Electromagnetic (ZTEM) was a newer technology that had found success in mapping deep conductivity changes for mining applications. ZTEM had also been used in limited tests for geothermal exploration. This newer technology provided the ability to cost effectively map large areas whilst detailing the electrical properties of the geological structures at depths. The ZTEM is passive and it uses naturally occurring audio frequency magnetic (AFMAG) signals as the electromagnetic triggering source. These geophysical methods were to be tested over a known geothermal site to determine whether or not the data provided the information required for accurately interpreting the subsurface geologic structure associated with a geothermal deposit. After successful acquisition and analysis of the known source area, an additional survey of a “greenfield” area was to be completed. The final step was to develop a combined interpretation model and determine if the combination produced a higher confident geophysical model compared to models developed using each of the technologies individually.« less

Loop optimization for tensor network renormalization

NASA Astrophysics Data System (ADS)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

Analysis of vortical structures in turbulent natural convection

NASA Astrophysics Data System (ADS)

Park, Sangro; Lee, Changhoon

2014-11-01

Natural convection of fluid within two parallel walls, Rayleigh-Bénard convection, is studied by direct numerical simulation using a spectral method. The flow is in soft turbulence regime with Rayleigh number 106, 107, 108, Prandtl number 0 . 7 and aspect ratio 4. We investigate the relations between thermal plumes and vortical structures through manipulating the evolution equations of vorticity and velocity gradient tensor. According to simulation results, horizontal vorticity occurs near the wall and changes into vertical vorticity by vertical stretching of fluid element which is caused by vertical movement of the thermal plume. Additionally, eigenvalues, eigenvectors and invariants of velocity gradient tensor show the topologies of vortical structures, including how vortical structures are tilted or stretched. Difference of velocity gradient tensor between inside thermal plumes and background region is also investigated, and the result indicates that thermal plumes play an important role in changing the distribution of vortical structures. The results of this study are consistent with other researches which suggest that vertical vorticity is stronger in high Rayleigh number flows. Details will be presented in the meeting.

The influence of installation angle of GGIs on full-tensor gravity gradient measurement

NASA Astrophysics Data System (ADS)

Wei, Hongwei; Wu, Meiping

2018-03-01

Gravity gradient plays an important role in many disciplines as a fundamental signal to reflect the information of the earth. Full-tensor gravity gradient measurement (FGGM) is an effective way to obtain the gravity gradient signal. In this paper, the installation mode of GGIs in FGGM is studied. It is expected that the accuracy of FGGM will be improved by optimizing the installation mode of GGIs. In addition, we analysed the relationship between GGIs’ installation angle and FGGM by establishing the measurement model of FGGM. Then the following conclusions was proved that there was no relationship between GGIs’ installation angle and the measurement result. This conclusion showed that there was no optimal angle for the GGIs’ installation in FGGM, and the installation angle only need to satisfy the relationship shown in the conclusion section of this paper. Finally, this conclusion was demonstrated by computer simulations.

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories.

PubMed

Dong, Xi

2016-06-24

We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy S_{n} is described by two coefficients: f_{b}(n) for traceless extrinsic curvature deformations and f_{c}(n) for Weyl tensor deformations. We provide the first calculation of the coefficient f_{b}(n) in interacting theories by relating it to the stress tensor one-point function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture f_{b}(n)=f_{c}(n), motivated by surprising evidence from a variety of free field theories and studies of conical defects, fails holographically.

Study of the velocity gradient tensor in turbulent flow

NASA Technical Reports Server (NTRS)

Cheng, Wei-Ping; Cantwell, Brian

1996-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-05-01

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

Symmetries, supersymmetries and cohomologies in gauge theories

NASA Astrophysics Data System (ADS)

Bǎbǎlîc, Elena-Mirela

2009-12-01

The main subjects approached in the thesis are the following: a) the derivation of the interactions in two space-time dimensions in a particular class of topological BF models; b) the construction of the couplings in D ≥ 5 dimensions between one massless tensor field with the mixed symmetry (3, 1) and one with the mixed symmetry of the Riemann tensor; c) the evaluation of the existence of interactions in D ≥ 5 dimensions between two different collections of massless tensor fields with the mixed symmetries (3, 1) and (2, 2); d) the analysis of the relation between the BRST charges obtained in the pure-spinor formalism, respectively in the κ-symmetric one for the supermembrane in eleven dimensions. Our procedure for the first three subjects is based on solving the equations that describe the deformation of the solution to the master equation by means of specific cohomological techniques, while for the fourth one we will use techniques specific to the BRST Hamiltonian approach in order to write the BRST charge. The interactions are obtained under the following hypotheses: locality, Lorentz covariance, Poincare invariance, analyticity of the deformations, and preservation of the number of derivatives on each field. The first three assumptions imply that the interacting theory is local in space-time, Lorentz covariant and Poincare invariant. The analyticity of the deformations refers to the fact that the deformed solution to the master equation is analytical in the coupling constant and reduces to the original solution in the free limit. The conservation of the number of derivatives on each field with respect to the free theory means here that the following two requirements are simultaneously satisfied: (i) the derivative order of the equations of motion on each field is the same for the free and respectively for the interacting theory; (ii) the maximum number of derivatives in the interaction vertices is equal to two, i.e. the maximum number of derivatives from the free Lagrangian. The main results of the thesis are: interactions in two space-time dimensions for a particular class of BF models; interactions between one massless tensor field with the mixed symmetry (3, 1) and one with the mixed symmetry of the Riemann tensor; interactions between collections of massless tensor fields with the mixed symmetries (3, 1) and (2, 2); relating the kappa-symmetric and pure-spinor versions of the supermembrane in eleven dimensions.

Analytical Expressions for Deformation from an Arbitrarily Oriented Spheroid in a Half-Space

NASA Astrophysics Data System (ADS)

Cervelli, P. F.

2013-12-01

Deformation from magma chambers can be modeled by an elastic half-space with an embedded cavity subject to uniform pressure change along its interior surface. For a small number of cavity shapes, such as a sphere or a prolate spheroid, closed-form, analytical expressions for deformation have been derived, although these only approximate the uniform-pressure-change boundary condition, with the approximation becoming more accurate as the ratio of source depth to source dimension increases. Using the method of Elshelby [1957] and Yang [1988], which consists of a distribution of double forces and centers of dilatation along the vertical axis, I have derived expressions for displacement from a finite spheroid of arbitrary orientation and aspect ratio that are exact in an infinite elastic medium and approximate in a half-space. The approximation, like those for other cavity shapes, becomes increasingly accurate as the depth to source ratio grows larger, and is accurate to within a few percent in most real-world cases. I have also derived expressions for the deformation-gradient tensor, i.e., the derivatives of each component of displacement with respect to each coordinate direction. These can be transformed easily into the strain and stress tensors. The expressions give deformation both at the surface and at any point within the half-space, and include conditional statements that account for limiting cases that would otherwise prove singular. I have developed MATLAB code for these expressions (and their derivatives), which I use to demonstrate the accuracy of the approximation by showing how well the uniform-pressure-change boundary condition is satisfied in a variety of cases. I also show that a vertical, oblate spheroid with a zero-length vertical axis is equivalent to the penny-shaped crack of Fialko [2001] in an infinite medium and an excellent approximation in a half-space. Finally, because, in many cases, volume change is more tangible than pressure change, I have derived an equation that relates these two quantities for the spheroid: volume change equals pressure change × 2/3 × π/μ × a constant that depends on Poisson's ratio and the spheroid geometry. Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R. Soc. London, Ser. A, 241, 376-396, 1957. Fialko, Y., Khazan, Y, and Simons, M. Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy, Geophys. J. Int., no. 146, 181-190, 2001. Yang, X., Davis, P. M., and Dieterich, J.H, Deformation from inflation of a dipping finite prolate spheroid in an Elastic Half-Space as a model for volcanic stressing, J. Geophys. Res., vol. 93, no. B5, 4249-4257, 1988.

Study of grain-level deformation and residual stresses in Ti-7Al under combined bending and tension using high energy diffraction microscopy (HEDM)

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

Chatterjee, K.; Venkataraman, A.; Garbaciak, T.

In-situ high energy diffraction microscopy (HEDM) experiments are carried out to analyze the state of combined bending and tension in a Ti-7Al alloy under room temperature creep. Grain-level elastic strain tensors are evaluated from HEDM data. Atomistic calculations are used to predict elastic constants of Ti-7Al, to be used in determination of stress from strain. The stress gradient and residual stresses are successfully determined, which allows the demarcation between macro-/micro-level residual stresses. A cluster of three neighboring grains are identified that highlight the variation of mean and effective stress between grains. Crystallographic orientations and slip characteristics are analyzed for themore » selected grains. It is inferred that the interfaces between loaded grains with markedly different stress triaxiality and slip tendency are potential spots for material damage.« less

Voting based object boundary reconstruction

NASA Astrophysics Data System (ADS)

Tian, Qi; Zhang, Like; Ma, Jingsheng

2005-07-01

A voting-based object boundary reconstruction approach is proposed in this paper. Morphological technique was adopted in many applications for video object extraction to reconstruct the missing pixels. However, when the missing areas become large, the morphological processing cannot bring us good results. Recently, Tensor voting has attracted people"s attention, and it can be used for boundary estimation on curves or irregular trajectories. However, the complexity of saliency tensor creation limits its applications in real-time systems. An alternative approach based on tensor voting is introduced in this paper. Rather than creating saliency tensors, we use a "2-pass" method for orientation estimation. For the first pass, Sobel d*etector is applied on a coarse boundary image to get the gradient map. In the second pass, each pixel puts decreasing weights based on its gradient information, and the direction with maximum weights sum is selected as the correct orientation of the pixel. After the orientation map is obtained, pixels begin linking edges or intersections along their direction. The approach is applied to various video surveillance clips under different conditions, and the experimental results demonstrate significant improvement on the final extracted objects accuracy.

Local deformation gradients in epitaxial Pb(Zr0.2Ti0.8)O3 layers investigated by transmission electron microscopy

NASA Astrophysics Data System (ADS)

Denneulin, T.; Wollschläger, N.; Everhardt, A. S.; Farokhipoor, S.; Noheda, B.; Snoeck, E.; Hÿtch, M.

2018-05-01

Lead zirconate titanate samples are used for their piezoelectric and ferroelectric properties in various types of micro-devices. Epitaxial layers of tetragonal perovskites have a tendency to relax by forming ferroelastic domains. The accommodation of the a/c/a/c polydomain structure on a flat substrate leads to nanoscale deformation gradients which locally influence the polarization by flexoelectric effect. Here, we investigated the deformation fields in epitaxial layers of Pb(Zr0.2Ti0.8)O3 grown on SrTiO3 substrates using transmission electron microscopy (TEM). We found that the deformation gradients depend on the domain walls inclination ( or to the substrate interface) of the successive domains and we describe three different a/c/a domain configurations: one configuration with parallel a-domains and two configurations with perpendicular a-domains (V-shaped and hat--shaped). In the parallel configuration, the c-domains contain horizontal and vertical gradients of out-of-plane deformation. In the V-shaped and hat--shaped configurations, the c-domains exhibit a bending deformation field with vertical gradients of in-plane deformation. Each of these configurations is expected to have a different influence on the polarization and so the local properties of the film. The deformation gradients were measured using dark-field electron holography, a TEM technique, which offers a good sensitivity (0.1%) and a large field-of-view (hundreds of nanometers). The measurements are compared with finite element simulations.

Simultaneous concentration and purification through gradient deformation chromatography

NASA Technical Reports Server (NTRS)

Velayudhan, A.; Hendrickson, R. L.; Ladisch, M. R.; Mitchell, C. A. (Principal Investigator)

1995-01-01

Mobile-phase additives, commonly used to modulate absorbate retention in gradient elution chromatography, are usually assumed to be either linearly retained or unretained. Previous theoretical work from our laboratory has shown that these modulators, such as salts in ion-exchange and hydrophobic interaction chromatography and organic modifiers in reversed-phase chromatography, can absorb nonlinearly, giving rise to gradient deformation. Consequently, adsorbate peaks that elute in the vicinity of the head of the deformed gradient may exhibit unusual shapes, form shoulders, and/or be concentrated. These effects for a reversed-phase sorbent with aqueous acetonitrile (ACN) as the modulator are verified experimentally. Gradient deformation is demonstrated experimentally and agrees with simulations based on ACN isotherm parameters that are independently determined from batch equilibrium studies using the layer model. Unusual absorbate peak shapes were found experimentally for single-component injections of phenylalanine, similar to those calculated by the simulations. A binary mixture of tryptophan and phenylalanine is used to demonstrate simultaneous concentration and separation, again in agreement with simulations. The possibility of gradient deformation in ion-exchange and hydrophobic interaction chromatography is discussed.

Emergent gravity from a mass deformation in warped spacetime

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

Gherghetta, Tony; Peloso, Marco; Poppitz, Erich

2005-11-15

We consider a deformation of five-dimensional warped gravity with bulk and boundary mass terms to quadratic order in the action. We show that massless zero modes occur for special choices of the masses. The tensor zero mode is a smooth deformation of the Randall-Sundrum graviton wave function and can be localized anywhere in the bulk. There is also a vector zero mode with similar localization properties, which is decoupled from conserved sources at tree level. Interestingly, there are no scalar modes, and the model is ghost-free at the linearized level. When the tensor zero mode is localized near the IRmore » brane, the dual interpretation is a composite graviton describing an emergent (induced) theory of gravity at the IR scale. In this case Newton's law of gravity changes to a new power law below the millimeter scale, with an exponent that can even be irrational.« less

A metamodel for the apparent permeability tensor of three-dimensional porous media in the inertial regime

NASA Astrophysics Data System (ADS)

Luminari, Nicola; Airiau, Christophe; Bottaro, Alessandro

2017-11-01

In the description of the homogenized flow through a porous medium saturated by a fluid, the apparent permeability tensor is one of the most important parameters to evaluate. In this work we compute numerically the apparent permeability tensor for a 3D porous medium constituted by rigid cylinder using the VANS (Volume-Averaged Navier-Stokes) theory. Such a tensor varies with the Reynolds number, the mean pressure gradient orientation and the porosity. A database is created exploring the space of the above parameters. Including the two Euler angles that define the mean pressure gradient is extremely important to capture well possible 3D effects. Based on the database, a kriging interpolation metamodel is used to obtain an estimate of all the tensor components for any input parameters. Preliminary results of the flow in a porous channel based on the metamodel and the VANS closure are shown; the use of such a reduced order model together with a numerical code based on the equations at the macroscopic scale permit to maintain the computational times to within reasonable levels. The authors acknowledge the IDEX Foundation of the University of Toulouse 570 for the financial support Granted to the last author under the project Attractivity Chairs.

Toward more complete magnetic gradiometry with the Swarm mission

NASA Astrophysics Data System (ADS)

Kotsiaros, Stavros

2016-07-01

An analytical and numerical analysis of the spectral properties of the gradient tensor, initially performed by Rummel and van Gelderen (Geophys J Int 111(1):159-169, 1992) for the gravity potential, shows that when the tensor elements are grouped into sets of semi-tangential and pure-tangential parts, they produce almost identical signal content as the normal element. Moreover, simple eigenvalue relations can be derived between these sets and the spherical harmonic expansion of the potential. This theoretical development generally applies to any potential field. First, the analysis of Rummel and van Gelderen (1992) is adapted to the magnetic field case and then the elements of the magnetic gradient tensor are estimated by 2 years of Swarm data and grouped into \\varvec{Γ }^{(1)} = {[\\varvec{nabla } {{B}}]_{rθ },[\\varvec{nabla } {{B}}]_{r\\varphi }} resp. \\varvec{Γ }^{(2)} = {[\\varvec{nabla } {{B}}]_{θ θ }-[\\varvec{nabla } {{B}}]_{\\varphi \\varphi }, 2[\\varvec{nabla } {{B}}]_{θ \\varphi }}. It is shown that the estimated combinations \\varvec{Γ }^{(1)} and \\varvec{Γ }^{(2)} produce similar signal content as the theoretical radial gradient \\varvec{Γ }^{(0)} = {[\\varvec{nabla } {{B}}]_{rr}}. These results demonstrate the ability of multi-satellite missions such as Swarm, which cannot directly measure the radial gradient, to retrieve similar signal content by means of the horizontal gradients. Finally, lithospheric field models are derived using the gradient combinations \\varvec{Γ }^{(1)} and \\varvec{Γ }^{(2)} and compared with models derived from traditional vector and gradient data. The model resulting from \\varvec{Γ }^{(1)} leads to a very similar, and in particular cases improved, model compared to models retrieved by using approximately three times more data, i.e., a full set of vector, North-South and East-West gradients. This demonstrates the high information content of \\varvec{Γ }^{(1)}.

Two-body problem in scalar-tensor theories as a deformation of general relativity: An effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis; Deruelle, Nathalie

2017-06-01

In this paper we address the two-body problem in massless scalar-tensor (ST) theories within an effective-one-body (EOB) framework. We focus on the first building block of the EOB approach, that is, mapping the conservative part of the two-body dynamics onto the geodesic motion of a test particle in an effective external metric. To this end, we first deduce the second post-Keplerian (2PK) Hamiltonian of the two-body problem from the known 2PK Lagrangian. We then build, by means of a canonical transformation, a ST deformation of the general relativistic EOB Hamiltonian that allows us to incorporate the scalar-tensor (2PK) corrections to the currently best available general relativity EOB results. This EOB-ST Hamiltonian defines a resummation of the dynamics that may provide information on the strong-field regime, in particular, the ISCO location and associated orbital frequency, and can be compared to, other, e.g., tidal, corrections.

Reducing the two-body problem in scalar-tensor theories to the motion of a test particle: A scalar-tensor effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis

2018-01-01

Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a ν deformation (where ν =0 is the test mass limit) of the analytically known ST Hamiltonian of a test particle. This ST-EOB Hamiltonian leads to a simple (yet canonically equivalent) formulation of the conservative 2PK two-body problem, but also defines a resummation of the dynamics which is well-suited to ST regimes that depart strongly from general relativity (GR) and which may provide information on the strong field dynamics; in particular, the ST innermost stable circular orbit location and associated orbital frequency. Results will be compared and contrasted with those deduced from the ST-deformation of the (5PN) GR-EOB Hamiltonian previously obtained in [Phys. Rev. D 95, 124054 (2017), 10.1103/PhysRevD.95.124054].

Intermittency in small-scale turbulence: a velocity gradient approach

NASA Astrophysics Data System (ADS)

Meneveau, Charles; Johnson, Perry

2017-11-01

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

Condition Number as a Measure of Noise Performance of Diffusion Tensor Data Acquisition Schemes with MRI

NASA Astrophysics Data System (ADS)

Skare, Stefan; Hedehus, Maj; Moseley, Michael E.; Li, Tie-Qiang

2000-12-01

Diffusion tensor mapping with MRI can noninvasively track neural connectivity and has great potential for neural scientific research and clinical applications. For each diffusion tensor imaging (DTI) data acquisition scheme, the diffusion tensor is related to the measured apparent diffusion coefficients (ADC) by a transformation matrix. With theoretical analysis we demonstrate that the noise performance of a DTI scheme is dependent on the condition number of the transformation matrix. To test the theoretical framework, we compared the noise performances of different DTI schemes using Monte-Carlo computer simulations and experimental DTI measurements. Both the simulation and the experimental results confirmed that the noise performances of different DTI schemes are significantly correlated with the condition number of the associated transformation matrices. We therefore applied numerical algorithms to optimize a DTI scheme by minimizing the condition number, hence improving the robustness to experimental noise. In the determination of anisotropic diffusion tensors with different orientations, MRI data acquisitions using a single optimum b value based on the mean diffusivity can produce ADC maps with regional differences in noise level. This will give rise to rotational variances of eigenvalues and anisotropy when diffusion tensor mapping is performed using a DTI scheme with a limited number of diffusion-weighting gradient directions. To reduce this type of artifact, a DTI scheme with not only a small condition number but also a large number of evenly distributed diffusion-weighting gradients in 3D is preferable.

Local deformation gradients in epitaxial Pb(Zr0.2Ti0.8)O3 layers investigated by transmission electron microscopy.

PubMed

Denneulin, T; Wollschläger, N; Everhardt, A S; Farokhipoor, S; Noheda, B; Snoeck, E; Hÿtch, M

2018-05-31

Lead zirconate titanate samples are used for their piezoelectric and ferroelectric properties in various types of micro-devices. Epitaxial layers of tetragonal perovskites have a tendency to relax by forming [Formula: see text] ferroelastic domains. The accommodation of the a/c/a/c polydomain structure on a flat substrate leads to nanoscale deformation gradients which locally influence the polarization by flexoelectric effect. Here, we investigated the deformation fields in epitaxial layers of Pb(Zr 0.2 Ti 0.8 )O 3 grown on SrTiO 3 substrates using transmission electron microscopy (TEM). We found that the deformation gradients depend on the domain walls inclination ([Formula: see text] or [Formula: see text] to the substrate interface) of the successive [Formula: see text] domains and we describe three different a/c/a domain configurations: one configuration with parallel a-domains and two configurations with perpendicular a-domains (V-shaped and hat-[Formula: see text]-shaped). In the parallel configuration, the c-domains contain horizontal and vertical gradients of out-of-plane deformation. In the V-shaped and hat-[Formula: see text]-shaped configurations, the c-domains exhibit a bending deformation field with vertical gradients of in-plane deformation. Each of these configurations is expected to have a different influence on the polarization and so the local properties of the film. The deformation gradients were measured using dark-field electron holography, a TEM technique, which offers a good sensitivity (0.1%) and a large field-of-view (hundreds of nanometers). The measurements are compared with finite element simulations.

Edge remap for solids

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

Kamm, James R.; Love, Edward; Robinson, Allen C.

We review the edge element formulation for describing the kinematics of hyperelastic solids. This approach is used to frame the problem of remapping the inverse deformation gradient for Arbitrary Lagrangian-Eulerian (ALE) simulations of solid dynamics. For hyperelastic materials, the stress state is completely determined by the deformation gradient, so remapping this quantity effectively updates the stress state of the material. A method, inspired by the constrained transport remap in electromagnetics, is reviewed, according to which the zero-curl constraint on the inverse deformation gradient is implicitly satisfied. Open issues related to the accuracy of this approach are identified. An optimization-based approachmore » is implemented to enforce positivity of the determinant of the deformation gradient. The efficacy of this approach is illustrated with numerical examples.« less

Shell evolution above Z ,N =50 within Skyrme density functional theory: The impact of deformation and tensor interactions

NASA Astrophysics Data System (ADS)

Shi, Yue

2017-03-01

Background: Recent years have seen considerable effort in associating the shell evolution (SE) for a chain of isotones or isotopes with the underlying nuclear interactions. In particular, it has been fairly well established that the tensor part of the Skyrme interaction is indispensable for understanding certain SE above Z ,N =50 shell closures, as a function of nucleon numbers. Purpose: The purpose of the present work is twofold: (1) to study the effect of deformation due to blocking on the SE above Z ,N =50 shell closures and (2) to examine the optimal parametrizations in the tensor part which gives a proper description of the SE above Z ,N =50 shell closures. Methods: I use the Skyrme-Hartree-Fock-Bogoliubov (SHFB) method to compute the even-even vacua of the Z =50 isotopes and N =50 isotones. For Sb and odd-A Sn isotopes, I perform calculations with a blocking procedure which accounts for the polarization effects, including deformations. Results: The blocking SHFB calculations show that the light odd-A Sb isotopes, with only one valence proton occupying down-sloping Ω =11 /2- and Ω =7 /2+ Nilsson orbits, assume finite oblate deformations. This reduces the energy differences between 11 /2- and 7 /2+ states by about 500 keV for 51Sb56 -66 , bringing the energy-difference curve closer to the experimental one. With une2t1 energy density functional (EDF), which differs from unedf2 parametrization by tensor terms, a better description of the slope of Δ e (π 1 h11 /2-π 1 g7 /2) as a function of neutron number has been obtained. However, the trend of Δ e (π 1 g7 /2-π 2 d5 /2) curve is worse using une2t1 EDF. Δ e (ν 3 s1 /2-ν 2 d5 /2) and Δ e (ν 1 g7 /2-ν 2 d5 /2) curve for N =50 isotones using une2t1 seems to be consistent with experimental data. The neutron SE of Δ e (ν 1 h11 /2-ν 1 g7 /2) and Δ e (ν 1 g7 /2-ν 2 d5 /2) for Sn isotopes are shown to be sensive to αT tensor parameter. Conclusions: Within the Skyrme self-consistent mean-field model, the deformation degree of freedom has to be taken into account for Sb isotopes, N =51 isotones, and odd-A Sn isotopes when discussing variation of quantities like shell gap etc. The tensor terms are important for describing the strong variation of Δ E (Ωπ=11 /2--7 /2+) in Sb isotopes. The SE of 1 /2+ and 7 /2+ states in N =51 isotones may show signature for the existence of tensor interaction. The experimental excitation energies of 11 /2- and 7 /2+ states in odd-A Sn isotopes close to 132Sn give prospects for constraining the αT parameter.

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

NASA Astrophysics Data System (ADS)

di Lauro, C.

2018-03-01

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

An affine model of the dynamics of astrophysical discs

NASA Astrophysics Data System (ADS)

Ogilvie, Gordon I.

2018-06-01

Thin astrophysical discs are very often modelled using the equations of 2D hydrodynamics. We derive an extension of this model that describes more accurately the behaviour of a thin disc in the absence of self-gravity, magnetic fields, and complex internal motions. The ideal fluid theory is derived directly from Hamilton's Principle for a 3D fluid after making a specific approximation to the deformation gradient tensor. We express the equations in Eulerian form after projection on to a reference plane. The disc is thought of as a set of fluid columns, each of which is capable of a time-dependent affine transformation, consisting of a translation together with a linear transformation in three dimensions. Therefore, in addition to the usual 2D hydrodynamics in the reference plane, the theory allows for a deformation of the mid-plane (as occurs in warped discs) and for the internal shearing motions that accompany such deformations. It also allows for the vertical expansions driven in non-circular discs by a variation of the vertical gravitational field around the horizontal streamlines, or by a divergence of the horizontal velocity. The equations of the affine model embody conservation laws for energy and potential vorticity, even for non-planar discs. We verify that they reproduce exactly the linear theories of 3D warped and eccentric discs in a secular approximation. However, the affine model does not rely on any secular or small-amplitude assumptions and should be useful in more general circumstances.

Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition F =FeFi

NASA Astrophysics Data System (ADS)

Reina, Celia; Conti, Sergio

2017-10-01

The multiplicative decomposition of the total deformation F =FeFi between an elastic (Fe) and an inelastic component (Fi) is standard in the modeling of many irreversible processes such as plasticity, growth, thermoelasticity, viscoelasticty or phase transformations. The heuristic argument for such kinematic assumption is based on the chain rule for the compatible scenario (CurlFi = 0) where the individual deformation tensors are gradients of deformation mappings, i.e. F = D φ = D (φe ∘φi) = (Dφe) ∘φi (Dφi) =FeFi . Yet, the conditions for its validity in the general incompatible case (CurlFi ≠ 0) has so far remained uncertain. We show in this paper that detFi = 1 and CurlFi bounded are necessary and sufficient conditions for the validity of F =FeFi for a wide range of inelastic processes. In particular, in the context of crystal plasticity, we demonstrate via rigorous homogenization from discrete dislocations to the continuum level in two dimensions, that the volume preserving property of the mechanistics of dislocation glide, combined with a finite dislocation density, is sufficient to deliver F =FeFp at the continuum scale. We then generalize this result to general two-dimensional inelastic processes that may be described at a lower dimensional scale via a multiplicative decomposition while exhibiting a finite density of incompatibilities. The necessity of the conditions detFi = 1 and CurlFi bounded for such systems is demonstrated via suitable counterexamples.

The tensor distribution function.

PubMed

Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M

2009-01-01

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Deformations of the Almheiri-Polchinski model

NASA Astrophysics Data System (ADS)

Kyono, Hideki; Okumura, Suguru; Yoshida, Kentaroh

2017-03-01

We study deformations of the Almheiri-Polchinski (AP) model by employing the Yang-Baxter deformation technique. The general deformed AdS2 metric becomes a solution of a deformed AP model. In particular, the dilaton potential is deformed from a simple quadratic form to a hyperbolic function-type potential similarly to integrable deformations. A specific solution is a deformed black hole solution. Because the deformation makes the spacetime structure around the boundary change drastically and a new naked singularity appears, the holographic interpretation is far from trivial. The Hawking temperature is the same as the undeformed case but the Bekenstein-Hawking entropy is modified due to the deformation. This entropy can also be reproduced by evaluating the renormalized stress tensor with an appropriate counter-term on the regularized screen close to the singularity.

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.

3D inversion of full gravity gradient tensor data in spherical coordinate system using local north-oriented frame

NASA Astrophysics Data System (ADS)

Zhang, Yi; Wu, Yulong; Yan, Jianguo; Wang, Haoran; Rodriguez, J. Alexis P.; Qiu, Yue

2018-04-01

In this paper, we propose an inverse method for full gravity gradient tensor data in the spherical coordinate system. As opposed to the traditional gravity inversion in the Cartesian coordinate system, our proposed method takes the curvature of the Earth, the Moon, or other planets into account, using tesseroid bodies to produce gravity gradient effects in forward modeling. We used both synthetic and observed datasets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts the depth of the density anomalous body efficiently and accurately. Using observed gravity data for the Mare Smythii area on the moon, the density distribution of the crust in this area reveals its geological structure. These results validate the proposed method and potential application for large area data inversion of planetary geological structures.[Figure not available: see fulltext.

A defect in holographic interpretations of tensor networks

NASA Astrophysics Data System (ADS)

Czech, Bartlomiej; Nguyen, Phuc H.; Swaminathan, Sivaramakrishnan

2017-03-01

We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.

Localized Flow of Frictional Or Creeping Materials In A Lower Flat Thrust To Ramp Transition

NASA Astrophysics Data System (ADS)

Maillot, B.; Leroy, Y.

The passage of rock through zones of localized shear deformation in the form of back- thrusts or kink planes is common in fold and thrust belts. The stationary flow through these two types of hinges is examined for the particular case of a lower flat to ramp transition of a fault-bend fold. The simple shear transformation resulting in strain lo- calization is studied both analytically and numerically. The overall equilibrium of the hanging wall, accounting for friction over the ramp, constrains the shear and normal forces acting on the hinge boundaries. For frictional materials, the localization oc- curs in the form of a velocity discontinuity, defining the backthrust, with a dip which is shown not to bissect ramp angle nor to conserve the thrust nappe thickness, if a criteria based on a minimization of the total dissipation is considered. For creeping materials, the strain localization as a kink plane is shown to require a destabilizing deformation mechanism, selected here to be flexural slip. The rotation of the stress tensor due to the gradient in pressure, the thicknening and thinning of the creeping material, the rate and amount of flexural slip through the hinge are analyzed to define potential tectonic markers.

Localization of the cutaneus trunci muscle reflex in horses.

PubMed

Essig, Cynthia M; Merritt, Jonathan S; Stubbs, Narelle C; Clayton, Hilary M

2013-11-01

To determine the magnitude and location of skin movement attributable to the cutaneus trunci muscle reflex in response to localized stimulation of the skin of the dorsolateral aspect of the thoracic wall in horses. 8 horses. A grid of 56 reflective markers was applied to the lateral aspect of the body wall of each horse; markers were placed at 10-cm intervals in 7 rows and 8 columns. A motion analysis system with 10 infrared cameras was used to track movements of the markers in response to tactile stimulation of the dorsolateral aspect of the thoracic wall at the levels of T6, T11, and T16. Marker movement data determined after skin stimulation were used to create a skin deformation gradient tensor field, which was analyzed with custom software. The sites of maximal skin deformation were located close to the stimulation sites; the centers of the twitch responses were located a mean distance of 7.7 to 12.8 cm ventral and between 6.6 cm cranial and 3.1 cm caudal to the stimulation sites. Findings of this study may have implications for assessment of nerve conduction velocities of the cutaneus trunci muscle reflex and may enhance understanding of the responses of horses to placement of tack or other equipment on skin over the cutaneus trunci muscles.

Dispersive transport and symmetry of the dispersion tensor in porous media

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

On the usefulness of gradient information in multi-objective deformable image registration using a B-spline-based dual-dynamic transformation model: comparison of three optimization algorithms

NASA Astrophysics Data System (ADS)

Pirpinia, Kleopatra; Bosman, Peter A. N.; Sonke, Jan-Jakob; van Herk, Marcel; Alderliesten, Tanja

2015-03-01

The use of gradient information is well-known to be highly useful in single-objective optimization-based image registration methods. However, its usefulness has not yet been investigated for deformable image registration from a multi-objective optimization perspective. To this end, within a previously introduced multi-objective optimization framework, we use a smooth B-spline-based dual-dynamic transformation model that allows us to derive gradient information analytically, while still being able to account for large deformations. Within the multi-objective framework, we previously employed a powerful evolutionary algorithm (EA) that computes and advances multiple outcomes at once, resulting in a set of solutions (a so-called Pareto front) that represents efficient trade-offs between the objectives. With the addition of the B-spline-based transformation model, we studied the usefulness of gradient information in multiobjective deformable image registration using three different optimization algorithms: the (gradient-less) EA, a gradientonly algorithm, and a hybridization of these two. We evaluated the algorithms to register highly deformed images: 2D MRI slices of the breast in prone and supine positions. Results demonstrate that gradient-based multi-objective optimization significantly speeds up optimization in the initial stages of optimization. However, allowing sufficient computational resources, better results could still be obtained with the EA. Ultimately, the hybrid EA found the best overall approximation of the optimal Pareto front, further indicating that adding gradient-based optimization for multiobjective optimization-based deformable image registration can indeed be beneficial

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.

Reducing tensor magnetic gradiometer data for unexploded ordnance detection

USGS Publications Warehouse

Bracken, Robert E.; Brown, Philip J.

2005-01-01

We performed a survey to demonstrate the effectiveness of a prototype tensor magnetic gradiometer system (TMGS) for detection of buried unexploded ordnance (UXO). In order to achieve a useful result, we designed a data-reduction procedure that resulted in a realistic magnetic gradient tensor and devised a simple way of viewing complicated tensor data, not only to assess the validity of the final resulting tensor, but also to preview the data at interim stages of processing. The final processed map of the surveyed area clearly shows a sharp anomaly that peaks almost directly over the target UXO. This map agrees well with a modeled map derived from dipolar sources near the known target locations. From this agreement, it can be deduced that the reduction process is valid, making the prototype TMGS a foundation for development of future systems and processes.

Spectral edge: gradient-preserving spectral mapping for image fusion.

PubMed

Connah, David; Drew, Mark S; Finlayson, Graham D

2015-12-01

This paper describes a novel approach to image fusion for color display. Our goal is to generate an output image whose gradient matches that of the input as closely as possible. We achieve this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is then reintegrated to form an output. Constraints on output colors are provided by an initial RGB rendering. Initially, we motivate our solution with a simple "ansatz" (educated guess) for projecting higher-D contrast onto color gradients, which we expand to a more rigorous theorem to incorporate color constraints. The solution to these constrained optimizations is closed-form, allowing for simple and hence fast and efficient algorithms. The approach can map any N-D image data to any M-D output and can be used in a variety of applications using the same basic algorithm. In this paper, we focus on the problem of mapping N-D inputs to 3D color outputs. We present results in five applications: hyperspectral remote sensing, fusion of color and near-infrared or clear-filter images, multilighting imaging, dark flash, and color visualization of magnetic resonance imaging diffusion-tensor imaging.

Infrared modified gravity with propagating torsion: Instability of torsionfull de Sitter-like solutions

NASA Astrophysics Data System (ADS)

Nikiforova, Vasilisa; Damour, Thibault

2018-06-01

We continue the exploration of the consistency of a modified-gravity theory that generalizes general relativity by including a dynamical torsion in addition to the dynamical metric. The six-parameter theory we consider was found to be consistent around arbitrary torsionless Einstein backgrounds, in spite of its containing a (notoriously delicate) massive spin-2 excitation. At zero bare cosmological constant, this theory was found to admit a self-accelerating solution whose exponential expansion is sustained by a nonzero torsion background. The scalar-type perturbations of the latter torsionfull self-accelerating solution were recently studied and were found to preserve the number of propagating scalar degrees of freedom, but to exhibit, for some values of the torsion background, some exponential instabilities (of a rather mild type). Here, we study the tensor-type and vector-type perturbations of the torsionfull self-accelerating solution, and of its deformation by a nonzero bare cosmological constant. We find strong, "gradient" instabilities in the vector sector. No tuning of the parameters of the theory can kill these instabilities without creating instabilities in the other sectors. Further work is needed to see whether generic torsionfull backgrounds are prone to containing gradient instabilities, or if the instabilities we found are mainly due to the (generalized) self-accelerating nature of the special de Sitter backgrounds we considered.

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

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.

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.

Thermoelastic enhancement of the magnonic spin Seebeck effect in thin films and bulk samples

NASA Astrophysics Data System (ADS)

Chotorlishvili, L.; Wang, X.-G.; Toklikishvili, Z.; Berakdar, J.

2018-04-01

A nonuniform temperature profile may generate a pure spin current in magnetic films, as observed, for instance, in the spin Seebeck effect. In addition, thermally induced elastic deformations may set in that could affect the spin current. A self-consistent theory of the magnonic spin Seebeck effect including thermally activated magnetoelastic effects is presented, and analytical expressions for the thermally activated deformation tensor and dispersion relations for coupled magnetoelastic modes are obtained. We derive analytical results for bulk (three-dimensional) systems and thin magnetic (two-dimensional) films. We observe that the displacement vector and the deformation tensor in bulk systems decay asymptotically as u ˜1 /R2 and ɛ ˜1 /R3 , respectively, while the decays in thin magnetic films proceed slower, following u ˜1 /R and ɛ ˜1 /R2 . The dispersion relations evidence a strong anisotropy in the magnetic excitations. We observe that a thermoelastic steady-state deformation may lead to both an enchantment and a reduction of the gap in the magnonic spectrum. The reduction of the gap increases the number of magnons contributing to the spin Seebeck effect and offers new possibilities for the thermoelastic control of the spin Seebeck effect.

Current deformation in Central Afar and triple junction kinematics deduced from GPS and InSAR measurements

NASA Astrophysics Data System (ADS)

Doubre, Cécile; Déprez, Aline; Masson, Frédéric; Socquet, Anne; Lewi, Elias; Grandin, Raphaël; Nercessian, Alexandre; Ulrich, Patrice; De Chabalier, Jean-Bernard; Saad, Ibrahim; Abayazid, Ahmadine; Peltzer, Gilles; Delorme, Arthur; Calais, Eric; Wright, Tim

2017-02-01

Kinematics of divergent boundaries and Rift-Rift-Rift junctions are classically studied using long-term geodetic observations. Since significant magma-related displacements are expected, short-term deformation provides important constraints on the crustal mechanisms involved both in active rifting and in transfer of extensional deformation between spreading axes. Using InSAR and GPS data, we analyse the surface deformation in the whole Central Afar region in detail, focusing on both the extensional deformation across the Quaternary magmato-tectonic rift segments, and on the zones of deformation transfer between active segments and spreading axes. The largest deformation occurs across the two recently activated Asal-Ghoubbet (AG) and Manda Hararo-Dabbahu (MH-D) magmato-tectonic segments with very high strain rates, whereas the other Quaternary active segments do not concentrate any large strain, suggesting that these rifts are either sealed during interdyking periods or not mature enough to remain a plate boundary. Outside of these segments, the GPS horizontal velocity field shows a regular gradient following a clockwise rotation of the displacements from the Southeast to the East of Afar, with respect to Nubia. Very few shallow creeping structures can be identified as well in the InSAR data. However, using these data together with the strain rate tensor and the rotations rates deduced from GPS baselines, the present-day strain field over Central Afar is consistent with the main tectonic structures, and therefore with the long-term deformation. We investigate the current kinematics of the triple junction included in our GPS data set by building simple block models. The deformation in Central Afar can be described by adding a central microblock evolving separately from the three surrounding plates. In this model, the northern block boundary corresponds to a deep EW-trending trans-tensional dislocation, locked from the surface to 10-13 km and joining at depth the active spreading axes of the Red Sea and the Aden Ridge, from AG to MH-D rift segments. Over the long-term, this plate configuration could explain the presence of the en-échelon magmatic basins and subrifts. However, the transient behaviour of the spreading axes implies that the deformation in Central Afar evolves depending on the availability of magma supply within the well-established segments.

Transformations of the dislocation structure of nickel single crystals

NASA Astrophysics Data System (ADS)

Alfyorova, E. A.; Lychagin, D. V.; Lychagina, L. L.; Tsvetkov, N. A.

2017-12-01

A relationship between different-scale deformations of crystals has not been established yet. In order to solve this task, we investigate the development of a deformation relief and dislocation structure in nickel single crystals after deformation. The stress tensor, crystallography, and geometry of specimens affect the organization of some shear along corresponding systems of sliding. The organization of shear shows some features of self-organization. It is associated with the self-organization in the dislocation subsystem analyzed previously. The effectiveness of reducing external and internal stresses determines patterns of deformation processes at different scale levels.

Diffusion Tensor Magnetic Resonance Imaging Strategies for Color Mapping of Human Brain Anatomy

PubMed Central

Boujraf, Saïd

2018-01-01

Background: A color mapping of fiber tract orientation using diffusion tensor imaging (DTI) can be prominent in clinical practice. The goal of this paper is to perform a comparative study of visualized diffusion anisotropy in the human brain anatomical entities using three different color-mapping techniques based on diffusion-weighted imaging (DWI) and DTI. Methods: The first technique is based on calculating a color map from DWIs measured in three perpendicular directions. The second technique is based on eigenvalues derived from the diffusion tensor. The last technique is based on three eigenvectors corresponding to sorted eigenvalues derived from the diffusion tensor. All magnetic resonance imaging measurements were achieved using a 1.5 Tesla Siemens Vision whole body imaging system. A single-shot DW echoplanar imaging sequence used a Stejskal–Tanner approach. Trapezoidal diffusion gradients are used. The slice orientation was transverse. The basic measurement yielded a set of 13 images. Each series consists of a single image without diffusion weighting, besides two DWIs for each of the next six noncollinear magnetic field gradient directions. Results: The three types of color maps were calculated consequently using the DWI obtained and the DTI. Indeed, we established an excellent similarity between the image data in the color maps and the fiber directions of known anatomical structures (e.g., corpus callosum and gray matter). Conclusions: In the meantime, rotationally invariant quantities such as the eigenvectors of the diffusion tensor reflected better, the real orientation found in the studied tissue. PMID:29928631

A Mechanobiological model for damage-induced growth in arterial tissue with application to in-stent restenosis

NASA Astrophysics Data System (ADS)

Fereidoonnezhad, B.; Naghdabadi, R.; Sohrabpour, S.; Holzapfel, G. A.

In-stent restenosis (ISR) is one of the main drawbacks of stent implementation which limits the long-term success of the procedure. Morphological changes occurring within the arterial wall due to stent-induced mechanical injury are a major cause for activation of vascular smooth muscle cells (VSMCs), and the subsequent development of ISR. Considering the theory of volumetric mass growth and adopting a multiplicative decomposition of the deformation gradient into an elastic part and a growth part, we present a mechanobiological model for ISR. An evolution equation is developed for mass growth of the neointima, in which the activation of VSMCs due to stent-induced damage (injury) and the proliferation rate of the activated cells are considered. By introducing the mass evolution into the mass balance equation, we obtain the evolution of the growth tensor over time. The model is implemented in a finite element code and the procedure of angioplasty is simulated, whereby the features of the proposed growth model are illustrated.

Effective friction of granular flows made of non-spherical particles

NASA Astrophysics Data System (ADS)

Somfai, Ellák; Nagy, Dániel B.; Claudin, Philippe; Favier, Adeline; Kálmán, Dávid; Börzsönyi, Tamás

2017-06-01

Understanding the rheology of dense granular matter is a long standing problem and is important both from the fundamental and the applied point of view. As the basic building blocks of granular materials are macroscopic particles, the nature of both the response to deformations and the dissipation is very different from that of molecular materials. In the absence of large gradients, the best approach formulates the constitutive equation as an effective friction: for sheared granular matter the ratio of the off-diagonal and the diagonal elements of the stress tensor depends only on dynamical parameters, in particular the inertial number. In this work we employ numerical simulations to extend this formalism to granular packings made of frictionless elongated particles. We measured how the shape of the particles affects the effective friction, volume fraction and first normal stress difference, and compared it to the spherical particle case. We had to introduce polydispersity in particle size in order to keep the systems of the more elongated particles disordered.

An introduction to tensor calculus, relativity and cosmology /3rd edition/

NASA Astrophysics Data System (ADS)

Lawden, D. F.

This textbook introduction to the principles of special relativity proceeds within the context of cartesian tensors. Newton's laws of motion are reviewed, as are the Lorentz transformations, Minkowski space-time, and the Fitzgerald contraction. Orthogonal transformations are described, and invariants, gradients, tensor derivatives, contraction, scalar products, divergence, pseudotensors, vector products, and curl are defined. Special relativity mechanics are explored in terms of mass, momentum, the force vector, the Lorentz transformation equations for force, calculations for photons and neutrinos, the development of the Lagrange and Hamilton equations, and the energy-momentum tensor. Electrodynamics is investigated, together with general tensor calculus and Riemmanian space. The General Theory of Relativity is presented, along with applications to astrophysical phenomena such as black holes and gravitational waves. Finally, analytical discussions of cosmological problems are reviewed, particularly Einstein, de Sitter, and Friedmann universes, redshifts, event horizons, and the redshift.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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.

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

Werner-Wheeler mass tensor for fusionlike configuration

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

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

2005-08-01

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

Distance-preserving rigidity penalty on deformable image registration of multiple skeletal components in the neck

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

Kim, Jihun, E-mail: jihun@umich.edu; Saitou, Kazuhiro; Matuszak, Martha M.

Purpose: This study aims at developing and testing a novel rigidity penalty suitable for the deformable registration of tightly located skeletal components in the head and neck from planning computed tomography (CT) and daily cone-beam CT (CBCT) scans of patients undergoing radiotherapy. Methods: The proposed rigidity penalty is designed to preserve intervoxel distances within each bony structure. This penalty was tested in the intensity-based B-spline deformable registration of five cervical vertebral bodies (C1–C5). The displacement vector fields (DVFs) from the registrations were compared to the DVFs generated by using rigid body motions of the cervical vertebrae, measured by the surfacemore » registration of vertebrae delineated on CT and CBCT images. Twenty five pairs of planning CT (reference) and treatment CBCTs (target) from five patients were aligned without and with the penalty. An existing penalty based on the orthonormality of the deformation gradient tensor was also tested and the effects of the penalties compared. Results: The mean magnitude of the maximum registration error with the proposed distance-preserving penalty was (0.86, 1.12, 1.33) mm compared to (2.11, 2.49, 2.46) without penalty and (1.53, 1.64, 1.64) with the existing orthonormality-based penalty. The improvement in the accuracy of the deformable image registration was also verified by comparing the Procrustes distance between the DVFs. With the proposed penalty, the average distance was 0.11 (σ 0.03 mm) which is smaller than 0.53 (0.1 mm) without penalty and 0.28 (0.04 mm) with the orthonormality-based penalty. Conclusions: The accuracy of aligning multiple bony elements was improved by using the proposed distance-preserving rigidity penalty. The voxel-based statistical analysis of the registration error shows that the proposed penalty improved the integrity of the DVFs within the vertebral bodies.« less

Distance-preserving rigidity penalty on deformable image registration of multiple skeletal components in the neck

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

Kim, Jihun, E-mail: jihun@umich.edu; Saitou, Kazuhiro; Matuszak, Martha M.

2013-12-15

Purpose: This study aims at developing and testing a novel rigidity penalty suitable for the deformable registration of tightly located skeletal components in the head and neck from planning computed tomography (CT) and daily cone-beam CT (CBCT) scans of patients undergoing radiotherapy. Methods: The proposed rigidity penalty is designed to preserve intervoxel distances within each bony structure. This penalty was tested in the intensity-based B-spline deformable registration of five cervical vertebral bodies (C1–C5). The displacement vector fields (DVFs) from the registrations were compared to the DVFs generated by using rigid body motions of the cervical vertebrae, measured by the surfacemore » registration of vertebrae delineated on CT and CBCT images. Twenty five pairs of planning CT (reference) and treatment CBCTs (target) from five patients were aligned without and with the penalty. An existing penalty based on the orthonormality of the deformation gradient tensor was also tested and the effects of the penalties compared. Results: The mean magnitude of the maximum registration error with the proposed distance-preserving penalty was (0.86, 1.12, 1.33) mm compared to (2.11, 2.49, 2.46) without penalty and (1.53, 1.64, 1.64) with the existing orthonormality-based penalty. The improvement in the accuracy of the deformable image registration was also verified by comparing the Procrustes distance between the DVFs. With the proposed penalty, the average distance was 0.11 (σ 0.03 mm) which is smaller than 0.53 (0.1 mm) without penalty and 0.28 (0.04 mm) with the orthonormality-based penalty. Conclusions: The accuracy of aligning multiple bony elements was improved by using the proposed distance-preserving rigidity penalty. The voxel-based statistical analysis of the registration error shows that the proposed penalty improved the integrity of the DVFs within the vertebral bodies.« less

Mechanics of deformations in terms of scalar variables

NASA Astrophysics Data System (ADS)

Ryabov, Valeriy A.

2017-05-01

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

The tensor hierarchy algebra

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

Palmkvist, Jakob, E-mail: palmkvist@ihes.fr

We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of ourmore » Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.« less

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.

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

An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment.

PubMed

Gültekin, Osman; Sommer, Gerhard; Holzapfel, Gerhard A

2016-11-01

This study deals with the viscoelastic constitutive modeling and the respective computational analysis of the human passive myocardium. We start by recapitulating the locally orthotropic inner structure of the human myocardial tissue and model the mechanical response through invariants and structure tensors associated with three orthonormal basis vectors. In accordance with recent experimental findings the ventricular myocardial tissue is assumed to be incompressible, thick-walled, orthotropic and viscoelastic. In particular, one spring element coupled with Maxwell elements in parallel endows the model with viscoelastic features such that four dashpots describe the viscous response due to matrix, fiber, sheet and fiber-sheet fragments. In order to alleviate the numerical obstacles, the strictly incompressible model is altered by decomposing the free-energy function into volumetric-isochoric elastic and isochoric-viscoelastic parts along with the multiplicative split of the deformation gradient which enables the three-field mixed finite element method. The crucial aspect of the viscoelastic formulation is linked to the rate equations of the viscous overstresses resulting from a 3-D analogy of a generalized 1-D Maxwell model. We provide algorithmic updates for second Piola-Kirchhoff stress and elasticity tensors. In the sequel, we address some numerical aspects of the constitutive model by applying it to elastic, cyclic and relaxation test data obtained from biaxial extension and triaxial shear tests whereby we assess the fitting capacity of the model. With the tissue parameters identified, we conduct (elastic and viscoelastic) finite element simulations for an ellipsoidal geometry retrieved from a human specimen.

An Exploration into Diffusion Tensor Imaging in the Bovine Ocular Lens

PubMed Central

Vaghefi, Ehsan; Donaldson, Paul J.

2013-01-01

We describe our development of the diffusion tensor imaging modality for the bovine ocular lens. Diffusion gradients were added to a spin-echo pulse sequence and the relevant parameters of the sequence were refined to achieve good diffusion weighting in the lens tissue, which demonstrated heterogeneous regions of diffusive signal attenuation. Decay curves for b-value (loosely summarizes the strength of diffusion weighting) and TE (determines the amount of magnetic resonance imaging-obtained signal) were used to estimate apparent diffusion coefficients (ADC) and T2 in different lens regions. The ADCs varied by over an order of magnitude and revealed diffusive anisotropy in the lens. Up to 30 diffusion gradient directions, and 8 signal acquisition averages, were applied to lenses in culture in order to improve maps of diffusion tensor eigenvalues, equivalent to ADC, across the lens. From these maps, fractional anisotropy maps were calculated and compared to known spatial distributions of anisotropic molecular fluxes in the lens. This comparison suggested new hypotheses and experiments to quantitatively assess models of circulation in the avascular lens. PMID:23459990

On Anholonomic Deformation, Geometry, and Differentiation

DTIC Science & Technology

2013-02-01

αβχ are not necessarily Levi - Civita connection coefficients). The vector cross product × obeys, for two vectors V and W and two covectors α and β , V...three-dimensional space. 2.2.5. Euclidean space. Let GAB(X ) = GA · GB be the metric tensor of the space. The Levi - Civita connection coefficients of GAB...curvature tensor of the Levi - Civita connection vanishes identically: G R A BCD = 2 ( ∂[B G A C]D + G A[B|E|G EC]D ) = 0. (43) In n

Chemical shift and electric field gradient tensors for the amide and carboxyl hydrogens in the model peptide N-acetyl-D,L-valine. Single-crystal deuterium NMR study.

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

Gerald, R. E., II; Bernhard, T.; Haeberlen, U.

1993-01-01

Solid-state NMR spectroscopy is well established as a method for describing molecular structure with resolution on the atomic scale. Many of the NMR observables result from anisotropic interactions between the nuclear spin and its environment. These observables can be described by second-rank tensors. For example, the eigenvalues of the traceless symmetric part of the hydrogen chemical shift (CS) tensor provide information about the strength of inter- or intramolecular hydrogen bonding. On the other hand, the eigenvectors of the deuterium electric field gradient (EFG) tensor give deuteron/proton bond directions with an accuracy rivalled only by neutron diffraction. In this paper themore » authors report structural information of this type for the amide and carboxyl hydrogen sites in a single crystal of the model peptide N-acetyl-D,L-valine (NAV). They use deuterium NMR to infer both the EFG and CS tensors at the amide and carboxyl hydrogen sites in NAV. Advantages of this technique over multiple-pulse proton NMR are that it works in the presence of {sup 14}N spins which are very hard to decouple from protons and that additional information in form of the EFG tensors can be derived. The change in the CS and EFG tensors upon exchange of a deuteron for a proton (the isotope effect) is anticipated to be very small; the effect on the CS tensors is certainly smaller than the experimental errors. NAV has served as a model peptide before in a variety of NMR studies, including those concerned with developing solid-state NMR spectroscopy as a method for determining the structure of proteins. NMR experiments on peptide or protein samples which are oriented in at least one dimension can provide important information about the three-dimensional structure of the peptide or the protein. In order to interpret the NMR data in terms of the structure of the polypeptide, the relationship of the CS and EFG tensors to the local symmetry elements of an amino acide, e.g., the peptide plane, is essential. The main purpose of this work is to investigate this relationship for the amide hydrogen CS tensor. The amide hydrogen CS tensor will also provide orientational information for peptide bonds in proteins complementary to that from the nitrogen CS and EFG tensors and the nitrogen-hydrogen heteronuclear dipole-dipole coupling which have been used previously to determine protein structures by solid-state NMR spectroscopy. This information will be particularly valuable because the amide hydrogen CS tensor is not axially symmetric. In addition, the use of the amide hydrogen CS interaction in high-field solid-state NMR experiments will increase the available resolution among peptide sites.« less

Controls and implications of anisotropy across a strain gradient within granodiorite, Serifos, Western Cyclades

NASA Astrophysics Data System (ADS)

Gaudreau, Élyse; Lagroix, France; Cossette, Élise; Schneider, David; Grasemann, Bernhard

2016-04-01

In order to evaluate the assumption that the crust behaves as an isotropic material in complex structural settings, we integrate crystallographic preferred orientation (CPO) and anisotropy of magnetic susceptibility (AMS) data across a strain gradient within a Miocene granodioritic intrusion on Serifos island, Western Cyclades. One of the consequences of anisotropic crust is the variation in seismic wave velocity with the direction of propagation, which is largely controlled by the CPO of anisotropic minerals such as micas. The magnetic fabric of variably deformed granodiorite is used to characterize weakly defined tectonic fabric and thus complements the CPO data. Granodiorite samples exhibit very low strain to mylonitic fabric across the crustal-scale shear zone, recording progressive deformation through the ductile to brittle transition. CPO data was collected using electron backscatter diffraction and seismic properties were calculated using Voigt-Reuss-Hill averaging of the single minerals' elastic stiffness tensor. Quartz CPO is very strong in the weakly deformed samples recording basal and prism {0001} slip. Furthermore, bulging recrystallization and undulose extinction in quartz as well as feldspar grains that exhibit brittle deformation structures are indicative of 300-400 °C temperatures. The mylonite has a very weak CPO for the quartz phase and exhibits prism {0001} slip. The higher strain samples also reveal dynamic recrystallization and grain size reduction of quartz, plagioclase, potassium feldspar and biotite, which are characteristic of 400-500 °C temperatures. Orthoclase and anorthite possess a weak CPO in all samples. The S-wave anisotropy calculated from the CPO data of the weakly deformed granodiorite is the highest of all samples (max: 8%), and the anisotropy of the mylonite is the weakest of all samples (max: <3%). AMS data yields mainly oblate fabrics and the magnetic foliations and lineations correlate with microscopic and macroscopic structural observations. Most samples exhibit a bulk magnetic susceptibility between 30 and 5000 μSI, suggesting that the magnetic signature is due to both paramagnetic and ferrimagnetic minerals. Hysteresis loops and thermomagnetic curves specify pseudo-single domain magnetite as the main ferrimagnetic mineral. Paramagnetic and ferrimagnetic minerals can exhibit distinct subfabrics, and differentiating between the two using the anisotropy of remanence is essential for semi-quantifying local deformation. The magnetic fabric, coupled with the tectonic fabric inferred from CPO data, gives unique insight into the character of anisotropic minerals in a complex structural setting. For instance, the AMS foliations for samples with ill-defined syntectonic emplacement fabric have a similar orientation to that of fast P-wave propagation, a trait consistent with samples that have a macroscopic foliation. The analysis of anisotropic minerals is therefore fundamental for incorporating seismic anisotropy into large-scale geophysical models.

Deforming regular black holes

NASA Astrophysics Data System (ADS)

Neves, J. C. S.

2017-06-01

In this work, we have deformed regular black holes which possess a general mass term described by a function which generalizes the Bardeen and Hayward mass functions. By using linear constraints in the energy-momentum tensor to generate metrics, the solutions presented in this work are either regular or singular. That is, within this approach, it is possible to generate regular or singular black holes from regular or singular black holes. Moreover, contrary to the Bardeen and Hayward regular solutions, the deformed regular black holes may violate the weak energy condition despite the presence of the spherical symmetry. Some comments on accretion of deformed black holes in cosmological scenarios are made.

Composite Beam Theory with Material Nonlinearities and Progressive Damage

NASA Astrophysics Data System (ADS)

Jiang, Fang

Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping functions, and the 3D spatial gradients of these warping functions. Asymptotic analysis of the extended Hamiltonian's principle suggests dropping the terms of axial gradients of the warping functions. As a result, the solid mechanics problem resolved into a 3D continuum is dimensionally reduced to a problem of solving the warping functions on a 2D cross-sectional field by minimizing the information loss. The present theory is implemented using the finite element method (FEM) in Variational Asymptotic Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model in the form of the Euler-Bernoulli beam theory. The deformation gradient tensor is directly used to enable the capability of dealing with finite deformation, various strain definitions, and several types of material constitutive laws regarding the nonlinear elasticity and progressive damage. Analytical and numerical examples are given for various problems including the trapeze effect, Poynting effect, Brazier effect, extension-bending coupling effect, and free edge damage. By comparison with the predictions from 3D finite element analyses (FEA), 2D FEA based on plane stress assumptions, and experimental data, the structural and material responses are proven to be rigorously captured by the present theory and the computational cost is significantly reduced. Due to the semi-analytical feature of the code developed, the unrealistic numerical issues widely seen in the conventional FEA with strain softening material behaviors are prevented by VABS. In light of these intrinsic features, the nonlinear elastic and inelastic 3D material models can be economically calibrated by data-matching the VABS predictions directly with the experimental measurements from slender coupons. Furthermore, the global behavior of slender composite structures in meters can also be effectively characterized by VABS without unnecessary loss of important information of its local laminae in micrometers.

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.

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.

Evolution of axis ratios from phase space dynamics of triaxial collapse

NASA Astrophysics Data System (ADS)

Nadkarni-Ghosh, Sharvari; Arya, Bhaskar

2018-04-01

We investigate the evolution of axis ratios of triaxial haloes using the phase space description of triaxial collapse. In this formulation, the evolution of the triaxial ellipsoid is described in terms of the dynamics of eigenvalues of three important tensors: the Hessian of the gravitational potential, the tensor of velocity derivatives, and the deformation tensor. The eigenvalues of the deformation tensor are directly related to the parameters that describe triaxiality, namely, the minor-to-major and intermediate-to-major axes ratios (s and q) and the triaxiality parameter T. Using the phase space equations, we evolve the eigenvalues and examine the evolution of the probability distribution function (PDF) of the axes ratios as a function of mass scale and redshift for Gaussian initial conditions. We find that the ellipticity and prolateness increase with decreasing mass scale and decreasing redshift. These trends agree with previous analytic studies but differ from numerical simulations. However, the PDF of the scaled parameter {\\tilde{q}} = (q-s)/(1-s) follows a universal distribution over two decades in mass range and redshifts which is in qualitative agreement with the universality for conditional PDF reported in simulations. We further show using the phase space dynamics that, in fact, {\\tilde{q}} is a phase space invariant and is conserved individually for each halo. These results demonstrate that the phase space analysis is a useful tool that provides a different perspective on the evolution of perturbations and can be applied to more sophisticated models in the future.

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.

Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings

NASA Astrophysics Data System (ADS)

Ganor, Ori J.

2018-02-01

"Curvepole (2,0)-theory" is a deformation of the (2,0)-theory with nonlocal interactions. A curvepole is defined as a two-dimensional generalization of a dipole. It is an object of fixed two-dimensional shape of which the boundary is a charged curve that interacts with a 2-form gauge field. Curvepole theory was previously only defined indirectly via M-theory. Here, we propose a supersymmetric Lagrangian, constructed explicitly up to quartic terms, for an "Abelian" curvepole theory, which is an interacting deformation of the free (2,0) tensor multiplet. This theory contains fields of which the quanta are curvepoles (i.e., fixed-shape strings). Supersymmetry is preserved (at least up to quartic terms) if the shape of the curvepoles is (two-dimensional) planar. This nonlocal six-dimensional quantum field theory may also serve as a UV completion for certain (local) five-dimensional gauge theories.

Moment-tensor inversion for offshore earthquakes east of Taiwan and their implications to regional collision

NASA Astrophysics Data System (ADS)

Kao, Honn; Jian, Pei-Ru; Ma, Kuo-Fong; Huang, Bor-Shouh; Liu, Chun-Chi

Reliable determination of source parameters for offshore earthquakes east of Taiwan with mb<5.5 was a difficult task because of the poor azimuthal coverage by local network and the lack of signals at teleseismic distances. We take advantage of the recently established “Broadband Array in Taiwan for Seismology” (BATS) to invert seismic moment tensors for 7 such events occurred in 1996. To cope with different patterns of background noise and unknown structural details, we utilize variable frequency bands in the inversion and adapt a two-step procedure to select best velocity models for individual epicenter-station paths. Our results are consistent with the overall patterns of regional collision and indicate that the resulting compressive stress has caused significant intraplate deformation within the Philippine Sea plate. Simulation of the region's geological evolution and orogenic processes should take this factor into account and allow the Philippine Sea plate to deform internally.

Segmentation of the pectoral muscle in breast MR images using structure tensor and deformable model

NASA Astrophysics Data System (ADS)

Lee, Myungeun; Kim, Jong Hyo

2012-02-01

Recently, breast MR images have been used in wider clinical area including diagnosis, treatment planning, and treatment response evaluation, which requests quantitative analysis and breast tissue segmentation. Although several methods have been proposed for segmenting MR images, segmenting out breast tissues robustly from surrounding structures in a wide range of anatomical diversity still remains challenging. Therefore, in this paper, we propose a practical and general-purpose approach for segmenting the pectoral muscle boundary based on the structure tensor and deformable model. The segmentation work flow comprises four key steps: preprocessing, detection of the region of interest (ROI) within the breast region, segmenting the pectoral muscle and finally extracting and refining the pectoral muscle boundary. From experimental results we show that the proposed method can segment the pectoral muscle robustly in diverse patient cases. In addition, the proposed method will allow the application of the quantification research for various breast images.

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.

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.

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

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

Polychromatic microdiffraction characterization of defect gradients in severely deformed materials.

PubMed

Barabash, Rozaliya I; Ice, Gene E; Liu, Wenjun; Barabash, Oleg M

2009-01-01

This paper analyzes local lattice rotations introduced in severely deformed polycrystalline titanium by friction stir welding. Nondestructive three-dimensional (3D) spatially resolved polychromatic X-ray microdiffraction, is used to resolve the local crystal structure of the restructured surface from neighboring local structures in the sample material. The measurements reveal strong gradients of strain and geometrically necessary dislocations near the surface and illustrate the potential of polychromatic microdiffraction for the study of deformation in complex materials systems.

Effects of torsional deformation on the microstructures and mechanical properties of a CoCrFeNiMo0.15 high-entropy alloy

NASA Astrophysics Data System (ADS)

Wu, Wenqian; Guo, Lin; Liu, Bin; Ni, Song; Liu, Yong; Song, Min

2017-12-01

The effects of torsional deformation on the microstructures and mechanical properties of a CoCrFeNiMo0.15 high-entropy alloy have been investigated. The torsional deformation generates a gradient microstructure distribution due to the gradient torsional strain. Both dislocation activity and deformation twinning dominated the torsional deformation process. With increasing the torsional equivalent strain, the microstructural evolution can be described as follows: (1) formation of pile-up dislocations parallel to the trace of {1 1 1}-type slip planes; (2) formation of Taylor lattices; (3) formation of highly dense dislocation walls; (3) formation of microbands and deformation twins. The extremely high deformation strain (strained to fracture) results in the activation of wavy slip. The tensile strength is very sensitive to the torsional deformation, and increases significantly with increasing the torsional angle.

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.

Segmentation of DTI based on tensorial morphological gradient

NASA Astrophysics Data System (ADS)

Rittner, Leticia; de Alencar Lotufo, Roberto

2009-02-01

This paper presents a segmentation technique for diffusion tensor imaging (DTI). This technique is based on a tensorial morphological gradient (TMG), defined as the maximum dissimilarity over the neighborhood. Once this gradient is computed, the tensorial segmentation problem becomes an scalar one, which can be solved by conventional techniques, such as watershed transform and thresholding. Similarity functions, namely the dot product, the tensorial dot product, the J-divergence and the Frobenius norm, were compared, in order to understand their differences regarding the measurement of tensor dissimilarities. The study showed that the dot product and the tensorial dot product turned out to be inappropriate for computation of the TMG, while the Frobenius norm and the J-divergence were both capable of measuring tensor dissimilarities, despite the distortion of Frobenius norm, since it is not an affine invariant measure. In order to validate the TMG as a solution for DTI segmentation, its computation was performed using distinct similarity measures and structuring elements. TMG results were also compared to fractional anisotropy. Finally, synthetic and real DTI were used in the method validation. Experiments showed that the TMG enables the segmentation of DTI by watershed transform or by a simple choice of a threshold. The strength of the proposed segmentation method is its simplicity and robustness, consequences of TMG computation. It enables the use, not only of well-known algorithms and tools from the mathematical morphology, but also of any other segmentation method to segment DTI, since TMG computation transforms tensorial images in scalar ones.

A nonlocal strain gradient model for dynamic deformation of orthotropic viscoelastic graphene sheets under time harmonic thermal load

NASA Astrophysics Data System (ADS)

Radwan, Ahmed F.; Sobhy, Mohammed

2018-06-01

This work presents a nonlocal strain gradient theory for the dynamic deformation response of a single-layered graphene sheet (SLGS) on a viscoelastic foundation and subjected to a time harmonic thermal load for various boundary conditions. Material of graphene sheets is presumed to be orthotropic and viscoelastic. The viscoelastic foundation is modeled as Kelvin-Voigt's pattern. Based on the two-unknown plate theory, the motion equations are obtained from the dynamic version of the virtual work principle. The nonlocal strain gradient theory is established from Eringen nonlocal and strain gradient theories, therefore, it contains two material scale parameters, which are nonlocal parameter and gradient coefficient. These scale parameters have two different effects on the graphene sheets. The obtained deflection is compared with that predicted in the literature. Additional numerical examples are introduced to illustrate the influences of the two length scale coefficients and other parameters on the dynamic deformation of the viscoelastic graphene sheets.

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

Diffusion in shear flow

NASA Astrophysics Data System (ADS)

Dufty, J. W.

1984-09-01

Diffusion of a tagged particle in a fluid with uniform shear flow is described. The continuity equation for the probability density describing the position of the tagged particle is considered. The diffusion tensor is identified by expanding the irreversible part of the probability current to first order in the gradient of the probability density, but with no restriction on the shear rate. The tensor is expressed as the time integral of a nonequilibrium autocorrelation function for the velocity of the tagged particle in its local fluid rest frame, generalizing the Green-Kubo expression to the nonequilibrium state. The tensor is evaluated from results obtained previously for the velocity autocorrelation function that are exact for Maxwell molecules in the Boltzmann limit. The effects of viscous heating are included and the dependence on frequency and shear rate is displayed explicitly. The mode-coupling contributions to the frequency and shear-rate dependent diffusion tensor are calculated.

A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

NASA Astrophysics Data System (ADS)

Lagos, Macarena; Bellini, Emilio; Noller, Johannes; Ferreira, Pedro G.; Baker, Tessa

2018-03-01

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.

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

NASA Astrophysics Data System (ADS)

Vasquez, B. J.; Markovskii, S.

2011-12-01

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

Simulation of Blast Loading on an Ultrastructurally-based Computational Model of the Ocular Lens

DTIC Science & Technology

2013-10-01

gradient components in the axial ( F22 ) and radial (F11) directions. One can observe the very large deformation (approaching 800%) and 5 Figure 5...and (bottom left) show deformation gradient in axial ( F22 ) and radial (F11) directions. (bottom right) normalized force versus displacement curve for

Slip-rate increase at Parkfield in 1993 detected by high-precision EDM and borehole tensor strainmeters

USGS Publications Warehouse

Langbein, J.; Gwyther, R.L.; Hart, R.H.G.; Gladwin, M.T.

1999-01-01

On two of the instrument networks at Parkfield, California, the two-color Electronic Distance Meter (EDM) network and Borehole Tensor Strainmeter (BTSM) network, we have detected a rate change starting in 1993 that has persisted at least 5 years. These and other instruments capable of measuring crustal deformation were installed at Parkfield in anticipation of a moderate, M6, earthquake on the San Andreas fault. Many of these instruments have been in operation since the mid 1980s and have established an excellent baseline to judge changes in rate of deformation and the coherence of such changes between instruments. The onset of the observed rate change corresponds in time to two other changes at Parkfield. From late 1992 through late 1994, the Parkfield region had an increase in number of M4 to M5 earthquakes relative to the preceding 6 years. The deformation-rate change also coincides with the end of a 7-year period of sub-normal rainfall. Both the spatial coherence of the rate change and hydrological modeling suggest a tectonic explanation for the rate change. From these observations, we infer that the rate of slip increased over the period 1993-1998.On two of the instrument networks at Parkfield, California, the two-color Electronic Distance Meter (EDM) network and Borehole Tensor Strainmeter (BTSM) network, we have detected a rate change starting in 1993 that has persisted at least 5 years. These and other instruments capable of measuring crustal deformation were installed at Parkfield in anticipation of a moderate, M6, earthquake on the San Andreas fault. Many of these instruments have been in operation since the mid 1980s and have established an excellent baseline to judge changes in rate of deformation and the coherence of such changes between instruments. The onset of the observed rate change corresponds in time to two other changes at Parkfield. From late 1992 through late 1994, the Parkfield region had an increase in number of M4 to M5 earthquakes relative to the preceding 6 years. The deformation-rate change also coincides with the end of a 7-year period of sub-normal rainfall. Both the spatial coherence of the rate change and hydrological modeling suggest a tectonic explanation for the rate change. From these observations, we infer that the rate of slip increased over the period 1993-1998.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Joint eigenvector estimation from mutually anisotropic tensors improves susceptibility tensor imaging of the brain, kidney, and heart.

PubMed

Dibb, Russell; Liu, Chunlei

2017-06-01

To develop a susceptibility-based MRI technique for probing microstructure and fiber architecture of magnetically anisotropic tissues-such as central nervous system white matter, renal tubules, and myocardial fibers-in three dimensions using susceptibility tensor imaging (STI) tools. STI can probe tissue microstructure, but is limited by reconstruction artifacts because of absent phase information outside the tissue and noise. STI accuracy may be improved by estimating a joint eigenvector from mutually anisotropic susceptibility and relaxation tensors. Gradient-recalled echo image data were simulated using a numerical phantom and acquired from the ex vivo mouse brain, kidney, and heart. Susceptibility tensor data were reconstructed using STI, regularized STI, and the proposed algorithm of mutually anisotropic and joint eigenvector STI (MAJESTI). Fiber map and tractography results from each technique were compared with diffusion tensor data. MAJESTI reduced the estimated susceptibility tensor orientation error by 30% in the phantom, 36% in brain white matter, 40% in the inner medulla of the kidney, and 45% in myocardium. This improved the continuity and consistency of susceptibility-based fiber tractography in each tissue. MAJESTI estimation of the susceptibility tensors yields lower orientation errors for susceptibility-based fiber mapping and tractography in the intact brain, kidney, and heart. Magn Reson Med 77:2331-2346, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

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

NASA Astrophysics Data System (ADS)

Xia, K.; Wang, J.

2001-10-01

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

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.

Dependence of nuclear quadrupole resonance transitions on the electric field gradient asymmetry parameter for nuclides with half-integer spins

DOE PAGES

Cho, Herman

2016-02-28

Allowed transition energies and eigenstate expansions have been calculated and tabulated in numerical form as functions of the electric field gradient asymmetry parameter for the zero field Hamiltonian of quadrupolar nuclides with I = 3/2,5/2,7/2, and 9/2. These results are essential to interpret nuclear quadrupole resonance (NQR) spectra and extract accurate values of the electric field gradient tensors. Furthermore, applications of NQR methods to studies of electronic structure in heavy element systems are proposed.

Strain Gradient Solution for the Eshelby-Type Polyhedral Inclusion Problem

DTIC Science & Technology

2012-01-01

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

Secondary isocurvature perturbations from acoustic reheating

NASA Astrophysics Data System (ADS)

Ota, Atsuhisa; Yamaguchi, Masahide

2018-06-01

The superhorizon (iso)curvature perturbations are conserved if the following conditions are satisfied: (i) (each) non adiabatic pressure perturbation is zero, (ii) the gradient terms are ignored, that is, at the leading order of the gradient expansion (iii) (each) total energy momentum tensor is conserved. We consider the case with the violation of the last two requirements and discuss the generation of secondary isocurvature perturbations during the late time universe. Second order gradient terms are not necessarily ignored even if we are interested in the long wavelength modes because of the convolutions which may pick products of short wavelength perturbations up. We then introduce second order conserved quantities on superhorizon scales under the conditions (i) and (iii) even in the presence of the gradient terms by employing the full second order cosmological perturbation theory. We also discuss the violation of the condition (iii), that is, the energy momentum tensor is conserved for the total system but not for each component fluid. As an example, we explicitly evaluate second order heat conduction between baryons and photons due to the weak Compton scattering, which dominates during the period just before recombination. We show that such secondary effects can be recast into the isocurvature perturbations on superhorizon scales if the local type primordial non Gaussianity exists a priori.

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

Airborne full tensor magnetic gradiometry surveys in the Thuringian basin, Germany

NASA Astrophysics Data System (ADS)

Queitsch, M.; Schiffler, M.; Goepel, A.; Stolz, R.; Meyer, M.; Meyer, H.; Kukowski, N.

2013-12-01

In this contribution we introduce a newly developed fully operational full tensor magnetic gradiometer (FTMG) instrument based on Superconducting Quantum Interference Devices (SQUIDs) and show example data acquired in 2012 within the framework of the INFLUINS (Integrated Fluid Dynamics in Sedimentary basins) project. This multidisciplinary project aims for a better understanding of movements and interaction between shallow and deep fluids in the Thuringian Basin in the center of Germany. In contrast to mapping total magnetic field intensity (TMI) in conventional airborne magnetic surveys for industrial exploration of mineral deposits and sedimentary basins, our instrument measures all components of the magnetic field gradient tensor using highly sensitive SQUID gradiometers. This significantly constrains the solutions of the inverse problem. Furthermore, information on the ratio between induced and remanent magnetization is obtained. Special care has been taken to reduce motion noise while acquiring data in airborne operation. Therefore, the sensors are mounted in a nonmagnetic and aerodynamically shaped bird made of fiberglas with a high drag tail which stabilizes the bird even at low velocities. The system is towed by a helicopter and kept at 30m above ground during data acquisition. Additionally, the system in the bird incorporates an inertial unit for geo-referencing and enhanced motion noise compensation, a radar altimeter for topographic correction and a GPS system for high precision positioning. Advanced data processing techniques using reference magnetometer and inertial unit data result in a very low system noise of less than 60 pT/m peak to peak in airborne operation. To show the performance of the system we present example results from survey areas within the Thuringian basin and along its bordering highlands. The mapped gradient tensor components show a high correlation to existing geologic maps. Furthermore, the measured gradient components indicate that some of the observed magnetic anomalies have a strong remanent magnetization. One example of interpretation of the acquired data of a magnetic anomaly related to a larger gabbro formation is presented.

The spectral expansion of the elasticity random field

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

Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

2014-12-10

We consider a deformable body that occupies a region D in the plane. In our model, the body’s elasticity tensor H(x) is the restriction to D of a second-order mean-square continuous random field. Under translation, the expected value and the correlation tensor of the field H(x) do not change. Under action of an arbitrary element k of the orthogonal group O(2), they transform according to the reducible orthogonal representation k ⟼ S{sup 2}(S{sup 2}(k)) of the above group. We find the spectral expansion of the correlation tensor R(x) of the elasticity field as well as the expansion of the fieldmore » itself in terms of stochastic integrals with respect to a family of orthogonal scattered random measures.« less

Full Tensor Diffusion Imaging Is Not Required To Assess the White-Matter Integrity in Mouse Contusion Spinal Cord Injury

PubMed Central

Tu, Tsang-Wei; Kim, Joong H.; Wang, Jian

2010-01-01

Abstract In vivo diffusion tensor imaging (DTI) derived indices have been demonstrated to quantify accurately white-matter injury after contusion spinal cord injury (SCI) in rodents. In general, a full diffusion tensor analysis requires the acquisition of diffusion-weighted images (DWI) along at least six independent directions of diffusion-sensitizing gradients. Thus, DTI measurements of the rodent central nervous system are time consuming. In this study, diffusion indices derived using the two-direction DWI (parallel and perpendicular to axonal tracts) were compared with those obtained using six-direction DTI in a mouse model of SCI. It was hypothesized that the mouse spinal cord ventral-lateral white-matter (VLWM) tracts, T8–T10 in this study, aligned with the main magnet axis (z) allowing the apparent diffusion coefficient parallel and perpendicular to the axis of the spine to be derived with diffusion-weighting gradients in the z and y axes of the magnet coordinate respectively. Compared with six-direction full tensor DTI, two-direction DWI provided comparable diffusion indices in mouse spinal cords. The measured extent of spared white matter after injury, estimated by anisotropy indices, using both six-direction DTI and two-direction DWI were in close agreement and correlated well with histological staining and behavioral assessment. The results suggest that the two-direction DWI derived indices may be used, with significantly reduced imaging time, to estimate accurately spared white matter in mouse SCI. PMID:19715399

Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

PubMed Central

Li, Zhining; Zhang, Yingtang; Yin, Gang

2018-01-01

The measurement error of the differencing (i.e., using two homogenous field sensors at a known baseline distance) magnetic gradient tensor system includes the biases, scale factors, nonorthogonality of the single magnetic sensor, and the misalignment error between the sensor arrays, all of which can severely affect the measurement accuracy. In this paper, we propose a low-cost artificial vector calibration method for the tensor system. Firstly, the error parameter linear equations are constructed based on the single-sensor’s system error model to obtain the artificial ideal vector output of the platform, with the total magnetic intensity (TMI) scalar as a reference by two nonlinear conversions, without any mathematical simplification. Secondly, the Levenberg–Marquardt algorithm is used to compute the integrated model of the 12 error parameters by nonlinear least-squares fitting method with the artificial vector output as a reference, and a total of 48 parameters of the system is estimated simultaneously. The calibrated system outputs along the reference platform-orthogonal coordinate system. The analysis results show that the artificial vector calibrated output can track the orientation fluctuations of TMI accurately, effectively avoiding the “overcalibration” problem. The accuracy of the error parameters’ estimation in the simulation is close to 100%. The experimental root-mean-square error (RMSE) of the TMI and tensor components is less than 3 nT and 20 nT/m, respectively, and the estimation of the parameters is highly robust. PMID:29373544

Superconducting tensor gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

The employment of superconductivity and other material properties at cryogenic temperatures to fabricate sensitive, low-drift, gravity gradiometer is described. The device yields a reduction of noise of four orders of magnitude over room temperature gradiometers, and direct summation and subtraction of signals from accelerometers in varying orientations are possible with superconducting circuitry. Additional circuits permit determination of the linear and angular acceleration vectors independent of the measurement of the gravity gradient tensor. A dewar flask capable of maintaining helium in a liquid state for a year's duration is under development by NASA, and a superconducting tensor gravity gradiometer for the NASA Geodynamics Program is intended for a LEO polar trajectory to measure the harmonic expansion coefficients of the earth's gravity field up to order 300.

Brain tissue segmentation based on DTI data

PubMed Central

Liu, Tianming; Li, Hai; Wong, Kelvin; Tarokh, Ashley; Guo, Lei; Wong, Stephen T.C.

2008-01-01

We present a method for automated brain tissue segmentation based on the multi-channel fusion of diffusion tensor imaging (DTI) data. The method is motivated by the evidence that independent tissue segmentation based on DTI parametric images provides complementary information of tissue contrast to the tissue segmentation based on structural MRI data. This has important applications in defining accurate tissue maps when fusing structural data with diffusion data. In the absence of structural data, tissue segmentation based on DTI data provides an alternative means to obtain brain tissue segmentation. Our approach to the tissue segmentation based on DTI data is to classify the brain into two compartments by utilizing the tissue contrast existing in a single channel. Specifically, because the apparent diffusion coefficient (ADC) values in the cerebrospinal fluid (CSF) are more than twice that of gray matter (GM) and white matter (WM), we use ADC images to distinguish CSF and non-CSF tissues. Additionally, fractional anisotropy (FA) images are used to separate WM from non-WM tissues, as highly directional white matter structures have much larger fractional anisotropy values. Moreover, other channels to separate tissue are explored, such as eigenvalues of the tensor, relative anisotropy (RA), and volume ratio (VR). We developed an approach based on the Simultaneous Truth and Performance Level Estimation (STAPLE) algorithm that combines these two-class maps to obtain a complete tissue segmentation map of CSF, GM, and WM. Evaluations are provided to demonstrate the performance of our approach. Experimental results of applying this approach to brain tissue segmentation and deformable registration of DTI data and spoiled gradient-echo (SPGR) data are also provided. PMID:17804258

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

A Few Integrable Dynamical Systems, Recurrence Operators, Expanding Integrable Models and Hamiltonian Structures by the r-Matrix Method

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Muhammad, Iqbal; Yue, Chao

2017-10-01

We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov-Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the (2+1)-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of (2+1)-dimensional expanding dynamical model of the (2+1)-dimensional dynamical system is generated as well. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

Constrained H1-regularization schemes for diffeomorphic image registration

PubMed Central

Mang, Andreas; Biros, George

2017-01-01

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss–)Newton–Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient. PMID:29075361

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Quantitative analysis of hypertrophic myocardium using diffusion tensor magnetic resonance imaging

PubMed Central

Tran, Nicholas; Giannakidis, Archontis; Gullberg, Grant T.; Seo, Youngho

2016-01-01

Abstract. Systemic hypertension is a causative factor in left ventricular hypertrophy (LVH). This study is motivated by the potential to reverse or manage the dysfunction associated with structural remodeling of the myocardium in this pathology. Using diffusion tensor magnetic resonance imaging, we present an analysis of myocardial fiber and laminar sheet orientation in ex vivo hypertrophic (6 SHR) and normal (5 WKY) rat hearts using the covariance of the diffusion tensor. First, an atlas of normal cardiac microstructure was formed using the WKY b0 images. Then, the SHR and WKY b0 hearts were registered to the atlas. The acquired deformation fields were applied to the SHR and WKY heart tensor fields followed by the preservation of principal direction (PPD) reorientation strategy. A mean tensor field was then formed from the registered WKY tensor images. Calculating the covariance of the registered tensor images about this mean for each heart, the hypertrophic myocardium exhibited significantly increased myocardial fiber derangement (p=0.017) with a mean dispersion of 38.7 deg, and an increased dispersion of the laminar sheet normal (p=0.030) of 54.8 deg compared with 34.8 deg and 51.8 deg, respectively, in the normal hearts. Results demonstrate significantly altered myocardial fiber and laminar sheet structure in rats with hypertensive LVH. PMID:27872872

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

High Efficiency, Low Distortion 3D Diffusion Tensor Imaging with Variable Density Spiral Fast Spin Echoes (3D DW VDS RARE)

PubMed Central

Frank, Lawrence R.; Jung, Youngkyoo; Inati, Souheil; Tyszka, J. Michael; Wong, Eric C.

2009-01-01

We present an acquisition and reconstruction method designed to acquire high resolution 3D fast spin echo diffusion tensor images while mitigating the major sources of artifacts in DTI - field distortions, eddy currents and motion. The resulting images, being 3D, are of high SNR, and being fast spin echoes, exhibit greatly reduced field distortions. This sequence utilizes variable density spiral acquisition gradients, which allow for the implementation of a self-navigation scheme by which both eddy current and motion artifacts are removed. The result is that high resolution 3D DTI images are produced without the need for eddy current compensating gradients or B0 field correction. In addition, a novel method for fast and accurate reconstruction of the non-Cartesian data is employed. Results are demonstrated in the brains of normal human volunteers. PMID:19778618

Laser pumping Cs atom magnetometer of theory research based on gradient tensor measuring

NASA Astrophysics Data System (ADS)

Yang, Zhang; Chong, Kang; Wang, Qingtao; Lei, Cheng; Zheng, Caiping

2011-02-01

At present, due to space exploration, military technology, geological exploration, magnetic navigation, medical diagnosis and biological magnetic fields study of the needs of research and development, the magnetometer is given strong driving force. In this paper, it will discuss the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling, the hyperfine structure has been further split into Zeeman sublevels for the effects of magnetic field. To use laser pump and RF magnetic field make electrons transition in the hyperfine structure to produce the results of magneto-optical double resonance, and ultimately through the resonant frequency will be able to achieve accurate value of the external magnetic field. On this basis, we further have a discussion about magnetic gradient tensor measuring method. To a large extent, it increases the magnetic field measurement of information.

Electric field gradient in FeTiO3 by nuclear magnetic resonance and ab initio calculations.

PubMed

Procházka, V; Stěpánková, H; Chlan, V; Tuček, J; Cuda, J; Kouřil, K; Filip, J; Zbořil, R

2011-05-25

Temperature dependence of nuclear magnetic resonance (NMR) spectra of (47)Ti and (49)Ti in polycrystalline ilmenite FeTiO(3) was measured in the range from 5 to 300 K under an external magnetic field of 9.401 T. NMR spectra collected between 300 and 77 K exhibit a resolved quadrupole splitting. The electric field gradient (EFG) tensor was evaluated for Ti nuclei and the ratio of (47)Ti and (49)Ti nuclear quadrupole moments was refined during the fitting procedure. Below 77 K, the fine structure of quadrupole splitting disappears due to the enormous increase of anisotropy. As a counterpart, ab initio calculations were performed using full potential augmented plane waves + local orbitals. The calculated EFG tensors for Ti and Fe were compared to the experimental ones evaluated from NMR and the Mössbauer spectroscopy experiments.

On curve and surface stretching in turbulent flow

NASA Technical Reports Server (NTRS)

Etemadi, Nassrollah

1989-01-01

Cocke (1969) proved that in incompressible, isotropic turbulence the average material line (material surface) elements increase in comparison with their initial values. Good estimates of how much they increase in terms of the eigenvalues of the Green deformation tensor were rigorously obtained.

Deformation compatibility in a single crystalline Ni superalloy

PubMed Central

Zhang, Tiantian; Dunne, Fionn P. E.

2016-01-01

Deformation in materials is often complex and requires rigorous understanding to predict engineering component lifetime. Experimental understanding of deformation requires utilization of advanced characterization techniques, such as high spatial resolution digital image correlation (HR-DIC) and high angular resolution electron backscatter diffraction (HR-EBSD), combined with clear interpretation of their results to understand how a material has deformed. In this study, we use HR-DIC and HR-EBSD to explore the mechanical behaviour of a single-crystal nickel alloy and to highlight opportunities to understand the complete deformations state in materials. Coupling of HR-DIC and HR-EBSD enables us to precisely focus on the extent which we can access the deformation gradient, F, in its entirety and uncouple contributions from elastic deformation gradients, slip and rigid body rotations. Our results show a clear demonstration of the capabilities of these techniques, found within our experimental toolbox, to underpin fundamental mechanistic studies of deformation in polycrystalline materials and the role of microstructure. PMID:26997901

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.

Analysis and Modeling of Process of Residual Deformations Accumulation in Soils and Granular Materials

NASA Astrophysics Data System (ADS)

Aleksandrov, A. S.; Dolgih, G. V.; Kalinin, A. L.

2017-11-01

It is established that under the influence of repeated loads the process of plastic deformation in soils and discrete materials is hereditary. To perform the mathematical modeling of plastic deformation, the authors applied the integral equation by solution of which they manage to obtain the power and logarithmic dependencies connecting plastic deformation with the number of repeated loads, the parameters of the material and components of the stress tensor in the principal axes. It is shown that these dependences generalize a number of models proposed earlier in Russia and abroad. Based on the analysis of the experimental data obtained during material testing in the dynamic devices of triaxial compression at different values of the stress deviator, the coefficients in the proposed models of deformation are determined. The authors determined the application domain for logarithmic and degree dependences.

3D modeling of unconstrained HPT process: role of strain gradient on high deformed microstructure formation

NASA Astrophysics Data System (ADS)

Ben Kaabar, A.; Aoufi, A.; Descartes, S.; Desrayaud, C.

2017-05-01

During tribological contact’s life, different deformation paths lead to the formation of high deformed microstructure, in the near-surface layers of the bodies. The mechanical conditions (high pressure, shear) occurring under contact, are reproduced through unconstrained High Pressure Torsion configuration. A 3D finite element model of this HPT test is developed to study the local deformation history leading to high deformed microstructure with nominal pressure and friction coefficient. For the present numerical study the friction coefficient at the interface sample/anvils is kept constant at 0.3; the material used is high purity iron. The strain distribution in the sample bulk, as well as the main components of the strain gradients according to the spatial coordinates are investigated, with rotation angle of the anvil.

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.

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.

Gradient Plasticity Model and its Implementation into MARMOT

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

Barker, Erin I.; Li, Dongsheng; Zbib, Hussein M.

2013-08-01

The influence of strain gradient on deformation behavior of nuclear structural materials, such as boby centered cubic (bcc) iron alloys has been investigated. We have developed and implemented a dislocation based strain gradient crystal plasticity material model. A mesoscale crystal plasticity model for inelastic deformation of metallic material, bcc steel, has been developed and implemented numerically. Continuum Dislocation Dynamics (CDD) with a novel constitutive law based on dislocation density evolution mechanisms was developed to investigate the deformation behaviors of single crystals, as well as polycrystalline materials by coupling CDD and crystal plasticity (CP). The dislocation density evolution law in thismore » model is mechanism-based, with parameters measured from experiments or simulated with lower-length scale models, not an empirical law with parameters back-fitted from the flow curves.« less

An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.

Plastic deformation treated as material flow through adjustable crystal lattice

NASA Astrophysics Data System (ADS)

Minakowski, P.; Hron, J.; Kratochvíl, J.; Kružík, M.; Málek, J.

2014-08-01

Looking at severe plastic deformation experiments, it seems that crystalline materials at yield behave as a special kind of anisotropic, highly viscous fluids flowing through an adjustable crystal lattice space. High viscosity provides a possibility to describe the flow as a quasi-static process, where inertial and other body forces can be neglected. The flow through the lattice space is restricted to preferred crystallographic planes and directions causing anisotropy. In the deformation process the lattice is strained and rotated. The proposed model is based on the rate form of the decomposition rule: the velocity gradient consists of the lattice velocity gradient and the sum of the velocity gradients corresponding to the slip rates of individual slip systems. The proposed crystal plasticity model allowing for large deformations is treated as the flow-adjusted boundary value problem. As a test example we analyze a plastic flow of an single crystal compressed in a channel die. We propose three step algorithm of finite element discretization for a numerical solution in the Arbitrary Lagrangian Eulerian (ALE) configuration.

BOOK REVIEW: Introduction to Computational Plasticity

NASA Astrophysics Data System (ADS)

Hartley, P.

2006-04-01

The use of computational modelling in all areas of science and engineering has in recent years escalated to the point where it underpins much of current research. However, the distinction must be made between computer systems in which no knowledge of the underlying computer technology or computational theory is required and those areas of research where the mastery of computational techniques is of great value, almost essential, for final year undergraduates or masters students planning to pursue a career in research. Such a field of research in the latter category is continuum mechanics, and in particular non-linear material behaviour, which is the core topic of this book. The focus of the book on computational plasticity embodies techniques of relevance not only to academic researchers, but also of interest to industrialists engaged in the production of components using bulk or sheet forming processes. Of particular interest is the guidance on how to create modules for use with the commercial system Abaqus for specific types of material behaviour. The book is in two parts, the first of which contains six chapters, starting with microplasticity, but predominantly on continuum plasticity. The first chapter on microplasticty gives a brief description of the grain structure of metals and the existence of slip systems within the grains. This provides an introduction to the concept of incompressibility during plastic deformation, the nature of plastic yield and the importance of the critically resolved shear stress on the slip planes (Schmid's law). Some knowledge of the notation commonly used to describe slip systems is assumed, which will be familiar to students of metallurgy, but anyone with a more general engineering background may need to undertake additional reading to understand the various descriptions. Any lack of knowledge in this area however, is of no disadvantage as it serves only as an introduction and the book moves on quickly to continuum plasticity. Chapter two introduces one of several yield criteria, that normally attributed to von Mises (though historians of mechanics might argue over who was first to develop the theory of yielding associated with strain energy density), and its two or three-dimensional representation as a yield surface. The expansion of the yield surface during plastic deformation, its translation due to kinematic hardening and the Bauschinger effect in reversed loading are described with a direct link to the material stress-strain curve. The assumption, that the increment of strain is normal to the yield surface, the normality principle, is introduced. Uniaxial loading of an elastic-plastic material is used as an example in which to develop expressions to describe increments in stress and strain. The full presentation of numerous expressions, tensors and matrices with a clear explanation of their development, is a recurring, and commendable, feature of the book, which provides an invaluable introduction for those new to the subject. The chapter moves on from time-independent behaviour to introduce viscoplasticity and creep. Chapter three takes the theories of deformation another stage further to consider the problems associated with large deformation in which an important concept is the separation of the phenomenon into material stretch and rotation. The latter is crucial to allow correct measures of strain and stress to be developed in which the effects of rigid body rotation do not contribute to these variables. Hence, the introduction of 'objective' measures for stress and strain. These are described with reference to deformation gradients, which are clearly explained; however, the introduction of displacement gradients passes with little comment, although velocity gradients appear later in the chapter. The interpretation of different strain measures, e.g. Green--Lagrange and Almansi, is covered briefly, followed by a description of the spin tensor and its use in developing the objective Jaumann rate of stress. It is tempting here to suggest that a more complete description should be given together with other measures of strain and stress, of which there are several, but there would be a danger of changing the book from an `introduction' to a more comprehensive text, and examples of such exist already. Chapter four begins the process of developing the plasticity theories into a form suitable for inclusion in the finite-element method. The starting point is Hamilton's principle for equilibrium of a dynamic system. A very brief introduction to the finite-element method is then given, followed by the finite-element equilibrium equations and a description of how they are incorporated into Hamilton's principle. A useful clarification is provided by comparing tensor notation and the form normally used in finite-element expressions, i.e. Voigt notation. The chapter concludes with a brief overview of implicit integration methods, i.e. tangent stiffness, initial tangent stiffness and Newton Raphson. Chapter five deals with the more specialized topic of implicit and explicit integration of von Mises plasticity. One of the techniques described is the radial-return method which ensures that the stresses at the end of an increment of deformation always lie on the expanded yield surface. Although this method guarantees a solution it may not always be the most accurate for large deformation, this is one area where reference to alternative methods would have been a helpful addition. Chapter six continues with further detail of how the plasticity models may be incorporated into finite-element codes, with particular reference to the Abaqus package and the use of user-defined subroutines, introduced via a `UMAT' subroutine. This completes part I of the book. Part II focuses on plasticity models, each chapter dealing with a particular process or material model. For example, chapter seven deals with superplasticity, chapter eight with porous plasticity, chapter nine with creep and chapter ten with cyclic plasticity, creep and TMF. Examples of deep drawing, forming of titanium metal-matrix composites and creep damage are provided, together with further guidelines on the use of Abaqus to model these processes. Overall, the book is organised in a very logical and readable form. The use of simple one-dimensional examples, with full descriptions of tensors and vectors throughout the book, is particularly useful. It provides a good introduction to the topic, covering much of the theory and with applications to give a good grounding that can be taken further with more comprehensive advanced texts. An excellent starting point for anyone involved in research in computational plasticity.

The Weighted Burgers Vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials.

PubMed

Wheeler, J; Mariani, E; Piazolo, S; Prior, D J; Trimby, P; Drury, M R

2009-03-01

The Weighted Burgers Vector (WBV) is defined here as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) x (Burgers vector)]. Here we show that it can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has three advantages over other measures of local lattice distortion: it is a vector and hence carries more information than a scalar quantity, it has an explicit mathematical link to the individual Burgers vectors of dislocations and, since it is derived via tensor calculus, it is not dependent on the map coordinate system. If a sub-grain wall is included in the WBV calculation, the magnitude of the WBV becomes dependent on the step size but its direction still carries information on the Burgers vectors in the wall. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations.

An optimization-based framework for anisotropic simplex mesh adaptation

NASA Astrophysics Data System (ADS)

Yano, Masayuki; Darmofal, David L.

2012-09-01

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a discretization and any element-wise, localizable error estimate, our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom. Utilizing mesh-metric duality, we consider a continuous optimization problem of the Riemannian metric tensor field that provides an anisotropic description of element sizes. First, our method performs a series of local solves to survey the behavior of the local error function. This information is then synthesized using an affine-invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field. Finally, we perform gradient descent in the metric space to drive the mesh toward optimality. The method is first demonstrated to produce optimal anisotropic meshes minimizing the L2 projection error for a pair of canonical problems containing a singularity and a singular perturbation. The effectiveness of the framework is then demonstrated in the context of output-based adaptation for the advection-diffusion equation using a high-order discontinuous Galerkin discretization and the dual-weighted residual (DWR) error estimate. The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.

3-D Deformation analysis via invariant geodetic obsevations.

NASA Astrophysics Data System (ADS)

Ardalan, A.; Esmaeili, R.

2003-04-01

In this paper a new method for 3-D deformation analysis based on invariant observations like distances and spatial angles is presented. Displacement field that is used in the classical deformation analysis is not reliable because the stability of the coordinate systems between successive epochs of observations cannot be guaranteed. On the contrary distances and spatial angles, i.e. measurements that are related to geometry between the constituent points of an object is independent of the definition of coordinate system. In this paper we have devised a new approach for the calculation of elements of the strain tensor directly from the geometrical observations such as angels and distances. This new method besides enjoys 3-D nature and as such guarantees the complete deformation study in 3-D space.

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.

Harnessing Multivariate Statistics for Ellipsoidal Data in Structural Geology

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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.

Unraveling Deformation Mechanisms in Gradient Structured Metals

NASA Astrophysics Data System (ADS)

Moering, Jordan Alexander

Gradient structures have demonstrated high strength and high ductility, introducing new mechanisms to challenge conventional mechanics. This work develops a method for characterizing the shear strain in gradient structured steel and presents evidence of a texture gradient that develops in Surface Mechanical Attrition Treatment (SMAT). Mechanics underlying some theories of the strengthening mechanisms in gradient structured metals are introduced, followed by the fabrication and testing of gradient structured aluminum rod. The round geometry is intrinsically different from its flat counterparts, which leads to a multiaxial stress state evolving in tension. The aluminum exhibits strengthening beyond rule of mixtures, and texture evolution in the post-mortem sample indicates that out of plane stresses operate within the gradient. Finally, another gradient structured aluminum rod is shown to exhibit higher strength and higher elongation to failure in a variety of sample diameters and processing conditions. The GND density and microstructural evolution showed no significant changes during mechanical testing, and high resolution strain mapping was successfully completed within the core of the material. These discoveries and contributions to the field should help continue unraveling the deformation mechanisms of gradient structured metals.

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.

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.

Ostrogradsky in theories with multiple fields

NASA Astrophysics Data System (ADS)

de Rham, Claudia; Matas, Andrew

2016-06-01

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.

Dynamics of a gravity-gradient stabilized flexible spacecraft

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Juang, J. N.

1974-01-01

The dynamics of gravity-gradient stabilized flexible satellite in the neighborhood of a deformed equilibrium configuration are discussed. First the equilibrium configuration was determined by solving a set of nonlinear differential equations. Then stability of motion about the deformed equilibrium was tested by means of the Liapunov direct method. The natural frequencies of oscillation of the complete structure were calculated. The analysis is applicable to the RAE/B satellite.

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.

Real-time positioning technology in horizontal directional drilling based on magnetic gradient tensor measurement

NASA Astrophysics Data System (ADS)

Deng, Guoqing; Yao, Aiguo

2017-04-01

Horizontal directional drilling (HDD) technology has been widely used in Civil Engineering. The dynamic position of the drill bit during construction is one of significant facts determining the accuracy of the trajectory of HDD. A new method now has been proposed to detecting the position of drill bit by measuring the magnetic gradient tensor of the ground solenoid magnetic beacon. Compared with traditional HDD positioning technologies, this new model is much easier to apply with lower request for construction sites and higher positioning efficiency. A direct current (DC) solenoid as a magnetic dipole is placed on ground near the drill bit, and related sensors array which contains four Micro-electromechanical Systems (MEMS ) tri-axial magnetometers, one MEMS tri-axial accelerometer and one MEMS tri-axial gyroscope is set up for measuring the magnetic gradient tensor of the magnetic dipole. The related HDD positioning model has been established and simulation experiments have been carried out to verify the feasibility and reliability of the proposed method. The experiments show that this method has good positioning accuracy in horizontal and vertical direction, and totally avoid the impact of the environmental magnetic field. It can be found that the posture of the magnetic beacon will impact the remote positioning precision within valid positioning range, and the positioning accuracy is higher with longer baseline for limited space in drilling tools. The results prove that the relative error can be limited in 2% by adjusting position of the magnetic beacon, the layers of the enameled coil, the sensitive of magnetometers and the baseline distance. Conclusion can be made that this new method can be applied in HDD positioning with better effect and wider application range than traditional method.

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

PubMed

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

2006-01-26

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

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

Micromechanical analysis of volumetric growth in the context of open systems thermodynamics and configurational mechanics. Application to tumor growth

NASA Astrophysics Data System (ADS)

Ganghoffer, J. F.; Boubaker, M. B.

2017-03-01

We adopt in this paper the physically and micromechanically motivated point of view that growth (resp. resorption) occurs as the expansion (resp. contraction) of initially small tissue elements distributed within a host surrounding matrix, due to the interfacial motion of their boundary. The interface motion is controlled by the availability of nutrients and mechanical driving forces resulting from the internal stresses that built in during the growth. A general extremum principle of the zero potential for open systems witnessing a change of their mass due to the diffusion of nutrients is constructed, considering the framework of open systems thermodynamics. We postulate that the shape of the tissue element evolves in such a way as to minimize the zero potential among all possible admissible shapes of the growing tissue elements. The resulting driving force for the motion of the interface sets a surface growth models at the scale of the growing tissue elements, and is conjugated to a driving force identified as the interfacial jump of the normal component of an energy momentum tensor, in line with Hadamard's structure theorem. The balance laws associated with volumetric growth at the mesoscopic level result as the averaging of surface growth mechanisms occurring at the microscopic scale of the growing tissue elements. The average kinematics has been formulated in terms of the effective growth velocity gradient and elastic rate of deformation tensor, both functions of time. This formalism is exemplified by the simulation of the avascular growth of multicell spheroids in the presence of diffusion of nutrients, showing the respective influence of mechanical and chemical driving forces in relation to generation of internal stresses.

Crista egregia: a geometrical model of the crista ampullaris, a sensory surface that detects head rotations.

PubMed

Marianelli, Prisca; Berthoz, Alain; Bennequin, Daniel

2015-02-01

The crista ampullaris is the epithelium at the end of the semicircular canals in the inner ear of vertebrates, which contains the sensory cells involved in the transduction of the rotational head movements into neuronal activity. The crista surface has the form of a saddle, or a pair of saddles separated by a crux, depending on the species and the canal considered. In birds, it was described as a catenoid by Landolt et al. (J Comp Neurol 159(2):257-287, doi: 10.1002/cne.901590207 , 1972). In the present work, we establish that this particular form results from principles of invariance maximization and energy minimization. The formulation of the invariance principle was inspired by Takumida (Biol Sci Space 15(4):356-358, 2001). More precisely, we suppose that in functional conditions, the equations of linear elasticity are valid, and we assume that in a certain domain of the cupula, in proximity of the crista surface, (1) the stress tensor of the deformed cupula is invariant under the gradient of the pressure, (2) the dissipation of energy is minimum. Then, we deduce that in this domain the crista surface is a minimal surface and that it must be either a planar, or helicoidal Scherk surface, or a piece of catenoid, which is the unique minimal surface of revolution. If we add the hypothesis that the direction of invariance of the stress tensor is unique and that a bilateral symmetry of the crista exists, only the catenoid subsists. This finding has important consequences for further functional modeling of the role of the vestibular system in head motion detection and spatial orientation.

Identification of a constitutive law for trabecular bone samples under remodeling in the framework of irreversible thermodynamics

NASA Astrophysics Data System (ADS)

Louna, Zineeddine; Goda, Ibrahim; Ganghoffer, Jean-François

2018-01-01

We construct in the present paper constitutive models for bone remodeling based on micromechanical analyses at the scale of a representative unit cell (RUC) including a porous trabecular microstructure. The time evolution of the microstructure is simulated as a surface remodeling process by relating the surface growth remodeling velocity to a surface driving force incorporating a (surface) Eshelby tensor. Adopting the framework of irreversible thermodynamics, a 2D constitutive model based on the setting up of the free energy density and a dissipation potential is identified from FE simulations performed over a unit cell representative of the trabecular architecture obtained from real bone microstructures. The static and evolutive effective properties of bone at the scale of the RUC are obtained by combining a methodology for the evaluation of the average kinematic and static variables over a prototype unit cell and numerical simulations with controlled imposed first gradient rates. The formulated effective growth constitutive law at the scale of the homogenized set of trabeculae within the RUC is of viscoplastic type and relates the average growth strain rate to the homogenized stress tensor. The postulated model includes a power law function of an effective stress chosen to depend on the first and second stress invariants. The model coefficients are calibrated from a set of virtual testing performed over the RUC subjected to a sequence of loadings. Numerical simulations show that overall bone growth does not show any growth kinematic hardening. The obtained results quantify the strength and importance of different types of external loads (uniaxial tension, simple shear, and biaxial loading) on the overall remodeling process and the development of elastic deformations within the RUC.

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.

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).

Lattice-Boltzmann-based simulations of diffusiophoresis of colloids and cells

NASA Astrophysics Data System (ADS)

Kreft Pearce, Jennifer; Castigliego, Joshua

Increasing environmental degradation due to plastic pollutants requires innovative solutions that facilitate the extraction of pollutants without harming local biota. We present results from a lattice-Boltzmann-base Brownian Dynamics simulation on diffusiophoresis and the separation of particles within the system. A gradient in viscosity that simulates a concentration gradient in a dissolved polymer allows us to separate various types of particles based on their deformability. As seen in previous experiments, simulated particles that have a higher deformability react differently to the polymer matrix than those with a lower deformability. Therefore, the particles can be separated from each other. The system described above was simulated with various concentration gradients as well as various Soret coefficients in order to optimize the separation of the particles. This simulation, in particular, was intended to model an oceanic system where the particles of interest were motile and nonmotile plankton and microplastics. The separation of plankton from the microplastics was achieved.

Effects of asymmetric rolling process on ridging resistance of ultra-purified 17%Cr ferritic stainless steel

NASA Astrophysics Data System (ADS)

Lu, Cheng-zhuang; Li, Jing-yuan; Fang, Zhi

2018-02-01

In ferritic stainless steels, a significant non-uniform recrystallization orientation and a substantial texture gradient usually occur, which can degrade the ridging resistance of the final sheets. To improve the homogeneity of the recrystallization orientation and reduce the texture gradient in ultra-purified 17%Cr ferritic stainless steel, in this work, we performed conventional and asymmetric rolling processes and conducted macro and micro-texture analyses to investigate texture evolution under different cold-rolling conditions. In the conventional rolling specimens, we observed that the deformation was not uniform in the thickness direction, whereas there was homogeneous shear deformation in the asymmetric rolling specimens as well as the formation of uniform recrystallized grains and random orientation grains in the final annealing sheets. As such, the ridging resistance of the final sheets was significantly improved by employing the asymmetric rolling process. This result indicates with certainty that the texture gradient and orientation inhomogeneity can be attributed to non-uniform deformation, whereas the uniform orientation gradient in the thickness direction is explained by the increased number of shear bands obtained in the asymmetric rolling process.

Infiltration of MHD liquid into a deformable porous material

NASA Astrophysics Data System (ADS)

Naseem, Anum; Mahmood, Asif; Siddique, J. I.; Zhao, Lifeng

2018-03-01

We analyze the capillary rise dynamics for magnetohydrodynamics (MHD) fluid flow through deformable porous material in the presence of gravity effects. The modeling is performed using mixture theory approach and mathematical manipulation yields a nonlinear free boundary problem. Due to the capillary rise action, the pressure gradient in the liquid generates a stress gradient that results in the deformation of porous substrate. The capillary rise process for MHD fluid slows down as compared to Newtonian fluid case. Numerical solutions are obtained using a method of lines approach. The graphical results are presented for important physical parameters, and comparison is presented with Newtonian fluid case.

Susceptibility Tensor Imaging (STI) of the Brain

PubMed Central

Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu

2016-01-01

Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169

Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties

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

Crenshaw, Michael E., E-mail: michael.e.crenshaw4.civ@mail.mil

2014-04-15

In a continuum setting, the energy–momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy–momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derivemore » electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy–momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the Abraham–Minkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy–momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.« less

Effect of modulator sorption on gradient shape in ion-exchange chromatography

NASA Technical Reports Server (NTRS)

Velayudhan, A.; Ladisch, M. R.; Mitchell, C. A. (Principal Investigator)

1995-01-01

Mobile phase additives, or modulators, are used in gradient elution chromatography to facilitate separation and reduce separation time. The modulators are usually assumed to be linearly adsorbed or unadsorbed. Here, the consequences of nonlinear modulator adsorption are examined for ion-exchange gradient elution through a series of simulations. Even when the buffer salt is identical to the modulator salt, gradient deformation is observed; the extent of deformation increases as the volume of the feed is increased. When the modulator salt is different from the buffer salt, unusual effects are observed, and the chromatograms are quite different from those predicted by classical gradient elution theory. In particular, local increases in the buffer concentration are found between feed bands, and serve to improve the separation. These effects become more pronounced as the feed volume increases, and could therefore prove valuable in preparative applications.

DWI filtering using joint information for DTI and HARDI.

PubMed

Tristán-Vega, Antonio; Aja-Fernández, Santiago

2010-04-01

The filtering of the Diffusion Weighted Images (DWI) prior to the estimation of the diffusion tensor or other fiber Orientation Distribution Functions (ODF) has been proved to be of paramount importance in the recent literature. More precisely, it has been evidenced that the estimation of the diffusion tensor without a previous filtering stage induces errors which cannot be recovered by further regularization of the tensor field. A number of approaches have been intended to overcome this problem, most of them based on the restoration of each DWI gradient image separately. In this paper we propose a methodology to take advantage of the joint information in the DWI volumes, i.e., the sum of the information given by all DWI channels plus the correlations between them. This way, all the gradient images are filtered together exploiting the first and second order information they share. We adapt this methodology to two filters, namely the Linear Minimum Mean Squared Error (LMMSE) and the Unbiased Non-Local Means (UNLM). These new filters are tested over a wide variety of synthetic and real data showing the convenience of the new approach, especially for High Angular Resolution Diffusion Imaging (HARDI). Among the techniques presented, the joint LMMSE is proved a very attractive approach, since it shows an accuracy similar to UNLM (or even better in some situations) with a much lighter computational load. Copyright 2009 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

The relationship between a deformation-based eddy parameterization and the LANS-α turbulence model

NASA Astrophysics Data System (ADS)

Bachman, Scott D.; Anstey, James A.; Zanna, Laure

2018-06-01

A recent class of ocean eddy parameterizations proposed by Porta Mana and Zanna (2014) and Anstey and Zanna (2017) modeled the large-scale flow as a non-Newtonian fluid whose subgridscale eddy stress is a nonlinear function of the deformation. This idea, while largely new to ocean modeling, has a history in turbulence modeling dating at least back to Rivlin (1957). The new class of parameterizations results in equations that resemble the Lagrangian-averaged Navier-Stokes-α model (LANS-α, e.g., Holm et al., 1998a). In this note we employ basic tensor mathematics to highlight the similarities between these turbulence models using component-free notation. We extend the Anstey and Zanna (2017) parameterization, which was originally presented in 2D, to 3D, and derive variants of this closure that arise when the full non-Newtonian stress tensor is used. Despite the mathematical similarities between the non-Newtonian and LANS-α models which might provide insight into numerical implementation, the input and dissipation of kinetic energy between these two turbulent models differ.

Ross sea ice motion, area flux, and deformation

NASA Technical Reports Server (NTRS)

kwok, Ron

2005-01-01

The sea ice motion, area export, and deformation of the Ross Sea ice cover are examined with satellite passive microwave and RADARSAT observations. The record of high-resolution synthetic aperture radar (SAR) data, from 1998 and 2000, allows the estimation of the variability of ice deformation at the small scale (10 km) and to assess the quality of the longer record of passive microwave ice motion. Daily and subdaily deformation fields and RADARSAT imagery highlight the variability of motion and deformation in the Ross Sea. With the passive microwave ice motion, the area export at a flux gate positioned between Cape Adare and Land Bay is estimated. Between 1992 and 2003, a positive trend can be seen in the winter (March-November) ice area flux that has a mean of 990 x 103 km2 and ranges from a low of 600 x 103 km2 in 1992 to a peak of 1600 x 103 km2 in 2001. In the mean, the southern Ross Sea produces almost twice its own area of sea ice during the winter. Cross-gate sea level pressure (SLP) gradients explain 60% of the variance in the ice area flux. A positive trend in this gradient, from reanalysis products, suggests a 'spinup' of the Ross Sea Gyre over the past 12 yr. In both the NCEP-NCAR and ERA-40 surface pressure fields, longer-term trends in this gradient and mean SLP between 1979 and 2002 are explored along with positive anomalies in the monthly cross-gate SLP gradient associated with the positive phase of the Southern Hemisphere annular mode and the extrapolar Southern Oscillation.

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.

Anisotropic mesoscale eddy transport in ocean general circulation models

NASA Astrophysics Data System (ADS)

Reckinger, Scott; Fox-Kemper, Baylor; Bachman, Scott; Bryan, Frank; Dennis, John; Danabasoglu, Gokhan

2014-11-01

In modern climate models, the effects of oceanic mesoscale eddies are introduced by relating subgrid eddy fluxes to the resolved gradients of buoyancy or other tracers, where the proportionality is, in general, governed by an eddy transport tensor. The symmetric part of the tensor, which represents the diffusive effects of mesoscale eddies, is universally treated isotropically. However, the diffusive processes that the parameterization approximates, such as shear dispersion and potential vorticity barriers, typically have strongly anisotropic characteristics. Generalizing the eddy diffusivity tensor for anisotropy extends the number of parameters from one to three: major diffusivity, minor diffusivity, and alignment. The Community Earth System Model (CESM) with the anisotropic eddy parameterization is used to test various choices for the parameters, which are motivated by observations and the eddy transport tensor diagnosed from high resolution simulations. Simply setting the ratio of major to minor diffusivities to a value of five globally, while aligning the major axis along the flow direction, improves biogeochemical tracer ventilation and reduces temperature and salinity biases. These effects can be improved by parameterizing the oceanic anisotropic transport mechanisms.

Machine Learning Interface for Medical Image Analysis.

PubMed

Zhang, Yi C; Kagen, Alexander C

2017-10-01

TensorFlow is a second-generation open-source machine learning software library with a built-in framework for implementing neural networks in wide variety of perceptual tasks. Although TensorFlow usage is well established with computer vision datasets, the TensorFlow interface with DICOM formats for medical imaging remains to be established. Our goal is to extend the TensorFlow API to accept raw DICOM images as input; 1513 DaTscan DICOM images were obtained from the Parkinson's Progression Markers Initiative (PPMI) database. DICOM pixel intensities were extracted and shaped into tensors, or n-dimensional arrays, to populate the training, validation, and test input datasets for machine learning. A simple neural network was constructed in TensorFlow to classify images into normal or Parkinson's disease groups. Training was executed over 1000 iterations for each cross-validation set. The gradient descent optimization and Adagrad optimization algorithms were used to minimize cross-entropy between the predicted and ground-truth labels. Cross-validation was performed ten times to produce a mean accuracy of 0.938 ± 0.047 (95 % CI 0.908-0.967). The mean sensitivity was 0.974 ± 0.043 (95 % CI 0.947-1.00) and mean specificity was 0.822 ± 0.207 (95 % CI 0.694-0.950). We extended the TensorFlow API to enable DICOM compatibility in the context of DaTscan image analysis. We implemented a neural network classifier that produces diagnostic accuracies on par with excellent results from previous machine learning models. These results indicate the potential role of TensorFlow as a useful adjunct diagnostic tool in the clinical setting.

The instantaneous apparent resistivity tensor: a visualization scheme for LOTEM electric field measurements

NASA Astrophysics Data System (ADS)

Caldwell, T. Grant; Bibby, Hugh M.

1998-12-01

Long-offset transient electromagnetic (LOTEM) data have traditionally been represented as early- and late-time apparent resistivities. Time-varying electric field data recorded in a LOTEM survey made with multiple sources can be represented by an `instantaneous apparent resistivity tensor'. Three independent, coordinate-invariant, time-varying apparent resistivities can be derived from this tensor. For dipolar sources, the invariants are also independent of source orientation. In a uniform-resistivity half-space, the invariant given by the square root of the tensor determinant remains almost constant with time, deviating from the half-space resistivity by a maximum of 6 per cent. For a layered half-space, a distance-time pseudo-section of the determinant apparent resistivity produces an image of the layering beneath the measurement profile. As time increases, the instantaneous apparent resistivity tensor approaches the direct current apparent resistivity tensor. An approximate time-to-depth conversion can be achieved by integrating the diffusion depth formula with time, using the determinant apparent resistivity at each instant to represent the resistivity of the conductive medium. Localized near-surface inhomogeneities produce shifts in the time-domain apparent resistivity sounding curves that preserve the gradient, analogous to static shifts seen in magnetotelluric soundings. Instantaneous apparent resistivity tensors calculated for 3-D resistivity models suggest that profiles of LOTEM measurements across a simple 3-D structure can be used to create an image that reproduces the main features of the subsurface resistivity. Where measurements are distributed over an area, maps of the tensor invariants can be made into a sequence of images, which provides a way of `time slicing' down through the target structure.

Seismic anisotropy in localized shear zones versus distributed tectonic fabrics: examples from geologic and seismic observations in western North America and the European Alps

NASA Astrophysics Data System (ADS)

Mahan, Kevin H.; Schulte-Pelkum, Vera; Condit, Cailey; Leydier, Thomas; Goncalves, Philippe; Raju, Anissha; Brownlee, Sarah; Orlandini, Omero F.

2017-04-01

Modern methods for detecting seismic anisotropy offer an array of promising tools for imaging deep crustal deformation but also present challenges, especially with respect to potential biases in both the detection methods themselves as well as in competing processes for localized versus distributed deformation. We address some of these issues from the geophysical perspective by employing azimuthally dependent amplitude and polarity variations in teleseismic receiver functions combined with a compilation of published rock elasticity tensors from middle and deep crustal rocks, and from the geological perspective through studies of shear zone deformation processes. Examples are highlighted at regional and outcrop scales from western North America and the European Alps. First, in regional patterns, strikes of seismically detected fabric from receiver functions in California show a strong alignment with current strike-slip motion between the Pacific and North American plates, with high signal strength near faults and from depths below the brittle-ductile transition suggesting these faults have deep ductile roots. In contrast, despite NE-striking shear zones being the most prominent features portrayed on Proterozoic tectonic maps of the southwestern USA, receiver function anisotropy from the central Rocky Mountain region appears to more prominently reflect broadly distributed Proterozoic fabric domains that preceded late-stage localized shear zones. Possible causes for the discrepancy fall into two categories: those that involve a) bias in seismic sampling and/or b) deformation processes that lead to either weaker anisotropy in the shear zones compared to adjacent domains or to a symmetry that is different from that conventionally assumed. Most of these explanations imply that the seismically sampled domains contain important structural information that is distinct from the shear zones. The second set of examples stem from studies of outcrop-scale shear zones in upper amphibolite-facies (0.9-1.0 GPa, 700 °C) mafic metagabbro from Precambrian exposures in Montana (USA) and in greenschist-facies (0.7-0.8 GPa, 450-500 °C) metagranites from the External Crystalline Massifs of the European Central Alps. The shear zones are characterized by strain gradients from undeformed coarse-grained protoliths to very fine grained ultramylonite, and by microstructures dominated by CPO-producing deformation mechanisms in the protomylonite and CPO-weakening mechanisms such as dissolution-precipitation creep and grain boundary sliding in the ultramylonite. In the mafic mylonites, the result is a lower seismic anisotropy ( 2%) in the core of the shear zones despite a well-developed hornblende shape-preferred orientation. Preliminary observations of these examples suggest that marginal gradients may contribute as much or more to the bulk anisotropy signal compared to the higher strained cores of these structures. If true, a similar effect could explain some otherwise puzzling anisotropy studies of larger scale shear zones such as from the Himalaya where anisotropy tilt proximal to the Main Himalayan Thrust is notably steeper than expected. In conclusion, while some anisotropy studies of crustal scale deformation patterns are relatively straightforward, others will require careful consideration of the limitations and potential future improvements to seismic detection methods, including ground truthing based on samples and exposures as well as a better understanding of physical processes involved in deformation localization.

Hidden Symmetries in String Theory

NASA Astrophysics Data System (ADS)

Chervonyi, Iurii

In this thesis we study hidden symmetries within the framework of string theory. Symmetries play a very important role in physics: they lead to drastic simplifications, which allow one to compute various physical quantities without relying on perturbative techniques. There are two kinds of hidden symmetries investigated in this work: the first type is associated with dynamics of quantum fields and the second type is related to integrability of strings on various backgrounds. Integrability is a remarkable property of some theories that allows one to determine all dynamical properties of the system using purely analytical methods. The goals of this thesis are twofold: extension of hidden symmetries known in General Relativity to stringy backgrounds in higher dimensions and construction of new integrable string theories. In the context of the first goal we study hidden symmetries of stringy backgrounds, with and without supersymmetry. For supersymmetric geometries produced by D-branes we identify the backgrounds with solvable equations for geodesics, which can potentially give rise to integrable string theories. Relaxing the requirement of supersymmetry, we also study charged black holes in higher dimensions and identify their hidden symmetries encoded in so-called Killing(-Yano) tensors. We construct the explicit form of the Killing(-Yano) tensors for the charged rotating black hole in arbitrary number of dimensions, study behavior of such tensors under string dualities, and use the analysis of hidden symmetries to explain why exact solutions for black rings (black holes with non-spherical event horizons) in more than five dimensions remain elusive. As a byproduct we identify the standard parameterization of AdSp x Sq backgrounds with elliptic coordinates on a flat base. The second goal of this work is construction of new integrable string theories by applying continuous deformations of known examples. We use the recent developments called (generalized) lambda-deformation to construct new integrable backgrounds depending on several continuous parameters and study analytical properties of the such deformations.

3D PATTERN OF BRAIN ABNORMALITIES IN FRAGILE X SYNDROME VISUALIZED USING TENSOR-BASED MORPHOMETRY

PubMed Central

Lee, Agatha D.; Leow, Alex D.; Lu, Allen; Reiss, Allan L.; Hall, Scott; Chiang, Ming-Chang; Toga, Arthur W.; Thompson, Paul M.

2007-01-01

Fragile X syndrome (FraX), a genetic neurodevelopmental disorder, results in impaired cognition with particular deficits in executive function and visuo-spatial skills. Here we report the first detailed 3D maps of the effects of the Fragile X mutation on brain structure, using tensor-based morphometry. TBM visualizes structural brain deficits automatically, without time-consuming specification of regions-of-interest. We compared 36 subjects with FraX (age: 14.66+/−1.58SD, 18 females/18 males), and 33 age-matched healthy controls (age: 14.67+/−2.2SD, 17 females/16 males), using high-dimensional elastic image registration. All 69 subjects' 3D T1-weighted brain MRIs were spatially deformed to match a high-resolution single-subject average MRI scan in ICBM space, whose geometry was optimized to produce a minimal deformation target. Maps of the local Jacobian determinant (expansion factor) were computed from the deformation fields. Statistical maps showed increased caudate (10% higher; p=0.001) and lateral ventricle volumes (19% higher; p=0.003), and trend-level parietal and temporal white matter excesses (10% higher locally; p=0.04). In affected females, volume abnormalities correlated with reduction in systemically measured levels of the fragile X mental retardation protein (FMRP; Spearman's r<−0.5 locally). Decreased FMRP correlated with ventricular expansion (p=0.042; permutation test), and anterior cingulate tissue reductions (p=0.0026; permutation test) supporting theories that FMRP is required for normal dendritic pruning in fronto-striatal-limbic pathways. No sex differences were found; findings were confirmed using traditional volumetric measures in regions of interest. Deficit patterns were replicated using Lie group statistics optimized for tensor-valued data. Investigation of how these anomalies emerge over time will accelerate our understanding of FraX and its treatment. PMID:17161622

Ostrogradsky in theories with multiple fields

DOE PAGES

de Rham, Claudia; Matas, Andrew

2016-06-23

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamicalmore » or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.« less

Ostrogradsky in theories with multiple fields

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

de Rham, Claudia; Matas, Andrew

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamicalmore » or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.« less

Acoustic Radiation Pressure

NASA Technical Reports Server (NTRS)

Cantrell, John H.

2018-01-01

The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in Lagrangian coordinates (not Eulerian coordinates) and that the terms in the BST are not the momentum flux density and mean excess Eulerian stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in Eulerian coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean Eulerian pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the Eulerian pressure. It is shown that the transformation between Lagrangian and Eulerian quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the Lagrangian and Eulerian radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the Lagrangian radiation pressure in the propagation direction is equal to (2K) and the BST result that the Eulerian radiation pressure in that direction is the momentum flux density.

Analysis of deformable image registration accuracy using computational modeling

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

Zhong Hualiang; Kim, Jinkoo; Chetty, Indrin J.

2010-03-15

Computer aided modeling of anatomic deformation, allowing various techniques and protocols in radiation therapy to be systematically verified and studied, has become increasingly attractive. In this study the potential issues in deformable image registration (DIR) were analyzed based on two numerical phantoms: One, a synthesized, low intensity gradient prostate image, and the other a lung patient's CT image data set. Each phantom was modeled with region-specific material parameters with its deformation solved using a finite element method. The resultant displacements were used to construct a benchmark to quantify the displacement errors of the Demons and B-Spline-based registrations. The results showmore » that the accuracy of these registration algorithms depends on the chosen parameters, the selection of which is closely associated with the intensity gradients of the underlying images. For the Demons algorithm, both single resolution (SR) and multiresolution (MR) registrations required approximately 300 iterations to reach an accuracy of 1.4 mm mean error in the lung patient's CT image (and 0.7 mm mean error averaged in the lung only). For the low gradient prostate phantom, these algorithms (both SR and MR) required at least 1600 iterations to reduce their mean errors to 2 mm. For the B-Spline algorithms, best performance (mean errors of 1.9 mm for SR and 1.6 mm for MR, respectively) on the low gradient prostate was achieved using five grid nodes in each direction. Adding more grid nodes resulted in larger errors. For the lung patient's CT data set, the B-Spline registrations required ten grid nodes in each direction for highest accuracy (1.4 mm for SR and 1.5 mm for MR). The numbers of iterations or grid nodes required for optimal registrations depended on the intensity gradients of the underlying images. In summary, the performance of the Demons and B-Spline registrations have been quantitatively evaluated using numerical phantoms. The results show that parameter selection for optimal accuracy is closely related to the intensity gradients of the underlying images. Also, the result that the DIR algorithms produce much lower errors in heterogeneous lung regions relative to homogeneous (low intensity gradient) regions, suggests that feature-based evaluation of deformable image registration accuracy must be viewed cautiously.« less

Experimental investigation of cyclic thermomechanical deformation in torsion

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

On representations of U{sub q}osp(1{vert_bar}2) when q is a root of unity

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

Chung, W.; Suzuki, T.

1997-06-01

The infinite dimensional highest weight representations of U{sub q}osp(1{vert_bar}2) for the deformation parameter q being a root of unity are investigated. As in the cases of q-deformed nongraded Lie algebras, we find that every irreducible representation is isomorphic to the tensor product of a highest weight representation of sl{sub 2}(R) and a finite dimensional one of U{sub q}osp(1{vert_bar}2). The structure is investigated in detail. {copyright} {ital 1997 American Institute of Physics.}

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

Small deformations of extreme five dimensional Myers-Perry black hole initial data

NASA Astrophysics Data System (ADS)

Alaee, Aghil; Kunduri, Hari K.

2015-02-01

We demonstrate the existence of a one-parameter family of initial data for the vacuum Einstein equations in five dimensions representing small deformations of the extreme Myers-Perry black hole. This initial data set has `' symmetry and preserves the angular momenta and horizon geometry of the extreme solution. Our proof is based upon an earlier result of Dain and Gabach-Clement concerning the existence of -invariant initial data sets which preserve the geometry of extreme Kerr (at least for short times). In addition, we construct a general class of transverse, traceless symmetric rank 2 tensors in these geometries.

Contour propagation for lung tumor delineation in 4D-CT using tensor-product surface of uniform and non-uniform closed cubic B-splines

NASA Astrophysics Data System (ADS)

Jin, Renchao; Liu, Yongchuan; Chen, Mi; Zhang, Sheng; Song, Enmin

2018-01-01

A robust contour propagation method is proposed to help physicians delineate lung tumors on all phase images of four-dimensional computed tomography (4D-CT) by only manually delineating the contours on a reference phase. The proposed method models the trajectory surface swept by a contour in a respiratory cycle as a tensor-product surface of two closed cubic B-spline curves: a non-uniform B-spline curve which models the contour and a uniform B-spline curve which models the trajectory of a point on the contour. The surface is treated as a deformable entity, and is optimized from an initial surface by moving its control vertices such that the sum of the intensity similarities between the sampling points on the manually delineated contour and their corresponding ones on different phases is maximized. The initial surface is constructed by fitting the manually delineated contour on the reference phase with a closed B-spline curve. In this way, the proposed method can focus the registration on the contour instead of the entire image to prevent the deformation of the contour from being smoothed by its surrounding tissues, and greatly reduce the time consumption while keeping the accuracy of the contour propagation as well as the temporal consistency of the estimated respiratory motions across all phases in 4D-CT. Eighteen 4D-CT cases with 235 gross tumor volume (GTV) contours on the maximal inhale phase and 209 GTV contours on the maximal exhale phase are manually delineated slice by slice. The maximal inhale phase is used as the reference phase, which provides the initial contours. On the maximal exhale phase, the Jaccard similarity coefficient between the propagated GTV and the manually delineated GTV is 0.881 +/- 0.026, and the Hausdorff distance is 3.07 +/- 1.08 mm. The time for propagating the GTV to all phases is 5.55 +/- 6.21 min. The results are better than those of the fast adaptive stochastic gradient descent B-spline method, the 3D  +  t B-spline method and the diffeomorphic demons method. The proposed method is useful for helping physicians delineate target volumes efficiently and accurately.

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

From three-dimensional long-term tectonic numerical models to synthetic structural data: semi-automatic extraction of instantaneous & finite strain quantities

NASA Astrophysics Data System (ADS)

Duclaux, Guillaume; May, Dave

2017-04-01

Over the past three decades thermo-mechanical numerical modelling has transformed the way we look at deformation in the lithosphere. More than just generating aesthetically pleasing pictures, the output from a numerical models contains a rich source of quantitative information that can be used to measure deformation quantities in plan view or three-dimensions. Adding value to any numerical experiment requires a thorough post-processing of the modelling results. Such work aims to produce visual information that will resonate to seasoned structural geologists and assist with comparing experimental and observational data. Here we introduce two methods to generate synthetic structural data from numerical model outputs. We first present an image processing and shape recognition workflow developed to extract the active faults orientation from surface velocity gradients. In order to measure the active faults lengths and directions along with their distribution at the surface of the model we implemented an automated sequential mapping technique based on the second invariant of the strain rate tensor and using a suite a python functions. Active fault direction measurements are achieved using a probabilistic method for extracting linear features orientation from any surface. This method has the undeniable advantage to avoid interpretation bias. Strike measurements for individual segments are weighted according to their length and orientation distribution data are presented in an equal-area moving average rose diagrams produced using a weighted method. Finally, we discuss a method for mapping finite strain in three-dimensions. A high-resolution Lagrangian regular grid which advects during the numerical experiment is used to track the progressive deformation within the model. Thanks to this data we can measure the finite strain ellipsoids for any region of interest in the model. This method assumes that the finite strain is homogenous within one unit cell of the grid. We can compute individual ellipsoid's parameters (orientation, shape, etc.) and represent the finite deformation for any region of interest in a Flinn diagram. In addition, we can use the finite strain ellipsoids to estimate the prevailing foliation and/or lineation directions anywhere in the model. These two methods are applied to measure the instantaneous and finite deformation patterns within an oblique rift zone ongoing constant extension in the absence of surface processes.

A physical model for strain accumulation in the San Francisco Bay Region

USGS Publications Warehouse

Pollitz, F.F.; Nyst, M.

2005-01-01

Strain accumulation in tectonically active regions is generally a superposition of the effects of background tectonic loading, steady-state dislocation processes, such as creep, and transient deformation. In the San Francisco Bay region (SFBR), the most uncertain of these processes is transient deformation, which arises primarily in association with large earthquakes. As such, it depends upon the history of faulting and the rheology of the crust and mantle, which together determine the pattern of longer term (decade-scale) post-seismic response to earthquakes. We utilize a set of 102 GPS velocity vectors in the SFBR in order to characterize the strain rate field and construct a physical model of its present deformation. We first perform an inversion for the continuous velocity gradient field from the discrete GPS velocity field, from which both tensor strain rate and rotation rate may be extracted. The present strain rate pattern is well described as a nearly uniform shear strain rate oriented approximately N34??W (140 nanostrain yr-1) plus a N56??E uniaxial compression rate averaging 20 nanostrain yr-1 across the shear zone. We fit the velocity and strain rate fields to a model of time-dependent deformation within a 135-kin-wide, arcuate shear zone bounded by strong Pacific Plate and Sierra Nevada block lithosphere to the SW and NE, respectively. Driving forces are purely lateral, consisting of shear zone deformation imposed by the relative motions between the thick Pacific Plate and Sierra Nevada block lithospheres. Assuming a depth-dependent viscoelastic structure within the shear zone, we account for the effects of steady creep on faults and viscoelastic relaxation following the 1906 San Francisco and 1989 Loma Prieta earthquakes, subject to constant velocity boundary conditions on the edges of the shear zone. Fault creep is realized by evaluating dislocations on the creeping portions of faults in the fluid limit of the viscoelastic model. A priori plate-boundary(PB)-parallel motion is set to 38 mm yr -1. A grid search based on fitting the observed strain rate pattern yields a mantle viscosity of 1.2 ?? 1019 Pa s and a PB-perpendicular convergence rate of ???3 mm yr-1. Most of this convergence appears to be uniformly distributed in the Pacific-Sierra Nevada plate boundary zone. ?? 2005 RAS.

Geodetic Constraints on Fault Slip Rates and Seismic Hazard in the Greater Las Vegas Area

NASA Astrophysics Data System (ADS)

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

2014-12-01

We address fundamental questions about how contemporary tectonic deformation of the crust in the southern Great Basin occurs in the region around Las Vegas (LV) Nevada, western Arizona and eastern California. This area lies in the intersection of the eastern Walker Lane Belt, southern Great Basin and western Colorado Plateau (CP), sharing features of transtensional and extensional deformation associated with Pacific/North America relative motion. We use GPS data collected from 48 stations of the MAGNET semi-continuous network and 77 stations from continuous networks including BARGEN and EarthScope Plate Boundary Observatory. MAGNET stations have been observed for a minimum of 7 years, while most continuous stations have longer records. From these data we estimate the velocity of crustal motion for all stations with respect to the stable North America reference frame NA12. To correct for transients from recent large earthquakes including the 1999 Hector Mine and 2010 El Mayor-Cucapah events we use models of co- and post-seismic deformation, subtracting the predicted motions from the time series before estimating interseismic stain rates. We find approximately 2 mm/yr of relative motion distributed over 200 km centered on Las Vegas, with a mean strain accumulation rate of 10 × 10-9 yr-1, with lower rates of predominantly extensional strain to the east and higher rates of predominantly shear deformation to the west. The mean strain rate is lower than that of the western Walker Lane but about twice that of eastern Nevada where e.g., the Wells, NV MW 6.0 earthquake occurred in 2008. From this new velocity field we generated a horizontal tensor strain rate map and a crustal block motion model to portray the transition of active strain from the CP into the Walker Lane. For faults in the Las Vegas Valley, including the Eglington Fault and Frenchman Mountain Fault, the observed velocity gradients and model results are consistent with normal slip rates of 0.2 mm/yr, which are typical for the region. The Stateline Fault system experiences dextral slip of at least 0.4 mm/yr while normal faults south of LV collectively accommodate 0.9 mm/yr of east-west extension across a zone ~150 km wide. We see no evidence for concentrations of deformation or isolated rigid microplates within this zone.

Radial deformation of the solar current sheet as a cause of geomagnetic storms

NASA Technical Reports Server (NTRS)

Akasofu, S.-I.

1979-01-01

It is suggested that the solar current sheet, extending from a coronal streamer, develops a large-scale radial deformation, at times with a very steep gradient at the earth's distance. The associated magnetic field lines (namely, the interplanetary magnetic field (IMF) lines) are expected to have also a large gradient in the vicinity of the current sheet. It is also suggested that some of the major geomagnetic storms occur when the earth is located in the region where IMF field lines have a large dip angle with respect to the ecliptic plane for an extended period (6-48 h), as a result of a steep radial deformation of the current sheet.

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.

Improving Tensile and Compressive Properties of an Extruded AZ91 Rod by the Combined Use of Torsion Deformation and Aging Treatment

PubMed Central

Song, Bo; Wang, Chunpeng; Guo, Ning; Pan, Hucheng; Xin, Renlong

2017-01-01

In this study, AZ91 magnesium alloy rods were used to investigate the effects of torsion deformation on microstructure and subsequent aging behavior. Extruded AZ91 rod has a uniform microstructure and typical fiber texture. Torsion deformation can generate a gradient microstructure on the cross-section of the rod. After torsion, from the center to the edge in the cross-section of the rod, both stored dislocations and area fraction of {10-12} twins gradually increase, and the basal pole of the texture tends to rotate in the ED direction. Direct aging usually generates coarse discontinuous precipitates and fine continuous precipitates simultaneously. Both twin structures and dislocations via torsion deformation can be effective microstructures for the nucleation of continuous precipitates during subsequent aging. Thus, aging after torsion can promote continuous precipitation and generate gradient precipitation characteristics. Both aging treatment and torsion deformation can reduce yield asymmetry, and torsion deformation enhances the aging hardening effect by promoting continuous precipitation. Therefore, combined use of torsion deformation and aging treatment can effectively enhance the yield strength and almost eliminate the yield asymmetry of the present extruded AZ91 rod. Finally, the relevant mechanisms are discussed. PMID:28772638

Performance Analysis and Experimental Validation of the Direct Strain Imaging Method

Treesearch

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

2013-01-01

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

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.

The GOCE end-to-end system simulator

NASA Astrophysics Data System (ADS)

Catastini, G.; Cesare, S.; de Sanctis, S.; Detoma, E.; Dumontel, M.; Floberghagen, R.; Parisch, M.; Sechi, G.; Anselmi, A.

2003-04-01

The idea of an end-to-end simulator was conceived in the early stages of the GOCE programme, as an essential tool for assessing the satellite system performance, that cannot be fully tested on the ground. The simulator in its present form is under development at Alenia Spazio for ESA since the beginning of Phase B and is being used for checking the consistency of the spacecraft and of the payload specifications with the overall system requirements, supporting trade-off, sensitivity and worst-case analyses, and preparing and testing the on-ground and in-flight calibration concepts. The software simulates the GOCE flight along an orbit resulting from the application of Earth's gravity field, non-conservative environmental disturbances (atmospheric drag, coupling with Earth's magnetic field, etc.) and control forces/torques. The drag free control forces as well as the attitude control torques are generated by the current design of the dedicated algorithms. Realistic sensor models (star tracker, GPS receiver and gravity gradiometer) feed the control algorithms and the commanded forces are applied through realistic thruster models. The output of this stage of the simulator is a time series of Level-0 data, namely the gradiometer raw measurements and spacecraft ancillary data. The next stage of the simulator transforms Level-0 data into Level-1b (gravity gradient tensor) data, by implementing the following steps: - transformation of raw measurements of each pair of accelerometers into common and differential accelerations - calibration of the common and differential accelerations - application of the post-facto algorithm to rectify the phase of the accelerations and to estimate the GOCE angular velocity and attitude - computation of the Level-1b gravity gradient tensor from calibrated accelerations and estimated angular velocity in different reference frames (orbital, inertial, earth-fixed); computation of the spectral density of the error of the tensor diagonal components (measured gravity gradient minus input gravity gradient) in order to verify the requirement on the error of gravity gradient of 4 mE/sqrt(Hz) within the gradiometer measurement bandwidth (5 to 100 mHz); computation of the spectral density of the tensor trace in order to verify the requirement of 4 sqrt(3) mE/sqrt(Hz) within the measurement bandwidth - processing of GPS observations for orbit reconstruction within the required 10m accuracy and for gradiometer measurement geolocation. The current version of the end-to-end simulator, essentially focusing on the gradiometer payload, is undergoing detailed testing based on a time span of 10 days of simulated flight. This testing phase, ending in January 2003, will verify the current implementation and conclude the assessment of numerical stability and precision. Following that, the exercise will be repeated on a longer-duration simulated flight and the lesson learnt so far will be exploited to further improve the simulator's fidelity. The paper will describe the simulator's current status and will illustrate its capabilities for supporting the assessment of the quality of the scientific products resulting from the current spacecraft and payload design.

New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions.

PubMed

Bonhomme, Christian; Gervais, Christel; Coelho, Cristina; Pourpoint, Frédérique; Azaïs, Thierry; Bonhomme-Coury, Laure; Babonneau, Florence; Jacob, Guy; Ferrari, Maude; Canet, Daniel; Yates, Jonathan R; Pickard, Chris J; Joyce, Siân A; Mauri, Francesco; Massiot, Dominique

2010-12-01

In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), β-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, β-HMX and α-NTO are explosive compounds. Copyright © 2010 John Wiley & Sons, Ltd.

Calcium-43 chemical shift tensors as probes of calcium binding environments. Insight into the structure of the vaterite CaCO3 polymorph by 43Ca solid-state NMR spectroscopy.

PubMed

Bryce, David L; Bultz, Elijah B; Aebi, Dominic

2008-07-23

Natural-abundance (43)Ca solid-state NMR spectroscopy at 21.1 T and gauge-including projector-augmented-wave (GIPAW) DFT calculations are developed as tools to provide insight into calcium binding environments, with special emphasis on the calcium chemical shift (CS) tensor. The first complete analysis of a (43)Ca solid-state NMR spectrum, including the relative orientation of the CS and electric field gradient (EFG) tensors, is reported for calcite. GIPAW calculations of the (43)Ca CS and EFG tensors for a series of small molecules are shown to reproduce experimental trends; for example, the trend in available solid-state chemical shifts is reproduced with a correlation coefficient of 0.983. The results strongly suggest the utility of the calcium CS tensor as a novel probe of calcium binding environments in a range of calcium-containing materials. For example, for three polymorphs of CaCO3 the CS tensor span ranges from 8 to 70 ppm and the symmetry around calcium is manifested differently in the CS tensor as compared with the EFG tensor. The advantages of characterizing the CS tensor are particularly evident in very high magnetic fields where the effect of calcium CS anisotropy is augmented in hertz while the effect of second-order quadrupolar broadening is often obscured for (43)Ca because of its small quadrupole moment. Finally, as an application of the combined experimental-theoretical approach, the solid-state structure of the vaterite polymorph of calcium carbonate is probed and we conclude that the hexagonal P6(3)/mmc space group provides a better representation of the structure than does the orthorhombic Pbnm space group, thereby demonstrating the utility of (43)Ca solid-state NMR as a complementary tool to X-ray crystallographic methods.

Pressure evolution and deformation of confined granular media during pneumatic fracturing

NASA Astrophysics Data System (ADS)

Eriksen, Fredrik K.; Toussaint, Renaud; Turquet, Antoine Léo; Mâløy, Knut J.; Flekkøy, Eirik G.

2018-01-01

By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by the properties of the pore fluid, the granular medium, and the system size. However, before the diffusing pressure approaches the Laplace solution on the system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity μB and displacement thresholds ∇ ⃗Pc evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the dielectric breakdown model with η =2 , where fractal dimensions are found between 1.5 and 1.6 for the patterns.

Global simulation of the induction heating TSSG process of SiC for the effects of Marangoni convection, free surface deformation and seed rotation

NASA Astrophysics Data System (ADS)

Yamamoto, Takuya; Okano, Yasunori; Ujihara, Toru; Dost, Sadik

2017-07-01

A global numerical simulation was performed for the induction heating Top-Seeded Solution Growth (TSSG) process of SiC. Analysis included the furnace and growth melt. The effects of interfacial force due to free surface tension gradient, the RF coil-induced electromagnetic body force, buoyancy, melt free surface deformation, and seed rotation were examined. The simulation results showed that the contributions of free surface tension gradient and the electromagnetic body force to the melt flow are significant. Marangoni convection affects the growth process adversely by making the melt flow downward in the region under the seed crystal. This downward flow reduces carbon flux into the seed and consequently lowers growth rate. The effects of free surface deformation and seed rotation, although positive, are not so significant compared with those of free surface tension gradient and the electromagnetic body force. Due to the small size of the melt the contribution of buoyancy is also small.

Tensor methodology and computational geometry in direct computational experiments in fluid mechanics

NASA Astrophysics Data System (ADS)

Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Julia

2017-07-01

The paper considers a generalized functional and algorithmic construction of direct computational experiments in fluid dynamics. Notation of tensor mathematics is naturally embedded in the finite - element operation in the construction of numerical schemes. Large fluid particle, which have a finite size, its own weight, internal displacement and deformation is considered as an elementary computing object. Tensor representation of computational objects becomes strait linear and uniquely approximation of elementary volumes and fluid particles inside them. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the efficiency of the algorithms developed by numerical procedures with natural parallelism. It is shown that advantages of the proposed approach are achieved among them by considering representation of large particles of a continuous medium motion in dual coordinate systems and computing operations in the projections of these two coordinate systems with direct and inverse transformations. So new method for mathematical representation and synthesis of computational experiment based on large particle method is proposed.

Investigation of anisotropic thermal transport in cross-linked polymers

NASA Astrophysics Data System (ADS)

Simavilla, David Nieto

Thermal transport in lightly cross-linked polyisoprene and polybutadine subjected to uniaxial elongation is investigated experimentally. We employ two experimental techniques to assess the effect that deformation has on this class of materials. The first technique, which is based on Forced Rayleigh Scattering (FRS), allows us to measure the two independent components of the thermal diffusivity tensor as a function of deformation. These measurements along with independent measurements of the tensile stress and birefringence are used to evaluate the stress-thermal and stress-optic rules. The stress-thermal rule is found to be valid for the entire range of elongations applied. In contrast, the stress-optic rule fails for moderate to large stretch ratios. This suggests that the degree of anisotropy in thermal conductivity depends on both orientation and tension in polymer chain segments. The second technique, which is based on infrared thermography (IRT), allows us to measure anisotropy in thermal conductivity and strain induced changes in heat capacity. We validate this method measurements of anisotropic thermal conductivity by comparing them with those obtained using FRS. We find excellent agreement between the two techniques. Uncertainty in the infrared thermography method measurements is estimated to be about 2-5 %. The accuracy of the method and its potential application to non-transparent materials makes it a good alternative to extend current research on anisotropic thermal transport in polymeric materials. A second IRT application allows us to investigate the dependence of heat capacity on deformation. We find that heat capacity increases with stretch ratio in polyisoprene specimens under uniaxial extension. The deviation from the equilibrium value of heat capacity is consistent with an independent set of experiments comparing anisotropy in thermal diffusivity and conductivity employing FRS and IRT techniques. We identify finite extensibility and strain-induced crystallization as the possible causes explaining our observations and evaluate their contribution making use of classical rubber elasticity results. Finally, we study of the role of evaporation-induced thermal effects in the well-know phenomena of the tears of wine. We develop a transport model and support its predictions by experimentally measuring the temperature gradient present in wine and cognac films using IRT. Our results demonstrate that the Marangoni flow responsible for wine tears results from both composition and temperature gradients, whose relative contribution strongly depends on the thermodynamic properties of ethanol-water mixtures. The methods developed here can be used to obtain a deeper understanding of Marangoni flows, which are ubiquitous in nature and modern technology.

Determining moisture gradient profile using X-Ray technique

Treesearch

Zhiyong Cai

2007-01-01

Moisture gradients in wood are known to affect the internal stresses that could cause dimensional changes and defects. Severe deformation of finished products has the potential to damage a manufacturer’s reputation and significantly increase the cost of manufacturing. An innovative approach to nondestructively examine the moisture gradients of different wood species...

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.

A novel measure of reliability in Diffusion Tensor Imaging after data rejections due to subject motion.

PubMed

Sairanen, V; Kuusela, L; Sipilä, O; Savolainen, S; Vanhatalo, S

2017-02-15

Diffusion Tensor Imaging (DTI) is commonly challenged by subject motion during data acquisition, which often leads to corrupted image data. Currently used procedure in DTI analysis is to correct or completely reject such data before tensor estimations, however assessing the reliability and accuracy of the estimated tensor in such situations has evaded previous studies. This work aims to define the loss of data accuracy with increasing image rejections, and to define a robust method for assessing reliability of the result at voxel level. We carried out simulations of every possible sub-scheme (N=1,073,567,387) of Jones30 gradient scheme, followed by confirming the idea with MRI data from four newborn and three adult subjects. We assessed the relative error of the most commonly used tensor estimates for DTI and tractography studies, fractional anisotropy (FA) and the major orientation vector (V1), respectively. The error was estimated using two measures, the widely used electric potential (EP) criteria as well as the rotationally variant condition number (CN). Our results show that CN and EP are comparable in situations with very few rejections, but CN becomes clearly more sensitive to depicting errors when more gradient vectors and images were rejected. The error in FA and V1 was also found depend on the actual FA level in the given voxel; low actual FA levels were related to high relative errors in the FA and V1 estimates. Finally, the results were confirmed with clinical MRI data. This showed that the errors after rejections are, indeed, inhomogeneous across brain regions. The FA and V1 errors become progressively larger when moving from the thick white matter bundles towards more superficial subcortical structures. Our findings suggest that i) CN is a useful estimator of data reliability at voxel level, and ii) DTI preprocessing with data rejections leads to major challenges when assessing brain tissue with lower FA levels, such as all newborn brain, as well as the adult superficial, subcortical areas commonly traced in precise connectivity analyses between cortical regions. Copyright © 2016 Elsevier Inc. All rights reserved.

Gravity and thermal deformation of large primary mirror in space telescope

NASA Astrophysics Data System (ADS)

Wang, Xin; Jiang, Shouwang; Wan, Jinlong; Shu, Rong

2016-10-01

The technology of integrating mechanical FEA analysis with optical estimation is essential to simulate the gravity deformation of large main mirror and the thermal deformation such as static or temperature gradient of optical structure. We present the simulation results of FEA analysis, data processing, and image performance. Three kinds of support structure for large primary mirror which have the center holding structure, the edge glue fixation and back support, are designed and compared to get the optimal gravity deformation. Variable mirror materials Zerodur/SiC are chosen and analyzed to obtain the small thermal gradient distortion. The simulation accuracy is dependent on FEA mesh quality, the load definition of structure, the fitting error from discrete data to smooth surface. A main mirror with 1m diameter is designed as an example. The appropriate structure material to match mirror, the central supporting structure, and the key aspects of FEA simulation are optimized for space application.

Tectonic stress evolution in the Pan-African Lufilian Arc and its foreland (Katanga, DRC): orogenic bending, late orogenic extensional collapse and transition to rifting

NASA Astrophysics Data System (ADS)

Kipata, M. L.; Delvaux, D.; Sebagenzi, M. N.; Cailteux, J.; Sintubin, M.

2012-04-01

Between the paroxysm of the Lufilian orogeny at ~ 550 Ma and the late Neogene to Quaternary development of the south-western branch of the East African rift system, the tectonic evolution of the Lufilian Arc and Kundelungu foreland in the Katanga region of the Democratic Republic of Congo remains poorly unknown although it caused important Cu-dominated mineral remobilizations leading to world-class ore deposits. This long period is essentially characterized by brittle tectonic deformations that have been investigated by field studies in open mines spread over the entire arc and foreland. Paleostress tensors were computed for a database of 1450 fault-slip data by interactive stress tensor inversion and data subset separation, and the relative succession of 8 brittle deformation events established. The oldest brittle structures observed are related to the Lufilian brittle compressional climax (stage 1). They have been re-oriented during the orogenic bending that led to the arcuate shape of the belt. Unfolding the stress directions from the first stage allows to reconstruct a consistent NE-SW direction of compression for this stage. Constrictional deformation occurred in the central part of the arc, probably during orogenic bending (Stage 2). After the orogenic bending, a sequence of 3 deformation stages marks the progressive onset of late-orogenic extension: strike-slip deformations (stages 3-4) and late-orogenic arc-parallel extension (stage 5). It is proposed that these 3 stages correspond to orogenic collapse. In early Mesozoic, NW-SE compression was induced by a transpressional inversion, interpreted as induced by far-field stresses generated at the southern active margin of Gondwana (stage 6). Since then, this region was affected by rift-related extension, successively in a NE-SW direction (stage 7, Tanganyika trend) and NW-SE direction (stage 8, Moero trend).

Semi-automated segmentation of neuroblastoma nuclei using the gradient energy tensor: a user driven approach

NASA Astrophysics Data System (ADS)

Kromp, Florian; Taschner-Mandl, Sabine; Schwarz, Magdalena; Blaha, Johanna; Weiss, Tamara; Ambros, Peter F.; Reiter, Michael

2015-02-01

We propose a user-driven method for the segmentation of neuroblastoma nuclei in microscopic fluorescence images involving the gradient energy tensor. Multispectral fluorescence images contain intensity and spatial information about antigene expression, fluorescence in situ hybridization (FISH) signals and nucleus morphology. The latter serves as basis for the detection of single cells and the calculation of shape features, which are used to validate the segmentation and to reject false detections. Accurate segmentation is difficult due to varying staining intensities and aggregated cells. It requires several (meta-) parameters, which have a strong influence on the segmentation results and have to be selected carefully for each sample (or group of similar samples) by user interactions. Because our method is designed for clinicians and biologists, who may have only limited image processing background, an interactive parameter selection step allows the implicit tuning of parameter values. With this simple but intuitive method, segmentation results with high precision for a large number of cells can be achieved by minimal user interaction. The strategy was validated on handsegmented datasets of three neuroblastoma cell lines.

A critical comparison of second order closures with direct numerical simulation of homogeneous turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Lumley, John L.

1991-01-01

Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Tensor distribution function

NASA Astrophysics Data System (ADS)

Leow, Alex D.; Zhu, Siwei

2008-03-01

Diffusion weighted MR imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitizing gradients along a minimum of 6 directions, second-order tensors (represetnted by 3-by-3 positive definiite matrices) can be computed to model dominant diffusion processes. However, it has been shown that conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g. crossing fiber tracts. More recently, High Angular Resolution Diffusion Imaging (HARDI) seeks to address this issue by employing more than 6 gradient directions. To account for fiber crossing when analyzing HARDI data, several methodologies have been introduced. For example, q-ball imaging was proposed to approximate Orientation Diffusion Function (ODF). Similarly, the PAS method seeks to reslove the angular structure of displacement probability functions using the maximum entropy principle. Alternatively, deconvolution methods extract multiple fiber tracts by computing fiber orientations using a pre-specified single fiber response function. In this study, we introduce Tensor Distribution Function (TDF), a probability function defined on the space of symmetric and positive definite matrices. Using calculus of variations, we solve for the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, ODF can easily be computed by analytical integration of the resulting displacement probability function. Moreover, principle fiber directions can also be directly derived from the TDF.

On the evolution of the invariants of the velocity gradient tensor in single-square-grid-generated turbulence

NASA Astrophysics Data System (ADS)

Zhou, Yi; Nagata, Koji; Sakai, Yasuhiko; Ito, Yasumasa; Hayase, Toshiyuki

2015-07-01

Direct numerical simulations were performed to investigate the topological evolution of turbulence generated by a single square grid. Immediately behind the single square grid (i.e., in the irrotational dissipation region), the conditional mean trajectories (CMTs) of R and Q are distinctly different from those in homogeneous isotropic turbulence (HIT), where R and Q are the third and second invariants, respectively, of the velocity gradient tensor. In this region, the non-local influence of the pressure Hessian is dominant, which causes irrotational viscous dissipation. The anisotropic part of the pressure Hessian may be responsible for the irrotational viscous dissipation found at the turbulent/nonturbulent interface in turbulent jets [C. B. da Silva and J. C. F. Pereira, "Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets," Phys. Fluids 20, 055101 (2008) and Watanabe et al., "Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet," J. Fluid Mech. 758, 754 (2014)]. In the transition region, the CMTs of R and Q gradually acquire an evolution pattern similar to that in HIT. The expansion of the (R, Q) map at Q > 0 is associated with the effects of the restricted Euler term. Finally, in the fully turbulent region, the CMTs of R and Q demonstrate a clockwise evolution toward a point close to the origin. However, the cyclic spiraling seen in HIT is not found. The lack of the cyclic evolution may be attributed to the considerably large effect of the viscous term owing to the relatively small local Reynolds number. On average, the combined influences of the restricted Euler term and anisotropic part of the pressure Hessian contribute to the generation of small-scale motions, and the viscous term tends to remove small-scale motions.

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Obtaining molecular and structural information from 13C-14N systems with 13C FIREMAT experiments.

PubMed

Strohmeier, Mark; Alderman, D W; Grant, David M

2002-04-01

The effect of dipolar coupling to 14N on 13C FIREMAT (five pi replicated magic angle turning) experiments is investigated. A method is developed for fitting the 13C FIREMAT FID employing the full theory to extract the 13C-14N dipolar and 13C chemical shift tensor information. The analysis requires prior knowledge of the electric field gradient (EFG) tensor at the 14N nucleus. In order to validate the method the analysis is done for the amino acids alpha-glycine, gamma-glycine, l-alanine, l-asparagine, and l-histidine on FIREMAT FIDs recorded at 13C frequencies of 50 and 100 MHz. The dipolar and chemical shift data obtained with this analysis are in very good agreement with the previous single-crystal 13C NMR results and neutron diffraction data on alpha-glycine, l-alanine, and l-asparagine. The values for gamma-glycine and l-histidine obtained with this new method are reported for the first time. The uncertainties in the EFG tensor on the resultant 13C chemical shift and dipolar tensor values are assessed. (c) 2002 Elsevier Science (USA).

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.

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

PubMed

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

2006-01-01

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

Dependence of nuclear quadrupole resonance transitions on the electric field gradient asymmetry parameter for nuclides with half-integer spins

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

Cho, Herman

2016-09-01

Allowed transition energies and eigenstate expansions have been calculated and tabulated in numerical form as functions of the electric field gradient asymmetry parameter for the zero field Hamiltonian of quadrupolar nuclides with I = 3/2, 5/2, 7/2, and 9/2. These results may be used to interpret nuclear quadrupole resonance (NQR) spectra and extract accurate values of the electric field gradient tensors. Applications of NQR methods to studies of electronic structure in heavy element systems are proposed. This material is based upon work supported by the U.S. Department of Energy Office of Science, Office of Basic Energy Sciences, Heavy Element Chemistrymore » program.« less

Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories

NASA Astrophysics Data System (ADS)

Surana, K. S.; Joy, A. D.; Reddy, J. N.

2017-03-01

This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements ( ±b \\varvec{u}) and (ii) three internal rotations ({}_i ±b \\varvec{Θ}) about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations ({}_e ±b \\varvec{Θ}) about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to ±b \\varvec{u} and {}_e ±b \\varvec{{Θ} as six degrees of freedom at a material point. The internal rotations ({}_i ±b \\varvec{Θ}), often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations {}_i ±b \\varvec{Θ} are resisted by the deforming matter, conjugate moment tensor arises that together with {}_i ±b \\varvec{Θ} may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations {}_e ±b \\varvec{Θ} also result in conjugate moment tensor which, together with {}_e ±b \\varvec{Θ}, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed.

Modeling of surface effects in crystalline materials within the framework of gradient crystal plasticity

NASA Astrophysics Data System (ADS)

Peng, Xiang-Long; Husser, Edgar; Huang, Gan-Yun; Bargmann, Swantje

2018-03-01

A finite-deformation gradient crystal plasticity theory is developed, which takes into account the interaction between dislocations and surfaces. The model captures both energetic and dissipative effects for surfaces penetrable by dislocations. By taking advantage of the principle of virtual power, the surface microscopic boundary equations are obtained naturally. Surface equations govern surface yielding and hardening. A thin film under shear deformation serves as a benchmark problem for validation of the proposed model. It is found that both energetic and dissipative surface effects significantly affect the plastic behavior.

Symposium on Continuum Models and Discrete Systems (6th) Held in Dijon, France on June 26 - 29, 1989

DTIC Science & Technology

1986-01-01

regard the I’ Burgers’ vector and the dislocation density tensor as measures of defectiveness. This practice can be given a systematic flavour . To begin...behaviour aims at describing the two main mechanisms of deformation, namely plastic slip of two granules over one another and changes of microstructure as

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

PubMed

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

2007-06-01

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

Puncture mechanics of soft elastomeric membrane with large deformation by rigid cylindrical indenter

NASA Astrophysics Data System (ADS)

Liu, Junjie; Chen, Zhe; Liang, Xueya; Huang, Xiaoqiang; Mao, Guoyong; Hong, Wei; Yu, Honghui; Qu, Shaoxing

2018-03-01

Soft elastomeric membrane structures are widely used and commonly found in engineering and biological applications. Puncture is one of the primary failure modes of soft elastomeric membrane at large deformation when indented by rigid objects. In order to investigate the puncture failure mechanism of soft elastomeric membrane with large deformation, we study the deformation and puncture failure of silicone rubber membrane that results from the continuous axisymmetric indentation by cylindrical steel indenters experimentally and analytically. In the experiment, effects of indenter size and the friction between the indenter and the membrane on the deformation and puncture failure of the membrane are investigated. In the analytical study, a model within the framework of nonlinear field theory is developed to describe the large local deformation around the punctured area, as well as to predict the puncture failure of the membrane. The deformed membrane is divided into three parts and the friction contact between the membrane and indenter is modeled by Coulomb friction law. The first invariant of the right Cauchy-Green deformation tensor I1 is adopted to predict the puncture failure of the membrane. The experimental and analytical results agree well. This work provides a guideline in designing reliable soft devices featured with membrane structures, which are present in a wide variety of applications.

Global Earth Response to Loading by Ocean Tide Models

NASA Technical Reports Server (NTRS)

Estes, R. H.; Strayer, J. M.

1979-01-01

Mathematical and programming techniques to numerically calculate Earth response to global semidiurnal and diurnal ocean tide models were developed. Global vertical crustal deformations were evaluated for M sub 2, S sub 2, N sub 2, K sub 2, K sub 1, O sub 1, and P sub 1 ocean tide loading, while horizontal deformations were evaluated for the M sub 2 tidal load. Tidal gravity calculations were performed for M sub 2 tidal loads, and strain tensor elements were evaluated for M sub 2 loads. The M sub 2 solution used for the ocean tide included the effects of self-gravitation and crustal loading.

Medial-based deformable models in nonconvex shape-spaces for medical image segmentation.

PubMed

McIntosh, Chris; Hamarneh, Ghassan

2012-01-01

We explore the application of genetic algorithms (GA) to deformable models through the proposition of a novel method for medical image segmentation that combines GA with nonconvex, localized, medial-based shape statistics. We replace the more typical gradient descent optimizer used in deformable models with GA, and the convex, implicit, global shape statistics with nonconvex, explicit, localized ones. Specifically, we propose GA to reduce typical deformable model weaknesses pertaining to model initialization, pose estimation and local minima, through the simultaneous evolution of a large number of models. Furthermore, we constrain the evolution, and thus reduce the size of the search-space, by using statistically-based deformable models whose deformations are intuitive (stretch, bulge, bend) and are driven in terms of localized principal modes of variation, instead of modes of variation across the entire shape that often fail to capture localized shape changes. Although GA are not guaranteed to achieve the global optima, our method compares favorably to the prevalent optimization techniques, convex/nonconvex gradient-based optimizers and to globally optimal graph-theoretic combinatorial optimization techniques, when applied to the task of corpus callosum segmentation in 50 mid-sagittal brain magnetic resonance images.

Theoretical analysis of sheet metal formability

NASA Astrophysics Data System (ADS)

Zhu, Xinhai

Sheet metal forming processes are among the most important metal-working operations. These processes account for a sizable proportion of manufactured goods made in industrialized countries each year. Furthermore, to reduce the cost and increase the performance of manufactured products, in addition to the environmental concern, more and more light weight and high strength materials have been used as a substitute to the conventional steel. These materials usually have limited formability, thus, a thorough understanding of the deformation processes and the factors limiting the forming of sound parts is important, not only from a scientific or engineering viewpoint, but also from an economic point of view. An extensive review of previous studies pertaining to theoretical analyses of Forming Limit Diagrams (FLDs) is contained in Chapter I. A numerical model to analyze the neck evolution process is outlined in Chapter II. With the use of strain gradient theory, the effect of initial defect profile on the necking process is analyzed. In the third chapter, the method proposed by Storen and Rice is adopted to analyze the initiation of localized neck and predict the corresponding FLDs. In view of the fact that the width of the localized neck is narrow, the deformation inside the neck region is constrained by the material in the neighboring homogeneous region. The relative rotation effect may then be assumed to be small and is thus neglected. In Chapter IV, Hill's 1948 yield criterion and strain gradient theory are employed to obtain FLDs, for planar anisotropic sheet materials by using bifurcation analysis. The effects of the strain gradient coefficient c and the material anisotropic parameters R's on the orientation of the neck and FLDs are analyzed in a systematic manner and compared with experiments. In Chapter V, Hill's 79 non-quadratic yield criterion with a deformation theory of plasticity is used along with bifurcation analyses to derive a general analytical expression for calculating FLDs. In the final chapter, a method is proposed to construct forming limit diagrams for sheet metals under different deformation histories. This analysis employs Hill's 79 anisotropic yield function and uses strain gradient theory to describe the constitutive equation for the flow stress. In order to utilize an analytical method developed earlier for proportional loading, the concept of "virtual deformation" is introduced. The actual deformation path is divided into a sequence of linear paths and an effective "virtual deformation" path is defined having a strain ratio identical to that of the linear part in the final deformation stage, and a plastic work identical to that of the prior actual deformation it is replacing. (Abstract shortened by UMI.)

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

PubMed

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

2015-10-14

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

Piezo-optic tensor of crystals from quantum-mechanical calculations

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

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

2015-10-14

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

Diffusion tensor imaging using multiple coils for mouse brain connectomics.

PubMed

Nouls, John C; Badea, Alexandra; Anderson, Robert B J; Cofer, Gary P; Allan Johnson, G

2018-06-01

The correlation between brain connectivity and psychiatric or neurological diseases has intensified efforts to develop brain connectivity mapping techniques on mouse models of human disease. The neural architecture of mouse brain specimens can be shown non-destructively and three-dimensionally by diffusion tensor imaging, which enables tractography, the establishment of a connectivity matrix and connectomics. However, experiments on cohorts of animals can be prohibitively long. To improve throughput in a 7-T preclinical scanner, we present a novel two-coil system in which each coil is shielded, placed off-isocenter along the axis of the magnet and connected to a receiver circuit of the scanner. Preservation of the quality factor of each coil is essential to signal-to-noise ratio (SNR) performance and throughput, because mouse brain specimen imaging at 7 T takes place in the coil-dominated noise regime. In that regime, we show a shielding configuration causing no SNR degradation in the two-coil system. To acquire data from several coils simultaneously, the coils are placed in the magnet bore, around the isocenter, in which gradient field distortions can bias diffusion tensor imaging metrics, affect tractography and contaminate measurements of the connectivity matrix. We quantified the experimental alterations in fractional anisotropy and eigenvector direction occurring in each coil. We showed that, when the coils were placed 12 mm away from the isocenter, measurements of the brain connectivity matrix appeared to be minimally altered by gradient field distortions. Simultaneous measurements on two mouse brain specimens demonstrated a full doubling of the diffusion tensor imaging throughput in practice. Each coil produced images devoid of shading or artifact. To further improve the throughput of mouse brain connectomics, we suggested a future expansion of the system to four coils. To better understand acceptable trade-offs between imaging throughput and connectivity matrix integrity, studies may seek to clarify how measurement variability, post-processing techniques and biological variability impact mouse brain connectomics. Copyright © 2018 John Wiley & Sons, Ltd.

A Bayesian approach to distinguishing interdigitated tongue muscles from limited diffusion magnetic resonance imaging.

PubMed

Ye, Chuyang; Murano, Emi; Stone, Maureen; Prince, Jerry L

2015-10-01

The tongue is a critical organ for a variety of functions, including swallowing, respiration, and speech. It contains intrinsic and extrinsic muscles that play an important role in changing its shape and position. Diffusion tensor imaging (DTI) has been used to reconstruct tongue muscle fiber tracts. However, previous studies have been unable to reconstruct the crossing fibers that occur where the tongue muscles interdigitate, which is a large percentage of the tongue volume. To resolve crossing fibers, multi-tensor models on DTI and more advanced imaging modalities, such as high angular resolution diffusion imaging (HARDI) and diffusion spectrum imaging (DSI), have been proposed. However, because of the involuntary nature of swallowing, there is insufficient time to acquire a sufficient number of diffusion gradient directions to resolve crossing fibers while the in vivo tongue is in a fixed position. In this work, we address the challenge of distinguishing interdigitated tongue muscles from limited diffusion magnetic resonance imaging by using a multi-tensor model with a fixed tensor basis and incorporating prior directional knowledge. The prior directional knowledge provides information on likely fiber directions at each voxel, and is computed with anatomical knowledge of tongue muscles. The fiber directions are estimated within a maximum a posteriori (MAP) framework, and the resulting objective function is solved using a noise-aware weighted ℓ1-norm minimization algorithm. Experiments were performed on a digital crossing phantom and in vivo tongue diffusion data including three control subjects and four patients with glossectomies. On the digital phantom, effects of parameters, noise, and prior direction accuracy were studied, and parameter settings for real data were determined. The results on the in vivo data demonstrate that the proposed method is able to resolve interdigitated tongue muscles with limited gradient directions. The distributions of the computed fiber directions in both the controls and the patients were also compared, suggesting a potential clinical use for this imaging and image analysis methodology. Copyright © 2015 Elsevier Ltd. All rights reserved.

The drift force on an object in an inviscid weakly-varying rotational flow

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

Wallis, G.B.

The force on any stationary object in an inviscid incompressible extensive steady flow is derived in terms of the added mass tensor and gradient of velocity of the undisturbed fluid. Taylor`s theorem is extended to flows with weak vorticity. There are possible applications to constitutive equations for two-phase flow.

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

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.

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

Snyder-like modified gravity in Newton's spacetime

NASA Astrophysics Data System (ADS)

Leiva, Carlos

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder-like deformation in the background of the Kepler problem. In order to accomplish that task, a Newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion-free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity-independent that is a feature present in other classical approaches to the problem. In this sense, the effect of introducing a deformed algebra is examined and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.

Study of wavefront error and polarization of a side mounted infrared window

NASA Astrophysics Data System (ADS)

Liu, Jiaguo; Li, Lin; Hu, Xinqi; Yu, Xin

2008-03-01

The wavefront error and polarization of a side mounted infrared window made of ZnS are studied. The Infrared windows suffer from temperature gradient and stress during their launch process. Generally, the gradient in temperature changes the refractive index of the material whereas stress produces deformation and birefringence. In this paper, a thermal finite element analysis (FEA) of an IR window is presented. For this purpose, we employed an FEA program Ansys to obtain the time-varying temperature field. The deformation and stress of the window are derived from a structural FEA with the aerodynamic force and the temperature field previously obtained as being the loads. The deformation, temperature field, stress field, ray tracing and Jones Calculus are used to calculate the wavefront error and the change of polarization state.

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.

Search for Earthquake-Induced Prompt Gravity Signals in Gravimetric Data: Data Analysis and a New Observation Model

NASA Astrophysics Data System (ADS)

Kimura, M.; Kame, N.; Watada, S.; Ohtani, M.; Araya, A.; Imanishi, Y.; Ando, M.; Kunugi, T.

2017-12-01

Seismic waves radiated from an earthquake rupture induces density perturbations of the medium, which in turn generates prompt gravity changes at all distances before the arrival of seismic waves. Detection of the gravity signal before the seismic one is a challenge in seismology. In this study, we searched for the prompt gravity changes from the 2011 Tohoku-Oki earthquake in data recorded by gravimeters, seismometers, and tiltmeters. Predicted changes from the currently used simplified model were not identified using band-pass filtering and multi-station stacking even though sufficient signal-to-noise ratios were achieved. Our data analysis raised discrepancy between the data and the theoretical model. To interpret the absence of signals in the data, we investigated the effect of self-gravity deformation on the measurement of gravitational acceleration, which has been ignored in the existing theory. We analytically calculated the displacement of the observation station induced by the prompt gravity changes in an infinite homogeneous medium, and showed that before the arrival of P waves each point in the medium moves at an acceleration identical to the applied gravity change, i.e., free-falls. As a result of the opposite inertial force, gravity sensors attached to the medium lose their sensitivity to the prompt gravity changes. This new observation model incorporated with the self-gravity effect explains the absence of such prompt signals in the acceleration data. We have shown the negative observability in acceleration, but there remains a possibility of detection of its spatial gradients or spatial strain. For a future detection experiment, we derived an analytical expression of the theoretical gravity gradients from a general seismic source described as a moment tensor.

Soft phononic crystals with deformation-independent band gaps

PubMed Central

2017-01-01

Soft phononic crystals have the advantages over their stiff counterparts of being flexible and reconfigurable. Normally, the band gaps of soft phononic crystals will be modified after deformation due to both geometric and constitutive nonlinearity. Indeed these are important properties that can be exploited to tune the dynamic properties of the material. However, in some instances, it may be that one wishes to deform the medium while retaining the band gap structure. A special class of soft phononic crystals is described here with band gaps that are independent or almost-independent of the imposed mechanical deformation, which enables the design of phononic crystals with robust performance. This remarkable behaviour originates from transformation elasticity theory, which leaves the wave equation and the eigenfrequencies invariant after deformation. The necessary condition to achieve such a property is that the Lagrangian elasticity tensor of the hyperelastic material should be constant, i.e. independent of deformation. It is demonstrated that incompressible neo-Hookean materials exhibit such a unique property. Semilinear materials also possess this property under special loading conditions. Phononic crystals composed of these two materials are studied theoretically and the predictions of invariance, or the manner in which the response deviates from invariance, are confirmed via numerical simulation. PMID:28484331

On space of integrable quantum field theories

DOE PAGES

Smirnov, F. A.; Zamolodchikov, A. B.

2016-12-21

Here, we study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as “effective field theories”, with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields X s, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars X s are built from the components of the associated conserved currents in a universal way. The first of these scalars, X 1, coincides with the composite field View the MathMLmore » source(TT¯) built from the components of the energy–momentum tensor. The deformations of quantum field theories generated by X 1 are “solvable” in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations X s are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators X s in sine-Gordon theory. Lastly, we also make some remarks on the problem of UV completeness of such integrable deformations.« less

Real-time simulation and visualization of volumetric brain deformation for image-guided neurosurgery

NASA Astrophysics Data System (ADS)

Ferrant, Matthieu; Nabavi, Arya; Macq, Benoit M. M.; Kikinis, Ron; Warfield, Simon K.

2001-05-01

During neurosurgery, the challenge for the neurosurgeon is to remove as much as possible of a tumor without destroying healthy tissue. This can be difficult because healthy and diseased tissue can have the same visual appearance. To this aim, and because the surgeon cannot see underneath the brain surface, image-guided neurosurgery systems are being increasingly used. However, during surgery, deformation of the brain occurs (due to brain shift and tumor resection), therefore causing errors in the surgical planning with respect to preoperative imaging. In our previous work, we developed software for capturing the deformation of the brain during neurosurgery. The software also allows preoperative data to be updated according to the intraoperative imaging so as to reflect the shape changes of the brain during surgery. Our goal in this paper was to rapidly visualize and characterize this deformation over the course of surgery with appropriate tools. Therefore, we developed tools allowing the doctor to visualize (in 2D and 3D) deformations, as well as the stress tensors characterizing the deformation along with the updated preoperative and intraoperative imaging during the course of surgery. Such tools significantly add to the value of intraoperative imaging and hence could improve surgical outcomes.

A transverse isotropic constitutive model for the aortic valve tissue incorporating rate-dependency and fibre dispersion: Application to biaxial deformation.

PubMed

Anssari-Benam, Afshin; Tseng, Yuan-Tsan; Bucchi, Andrea

2018-05-26

This paper presents a continuum-based transverse isotropic model incorporating rate-dependency and fibre dispersion, applied to the planar biaxial deformation of aortic valve (AV) specimens under various stretch rates. The rate dependency of the mechanical behaviour of the AV tissue under biaxial deformation, the (pseudo-) invariants of the right Cauchy-Green deformation-rate tensor Ċ associated with fibre dispersion, and a new fibre orientation density function motivated by fibre kinematics are presented for the first time. It is shown that the model captures the experimentally observed deformation of the specimens, and characterises a shear-thinning behaviour associated with the dissipative (viscous) kinematics of the matrix and the fibres. The application of the model for predicting the deformation behaviour of the AV under physiological rates is illustrated and an example of the predicted σ-λ curves is presented. While the development of the model was principally motivated by the AV biomechanics requisites, the comprehensive theoretical approach employed in the study renders the model suitable for application to other fibrous soft tissues that possess similar rate-dependent and structural attributes. Crown Copyright © 2018. Published by Elsevier Ltd. All rights reserved.

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

A novel registration-based methodology for prediction of trabecular bone fabric from clinical QCT: A comprehensive analysis

PubMed Central

Reyes, Mauricio; Zysset, Philippe

2017-01-01

Osteoporosis leads to hip fractures in aging populations and is diagnosed by modern medical imaging techniques such as quantitative computed tomography (QCT). Hip fracture sites involve trabecular bone, whose strength is determined by volume fraction and orientation, known as fabric. However, bone fabric cannot be reliably assessed in clinical QCT images of proximal femur. Accordingly, we propose a novel registration-based estimation of bone fabric designed to preserve tensor properties of bone fabric and to map bone fabric by a global and local decomposition of the gradient of a non-rigid image registration transformation. Furthermore, no comprehensive analysis on the critical components of this methodology has been previously conducted. Hence, the aim of this work was to identify the best registration-based strategy to assign bone fabric to the QCT image of a patient’s proximal femur. The normalized correlation coefficient and curvature-based regularization were used for image-based registration and the Frobenius norm of the stretch tensor of the local gradient was selected to quantify the distance among the proximal femora in the population. Based on this distance, closest, farthest and mean femora with a distinction of sex were chosen as alternative atlases to evaluate their influence on bone fabric prediction. Second, we analyzed different tensor mapping schemes for bone fabric prediction: identity, rotation-only, rotation and stretch tensor. Third, we investigated the use of a population average fabric atlas. A leave one out (LOO) evaluation study was performed with a dual QCT and HR-pQCT database of 36 pairs of human femora. The quality of the fabric prediction was assessed with three metrics, the tensor norm (TN) error, the degree of anisotropy (DA) error and the angular deviation of the principal tensor direction (PTD). The closest femur atlas (CTP) with a full rotation (CR) for fabric mapping delivered the best results with a TN error of 7.3 ± 0.9%, a DA error of 6.6 ± 1.3% and a PTD error of 25 ± 2°. The closest to the population mean femur atlas (MTP) using the same mapping scheme yielded only slightly higher errors than CTP for substantially less computing efforts. The population average fabric atlas yielded substantially higher errors than the MTP with the CR mapping scheme. Accounting for sex did not bring any significant improvements. The identified fabric mapping methodology will be exploited in patient-specific QCT-based finite element analysis of the proximal femur to improve the prediction of hip fracture risk. PMID:29176881

Vision-Based Autonomous Sensor-Tasking in Uncertain Adversarial Environments

DTIC Science & Technology

2015-01-02

motion segmentation and change detection in crowd behavior. In particular we investigated Finite Time Lyapunov Exponents, Perron Frobenius Operator and...deformation tensor [11]. On the other hand, eigenfunctions of, the Perron Frobenius operator can be used to detect Almost Invariant Sets (AIS) which are... Perron Frobenius operator. Finally, Figure 1.12d shows the ergodic partitions (EP) obtained based on the eigenfunctions of the Koopman operator

Killing-Yano Symmetry in Supergravity Theories

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi

Killing-Yano symmetry has played an important role in the study of black hole physics. In supergravity theories, Killing-Yano symmetry is deformed by the presence of the fluxes which can be identified with skew-symmetric torsion. Therefore, we attempt to classify spacetimes admitting Killing-Yano symmetry with torsion. In particular, the classification problem of metrics admitting a principal Killing-Yano tensor with torsion is discussed.

Structural Crashworthiness and Failure

DTIC Science & Technology

1993-04-16

body motion occurs. This rigid -plastic idealization for dynamically loaded structures is based upon the fact that the plastic deformation of a...in general, for any tensor variable x, i represents the convective derivative. It should be noted that the rigid body rotation is included in the...clamped, impulsively loaded, rigid - plastic beam.’ (a) First phase of motion with stationary transverse plastic hinges at A and E and stationary plastic

Advective Mixing in a Nondivergent Barotropic Hurricane Model

DTIC Science & Technology

2010-01-20

voted to the mixing of fluid from different regions of a hurri- cane, which is considered as a fundamental mechanism that is intimately related to...range is governed by the Cauchy-Riemann deformation tensor , 1(x0,t0)= ( dx0φ t0+T t0 (x0) )∗( dx0φ t0+T t0 (x0) ) , and becomes maximal when ξ0 is

Timescales of isotropic and anisotropic cluster collapse

NASA Astrophysics Data System (ADS)

Bartelmann, M.; Ehlers, J.; Schneider, P.

1993-12-01

From a simple estimate for the formation time of galaxy clusters, Richstone et al. have recently concluded that the evidence for non-virialized structures in a large fraction of observed clusters points towards a high value for the cosmological density parameter Omega0. This conclusion was based on a study of the spherical collapse of density perturbations, assumed to follow a Gaussian probability distribution. In this paper, we extend their treatment in several respects: first, we argue that the collapse does not start from a comoving motion of the perturbation, but that the continuity equation requires an initial velocity perturbation directly related to the density perturbation. This requirement modifies the initial condition for the evolution equation and has the effect that the collapse proceeds faster than in the case where the initial velocity perturbation is set to zero; the timescale is reduced by a factor of up to approximately equal 0.5. Our results thus strengthens the conclusion of Richstone et al. for a high Omega0. In addition, we study the collapse of density fluctuations in the frame of the Zel'dovich approximation, using as starting condition the analytically known probability distribution of the eigenvalues of the deformation tensor, which depends only on the (Gaussian) width of the perturbation spectrum. Finally, we consider the anisotropic collapse of density perturbations dynamically, again with initial conditions drawn from the probability distribution of the deformation tensor. We find that in both cases of anisotropic collapse, in the Zel'dovich approximation and in the dynamical calculations, the resulting distribution of collapse times agrees remarkably well with the results from spherical collapse. We discuss this agreement and conclude that it is mainly due to the properties of the probability distribution for the eigenvalues of the Zel'dovich deformation tensor. Hence, the conclusions of Richstone et al. on the value of Omega0 can be verified and strengthened, even if a more general approach to the collapse of density perturbations is employed. A simple analytic formula for the cluster redshift distribution in an Einstein-deSitter universe is derived.

Medical image registration by combining global and local information: a chain-type diffeomorphic demons algorithm.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Zhu, Junming; Xu, Dongrong

2013-12-07

The demons algorithm is a popular algorithm for non-rigid image registration because of its computational efficiency and simple implementation. The deformation forces of the classic demons algorithm were derived from image gradients by considering the deformation to decrease the intensity dissimilarity between images. However, the methods using the difference of image intensity for medical image registration are easily affected by image artifacts, such as image noise, non-uniform imaging and partial volume effects. The gradient magnitude image is constructed from the local information of an image, so the difference in a gradient magnitude image can be regarded as more reliable and robust for these artifacts. Then, registering medical images by considering the differences in both image intensity and gradient magnitude is a straightforward selection. In this paper, based on a diffeomorphic demons algorithm, we propose a chain-type diffeomorphic demons algorithm by combining the differences in both image intensity and gradient magnitude for medical image registration. Previous work had shown that the classic demons algorithm can be considered as an approximation of a second order gradient descent on the sum of the squared intensity differences. By optimizing the new dissimilarity criteria, we also present a set of new demons forces which were derived from the gradients of the image and gradient magnitude image. We show that, in controlled experiments, this advantage is confirmed, and yields a fast convergence.

[Preliminary application of an improved Demons deformable registration algorithm in tumor radiotherapy].

PubMed

Zhou, Lu; Zhen, Xin; Lu, Wenting; Dou, Jianhong; Zhou, Linghong

2012-01-01

To validate the efficiency of an improved Demons deformable registration algorithm and evaluate its application in registration of the treatment image and the planning image in image-guided radiotherapy (IGRT). Based on Brox's gradient constancy assumption and Malis's efficient second-order minimization algorithm, a grey value gradient similarity term was added into the original energy function, and a formula was derived to calculate the update of transformation field. The limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm was used to optimize the energy function for automatic determination of the iteration number. The proposed algorithm was validated using mathematically deformed images, physically deformed phantom images and clinical tumor images. Compared with the original Additive Demons algorithm, the improved Demons algorithm achieved a higher precision and a faster convergence speed. Due to the influence of different scanning conditions in fractionated radiation, the density range of the treatment image and the planning image may be different. The improved Demons algorithm can achieve faster and more accurate radiotherapy.

Shear stress along the conduit wall as a plausible source of tilt at Soufrière Hills volcano, Montserrat

NASA Astrophysics Data System (ADS)

Green, D. N.; Neuberg, J.; Cayol, V.

2006-05-01

Surface deformations recorded in close proximity to the active lava dome at Soufrière Hills volcano, Montserrat, can be used to infer stresses within the uppermost 1000 m of the conduit system. Most deformation source models consider only isotropic pressurisation of the conduit. We show that tilt recorded during rapid magma extrusion in 1997 could have also been generated by shear stresses sustained along the conduit wall; these stresses are a consequence of pressure gradients that develop along the conduit. Numerical modelling, incorporating realistic topography, can reproduce both the morphology and half the amplitude of the measured deformation field using a realistic shear stress amplitude, equivalent to a pressure gradient of 3.5 × 104 Pa m-1 along a 1000 m long conduit with a 15 m radius. This shear stress model has advantages over the isotropic pressure models because it does not require either physically unattainable overpressures or source radii larger than 200 m to explain the same deformation.

A dislocation-based, strain–gradient–plasticity strengthening model for deformation processed metal–metal composites

DOE PAGES

Tian, Liang; Russell, Alan; Anderson, Iver

2014-01-03

Deformation processed metal–metal composites (DMMCs) are high-strength, high-electrical conductivity composites developed by severe plastic deformation of two ductile metal phases. The extraordinarily high strength of DMMCs is underestimated using the rule of mixture (or volumetric weighted average) of conventionally work-hardened metals. A dislocation-density-based, strain–gradient–plasticity model is proposed to relate the strain-gradient effect with the geometrically necessary dislocations emanating from the interface to better predict the strength of DMMCs. The model prediction was compared with our experimental findings of Cu–Nb, Cu–Ta, and Al–Ti DMMC systems to verify the applicability of the new model. The results show that this model predicts themore » strength of DMMCs better than the rule-of-mixture model. The strain-gradient effect, responsible for the exceptionally high strength of heavily cold worked DMMCs, is dominant at large deformation strain since its characteristic microstructure length is comparable with the intrinsic material length.« less

Using the full tensor of GOCE gravity gradients for regional gravity field modelling

NASA Astrophysics Data System (ADS)

Lieb, Verena; Bouman, Johannes; Dettmering, Denise; Fuchs, Martin; Schmidt, Michael

2013-04-01

With its 3-axis gradiometer GOCE delivers 3-dimensional (3D) information of the Earth's gravity field. This essential advantage - e.g. compared with the 1D gravity field information from GRACE - can be used for research on the Earth's interior and for geophysical exploration. To benefit from this multidimensional measurement system, the combination of all 6 GOCE gradients and additionally the consistent combination with other gravity observations mean an innovative challenge for regional gravity field modelling. As the individual gravity gradients reflect the gravity field depending on different spatial directions, observation equations are formulated separately for each of these components. In our approach we use spherical localizing base functions to display the gravity field for specified regions. Therefore the series expansions based on Legendre polynomials have to be adopted to obtain mathematical expressions for the second derivatives of the gravitational potential which are observed by GOCE in the Cartesian Gradiometer Reference Frame (GRF). We (1) have to transform the equations from the spherical terrestrial into a Cartesian Local North-Oriented Reference Frame (LNOF), (2) to set up a 3x3 tensor of observation equations and (3) finally to rotate the tensor defined in the terrestrial LNOF into the GRF. Thus we ensure the use of the original non-rotated and unaffected GOCE measurements within the analysis procedure. As output from the synthesis procedure we then obtain the second derivatives of the gravitational potential for all combinations of the xyz Cartesian coordinates in the LNOF. Further the implementation of variance component estimation provides a flexible tool to diversify the influence of the input gradiometer observations. On the one hand the less accurate xy and yz measurements are nearly excluded by estimating large variance components. On the other hand the yy measurements, which show systematic errors increasing at high latitudes, could be manually down-weighted in the corresponding regions. We choose different test areas to compute regional gravity field models at mean GOCE altitudes for different spectral resolutions and varying relative weights for the observations. Further we compare the regional models with the static global GOCO03S model. Especially the flexible handling and combination of the 3D measurements promise a great benefit for geophysical applications from GOCE gravity gradients, as they contain information on radial as well as on lateral gravity changes.

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

NASA Astrophysics Data System (ADS)

Lu, Biao; Luo, Zhicai; Zhong, Bo; Zhou, Hao; Flechtner, Frank; Förste, Christoph; Barthelmes, Franz; Zhou, Rui

2017-11-01

Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model's spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components V_{xy} and V_{yz} of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE's inclination of 96.7° . With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of V_{xy} and V_{yz} are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT_R1's accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/leveling data.

Global Solutions to Repulsive Hookean Elastodynamics

NASA Astrophysics Data System (ADS)

Hu, Xianpeng; Masmoudi, Nader

2017-01-01

The global existence of classical solutions to the three dimensional repulsive Hookean elastodynamics around an equilibrium is considered. By linearization and Hodge's decomposition, the compressible part of the velocity, the density, and the compressible part of the transpose of the deformation gradient satisfy Klein-Gordon equations with speed {√{2}}, while the incompressible parts of the velocity and of the transpose of the deformation gradient satisfy wave equations with speed one. The space-time resonance method combined with the vector field method is used in a novel way to obtain the decay of the solution and hence global existence.

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.

Ergodic actions of SμU(2) on C∗-algebras from II1 subfactors

NASA Astrophysics Data System (ADS)

Pinzari, Claudia; Roberts, John E.

2010-03-01

To a proper inclusion N⊂M of II factors of finite Jones index [M:N], we associate an ergodic C∗-action of the quantum group SμU(2) (or more generally of certain groups Ao(F)). The higher relative commutant N'∩M can be identified with the spectral space of the rth tensor power u of the defining representation of the quantum group. The index and the deformation parameter are related by -1≤μ<0 and [M:N]=|μ+μ-1|. This ergodic action may be thought of as a virtual subgroup of SμU(2) in the sense of Mackey arising from the tensor category generated by the N-bimodule NMN. μ is negative as NMN is a real bimodule.

The influence of normal fault geometry on porous sandstone deformation: Insights from mechanical models into conditions leading to Coulomb failure and shear-enhanced compaction

NASA Astrophysics Data System (ADS)

Allison, K.; Reinen, L. A.

2011-12-01

Slip on non-planar faults produces stress perturbations in the surrounding host rock that can yield secondary faults at a scale too small to be resolved on seismic surveys. Porosity changes during failure may affect the ability of the rock to transmit fluids through dilatant cracking or, in porous rocks, shear-enhanced compaction (i.e., cataclastic flow). Modeling the mechanical behavior of the host rock in response to slip on non-planar faults can yield insights into the role of fault geometry on regions of enhanced or inhibited fluid flow. To evaluate the effect of normal fault geometry on deformation in porous sandstones, we model the system as a linear elastic, homogeneous, whole or half space using the boundary-element modeling program Poly3D. We consider conditions leading to secondary deformation using the maximum Coulomb shear stress (MCSS) as an index of brittle deformation and proximity to an elliptical yield envelope (Y), determined experimentally for porous sandstone (Baud et al., JGR, 2006), for cataclastic flow. We model rectangular faults consisting of two segments: an upper leg with a constant dip of 60° and a lower leg with dips ranging 15-85°. We explore far-field stress models of constant and gradient uniaxial strain. We investigate the potential damage in the host rock in two ways: [1] the size of the damage zone, and [2] regions of enhanced deformation indicated by elevated MCSS or Y. Preliminary results indicate that, along a vertical transect passing through the fault kink, [1] the size of the damage zone increases in the footwall with increasing lower leg dip and remains constant in the hanging wall. [2] In the footwall, the amount of deformation does not change as a function of lower leg dip in constant stress models; in gradient stress models, both MCSS and Y increase with dip. In the hanging wall, Y decreases with increasing lower leg dip for both constant and gradient stress models. In contrast, MCSS increases: as lower leg dip increases for constant stress models, and as the difference between lower leg dip and 60° increases for gradient stress models. These preliminary results indicate that the dip of the lower fault segment significantly affects the amount and style of deformation in the host rock.

A Matlab user interface for the statistically assisted fluid registration algorithm and tensor-based morphometry

NASA Astrophysics Data System (ADS)

Yepes-Calderon, Fernando; Brun, Caroline; Sant, Nishita; Thompson, Paul; Lepore, Natasha

2015-01-01

Tensor-Based Morphometry (TBM) is an increasingly popular method for group analysis of brain MRI data. The main steps in the analysis consist of a nonlinear registration to align each individual scan to a common space, and a subsequent statistical analysis to determine morphometric differences, or difference in fiber structure between groups. Recently, we implemented the Statistically-Assisted Fluid Registration Algorithm or SAFIRA,1 which is designed for tracking morphometric differences among populations. To this end, SAFIRA allows the inclusion of statistical priors extracted from the populations being studied as regularizers in the registration. This flexibility and degree of sophistication limit the tool to expert use, even more so considering that SAFIRA was initially implemented in command line mode. Here, we introduce a new, intuitive, easy to use, Matlab-based graphical user interface for SAFIRA's multivariate TBM. The interface also generates different choices for the TBM statistics, including both the traditional univariate statistics on the Jacobian matrix, and comparison of the full deformation tensors.2 This software will be freely disseminated to the neuroimaging research community.

Evolution of plastic anisotropy for high-strain-rate computations

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

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

1994-12-01

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

Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements

NASA Astrophysics Data System (ADS)

Paschall, Randall N.; Anderson, David J.

1993-11-01

A linear quadratic Gaussian method is proposed for a deformable mirror adaptive optics system control. Estimates of system states describing the distortion are generated by a Kalman filter based on Hartmann wave front measurements of the wave front gradient.

A numerical investigation into the ability of the Poisson PDE to extract the mass-density from land-based gravity data: A case study of salt diapirs in the north coast of the Persian Gulf

NASA Astrophysics Data System (ADS)

AllahTavakoli, Yahya; Safari, Abdolreza

2017-08-01

This paper is counted as a numerical investigation into the capability of Poisson's Partial Differential Equation (PDE) at Earth's surface to extract the near-surface mass-density from land-based gravity data. For this purpose, first it focuses on approximating the gradient tensor of Earth's gravitational potential by means of land-based gravity data. Then, based on the concepts of both the gradient tensor and Poisson's PDE at the Earth's surface, certain formulae are proposed for the mass-density determination. Furthermore, this paper shows how the generalized Tikhonov regularization strategy can be used for enhancing the efficiency of the proposed approach. Finally, in a real case study, the formulae are applied to 6350 gravity stations located within a part of the north coast of the Persian Gulf. The case study numerically indicates that the proposed formulae, provided by Poisson's PDE, has the ability to convert land-based gravity data into the terrain mass-density which has been used for depicting areas of salt diapirs in the region of the case study.

Higher-Order Motion-Compensation for In Vivo Cardiac Diffusion Tensor Imaging in Rats

PubMed Central

Welsh, Christopher L.; DiBella, Edward V. R.; Hsu, Edward W.

2015-01-01

Motion of the heart has complicated in vivo applications of cardiac diffusion MRI and diffusion tensor imaging (DTI), especially in small animals such as rats where ultra-high-performance gradient sets are currently not available. Even with velocity compensation via, for example, bipolar encoding pulses, the variable shot-to-shot residual motion-induced spin phase can still give rise to pronounced artifacts. This study presents diffusion-encoding schemes that are designed to compensate for higher-order motion components, including acceleration and jerk, which also have the desirable practical features of minimal TEs and high achievable b-values. The effectiveness of these schemes was verified numerically on a realistic beating heart phantom, and demonstrated empirically with in vivo cardiac diffusion MRI in rats. Compensation for acceleration, and lower motion components, was found to be both necessary and sufficient for obtaining diffusion-weighted images of acceptable quality and SNR, which yielded the first in vivo cardiac DTI demonstrated in the rat. These findings suggest that compensation for higher order motion, particularly acceleration, can be an effective alternative solution to high-performance gradient hardware for improving in vivo cardiac DTI. PMID:25775486

Weakening gravity on redshift-survey scales with kinetic matter mixing

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

D'Amico, Guido; Huang, Zhiqi; Mancarella, Michele

We explore general scalar-tensor models in the presence of a kinetic mixing between matter and the scalar field, which we call Kinetic Matter Mixing. In the frame where gravity is de-mixed from the scalar this is due to disformal couplings of matter species to the gravitational sector, with disformal coefficients that depend on the gradient of the scalar field. In the frame where matter is minimally coupled, it originates from the so-called beyond Horndeski quadratic Lagrangian. We extend the Effective Theory of Interacting Dark Energy by allowing disformal coupling coefficients to depend on the gradient of the scalar field asmore » well. In this very general approach, we derive the conditions to avoid ghost and gradient instabilities and we define Kinetic Matter Mixing independently of the frame metric used to described the action. We study its phenomenological consequences for a ΛCDM background evolution, first analytically on small scales. Then, we compute the matter power spectrum and the angular spectra of the CMB anisotropies and the CMB lensing potential, on all scales. We employ the public version of COOP, a numerical Einstein-Boltzmann solver that implements very general scalar-tensor modifications of gravity. Rather uniquely, Kinetic Matter Mixing weakens gravity on short scales, predicting a lower σ{sub 8} with respect to the ΛCDM case. We propose this as a possible solution to the tension between the CMB best-fit model and low-redshift observables.« less

Coupled effects of impact and orogeny: Is the marine Lockne crater, Sweden, pristine?

NASA Astrophysics Data System (ADS)

Kenkmann, T.; Kiebach, F.; Rosenau, M.; Raschke, U.; Pigowske, A.; Mittelhaus, K.; Eue, D.

Our current understanding of marine-impact cratering processes is partly inferred from the geological structure of the Lockne crater. We present results of a mapping campaign and structural data indicating that this crater is not pristine. In the western part of the crater, pre-impact, impact, and post-impact rocks are incorporated in Caledonian thrust slices and are subjected to folding and faulting. A nappe outlier in the central crater depression is a relic of the Caledonian nappe cover that reached a thickness of more than 5 km. The overthrusted crater is gently deformed. Strike of strata and trend of fold axes deviate from standard Caledonian directions (northeast-southwest). Radially oriented crater depressions, which were previously regarded as marine resurge gullies formed when resurging seawater erosively cut through the crater brim, are interpreted to be open synclines in which resurge deposits were better preserved.The presence of the impact structure influenced orogenesis due to morphological and lithological anomalies of the crater: i) a raised crater brim zone acted as an obstacle during nappe propagation, (ii) the occurrence of a central crater depression caused downward sagging of nappes, and (iii) the lack of an appropriate detachment horizon (alum shale) within the crater led to an enhanced mechanical coupling and internal deformation of the nappe and the overthrusted foreland. Preliminary results of 3-D-analogue experiments suggest that a circular high-friction zone representing the crater locally hinders nappe propagation and initiates a circumferentially striking ramp fault that delineates the crater. Crustal shortening is also partitioned into the crater basement and decreases laterally outward. Deformation of the foreland affected the geometry of the detachment and could be associated with the activation of a deeper detachment horizon beneath the crater. Strain gradients both vertically and horizontally result in non-plane strain deformation in the vicinity of the crater. The strain tensors in the hanging and foot walls may deviate up to 90° from each other and rotated by up to 45° with respect to the standard regional orientation. The observed deflection of strata and fold axes within the Lockne crater area as revealed by field mapping is in agreement with the pattern of strain partitioning shown in the analogue models.

Calibrating a tensor magnetic gradiometer using spin data

USGS Publications Warehouse

Bracken, Robert E.; Smith, David V.; Brown, Philip J.

2005-01-01

Scalar magnetic data are often acquired to discern characteristics of geologic source materials and buried objects. It is evident that a great deal can be done with scalar data, but there are significant advantages to direct measurement of the magnetic gradient tensor in applications with nearby sources, such as unexploded ordnance (UXO). To explore these advantages, we adapted a prototype tensor magnetic gradiometer system (TMGS) and successfully implemented a data-reduction procedure. One of several critical reduction issues is the precise determination of a large group of calibration coefficients for the sensors and sensor array. To resolve these coefficients, we devised a spin calibration method, after similar methods of calibrating space-based magnetometers (Snare, 2001). The spin calibration procedure consists of three parts: (1) collecting data by slowly revolving the sensor array in the Earth?s magnetic field, (2) deriving a comprehensive set of coefficients from the spin data, and (3) applying the coefficients to the survey data. To show that the TMGS functions as a tensor gradiometer, we conducted an experimental survey that verified that the reduction procedure was effective (Bracken and Brown, in press). Therefore, because it was an integral part of the reduction, it can be concluded that the spin calibration was correctly formulated with acceptably small errors.

Application of a Pore Fraction Hot Tearing Model to Directionally Solidified and Direct Chill Cast Aluminum Alloys

NASA Astrophysics Data System (ADS)

Dou, Ruifeng; Phillion, A. B.

2016-08-01

Hot tearing susceptibility is commonly assessed using a pressure drop equation in the mushy zone that includes the effects of both tensile deformation perpendicular to the thermal gradient as well as shrinkage feeding. In this study, a Pore Fraction hot tearing model, recently developed by Monroe and Beckermann (JOM 66:1439-1445, 2014), is extended to additionally include the effect of strain rate parallel to the thermal gradient. The deformation and shrinkage pore fractions are obtained on the basis of the dimensionless Niyama criterion and a scaling variable method. First, the model is applied to the binary Al-Cu system under conditions of directional solidification. It is shown that for the same Niyama criterion, a decrease in the cooling rate increases both the deformation and shrinkage pore fractions because of an increase in the time spent in the brittle temperature region. Second, the model is applied to the industrial aluminum alloy AA5182 as part of a finite element simulation of the Direct Chill (DC) casting process. It is shown that an increase in the casting speed during DC casting increases the deformation and shrinkage pore fractions, causing the maximum point of pore fraction to move towards the base of the casting. These results demonstrate that including the strain rate parallel to the thermal gradient significantly improves the predictive quality of hot tearing criteria based on the pressure drop equation.

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

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar

Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R 1,d--1. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We also show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, andmore » proportional to the coefficient C T appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ/CT=π 2/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.« less

Diurnal polar motion

NASA Technical Reports Server (NTRS)

Mcclure, P.

1973-01-01

An analytical theory is developed to describe diurnal polar motion in the earth which arises as a forced response due to lunisolar torques and tidal deformation. Doodson's expansion of the tide generating potential is used to represent the lunisolar torques. Both the magnitudes and the rates of change of perturbations in the earth's inertia tensor are included in the dynamical equations for the polar motion so as to account for rotational and tidal deformation. It is found that in a deformable earth with Love's number k = 0.29, the angular momentum vector departs by as much as 20 cm from the rotation axis rather than remaining within 1 or 2 cm as it would in a rigid earth. This 20 cm separation is significant in the interpretation of submeter polar motion observations because it necessitates an additional coordinate transformation in order to remove what would otherwise be a 20 cm error source in the conversion between inertial and terrestrial reference systems.

Remote sensing image stitch using modified structure deformation

NASA Astrophysics Data System (ADS)

Pan, Ke-cheng; Chen, Jin-wei; Chen, Yueting; Feng, Huajun

2012-10-01

To stitch remote sensing images seamlessly without producing visual artifact which is caused by severe intensity discrepancy and structure misalignment, we modify the original structure deformation based stitching algorithm which have two main problems: Firstly, using Poisson equation to propagate deformation vectors leads to the change of the topological relationship between the key points and their surrounding pixels, which may bring in wrong image characteristics. Secondly, the diffusion area of the sparse matrix is too limited to rectify the global intensity discrepancy. To solve the first problem, we adopt Spring-Mass model and bring in external force to keep the topological relationship between key points and their surrounding pixels. We also apply tensor voting algorithm to achieve the global intensity corresponding curve of the two images to solve the second problem. Both simulated and experimental results show that our algorithm is faster and can reach better result than the original algorithm.

Classical Dynamics of Fullerenes

NASA Astrophysics Data System (ADS)

Sławianowski, Jan J.; Kotowski, Romuald K.

2017-06-01

The classical mechanics of large molecules and fullerenes is studied. The approach is based on the model of collective motion of these objects. The mixed Lagrangian (material) and Eulerian (space) description of motion is used. In particular, the Green and Cauchy deformation tensors are geometrically defined. The important issue is the group-theoretical approach to describing the affine deformations of the body. The Hamiltonian description of motion based on the Poisson brackets methodology is used. The Lagrange and Hamilton approaches allow us to formulate the mechanics in the canonical form. The method of discretization in analytical continuum theory and in classical dynamics of large molecules and fullerenes enable us to formulate their dynamics in terms of the polynomial expansions of configurations. Another approach is based on the theory of analytical functions and on their approximations by finite-order polynomials. We concentrate on the extremely simplified model of affine deformations or on their higher-order polynomial perturbations.

A study of microindentation hardness tests by mechanism-based strain gradient plasticity

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

Huang, Y.; Xue, Z.; Gao, H.

2000-08-01

We recently proposed a theory of mechanism-based strain gradient (MSG) plasticity to account for the size dependence of plastic deformation at micron- and submicron-length scales. The MSG plasticity theory connects micron-scale plasticity to dislocation theories via a multiscale, hierarchical framework linking Taylor's dislocation hardening model to strain gradient plasticity. Here we show that the theory of MSG plasticity, when used to study micro-indentation, indeed reproduces the linear dependence observed in experiments, thus providing an important self-consistent check of the theory. The effects of pileup, sink-in, and the radius of indenter tip have been taken into account in the indentation model.more » In accomplishing this objective, we have generalized the MSG plasticity theory to include the elastic deformation in the hierarchical framework. (c) 2000 Materials Research Society.« less

Reynolds and Maxwell stress measurements in the reversed field pinch experiment Extrap-T2R

NASA Astrophysics Data System (ADS)

Vianello, N.; Antoni, V.; Spada, E.; Spolaore, M.; Serianni, G.; Cavazzana, R.; Bergsåker, H.; Cecconello, M.; Drake, J. R.

2005-08-01

The complete Reynolds stress (RS) has been measured in the edge region of the Extrap-T2R reversed field pinch experiment. The RS exhibits a strong gradient in the region where a high E × B shear takes place. Experimental results show this gradient to be almost entirely due to the electrostatic contribution. This has been interpreted as experimental evidence of flow generation via turbulence mechanism. The scales involved in flow generation are deduced from the frequency decomposition of RS tensor. They are found related to magnetohydrodynamic activity but are different with respect to the scales responsible for turbulent transport.

Joint Inversion of Gravity and Gravity Tensor Data Using the Structural Index as Weighting Function Rate Decay

NASA Astrophysics Data System (ADS)

Ialongo, S.; Cella, F.; Fedi, M.; Florio, G.

2011-12-01

Most geophysical inversion problems are characterized by a number of data considerably higher than the number of the unknown parameters. This corresponds to solve highly underdetermined systems. To get a unique solution, a priori information must be therefore introduced. We here analyze the inversion of the gravity gradient tensor (GGT). Previous approaches to invert jointly or independently more gradient components are by Li (2001) proposing an algorithm using a depth weighting function and Zhdanov et alii (2004), providing a well focused inversion of gradient data. Both the methods give a much-improved solution compared with the minimum length solution, which is invariably shallow and not representative of the true source distribution. For very undetermined problems, this feature is due to the role of the depth weighting matrices used by both the methods. Recently, Cella and Fedi (2011) showed however that for magnetic and gravity data the depth weighting function has to be defined carefully, under a preliminary application of Euler Deconvolution or Depth from Extreme Point methods, yielding the appropriate structural index and then using it as the rate decay of the weighting function. We therefore propose to extend this last approach to invert jointly or independently the GGT tensor using the structural index as weighting function rate decay. In case of a joint inversion, gravity data can be added as well. This multicomponent case is also relevant because the simultaneous use of several components and gravity increase the number of data and reduce the algebraic ambiguity compared to the inversion of a single component. The reduction of such ambiguity was shown in Fedi et al, (2005) decisive to get an improved depth resolution in inverse problems, independently from any form of depth weighting function. The method is demonstrated to synthetic cases and applied to real cases, such as the Vredefort impact area (South Africa), characterized by a complex density distribution, well defining a central uplift area, ring structures and low density sediments. REFERENCES Cella F., and Fedi M., 2011, Inversion of potential field data using the structural index as weighting function rate decay, Geophysical Prospecting, doi: 10.1111/j.1365-2478.2011.00974.x Fedi M., Hansen P. C., and Paoletti V., 2005 Analysis of depth resolution in potential-field inversion. Geophysics, 70, NO. 6 Li, Y., 2001, 3-D inversion of gravity gradiometry data: 71st Annual Meeting, SEG, Expanded Abstracts, 1470-1473. Zhdanov, M. S., Ellis, R. G., and Mukherjee, S., 2004, Regularized focusing inversion of 3-D gravity tensor data: Geophysics, 69, 925-937.

Introduction to Vector Field Visualization

NASA Technical Reports Server (NTRS)

Kao, David; Shen, Han-Wei

2010-01-01

Vector field visualization techniques are essential to help us understand the complex dynamics of flow fields. These can be found in a wide range of applications such as study of flows around an aircraft, the blood flow in our heart chambers, ocean circulation models, and severe weather predictions. The vector fields from these various applications can be visually depicted using a number of techniques such as particle traces and advecting textures. In this tutorial, we present several fundamental algorithms in flow visualization including particle integration, particle tracking in time-dependent flows, and seeding strategies. For flows near surfaces, a wide variety of synthetic texture-based algorithms have been developed to depict near-body flow features. The most common approach is based on the Line Integral Convolution (LIC) algorithm. There also exist extensions of LIC to support more flexible texture generations for 3D flow data. This tutorial reviews these algorithms. Tensor fields are found in several real-world applications and also require the aid of visualization to help users understand their data sets. Examples where one can find tensor fields include mechanics to see how material respond to external forces, civil engineering and geomechanics of roads and bridges, and the study of neural pathway via diffusion tensor imaging. This tutorial will provide an overview of the different tensor field visualization techniques, discuss basic tensor decompositions, and go into detail on glyph based methods, deformation based methods, and streamline based methods. Practical examples will be used when presenting the methods; and applications from some case studies will be used as part of the motivation.

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

PubMed

Oshri, Oz; Diamant, Haim

2017-05-01

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

EQUIVALENCE BETWEEN SHORT-TIME BIPHASIC AND INCOMPRESSIBLE ELASTIC MATERIAL RESPONSES

PubMed Central

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

2009-01-01

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

Strain tensor selection and the elastic theory of incompatible thin sheets

NASA Astrophysics Data System (ADS)

Oshri, Oz; Diamant, Haim

2017-05-01

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

Brain structural changes following adaptive cognitive training assessed by Tensor-Based Morphometry (TBM)

PubMed Central

Colom, Roberto; Hua, Xue; Martínez, Kenia; Burgaleta, Miguel; Román, Francisco J.; Gunter, Jeffrey L.; Carmona, Susanna; Jaeggi, Susanne M.; Thompson, Paul M.

2016-01-01

Tensor-Based Morphometry (TBM) allows the automatic mapping of brain changes across time building 3D deformation maps. This technique has been applied for tracking brain degeneration in Alzheimer's and other neurodegenerative diseases with high sensitivity and reliability. Here we applied TBM to quantify changes in brain structure after completing a challenging adaptive cognitive training program based on the n-back task. Twenty-six young women completed twenty-four training sessions across twelve weeks and they showed, on average, large cognitive improvements. High-resolution MRI scans were obtained before and after training. The computed longitudinal deformation maps were analyzed for answering three questions: (a) Are there differential brain structural changes in the training group as compared with a matched control group? (b) Are these changes related to performance differences in the training program? (c) Are standardized changes in a set of psychological factors (fluid and crystallized intelligence, working memory, and attention control) measured before and after training, related to structural changes in the brain? Results showed (a) greater structural changes for the training group in the temporal lobe, (b) a negative correlation between these changes and performance across training sessions (the greater the structural change, the lower the cognitive performance improvements), and (c) negligible effects regarding the psychological factors measured before and after training. PMID:27477628

Near N-S paleo-extension in the western Deccan region, India: Does it link strike-slip tectonics with India-Seychelles rifting?

NASA Astrophysics Data System (ADS)

Misra, Achyuta Ayan; Bhattacharya, Gourab; Mukherjee, Soumyajit; Bose, Narayan

2014-09-01

This is the first detailed report and analyses of deformation from the W part of the Deccan large igneous province (DLIP), Maharashtra, India. This deformation, related to the India-Seychelles rifting during Late Cretaceous-Early Paleocene, was studied, and the paleostress tensors were deduced. Near N-S trending shear zones, lineaments, and faults were already reported without significant detail. An E-W extension was envisaged by the previous workers to explain the India-Seychelles rift at ~64 Ma. The direction of extension, however, does not match with their N-S brittle shear zones and also those faults (sub-vertical, ~NE-SW/~NW-SE, and few ~N-S) we report and emphasize in this work. Slickenside-bearing fault planes, brittle shear zones, and extension fractures in meso-scale enabled us to estimate the paleostress tensors (directions and relative magnitudes). The field study was complemented by remote sensing lineament analyses to map dykes and shear zones. Dykes emplaced along pre-existing ~N-S to ~NE-SW/~NW-SE shears/fractures. This information was used to derive regional paleostress trends. A ~NW-SE/NE-SW minimum compressive stress in the oldest Kalsubai Subgroup and a ~N-S direction for the younger Lonavala, Wai, and Salsette Subgroups were deciphered. Thus, a ~NW/NE to ~N-S extension is put forward that refutes the popular view of E-W India-Seychelles extension. Paleostress analyses indicate that this is an oblique rifted margin. Field criteria suggest only ~NE-SW and ~NW-SE, with some ~N-S strike-slip faults/brittle shear zones. We refer this deformation zone as the "Western Deccan Strike-slip Zone" (WDSZ). The observed deformation was matched with offshore tectonics deciphered mainly from faults interpreted on seismic profiles and from magnetic seafloor spreading anomalies. These geophysical findings too indicate oblique rifting in this part of the W Indian passive margin. We argue that the Seychelles microcontinent separated from India only after much of the DLIP erupted. Further studies of magma-rich passive margins with respect to timing and architecture of deformation and emplacement of volcanics are required.

Detailed fault structure of the 2000 Western Tottori, Japan, earthquake sequence

USGS Publications Warehouse

Fukuyama, E.; Ellsworth, W.L.; Waldhauser, F.; Kubo, A.

2003-01-01

We investigate the faulting process of the aftershock region of the 2000 western Tottori earthquake (Mw 6.6) by combining aftershock hypocenters and moment tensor solutions. Aftershock locations were precisely determined by the double difference method using P- and S-phase arrival data of the Japan Meteorological Agency unified catalog. By combining the relocated hypocenters and moment tensor solutions of aftershocks by broadband waveform inversion of FREESIA (F-net), we successfully resolved very detailed fault structures activated by the mainshock. The estimated fault model resolves 15 individual fault segments that are consistent with both aftershock distribution and focal mechanism solutions. Rupture in the mainshock was principally confined to the three fault elements in the southern half of the zone, which is also where the earliest aftershocks concentrate. With time, the northern part of the zone becomes activated, which is also reflected in the postseismic deformation field. From the stress tensor analysis of aftershock focal mechanisms, we found a rather uniform stress field in the aftershock region, although fault strikes were scattered. The maximum stress direction is N107??E, which is consistent with the tectonic stress field in this region. In the northern part of the fault, where no slip occurred during the mainshock but postseismic slip was observed, the maximum stress direction of N130??E was possible as an alternative solution of stress tensor inversion.

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.

Lifetime of oil drops pressed by buoyancy against a planar interface: Large drops

NASA Astrophysics Data System (ADS)

Rojas, Clara; García-Sucre, Máximo; Urbina-Villalba, Germán

2010-11-01

In a previous report [C. Rojas, G. Urbina-Villalba, and M. García-Sucre, Phys. Rev. E 81, 016302 (2010)10.1103/PhysRevE.81.016302] it was shown that emulsion stability simulations are able to reproduce the lifetime of micrometer-size drops of hexadecane pressed by buoyancy against a planar water-hexadecane interface. It was confirmed that small drops (ri<10μm) stabilized with β -casein behave as nondeformable particles, moving with a combination of Stokes and Taylor tensors as they approach the interface. Here, a similar methodology is used to parametrize the potential of interaction of drops of soybean oil stabilized with bovine serum albumin. The potential obtained is then employed to study the lifetime of deformable drops in the range 10≤ri≤1000μm . It is established that the average lifetime of these drops can be adequately replicated using the model of truncated spheres. However, the results depend sensibly on the expressions of the initial distance of deformation and the maximum film radius used in the calculations. The set of equations adequate for large drops is not satisfactory for medium-size drops (10≤ri≤100μm) , and vice versa. In the case of large particles, the increase in the interfacial area as a consequence of the deformation of the drops generates a very large repulsive barrier which opposes coalescence. Nevertheless, the buoyancy force prevails. As a consequence, it is the hydrodynamic tensor of the drops which determine the characteristic behavior of the lifetime as a function of the particle size. While the average values of the coalescence time of the drops can be justified by the mechanism of film thinning, the scattering of the experimental data of large drops cannot be rationalized using the methodology previously described. A possible explanation of this phenomenon required elaborate simulations which combine deformable drops, capillary waves, repulsive interaction forces, and a time-dependent surfactant adsorption.

On the energetics of tensile and shear void coalescences

NASA Astrophysics Data System (ADS)

Wong, W. H.; Guo, T. F.

2015-09-01

This paper investigates the mechanisms of tensile and shear void coalescences in ductile materials from energetics perspective. By examining and comparing the elastic and plastic energies of a voided cell throughout its deformation history, the onset of and final coalescence can be distinctly established. This energy-based approach offers a single unified method and criterion for determining the occurrences of both mechanisms. This paper also reports a novel micromechanics model that considers general stress states described by three macroscopic normal stresses and one macroscopic shear stress. Detailed formulation of the model is presented that includes the homogenization-based derivation and implementation of a 4×4 orthogonal transformation matrix, which relates the macroscopic deformation rate of the cell to displacement rates of non-physical degrees-of-freedom (DOFs), and the polar decomposition of the macroscopic deformation gradient tensor which admits the explicit determination of the logarithmic strain measures and rotation angle. In terms of stress ratios, ρ1 (=Σ11 /Σ22) ,ρ2 (=Σ12 /Σ22) ,ρ3 (=Σ33 /Σ22), it is analytically shown that multiple macroscopic stress states {ρ1 ,ρ2 ,ρ3 } can exist that result in the same stress triaxiality T and Lode parameter L. Specifically, it is shown that for a prescribed pair of T and L and in the absence of shear stress, at most six stress states {ρ1 , 0 ,ρ3 } are possible. On the other extreme in the presence of shear stress, an infinite number of stress states is possible, due to the existence of Mohr's circle for this stress state. This model, together with the proposed energy-based criteria, is used to examine void coalescence under multiple stress-state conditions for any given T and L. Numerical results have shown that the presence of shear stress has a significant effect of reducing the effective strains for the onset of and final void coalescences. In addition, a relationship has also been established between shear angle and effective strain at the onset of shear void coalescence.

InSAR constraints on the kinematics and magnitude of the 2001 Bhuj earthquake

NASA Astrophysics Data System (ADS)

Schmidt, D.; Bürgmann, R.

2005-12-01

The Mw 7.6 Bhuj intraplate event occurred along a blind thrust within the Kutch Rift basin of western India in January of 2001. The lack of any surface rupture and limited geodetic data have made it difficult to place the event on a known fault and constrain its source parameters. Moment tensor solutions and aftershock relocations indicate that the earthquake was a reverse event along an east-west striking, south dipping fault. In an effort to image the surface deformation, we have processed a total of 9 interferograms that span the coseismic event. Interferometry has proven difficult for the region because of technical difficulties experienced by the ERS Satellite around the time of the earthquake and because of low coherence. The stabilization of the orbital control by the European Space Agency beginning in 2002 has allowed us to interfere more recent SAR data with pre-earthquake data. Therefore, all available interferograms of the event include the first year of any postseismic deformation. The source region is characterized by broad floodplains interrupted by isolated highlands. Coherence is limited to the surrounding highlands and no data is available directly over the epicenter. Using the InSAR data along two descending and one ascending tracks, we perform a gridded search for the optimal source parameters of the earthquake. The deformation pattern is modeled assuming uniform slip on an elastic dislocation. Since the highland regions are discontinuous, the coherent InSAR phase is isolated to several individual patches. For each iteration of the gridded search algorithm, we optimize the fit to the data by solving for number of 2π phase cycles between coherent patches and the orbital gradient across each interferogram. Since the look angle varies across a SAR scene, a variable unit vector is calculated for each track. Inversion results place the center of the fault plane at 70.33° E/23.42° N at a depth of 21 km, and are consistent with the strike and dip suggested by the relocated aftershocks. The data also constrain the magnitude, rake, and finiteness of the event.

Size-dependent axial instability of microtubules surrounded by cytoplasm of a living cell based on nonlocal strain gradient elasticity theory.

PubMed

Sahmani, S; Aghdam, M M

2017-06-07

Microtubules including tubulin heterodimers arranging in a parallel shape of cylindrical hollow plays an important role in the mechanical stiffness of a living cell. In the present study, the nonlocal strain gradient theory of elasticity including simultaneously the both nonlocality and strain gradient size dependency is put to use within the framework of a refined orthotropic shell theory with hyperbolic distribution of shear deformation to analyze the size-dependent buckling and postbuckling characteristics of microtubules embedded in cytoplasm under axial compressive load. The non-classical governing differential equations are deduced via boundary layer theory of shell buckling incorporating the nonlinear prebuckling deformation and microtubule-cytoplasm interaction in the living cell environment. Finally, with the aid of a two-stepped perturbation solution methodology, the explicit analytical expressions for nonlocal strain gradient stability paths of axially loaded microtubules are achieved. It is illustrated that by taking the nonlocal size effect into consideration, the critical buckling load of microtubule and its maximum deflection associated with the minimum postbuckling load decreases, while the strain gradient size dependency causes to increase them. Copyright © 2017 Elsevier Ltd. All rights reserved.

Adaptive distance metric learning for diffusion tensor image segmentation.

PubMed

Kong, Youyong; Wang, Defeng; Shi, Lin; Hui, Steve C N; Chu, Winnie C W

2014-01-01

High quality segmentation of diffusion tensor images (DTI) is of key interest in biomedical research and clinical application. In previous studies, most efforts have been made to construct predefined metrics for different DTI segmentation tasks. These methods require adequate prior knowledge and tuning parameters. To overcome these disadvantages, we proposed to automatically learn an adaptive distance metric by a graph based semi-supervised learning model for DTI segmentation. An original discriminative distance vector was first formulated by combining both geometry and orientation distances derived from diffusion tensors. The kernel metric over the original distance and labels of all voxels were then simultaneously optimized in a graph based semi-supervised learning approach. Finally, the optimization task was efficiently solved with an iterative gradient descent method to achieve the optimal solution. With our approach, an adaptive distance metric could be available for each specific segmentation task. Experiments on synthetic and real brain DTI datasets were performed to demonstrate the effectiveness and robustness of the proposed distance metric learning approach. The performance of our approach was compared with three classical metrics in the graph based semi-supervised learning framework.

Adaptive Distance Metric Learning for Diffusion Tensor Image Segmentation

PubMed Central

Kong, Youyong; Wang, Defeng; Shi, Lin; Hui, Steve C. N.; Chu, Winnie C. W.

2014-01-01

High quality segmentation of diffusion tensor images (DTI) is of key interest in biomedical research and clinical application. In previous studies, most efforts have been made to construct predefined metrics for different DTI segmentation tasks. These methods require adequate prior knowledge and tuning parameters. To overcome these disadvantages, we proposed to automatically learn an adaptive distance metric by a graph based semi-supervised learning model for DTI segmentation. An original discriminative distance vector was first formulated by combining both geometry and orientation distances derived from diffusion tensors. The kernel metric over the original distance and labels of all voxels were then simultaneously optimized in a graph based semi-supervised learning approach. Finally, the optimization task was efficiently solved with an iterative gradient descent method to achieve the optimal solution. With our approach, an adaptive distance metric could be available for each specific segmentation task. Experiments on synthetic and real brain DTI datasets were performed to demonstrate the effectiveness and robustness of the proposed distance metric learning approach. The performance of our approach was compared with three classical metrics in the graph based semi-supervised learning framework. PMID:24651858

The self-similarly expanding Eshelby ellipsoidal inclusion: II. The Dynamic Eshelby Tensor for the expanding sphere

NASA Astrophysics Data System (ADS)

Ni, Luqun; Markenscoff, Xanthippi

2016-11-01

The field solution of a self-similarly (subsonically) expanding Eshelby ellipsoidal inclusion obtained in Part I is evaluated for the case of the expanding spherical inclusion under general uniform eigenstrain ɛij* in self-similar motion R = υt, starting from zero dimension. The particle velocity in the interior domain vanishes and the displacement gradient is constant exhibiting the Eshelby property in the self-similar dynamic case. All components of the interior and exterior Dynamic Eshelby Tensor are obtained for the sphere, with the interior ones depending on the wave speeds and the expansion speed of the inclusion, while the exterior ones depend, in addition, on the variable of self-similarity r / t and the direction of the field point. By a limiting procedure the static Eshelby tensor both interior and exterior is retrieved, thus making the static inclusion a special limit of the dynamic self-similarly expanding one. The jump of the particle velocity across the moving inclusion boundary is obtained, and it depends only on the wave and expansion speeds and the direction of the normal.

Evaluating gyro-viscosity in the Kelvin-Helmholtz instability by kinetic simulations

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

Umeda, Takayuki, E-mail: taka.umeda@nagoya-u.jp; Yamauchi, Natsuki; Wada, Yasutaka

2016-05-15

In the present paper, the finite-Larmor-radius (gyro-viscous) term [K. V. Roberts and J. B. Taylor, Phys. Rev. Lett. 8, 197–198 (1962)] is evaluated by using a full kinetic Vlasov simulation result of the Kelvin-Helmholtz instability (KHI). The velocity field and the pressure tensor are calculated from the high-resolution data of the velocity distribution functions obtained by the Vlasov simulation, which are used to approximate the Finite-Larmor-Radius (FLR) term according to Roberts and Taylor [Phys. Rev. Lett. 8, 197–198 (1962)]. The direct comparison between the pressure tensor and the FLR term shows an agreement. It is also shown that the anisotropicmore » pressure gradient enhanced the linear growth of the KHI when the inner product between the vorticity of the primary velocity shear layer and the magnetic field is negative, which is consistent with the previous FLR-magnetohydrodynamic simulation result. This result suggests that it is not sufficient for reproducing the kinetic simulation result by fluid simulations to include the FLR term (or the pressure tensor) only in the equation of motion for fluid.« less

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

IBMISPS (International Brain Mapping & Intraoperative Surgical Planning Symposium)

DTIC Science & Technology

2005-12-01

they received the 2005 Excellence in R, D & E award for their contribution in the feild of prosthetics and brain imaging. Excellence in Educational...specific bipolar magnetic gradient pulses which measure the velocity vector components of motion. Presented here are the development of dynamic MR...movies of quantitative velocity vector components, 30 frames per second. The 3 velocity vector maps with tensor analysis produced maps of the

Rastall's and related theories are conservative gravitational theories although physically inequivalent to general relativity

NASA Technical Reports Server (NTRS)

Smalley, L. L.

1983-01-01

The proper framework for testing Rastall's theory and its generalizations is in the case of non-negligible (i.e. discernible) gravitational effects such as gravity gradients. These theories have conserved integral four-momentum and angular momentum. The Nordtvedt effect then provides limits on the parameters which arise as the result of the non-zero divergence of the energy-momentum tensor.

The Interior Lowland Plains Unit of Mars: Evidence for a Possible Mud Ocean and Induced Tectonic Deformation

NASA Technical Reports Server (NTRS)

Tanaka, K. L.; Banerdt, W. B.

2000-01-01

We conclude from MOC and MOLA data that the northern plains of Mars were infilled by a sediment-rich, mud ocean. Evidence for subsidence within the north polar basin and reversed channel-floor gradients are consistent with tectonic deformation due to the sediment load.

Ultrasonographic study of mechanosensory properties in human esophagus during mechanical distension

PubMed Central

Larsen, Ejnar; Reddy, Hariprasad; Drewes, Asbjørn Mohr; Arendt-Nielsen, Lars; Gregersen, Hans

2006-01-01

AIM: To study the esophageal geometry and mechanosensation using endoscopic ultrasonography during volume-controlled ramp distensions in the distal esophagus. METHODS: Twelve healthy volunteers underwent distension of a bag. During distension up to moderate pain the sensory intensity was assessed on a visual analogue scale (VAS). The esophageal deformation in terms of multidimensional stretch ratios and strains was calculated at different volumes and VAS levels. Distensions were done before and during administration of the anti-cholinergic drug butylscopolamine. RESULTS: The stimulus-response (volume-VAS) curve did not differ without or with the administration of butylscopolamine. Analysis of stretch ratios demonstrated tensile stretch in circumferential direction, compression in radial direction and a small tensile stretch in longitudinal direction. A strain gradient existed throughout the esophageal wall with the largest circumferential deformation at the mucosal surface. The sensation intensity increased exponentially as function of the strains. CONCLUSION: The method provides information of esophageal deformation gradients that correlate to the sensation intensity. Hence, it can be used to study mechanosensation in the human esophagus. Further studies are needed to determine the exact deformation stimulus for the esophageal mechanoreceptors. PMID:16874864

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

H.E. Mynick, N. Pomphrey and P. Xanthopoulos

Recent progress in reducing turbulent transport in stellarators and tokamaks by 3D shaping using a stellarator optimization code in conjunction with a gyrokinetic code is presented. The original applications of the method focussed on ion temperature gradient transport in a quasi-axisymmetric stellarator design. Here, an examination of both other turbulence channels and other starting configurations is initiated. It is found that the designs evolved for transport from ion temperature gradient turbulence also display reduced transport from other transport channels whose modes are also stabilized by improved curvature, such as electron temperature gradient and ballooning modes. The optimizer is also appliedmore » to evolving from a tokamak, finding appreciable turbulence reduction for these devices as well. From these studies, improved understanding is obtained of why the deformations found by the optimizer are beneficial, and these deformations are related to earlier theoretical work in both stellarators and tokamaks.« less

A spin echo sequence with a single-sided bipolar diffusion gradient pulse to obtain snapshot diffusion weighted images in moving media

NASA Astrophysics Data System (ADS)

Freidlin, R. Z.; Kakareka, J. W.; Pohida, T. J.; Komlosh, M. E.; Basser, P. J.

2012-08-01

In vivo MRI data can be corrupted by motion. Motion artifacts are particularly troublesome in Diffusion Weighted MRI (DWI), since the MR signal attenuation due to Brownian motion can be much less than the signal loss due to dephasing from other types of complex tissue motion, which can significantly degrade the estimation of self-diffusion coefficients, diffusion tensors, etc. This paper describes a snapshot DWI sequence, which utilizes a novel single-sided bipolar diffusion sensitizing gradient pulse within a spin echo sequence. The proposed method shortens the diffusion time by applying a single refocused bipolar diffusion gradient on one side of a refocusing RF pulse, instead of a set of diffusion sensitizing gradients, separated by a refocusing RF pulse, while reducing the impact of magnetic field inhomogeneity by using a spin echo sequence. A novel MRI phantom that can exhibit a range of complex motions was designed to demonstrate the robustness of the proposed DWI sequence.

Active crustal deformation across the Basin and Range province, western United States, measured with the Global Positioning System, 1992-2002

NASA Astrophysics Data System (ADS)

Hammond, W.; Thatcher, W.

2003-04-01

The Basin and Range province of the western United States is a region of active tectonic extension and dextral shear, accommodating roughly 25% of the motion between non-deforming North America (NA) and the Pacific Plate (PA). The orientation of dextral shear is consistent with that of NA/PA relative plate motion, suggesting that this high elevation interior province is an important part of the plate boundary system. We present an analysis of Global Positioning System (GPS) data collected from 1992 to 2002. An 800 km long network of campaign-style geodetic benchmarks extends from east of the Wasatch fault zone (WFZ) in central Utah to west of the Genoa fault zone and Lake Tahoe in the northern Sierra Nevada mountains. From the new data collected in September 2002 and from data collected in 1992, 1996, and 1998, velocities have been estimated at 92 GPS sites, nearly double the number previously presented by Thatcher et al. [1999]. This new data reduces the uncertainty in site velocities and increases the spatial detail compared to earlier results, and now allows resolution of distinct domains in the tensor strain rate field. To process the data we use the GIPSY/OASIS and Quasi-Observation Combination Analysis (Dong et al. [1998]) software packages and incorporate data from continuously recording GPS stations in California and Nevada. The results show that most of the approximately 12 mm/yr of Sierra Nevada block motion is accommodated by right lateral shear and extensional deformation concentrated in the westernmost 200 km of Nevada, in the vicinity of the Walker Lane (WL). A lesser amount of velocity variation (roughly 3 mm/yr) is localized at the easternmost edge of the network, in the vicinity of the Wasatch Fault Zone (WFZ). Estimates of tensor strain rates show transitions in the style of deformation. Near the WFZ only uniaxial, roughly east-west extension can be resolved. Between longitude -112 and -117.5 no deformation is resolvable. Near longitude -118, in the vicinity of the historic ruptures of the Fairview Peak, Dixie Valley, and Rainbow Mountain earthquakes in the Central Nevada Seismic Zone, the deformation is mostly uniaxial extension oriented roughly NW/SE, in agreement with the roughly NE/SW strike of the normal faults. At the WL between longitude -118.5 and -119.5, deformation is best characterized by right lateral simple shear, which transitions westward to a blend of right lateral shear and uniaxial extension at the westernmost end of our network.

Running of the spectral index in deformed matter bounce scenarios with Hubble-rate-dependent dark energy

NASA Astrophysics Data System (ADS)

Arab, M.; Khodam-Mohammadi, A.

2018-03-01

As a deformed matter bounce scenario with a dark energy component, we propose a deformed one with running vacuum model (RVM) in which the dark energy density ρ _{Λ } is written as a power series of H^2 and \\dot{H} with a constant equation of state parameter, same as the cosmological constant, w=-1. Our results in analytical and numerical point of views show that in some cases same as Λ CDM bounce scenario, although the spectral index may achieve a good consistency with observations, a positive value of running of spectral index (α _s) is obtained which is not compatible with inflationary paradigm where it predicts a small negative value for α _s. However, by extending the power series up to H^4, ρ _{Λ }=n_0+n_2 H^2+n_4 H^4, and estimating a set of consistent parameters, we obtain the spectral index n_s, a small negative value of running α _s and tensor to scalar ratio r, which these reveal a degeneracy between deformed matter bounce scenario with RVM-DE and inflationary cosmology.

Determination of Stress Coefficient Terms in Cracked Solids for Monoclinic Materials with Plane Symmetry at x3 = 0

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1998-01-01

Determination of all the coefficients in the crack tip field expansion for monoclinic materials under two-dimensional deformation is presented in this report. For monoclinic materials with a plane of material symmetry at x(sub 3) = 0, the in-plane deformation is decoupled from the anti-plane deformation. In the case of in-plane deformation, utilizing conservation laws of elasticity and Betti's reciprocal theorem, together with selected auxiliary fields, T-stress and third-order stress coefficients near the crack tip are evaluated first from path-independent line integrals. To determine the T-stress terms using the J-integral and Betti's reciprocal work theorem, auxiliary fields under a concentrated force and moment acting at the crack tip are used respectively. Through the use of Stroh formalism in anisotropic elasticity, analytical expressions for all the coefficients including the stress intensity factors are derived in a compact form that has surprisingly simple structure in terms of the Barnett-Lothe tensors, L. The solution forms for degenerated materials, orthotropic, and isotropic materials are presented.

DTI segmentation by statistical surface evolution.

PubMed

Lenglet, Christophe; Rousson, Mikaël; Deriche, Rachid

2006-06-01

We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images (DTI). A DTI produces, from a set of diffusion-weighted MR images, tensor-valued images where each voxel is assigned with a 3 x 3 symmetric, positive-definite matrix. This second order tensor is simply the covariance matrix of a local Gaussian process, with zero-mean, modeling the average motion of water molecules. As we will show in this paper, the definition of a dissimilarity measure and statistics between such quantities is a nontrivial task which must be tackled carefully. We claim and demonstrate that, by using the theoretically well-founded differential geometrical properties of the manifold of multivariate normal distributions, it is possible to improve the quality of the segmentation results obtained with other dissimilarity measures such as the Euclidean distance or the Kullback-Leibler divergence. The main goal of this paper is to prove that the choice of the probability metric, i.e., the dissimilarity measure, has a deep impact on the tensor statistics and, hence, on the achieved results. We introduce a variational formulation, in the level-set framework, to estimate the optimal segmentation of a DTI according to the following hypothesis: Diffusion tensors exhibit a Gaussian distribution in the different partitions. We must also respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the DTI. We show how to express all the statistical quantities for the different probability metrics. We validate and compare the results obtained on various synthetic data-sets, a biological rat spinal cord phantom and human brain DTIs.

Wide-range simulation of elastoplastic wave fronts and failure of solids under high-speed loading

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

Saveleva, Natalia, E-mail: saveleva@icmm.ru; Bayandin, Yuriy, E-mail: buv@icmm.ru; Naimark, Oleg, E-mail: naimark@icmm.ru

2015-10-27

The aim of this paper is numerical study of deformation processes and failure of vanadium under shock-wave loading. According developed statistical theory of solid with mesoscopic defects the constitutive equations were proposed in terms of two structural variables characterizing behavior of defects ensembles: defect density tensor and structural scaling parameter. On the basis of wide-range constitutive equations the mathematical model of deformation behavior and failure of vanadium was developed taking into account the bond relaxation mechanisms, multistage of fracture and nonlinearity kinetic of defects. Results of numerical simulation allow the description of the major effects of shock wave propagation (elasticmore » precursor decay, grow of spall strength under grow strain rate)« less

Static black holes with back reaction from vacuum energy

NASA Astrophysics Data System (ADS)

Ho, Pei-Ming; Matsuo, Yoshinori

2018-03-01

We study spherically symmetric static solutions to the semi-classical Einstein equation sourced by the vacuum energy of quantum fields in the curved space-time of the same solution. We found solutions that are small deformations of the Schwarzschild metric for distant observers, but without horizon. Instead of being a robust feature of objects with high densities, the horizon is sensitive to the energy–momentum tensor in the near-horizon region.

Combined Near and Far Field High Energy Diffraction Microscopy Dataset for Ti-7Al Tensile Specimen Elastically Loaded In Situ

DOE Data Explorer

Turner, Todd J.; Shade, Paul A; Bernier, Joel V.; Li, Shiu Fai; Schuren, Jay C.; Lind, Jonathan F.; Lienert, Ulrich; Kenesei, Peter; Suter, Robert; Blank, Basil; Almer, Jonathan

2016-01-01

We present both near-field HEDM data that maps out the grain morphology and intragranular crystallographic orientations and far-field HEDM data that provides the grain centroid, grain average crystallographic orientation, and grain average elastic strain tensor for each grain. Finally, we provide a finite element mesh that can be utilized to simulate deformation in the volume of this Ti-7Al specimen.

Microstructures and Mechanical Properties of Commercially Pure Ti Processed by Rotationally Accelerated Shot Peening

PubMed Central

Huang, Zhaowen; Cao, Yang; Nie, Jinfeng; Zhou, Hao; Li, Yusheng

2018-01-01

Gradient structured materials possess good combinations of strength and ductility, rendering the materials attractive in industrial applications. In this research, a surface nanocrystallization (SNC) technique, rotationally accelerated shot peening (RASP), was employed to produce a gradient nanostructured pure Ti with a deformation layer that had a thickness of 2000 μm, which is thicker than those processed by conventional SNC techniques. It is possible to fabricate a gradient structured Ti workpiece without delamination. Moreover, based on the microstructural features, the microstructure of the processed sample can be classified into three regions, from the center to the surface of the RASP-processed sample: (1) a twinning-dominated core region; (2) a “twin intersection”-dominated twin transition region; and (3) the nanostructured region, featuring nanograins. A microhardness gradient was detected from the RASP-processed Ti. The surface hardness was more than twice that of the annealed Ti sample. The RASP-processed Ti sample exhibited a good combination of yield strength and uniform elongation, which may be attributed to the high density of deformation twins and a strong back stress effect. PMID:29498631

Calcium-43 chemical shift and electric field gradient tensor interplay: a sensitive probe of structure, polymorphism, and hydration.

PubMed

Widdifield, Cory M; Moudrakovski, Igor; Bryce, David L

2014-07-14

Calcium is the 5th most abundant element on earth, and is found in numerous biological tissues, proteins, materials, and increasingly in catalysts. However, due to a number of unfavourable nuclear properties, such as a low magnetogyric ratio, very low natural abundance, and its nuclear electric quadrupole moment, development of solid-state (43)Ca NMR has been constrained relative to similar nuclides. In this study, 12 commonly-available calcium compounds are analyzed via(43)Ca solid-state NMR and the information which may be obtained by the measurement of both the (43)Ca electric field gradient (EFG) and chemical shift tensors (the latter of which are extremely rare with only a handful of literature examples) is discussed. Combined with density functional theory (DFT) computations, this 'tensor interplay' is, for the first time for (43)Ca, illustrated to be diagnostic in distinguishing polymorphs (e.g., calcium formate), and the degree of hydration (e.g., CaCl2·2H2O and calcium tartrate tetrahydrate). For Ca(OH)2, we outline the first example of (1)H to (43)Ca cross-polarization on a sample at natural abundance in (43)Ca. Using prior knowledge of the relationship between the isotropic calcium chemical shift and the calcium quadrupolar coupling constant (CQ) with coordination number, we postulate the coordination number in a sample of calcium levulinate dihydrate, which does not have a known crystal structure. Natural samples of CaCO3 (aragonite polymorph) are used to show that the synthetic structure is present in nature. Gauge-including projector augmented-wave (GIPAW) DFT computations using accepted crystal structures for many of these systems generally result in calculated NMR tensor parameters which are in very good agreement with the experimental observations. This combination of (43)Ca NMR measurements with GIPAW DFT ultimately allows us to establish clear correlations between various solid-state (43)Ca NMR observables and selected structural parameters, such as unit cell dimensions and average Ca-O bond distances.

Present-day deformation across the Basin and Range Province, western United States

USGS Publications Warehouse

Thatcher, W.; Foulger, G.R.; Julian, B.R.; Svarc, J.; Quilty, E.; Bawden, G.W.

1999-01-01

The distribution of deformation within the Basin and Range province was determined from 1992, 1996, and 1998 surveys of a dense, 800-kilometer- aperture, Global Positioning System network, Internal deformation generally follows the pattern of Holocene fault distribution and is concentrated near the western extremity of the province, with lesser amounts focused near the eastern boundary. Little net deformation occurs across the central 500 kilometers of the network in western Utah and eastern Nevada. Concentration of deformation adjacent to the rigid Sierra Nevada block indicates that external plate-driving forces play an important role in driving deformation, modulating the extensional stress field generated by internal buoyancy forces that are due to lateral density gradients and topography near the province boundaries.

Dynamic deformations of shallow sediments in the Valley of Mexico, Part II: Single-station estimates

USGS Publications Warehouse

Singh, S.K.; Santoyo, M.; Bodin, P.; Gomberg, J.

1997-01-01

We develop simple relations to estimate dynamic displacement gradients (and hence the strains and rotations) during earthquakes in the lake-bed zone of the Valley of Mexico, where the presence of low-velocity, high-water content clays in the uppermost layers cause dramatic amplification of seismic waves and large strains. The study uses results from a companion article (Bodin et al., 1997) in which the data from an array at Roma, a lake-bed site, were analyzed to obtain displacement gradients. In this article, we find that the deformations at other lake-bed sites may differ from those at Roma by a factor of 2 to 3. More accurate estimates of the dominant components of the deformation at an individual instrumented lake-bed site may be obtained from the maximum horizontal velocity and displacement, ??max and umax, at the surface. The maximum surface strain ??max is related to ??max by ??max = ??max/C, with C ??? 0.6 km/sec. From the analysis of data from sites equipped with surface and borehole sensors, we find that the vertical gradient of peak horizontal displacement (??umax/??z) computed from sensors at 0 and 30 m equals (umax)z = 0/??z, ??z = 30 m, within a factor of 1.5. This is the largest gradient component, and the latter simple relation permits its estimation from surface records alone. The observed profiles of umax versus depth suggest a larger gradient in some depth range of 10 to 20 m, in agreement with synthetic calculations presented in Bodin et al. (1997). From the free-field recordings of the 19 September 1985 Michoacan earthquake, we estimate a maximum surface strain, ??max, between 0.05% and 0.11%, and a lower bound for the peak vertical gradient (??umax/??z) between 0.3% and 1.3%. This implies that (1) the extensive failure of water pipe joints during the Michoacan earthquake in the valley occurred at axial strains of about 0.1%, not 0.38% as previously reported, and (2) the clays of the valley behave almost linearly even at shear strain of about 1%, in agreement with laboratory tests. The available data in the valley can be used to predict deformations during future earthquakes using self-similar earthquake scaling.

Late Pan-African and early Mesozoic brittle compressions in East and Central Africa: lithospheric deformation within the Congo-Tanzania Cratonic area

NASA Astrophysics Data System (ADS)

Delvaux, D.; Kipata, M. L.; Macheyeki, A. S.

2012-04-01

Tectonic reconstructions leading to the formation of the Central-African part of Gondwana have so far not much taken into account constraints provided by the evolution of brittle structures and related stress field. This is largely because little is known on continental brittle deformation in Equatorial Africa before the onset of the Mesozoic Central-African and Late Cenozoic East-African rifts. We present a synthesis of fault-kinematic data and paleostress inversion results from field surveys covering parts of Tanzania, Zambia and the Democratic Republic of Congo. It is based on investigations along the eastern margin of the Tanzanian craton, in the Ubendian belt between the Tanzanian craton and Bangweulu block, in the Lufilian Arc between the Kalahari and Congo cratons and along the Congo intracratonic basin. Paleostress tensors were computed for a substantial database by interactive stress tensor inversion and data subset separation, and the relative succession of major brittle events established. Two of them appear to be of regional importance and could be traced from one region to the other. The oldest one is the first brittle event recorded after the paroxysm of the Terminal Pan-African event that led to the amalgamation Gondwana at the Precambrian-Cambrian transition. It is related to compressional deformation with horizontal stress trajectories fluctuating from an E-W compression in Central Tanzania to NE-SW in the Ubende belt and Lufilian Arc. The second event is a transpressional inversion with a consistent NW-SE compression that we relate to the far-field effects of the active margin south of Gondwana during the late Triassic - early Jurassic.

Universal two-dimensional characteristics in perovskite-type oxyhydrides ATiO2H (A = Li, Na, K, Rb, Cs)

NASA Astrophysics Data System (ADS)

Sato, Nobuya; Akashi, Ryosuke; Tsuneyuki, Shinji

2017-07-01

A series of unsynthesized perovskite-type oxyhydrides ATiO2H (A = Li, Na, K, Rb, Cs) are investigated by the density functional calculations. These oxyhydrides are stable in the sense of the formation energies for some possible synthesis reactions. They are crystallized into quite similar crystal structures with the long c-axis, and the corner-sharing TiO4H2 octahedra of the ideal perovskite-type structure are deformed into the 5-fold coordinated titanium atoms with the OH plane and the apical oxygen atoms. All of these oxyhydrides exhibit two-dimensional electronic states at the valence band maximum characterized by the in-plane oxygen 2p and the hydrogen 1s orbitals. While the c-axis becomes short as the ionic radius of the A atom becomes small and the two-dimensional characteristics are weakened, the electronic state at the valence band maximum is still characterized as the O-H in-plane state. Additionally, the Born effective charge tensors, spontaneous electric polarizations, dielectric tensors, and piezoelectric tensors are evaluated. It is found that the spontaneous electric polarizations of these oxyhydrides are much larger than that of tetragonal BaTiO3.

Modeling the effects of structure on seismic anisotropy in the Chester gneiss dome, southeast Vermont

NASA Astrophysics Data System (ADS)

Saif, S.; Brownlee, S. J.

2017-12-01

Compositional and structural heterogeneity in the continental crust are factors that contribute to the complex expression of crustal seismic anisotropy. Understanding deformation and flow in the crust using seismic anisotropy has thus proven difficult. Seismic anisotropy is affected by rock microstructure and mineralogy, and a number of studies have begun to characterize the full elastic tensors of crustal rocks in an attempt to increase our understanding of these intrinsic factors. However, there is still a large gap in length-scale between laboratory characterization on the scale of centimeters and seismic wavelengths on the order of kilometers. To address this length-scale gap we are developing a 3D crustal model that will help us determine the effects of rotating laboratory-scale elastic tensors into field-scale structures. The Chester gneiss dome in southeast Vermont is our primary focus. The model combines over 2000 structural data points from field measurements and published USGS structural data with elastic tensors of Chester dome rocks derived from electron backscatter diffraction data. We created a uniformly spaced grid by averaging structural measurements together in equally spaced grid boxes. The surface measurements are then projected into the third dimension using existing subsurface interpretations. A measured elastic tensor for the specific rock type is rotated according to its unique structural input at each point in the model. The goal is to use this model to generate artificial seismograms using existing numerical wave propagation codes. Once completed, the model input can be varied to examine the effects of different subsurface structure interpretations, as well as heterogeneity in rock composition and elastic tensors. Our goal is to be able to make predictions for how specific structures will appear in seismic data, and how that appearance changes with variations in rock composition.

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.

Deformation rates across the San Andreas Fault system, central California determined by geology and geodesy

NASA Astrophysics Data System (ADS)

Titus, Sarah J.

The San Andreas fault system is a transpressional plate boundary characterized by sub-parallel dextral strike-slip faults separating internally deformed crustal blocks in central California. Both geodetic and geologic tools were used to understand the short- and long-term partitioning of deformation in both the crust and the lithospheric mantle across the plate boundary system. GPS data indicate that the short-term discrete deformation rate is ˜28 mm/yr for the central creeping segment of the San Andreas fault and increases to 33 mm/yr at +/-35 km from the fault. This gradient in deformation rates is interpreted to reflect elastic locking of the creeping segment at depth, distributed off-fault deformation, or some combination of these two mechanisms. These short-term fault-parallel deformation rates are slower than the expected geologic slip rate and the relative plate motion rate. Structural analysis of folds and transpressional kinematic modeling were used to quantify long-term distributed deformation adjacent to the Rinconada fault. Folding accommodates approximately 5 km of wrench deformation, which translates to a deformation rate of ˜1 mm/yr since the start of the Pliocene. Integration with discrete offset on the Rinconada fault indicates that this portion of the San Andreas fault system is approximately 80% strike-slip partitioned. This kinematic fold model can be applied to the entire San Andreas fault system and may explain some of the across-fault gradient in deformation rates recorded by the geodetic data. Petrologic examination of mantle xenoliths from the Coyote Lake basalt near the Calaveras fault was used to link crustal plate boundary deformation at the surface with models for the accommodation of deformation in the lithospheric mantle. Seismic anisotropy calculations based on xenolith petrofabrics suggest that an anisotropic mantle layer thickness of 35-85 km is required to explain the observed shear wave splitting delay times in central California. The available data are most consistent with models for a broad zone of distributed deformation in the lithospheric mantle.

A new sequence for single-shot diffusion-weighted NMR spectroscopy by the trace of the diffusion tensor.

PubMed

Valette, Julien; Giraudeau, Céline; Marchadour, Charlotte; Djemai, Boucif; Geffroy, Françoise; Ghaly, Mohamed Ahmed; Le Bihan, Denis; Hantraye, Philippe; Lebon, Vincent; Lethimonnier, Franck

2012-12-01

Diffusion-weighted spectroscopy is a unique tool for exploring the intracellular microenvironment in vivo. In living systems, diffusion may be anisotropic, when biological membranes exhibit particular orientation patterns. In this work, a volume selective diffusion-weighted sequence is proposed, allowing single-shot measurement of the trace of the diffusion tensor, which does not depend on tissue anisotropy. With this sequence, the minimal echo time is only three times the diffusion time. In addition, cross-terms between diffusion gradients and other gradients are cancelled out. An adiabatic version, similar to localization by adiabatic selective refocusing sequence, is then derived, providing partial immunity against cross-terms. Proof of concept is performed ex vivo on chicken skeletal muscle by varying tissue orientation and intra-voxel shim. In vivo performance of the sequence is finally illustrated in a U87 glioblastoma mouse model, allowing the measurement of the trace apparent diffusion coefficient for six metabolites, including J-modulated metabolites. Although measurement performed along three separate orthogonal directions would bring similar accuracy on trace apparent diffusion coefficient under ideal conditions, the method described here should be useful for probing intimate properties of the cells with minimal experimental bias. Copyright © 2012 Wiley Periodicals, Inc.

Numerical studies of surface tensions

NASA Technical Reports Server (NTRS)

Hung, R. J.

1995-01-01

Liquid-vapor (bubble) interface disturbances caused by various types of accelerations, including centrifugal, lateral and axial impulses, gravity gradient and g-jitter accelerations associated with spinning and slew motion in microgravity, are reviewed. Understanding of bubble deformations and fluctuations is important in the development of spacecraft orbital and attitude control techniques to secure its normal operation. This review discusses bubble deformations and oscillations driven by various forces in the microgravity environment. The corresponding bubble mass center fluctuations and slosh reaction forces and torques due to bubble deformations are also reviewed.

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

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

Ringholm, Magnus; Ruud, Kenneth; Bast, Radovan

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields,more » reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.« less

Computational aeroelastic analysis of aircraft wings including geometry nonlinearity

NASA Astrophysics Data System (ADS)

Tian, Binyu

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

Diffusion tensor imaging of the sural nerve in normal controls☆

PubMed Central

Kim, Boklye; Srinivasan, Ashok; Sabb, Brian; Feldman, Eva L; Pop-Busui, Rodica

2016-01-01

Objective To develop a diffusion tensor imaging (DTI) protocol for assessing the sural nerve in healthy subjects. Methods Sural nerves in 25 controls were imaged using DTI at 3 T with 6, 15, and 32 gradient directions. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were computed from nerve regions of interest co-registered with T2-weighted images. Results Coronal images with 0.5(RL)×2.0(FH)×0.5(AP) mm3 resolution successfully localized the sural nerve. FA maps showed less variability with 32 directions (0.559±0.071) compared to 15(0.590±0.080) and 6(0.659±0.109). Conclusions Our DTI protocol was effective in imaging sural nerves in controls to establish normative FA/ADC, with potential to be used non-invasively in diseased nerves of patients. PMID:24908367

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

On the multi-scale description of micro-structured fluids composed of aggregating rods

NASA Astrophysics Data System (ADS)

Perez, Marta; Scheuer, Adrien; Abisset-Chavanne, Emmanuelle; Ammar, Amine; Chinesta, Francisco; Keunings, Roland

2018-05-01

When addressing the flow of concentrated suspensions composed of rods, dense clusters are observed. Thus, the adequate modelling and simulation of such a flow requires addressing the kinematics of these dense clusters and their impact on the flow in which they are immersed. In a former work, we addressed a first modelling framework of these clusters, assumed so dense that they were considered rigid and their kinematics (flow-induced rotation) were totally defined by a symmetric tensor c with unit trace representing the cluster conformation. Then, the rigid nature of the clusters was relaxed, assuming them deformable, and a model giving the evolution of both the cluster shape and its microstructural orientation descriptor (the so-called shape and orientation tensors) was proposed. This paper compares the predictions coming from those models with finer-scale discrete simulations inspired from molecular dynamics modelling.

The study of Thai stock market across the 2008 financial crisis

NASA Astrophysics Data System (ADS)

Kanjamapornkul, K.; Pinčák, Richard; Bartoš, Erik

2016-11-01

The cohomology theory for financial market can allow us to deform Kolmogorov space of time series data over time period with the explicit definition of eight market states in grand unified theory. The anti-de Sitter space induced from a coupling behavior field among traders in case of a financial market crash acts like gravitational field in financial market spacetime. Under this hybrid mathematical superstructure, we redefine a behavior matrix by using Pauli matrix and modified Wilson loop for time series data. We use it to detect the 2008 financial market crash by using a degree of cohomology group of sphere over tensor field in correlation matrix over all possible dominated stocks underlying Thai SET50 Index Futures. The empirical analysis of financial tensor network was performed with the help of empirical mode decomposition and intrinsic time scale decomposition of correlation matrix and the calculation of closeness centrality of planar graph.

On the combined gradient-stochastic plasticity model: Application to Mo-micropillar compression

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

Konstantinidis, A. A., E-mail: akonsta@civil.auth.gr; Zhang, X., E-mail: zhangxu26@126.com; Aifantis, E. C., E-mail: mom@mom.gen.auth.gr

2015-02-17

A formulation for addressing heterogeneous material deformation is proposed. It is based on the use of a stochasticity-enhanced gradient plasticity model implemented through a cellular automaton. The specific application is on Mo-micropillar compression, for which the irregularities of the strain bursts observed have been experimentally measured and theoretically interpreted through Tsallis' q-statistics.

The generalized Hill model: A kinematic approach towards active muscle contraction

NASA Astrophysics Data System (ADS)

Göktepe, Serdar; Menzel, Andreas; Kuhl, Ellen

2014-12-01

Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion.

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

Quantum κ-deformed differential geometry and field theory

NASA Astrophysics Data System (ADS)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Brain structural changes following adaptive cognitive training assessed by Tensor-Based Morphometry (TBM).

PubMed

Colom, Roberto; Hua, Xue; Martínez, Kenia; Burgaleta, Miguel; Román, Francisco J; Gunter, Jeffrey L; Carmona, Susanna; Jaeggi, Susanne M; Thompson, Paul M

2016-10-01

Tensor-Based Morphometry (TBM) allows the automatic mapping of brain changes across time building 3D deformation maps. This technique has been applied for tracking brain degeneration in Alzheimer's and other neurodegenerative diseases with high sensitivity and reliability. Here we applied TBM to quantify changes in brain structure after completing a challenging adaptive cognitive training program based on the n-back task. Twenty-six young women completed twenty-four training sessions across twelve weeks and they showed, on average, large cognitive improvements. High-resolution MRI scans were obtained before and after training. The computed longitudinal deformation maps were analyzed for answering three questions: (a) Are there differential brain structural changes in the training group as compared with a matched control group? (b) Are these changes related to performance differences in the training program? (c) Are standardized changes in a set of psychological factors (fluid and crystallized intelligence, working memory, and attention control) measured before and after training, related to structural changes in the brain? Results showed (a) greater structural changes for the training group in the temporal lobe, (b) a negative correlation between these changes and performance across training sessions (the greater the structural change, the lower the cognitive performance improvements), and (c) negligible effects regarding the psychological factors measured before and after training. Copyright © 2016 Elsevier Ltd. All rights reserved.

Functional MRI registration with tissue-specific patch-based functional correlation tensors.

PubMed

Zhou, Yujia; Zhang, Han; Zhang, Lichi; Cao, Xiaohuan; Yang, Ru; Feng, Qianjin; Yap, Pew-Thian; Shen, Dinggang

2018-06-01

Population studies of brain function with resting-state functional magnetic resonance imaging (rs-fMRI) rely on accurate intersubject registration of functional areas. This is typically achieved through registration using high-resolution structural images with more spatial details and better tissue contrast. However, accumulating evidence has suggested that such strategy cannot align functional regions well because functional areas are not necessarily consistent with anatomical structures. To alleviate this problem, a number of registration algorithms based directly on rs-fMRI data have been developed, most of which utilize functional connectivity (FC) features for registration. However, most of these methods usually extract functional features only from the thin and highly curved cortical grey matter (GM), posing great challenges to accurate estimation of whole-brain deformation fields. In this article, we demonstrate that additional useful functional features can also be extracted from the whole brain, not restricted to the GM, particularly the white-matter (WM), for improving the overall functional registration. Specifically, we quantify local anisotropic correlation patterns of the blood oxygenation level-dependent (BOLD) signals using tissue-specific patch-based functional correlation tensors (ts-PFCTs) in both GM and WM. Functional registration is then performed by integrating the features from different tissues using the multi-channel large deformation diffeomorphic metric mapping (mLDDMM) algorithm. Experimental results show that our method achieves superior functional registration performance, compared with conventional registration methods. © 2018 Wiley Periodicals, Inc.

Magnetic potential, vector and gradient tensor fields of a tesseroid in a geocentric spherical coordinate system

NASA Astrophysics Data System (ADS)

Du, Jinsong; Chen, Chao; Lesur, Vincent; Lane, Richard; Wang, Huilin

2015-06-01

We examined the mathematical and computational aspects of the magnetic potential, vector and gradient tensor fields of a tesseroid in a geocentric spherical coordinate system (SCS). This work is relevant for 3-D modelling that is performed with lithospheric vertical scales and global, continent or large regional horizontal scales. The curvature of the Earth is significant at these scales and hence, a SCS is more appropriate than the usual Cartesian coordinate system (CCS). The 3-D arrays of spherical prisms (SP; `tesseroids') can be used to model the response of volumes with variable magnetic properties. Analytical solutions do not exist for these model elements and numerical or mixed numerical and analytical solutions must be employed. We compared various methods for calculating the response in terms of accuracy and computational efficiency. The methods were (1) the spherical coordinate magnetic dipole method (MD), (2) variants of the 3-D Gauss-Legendre quadrature integration method (3-D GLQI) with (i) different numbers of nodes in each of the three directions, and (ii) models where we subdivided each SP into a number of smaller tesseroid volume elements, (3) a procedure that we term revised Gauss-Legendre quadrature integration (3-D RGLQI) where the magnetization direction which is constant in a SCS is assumed to be constant in a CCS and equal to the direction at the geometric centre of each tesseroid, (4) the Taylor's series expansion method (TSE) and (5) the rectangular prism method (RP). In any realistic application, both the accuracy and the computational efficiency factors must be considered to determine the optimum approach to employ. In all instances, accuracy improves with increasing distance from the source. It is higher in the percentage terms for potential than the vector or tensor response. The tensor errors are the largest, but they decrease more quickly with distance from the source. In our comparisons of relative computational efficiency, we found that the magnetic potential takes less time to compute than the vector response, which in turn takes less time to compute than the tensor gradient response. The MD method takes less time to compute than either the TSE or RP methods. The efficiency of the (GLQI and) RGLQI methods depends on the polynomial order, but the response typically takes longer to compute than it does for the other methods. The optimum method is a complex function of the desired accuracy, the size of the volume elements, the element latitude and the distance between the source and the observation. For a model of global extent with typical model element size (e.g. 1 degree horizontally and 10 km radially) and observations at altitudes of 10s to 100s of km, a mixture of methods based on the horizontal separation of the source and observation separation would be the optimum approach. To demonstrate the RGLQI method described within this paper, we applied it to the computation of the response for a global magnetization model for observations at 300 and 30 km altitude.

The Remote Detection of Incipient Catastrophic Failure in Large Landslides

NASA Astrophysics Data System (ADS)

Petley, D.; Bulmer, M. H.; Murphy, W.; Mantovani, F.

2001-12-01

Landslide movement is commonly associated with brittle failure and ductile deformation. Kilburn and Petley (2001) proposed that cracking in landslides occurs due to downslope stress acting on the deforming horizon. If the assumption that a given crack event breaks a fixed distance of unbroken rock or soil the rate of cracking becomes equivalent to the number of crack events per unit time. Where crack growth (not nucleation) is occurring, the inverse rate of displacement changes linearly with time. Failure can be assumed to be the time at which displacement rates become infinitely large. Thus, for a slope heading towards catastrophic failure due to the development of a failure plane, this relationship would be linear, with the point at which failure will occur being the time when the line intercepts the x-axis. Increasing rates of deformation associated with ductile processes of crack nucleation would yield a curve with a negative gradient asymptopic to the x-axis. This hypothesis is being examined. In the 1960 movement of the Vaiont slide, Italy, although the rate of movement was accelerating, the plot of 1/deformation against time shows that it was increasing towards a steady state deformation. This movement has been associated with a low accumulated strain ductile phase of movement. In the 1963 movement event, the trend is linear. This was associated with a brittle phase of movement. A plot of 1/deformation against time for movement of the debris flow portion of the Tessina landslide (1998) shows a curve with a negative gradient asymptopic to the x-axis. This indicates that the debris flow moved as a result of ductile deformation processes. Plots of movement data for the Black Ven landslide over 1999 and 2001 also show curves that correlate with known deformation and catastrophic phases. The model results suggest there is a definable deformation pattern that is diagnostic of landslides approaching catastrophic failure. This pattern can be differentiated from landslides that are undergoing ductile deformation and those that are suffering crack nucleation.

Shape dependence of entanglement entropy in conformal field theories

DOE PAGES

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar

2016-04-14

Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R 1,d--1. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We also show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, andmore » proportional to the coefficient C T appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ/CT=π 2/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.« less

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics

DTIC Science & Technology

2014-02-01

aluminum, copper, and magnesium . 15. SUBJECT TERMS impact physics, shock compression, elasticity, plasticity 16. SECURITY CLASSIFICATION OF: 17... deformation wave propagation code accounting for dissipative inelastic mechanisms. • Accuracy of the new nonlinear elastic- plastic model(s) will be...gradient and its transpose. A new general thermomechanical theory accounting for both elastic and plastic deformations has been briefly outlined in

Validation of an improved 'diffeomorphic demons' algorithm for deformable image registration in image-guided radiation therapy.

PubMed

Zhou, Lu; Zhou, Linghong; Zhang, Shuxu; Zhen, Xin; Yu, Hui; Zhang, Guoqian; Wang, Ruihao

2014-01-01

Deformable image registration (DIR) was widely used in radiation therapy, such as in automatic contour generation, dose accumulation, tumor growth or regression analysis. To achieve higher registration accuracy and faster convergence, an improved 'diffeomorphic demons' registration algorithm was proposed and validated. Based on Brox et al.'s gradient constancy assumption and Malis's efficient second-order minimization (ESM) algorithm, a grey value gradient similarity term and a transformation error term were added into the demons energy function, and a formula was derived to calculate the update of transformation field. The limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm was used to optimize the energy function so that the iteration number could be determined automatically. The proposed algorithm was validated using mathematically deformed images and physically deformed phantom images. Compared with the original 'diffeomorphic demons' algorithm, the registration method proposed achieve a higher precision and a faster convergence speed. Due to the influence of different scanning conditions in fractionated radiation, the density range of the treatment image and the planning image may be different. In such a case, the improved demons algorithm can achieve faster and more accurate radiotherapy.

Method of determining effects of heat-induced irregular refractive index on an optical system.

PubMed

Song, Xifa; Li, Lin; Huang, Yifan

2015-09-01

The effects of an irregular refractive index on optical performance are examined. A method was developed to express a lens's irregular refractive index distribution. An optical system and its mountings were modeled by a thermomechanical finite element (FE) program in the predicted operating temperature range, -45°C-50°C. FE outputs were elaborated using a MATLAB optimization routine; a nonlinear least squares algorithm was adopted to determine which gradient equation best fit each lens's refractive index distribution. The obtained gradient data were imported into Zemax for sequential ray-tracing analysis. The root mean square spot diameter, modulation transfer function, and diffraction ensquared energy were computed for an optical system under an irregular refractive index and under thermoelastic deformation. These properties are greatly reduced by the irregular refractive index effect, which is one-third to five-sevenths the size of the thermoelastic deformation effect. Thus, thermal analyses of optical systems should consider not only thermoelastic deformation but also refractive index irregularities caused by inhomogeneous temperature.

A study of perturbations in scalar-tensor theory using 1 + 3 covariant approach

NASA Astrophysics Data System (ADS)

Ntahompagaze, Joseph; Abebe, Amare; Mbonye, Manasse

This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke sub-class, and one that also takes note of the latter’s equivalence with f(R) gravitation theories. A 1 + 3 covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann-Laimaître-Robertson-Walker (FLRW) spacetime. Linear perturbation equations are developed based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar-tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for Rn models. For the matter-dominated era, it is shown that the dust energy density perturbations grow exponentially, a result which agrees with those already existing in the literatures. In the radiation-dominated era, it is found that the behavior of the radiation energy-density perturbations is oscillatory, with growing amplitudes for n > 1, and with decaying amplitudes for 0 < n < 1. This is a new result.

Nonlinear motion of cantilevered SWNT and Its Meaning to Phonon Dynamics

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Comparison between iterative wavefront control algorithm and direct gradient wavefront control algorithm for adaptive optics system

NASA Astrophysics Data System (ADS)

Cheng, Sheng-Yi; Liu, Wen-Jin; Chen, Shan-Qiu; Dong, Li-Zhi; Yang, Ping; Xu, Bing

2015-08-01

Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ˜ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ˜ (O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits. Project supported by the National Key Scientific and Research Equipment Development Project of China (Grant No. ZDYZ2013-2), the National Natural Science Foundation of China (Grant No. 11173008), and the Sichuan Provincial Outstanding Youth Academic Technology Leaders Program, China (Grant No. 2012JQ0012).

A Gradient-Based Multistart Algorithm for Multimodal Aerodynamic Shape Optimization Problems Based on Free-Form Deformation

NASA Astrophysics Data System (ADS)

Streuber, Gregg Mitchell

Environmental and economic factors motivate the pursuit of more fuel-efficient aircraft designs. Aerodynamic shape optimization is a powerful tool in this effort, but is hampered by the presence of multimodality in many design spaces. Gradient-based multistart optimization uses a sampling algorithm and multiple parallel optimizations to reliably apply fast gradient-based optimization to moderately multimodal problems. Ensuring that the sampled geometries remain physically realizable requires manually developing specialized linear constraints for each class of problem. Utilizing free-form deformation geometry control allows these linear constraints to be written in a geometry-independent fashion, greatly easing the process of applying the algorithm to new problems. This algorithm was used to assess the presence of multimodality when optimizing a wing in subsonic and transonic flows, under inviscid and viscous conditions, and a blended wing-body under transonic, viscous conditions. Multimodality was present in every wing case, while the blended wing-body was found to be generally unimodal.

Unraveling submicron-scale mechanical heterogeneity by three-dimensional X-ray microdiffraction

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

Li, Runguang; Xie, Qingge; Wang, Yan-Dong

Shear banding is a ubiquitous phenomenon of severe plastic deformation, and damage accumulation in shear bands often results in the catastrophic failure of a material. Despite extensive studies, the microscopic mechanisms of strain localization and deformation damage in shear bands remain elusive due to their spatial-temporal complexities embedded in bulk materials. Here we conducted synchrotron-based X-ray microdiffraction (μXRD) experiments to map out the 3D lattice strain field with a submicron resolution around fatigue shear bands in a stainless steel. Both in situ and postmortem μXRD results revealed large lattice strain gradients at intersections of the primary and secondary shear bands.more » Such strain gradients resulted in severe mechanical heterogeneities across the fatigue shear bands, leading to reduced fatigue limits in the high-cycle regime. The ability to spatially quantify the localized strain gradients with submicron resolution through μXRD opens opportunities for understanding the microscopic mechanisms of damage and failure in bulk materials.« less

Unraveling submicron-scale mechanical heterogeneity by three-dimensional X-ray microdiffraction

DOE PAGES

Li, Runguang; Xie, Qingge; Wang, Yan-Dong; ...

2017-12-28

Shear banding is a ubiquitous phenomenon of severe plastic deformation, and damage accumulation in shear bands often results in the catastrophic failure of a material. Despite extensive studies, the microscopic mechanisms of strain localization and deformation damage in shear bands remain elusive due to their spatial-temporal complexities embedded in bulk materials. Here we conducted synchrotron-based X-ray microdiffraction (μXRD) experiments to map out the 3D lattice strain field with a submicron resolution around fatigue shear bands in a stainless steel. Both in situ and postmortem μXRD results revealed large lattice strain gradients at intersections of the primary and secondary shear bands.more » Such strain gradients resulted in severe mechanical heterogeneities across the fatigue shear bands, leading to reduced fatigue limits in the high-cycle regime. The ability to spatially quantify the localized strain gradients with submicron resolution through μXRD opens opportunities for understanding the microscopic mechanisms of damage and failure in bulk materials.« less

[Accurate 3D free-form registration between fan-beam CT and cone-beam CT].

PubMed

Liang, Yueqiang; Xu, Hongbing; Li, Baosheng; Li, Hongsheng; Yang, Fujun

2012-06-01

Because the X-ray scatters, the CT numbers in cone-beam CT cannot exactly correspond to the electron densities. This, therefore, results in registration error when the intensity-based registration algorithm is used to register planning fan-beam CT and cone-beam CT. In order to reduce the registration error, we have developed an accurate gradient-based registration algorithm. The gradient-based deformable registration problem is described as a minimization of energy functional. Through the calculus of variations and Gauss-Seidel finite difference method, we derived the iterative formula of the deformable registration. The algorithm was implemented by GPU through OpenCL framework, with which the registration time was greatly reduced. Our experimental results showed that the proposed gradient-based registration algorithm could register more accurately the clinical cone-beam CT and fan-beam CT images compared with the intensity-based algorithm. The GPU-accelerated algorithm meets the real-time requirement in the online adaptive radiotherapy.

Unraveling submicron-scale mechanical heterogeneity by three-dimensional X-ray microdiffraction

PubMed Central

Li, Runguang; Xie, Qingge; Wang, Yan-Dong; Liu, Wenjun; Wang, Mingguang; Wu, Guilin; Li, Xiaowu; Zhang, Minghe; Lu, Zhaoping; Geng, Chang; Zhu, Ting

2018-01-01

Shear banding is a ubiquitous phenomenon of severe plastic deformation, and damage accumulation in shear bands often results in the catastrophic failure of a material. Despite extensive studies, the microscopic mechanisms of strain localization and deformation damage in shear bands remain elusive due to their spatial−temporal complexities embedded in bulk materials. Here we conducted synchrotron-based X-ray microdiffraction (μXRD) experiments to map out the 3D lattice strain field with a submicron resolution around fatigue shear bands in a stainless steel. Both in situ and postmortem μXRD results revealed large lattice strain gradients at intersections of the primary and secondary shear bands. Such strain gradients resulted in severe mechanical heterogeneities across the fatigue shear bands, leading to reduced fatigue limits in the high-cycle regime. The ability to spatially quantify the localized strain gradients with submicron resolution through μXRD opens opportunities for understanding the microscopic mechanisms of damage and failure in bulk materials. PMID:29284751

Formation of Gradient Structures in the Zone of Joining a Deformable Nickel Alloy and a Single-Crystal Intermetallic Alloy during Thermodiffusion Pressure Welding and Subsequent Heat Treatment

NASA Astrophysics Data System (ADS)

Povarova, K. B.; Valitov, V. A.; Drozdov, A. A.; Bazyleva, O. A.; Galieva, E. V.; Arginbaeva, E. G.

2018-01-01

The possibility of formation of a high-quality solid-phase joint of an Ni3Al-based single-crystal intermetallic VKNA-25 blade alloy with a high-temperature deformable EP975 disk alloy by pressure welding is studied to create high-performance one-piece blisk unit for the next-generation aviation gas turbine engines and to decrease the unit mass. The influence of the conditions of thermodiffusion pressure welding under the hightemperature superplasticity of the disk alloy and the influence of heat treatment of welded joints on the gradient structures in the welded joint zone and the structure at the periphery of the welded samples are investigated.

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

Hirano, Shin'ichi; Nishi, Sakine; Kobayashi, Tsutomu, E-mail: s.hirano@rikkyo.ac.jp, E-mail: sakine@rikkyo.ac.jp, E-mail: tsutomu@rikkyo.ac.jp

We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar perturbations. To seek for an instability-free extension of imperfect dark matter, we develop an effective theory of cosmological perturbations subject to the constraint on the scalar field's kinetic term. This is done by using the unifying framework of general scalar-tensor theories based on the ADM formalism. We demonstrate that it is indeed possible to construct a model of imperfect dark matter which ismore » free from ghost and gradient instabilities. As a side remark, we also show that mimetic F (R) theory is plagued with the Ostrogradsky instability.« less

Microstructure-property relationships and constitutive response of plastically graded case hardened steels

NASA Astrophysics Data System (ADS)

Klecka, Michael A.

Case hardened materials, popularly used in many demanding engineering applications such as bearings, gears, and wear/impact surfaces, have high surface hardness and a gradient in material properties (hardness, yield strength, etc.) as a function of depth; therefore, they behave as plastically graded materials. In the current study, two different commercially available case carburized steels along with two through hardened steels are characterized to obtain relationships among the volume fraction of subsurface carbides, indentation hardness, elastic modulus, and yield strength as a function of depth. A variety of methods including microindentation, nanoindentation, ultrasonic measurements, compression testing, rule of mixtures, and upper and lower bound models are used to determine the relationships for elastic modulus and compare the experimental results with model predictions. In addition, the morphology, composition, and properties of the carbide particles are also determined. The gradient in hardness with depth in graded materials is commonly determined using microindentation on the cross-section of the material which contains the gradation in microstructure or composition. In the current study, a novel method is proposed to predict the hardness gradient profile using solely surface indentations at a range of loads. The method does not require the graded material to be sectioned, and has practical utility in the surface heat-treatment industry. For a material with a decreasing gradient in hardness, higher indent loads result in a lower measured hardness due to the influence of the softer subsurface layers. A power-law model is presented which relates the measured surface indentation hardness under increasing load to the subsurface gradient in hardness. A coordinated experimental and numerical study is presented to extract the constitutive response of graded materials, utilizing relationships between hardness, plastic deformation, and strain hardening response. The average plastic strain induced by an indent is shown to be an effective measure of the representative plastic strain, which is used in order to relate hardness to yield strength in both virgin and plastically deformed materials. It is shown that the two carburized steels contain gradients in yield strength, but constant strain hardening exponent with depth. The resulting model of material behavior is used to characterize the influence of specific gradients in material properties on the surface indentation behavior under increasing indentation loads. It is also shown that the response of the material is not greatly influenced by strain hardening exponent, while a gradient in strain hardening ability only has minimal impact. Gradients in elastic properties are also shown to have negligible influence for a fixed gradient in hardness. The depth of subsurface plastic deformation is shown to increase with sharper gradients in hardness, but is not altered by gradients in elastic properties. The proposed approach is not specific to case hardened materials and can be used to determine the subsurface hardness gradient for any graded material.

The use of a deformable photonic crystal for millimeter-wave beam steering

NASA Astrophysics Data System (ADS)

Lin, Shawn-Yu; Yang, Zu-Po; Chen, Mingfeng; Bur, James A.; Levitan, A.; Kosowsky, Lester H.

2008-01-01

A deformable photonic band gap (PBG) material is theoretically proposed as a transmissive element for beam steering at 77GHz. The deformation may be achieved by integrating microsprings (as spacers) into a one-dimensional PBG structure. This PBG material can produce a specific phase shift dependent on its spacer thickness. By varying the spacer thickness, we generate a continuous phase gradient across the element. Such a PBG device is experimentally realized, capable of beam deflection of up to ±15° and suitable for beam scanning for smart automobile radar application.

Turbulent transport of heat and momentum in a boundary layer subject to deceleration, suction and variable wall temperature

NASA Technical Reports Server (NTRS)

Orlando, A. F.; Moffat, R. J.; Kays, W. M.

1974-01-01

The relationship between the turbulent transport of heat and momentum in an adverse pressure gradient boundary layer was studied. An experimental study was conducted of turbulent boundary layers subject to strong adverse pressure gradients with suction. Near-equilibrium flows were attained, evidenced by outer-region similarity in terms of defect temperature and defect velocity profiles. The relationship between Stanton number and enthalpy thickness was shown to be the same as for a flat plate flow both for constant wall temperature boundary conditions and for steps in wall temperature. The superposition principle used with the step-wall-temperature experimental result was shown to accurately predict the Stanton number variation for two cases of arbitrarily varying wall temperature. The Reynolds stress tensor components were measured for strong adverse pressure gradient conditions and different suction rates. Two peaks of turbulence intensity were found: one in the inner and one in the outer regions. The outer peak is shown to be displaced outward by an adverse pressure gradient and suppressed by suction.

Surface enhanced Raman optical activity of molecules on orientationally averaged substrates: theory of electromagnetic effects.

PubMed

Janesko, Benjamin G; Scuseria, Gustavo E

2006-09-28

We present a model for electromagnetic enhancements in surface enhanced Raman optical activity (SEROA) spectroscopy. The model extends previous treatments of SEROA to substrates, such as metal nanoparticles in solution, that are orientationally averaged with respect to the laboratory frame. Our theoretical treatment combines analytical expressions for unenhanced Raman optical activity with molecular polarizability tensors that are dressed by the substrate's electromagnetic enhancements. We evaluate enhancements from model substrates to determine preliminary scaling laws and selection rules for SEROA. We find that dipolar substrates enhance Raman optical activity (ROA) scattering less than Raman scattering. Evanescent gradient contributions to orientationally averaged ROA scale to first or higher orders in the gradient of the incident plane-wave field. These evanescent gradient contributions may be large for substrates with quadrupolar responses to the plane-wave field gradient. Some substrates may also show a ROA contribution that depends only on the molecular electric dipole-electric dipole polarizability. These conclusions are illustrated via numerical calculations of surface enhanced Raman and ROA spectra from (R)-(-)-bromochlorofluoromethane on various model substrates.

Micro-mechanics of fiber reinforced bounded and unbounded solids: effective local and non-local thermo-elastic properties, stress concentration factors, and edge effect

DTIC Science & Technology

2005-07-01

second order tensors of local eigenstresses and eigenstrains (transformation fields) which may arise by thermal expansion, plastic deformation, phase...with properties different from those of the homogeneous matrix) can be related to specified eigenstrain *( )e x by replacing the inhomogeneities...homogeneous matrix material only. rλ and mλ could be isotropic or anisotropic if the eigenstrain field *( )e x is uniform in Iv . So the strain at

Kundt solutions of minimal massive 3D gravity

NASA Astrophysics Data System (ADS)

Deger, Nihat Sadik; Sarıoǧlu, Ã.-zgür

2015-11-01

We construct Kundt solutions of minimal massive gravity theory and show that, similar to topologically massive gravity (TMG), most of them are constant scalar invariant (CSI) spacetimes that correspond to deformations of round and warped (A)dS. We also find an explicit non-CSI Kundt solution at the merger point. Finally, we give their algebraic classification with respect to the traceless Ricci tensor (Segre classification) and show that their Segre types match with the types of their counterparts in TMG.

Experimental Validation of a Time-Accurate Finite Element Model for Coupled Multibody Dynamics and Liquid Sloshing

DTIC Science & Technology

2007-04-16

velocity of the fluid mesh, P is the relative pressure, xr is the position vector, τ is the deviatoric stress tensor, D is the rate of deformation...corresponds to a slip factor of zero. The slip factor determines how much of the fluid and structure forces are mutually exchanged. Equations 22 and 23...updated from last to first. viii.Average the fluid pressure (This step eliminates the pressure checker-boarding effect and allows use of equal

Seismicity, shear failure and modes of deformation in deep subduction zones

NASA Technical Reports Server (NTRS)

Lundgren, Paul R.; Giardini, Domenico

1992-01-01

The joint hypocentral determination method is used to relocate deep seismicity reported in the International Seismological Center catalog for earthquakes deeper than 400 km in the Honshu, Bonin, Mariannas, Java, Banda, and South America subduction zones. Each deep seismic zone is found to display planar features of seismicity parallel to the Harvard centroid-moment tensor nodal planes, which are identified as planes of shear failure. The sense of displacement on these planes is one of resistance to deeper penetration.

Anisotropic Mesoscale Eddy Transport in Ocean General Circulation Models

NASA Astrophysics Data System (ADS)

Reckinger, S. J.; Fox-Kemper, B.; Bachman, S.; Bryan, F.; Dennis, J.; Danabasoglu, G.

2014-12-01

Modern climate models are limited to coarse-resolution representations of large-scale ocean circulation that rely on parameterizations for mesoscale eddies. The effects of eddies are typically introduced by relating subgrid eddy fluxes to the resolved gradients of buoyancy or other tracers, where the proportionality is, in general, governed by an eddy transport tensor. The symmetric part of the tensor, which represents the diffusive effects of mesoscale eddies, is universally treated isotropically in general circulation models. Thus, only a single parameter, namely the eddy diffusivity, is used at each spatial and temporal location to impart the influence of mesoscale eddies on the resolved flow. However, the diffusive processes that the parameterization approximates, such as shear dispersion, potential vorticity barriers, oceanic turbulence, and instabilities, typically have strongly anisotropic characteristics. Generalizing the eddy diffusivity tensor for anisotropy extends the number of parameters to three: a major diffusivity, a minor diffusivity, and the principal axis of alignment. The Community Earth System Model (CESM) with the anisotropic eddy parameterization is used to test various choices for the newly introduced parameters, which are motivated by observations and the eddy transport tensor diagnosed from high resolution simulations. Simply setting the ratio of major to minor diffusivities to a value of five globally, while aligning the major axis along the flow direction, improves biogeochemical tracer ventilation and reduces global temperature and salinity biases. These effects can be improved even further by parameterizing the anisotropic transport mechanisms in the ocean.

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

NASA Astrophysics Data System (ADS)

Victor, P.; Sobiesiak, M.

2005-12-01

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

Cerebral White Matter Integrity and Cognitive Aging: Contributions from Diffusion Tensor Imaging

PubMed Central

Madden, David J.; Bennett, Ilana J.; Song, Allen W.

2009-01-01

The integrity of cerebral white matter is critical for efficient cognitive functioning, but little is known regarding the role of white matter integrity in age-related differences in cognition. Diffusion tensor imaging (DTI) measures the directional displacement of molecular water and as a result can characterize the properties of white matter that combine to restrict diffusivity in a spatially coherent manner. This review considers DTI studies of aging and their implications for understanding adult age differences in cognitive performance. Decline in white matter integrity contributes to a disconnection among distributed neural systems, with a consistent effect on perceptual speed and executive functioning. The relation between white matter integrity and cognition varies across brain regions, with some evidence suggesting that age-related effects exhibit an anterior-posterior gradient. With continued improvements in spatial resolution and integration with functional brain imaging, DTI holds considerable promise, both for theories of cognitive aging and for translational application. PMID:19705281

Increasing Accuracy of Tissue Shear Modulus Reconstruction Using Ultrasonic Strain Tensor Measurement

NASA Astrophysics Data System (ADS)

Sumi, C.

Previously, we developed three displacement vector measurement methods, i.e., the multidimensional cross-spectrum phase gradient method (MCSPGM), the multidimensional autocorrelation method (MAM), and the multidimensional Doppler method (MDM). To increase the accuracies and stabilities of lateral and elevational displacement measurements, we also developed spatially variant, displacement component-dependent regularization. In particular, the regularization of only the lateral/elevational displacements is advantageous for the lateral unmodulated case. The demonstrated measurements of the displacement vector distributions in experiments using an inhomogeneous shear modulus agar phantom confirm that displacement-component-dependent regularization enables more stable shear modulus reconstruction. In this report, we also review our developed lateral modulation methods that use Parabolic functions, Hanning windows, and Gaussian functions in the apodization function and the optimized apodization function that realizes the designed point spread function (PSF). The modulations significantly increase the accuracy of the strain tensor measurement and shear modulus reconstruction (demonstrated using an agar phantom).

Extended Czjzek model applied to NMR parameter distributions in sodium metaphosphate glass

NASA Astrophysics Data System (ADS)

Vasconcelos, Filipe; Cristol, Sylvain; Paul, Jean-François; Delevoye, Laurent; Mauri, Francesco; Charpentier, Thibault; Le Caër, Gérard

2013-06-01

The extended Czjzek model (ECM) is applied to the distribution of NMR parameters of a simple glass model (sodium metaphosphate, NaPO3) obtained by molecular dynamics (MD) simulations. Accurate NMR tensors, electric field gradient (EFG) and chemical shift anisotropy (CSA) are calculated from density functional theory (DFT) within the well-established PAW/GIPAW framework. The theoretical results are compared to experimental high-resolution solid-state NMR data and are used to validate the considered structural model. The distributions of the calculated coupling constant CQ ∝ |Vzz| and the asymmetry parameter ηQ that characterize the quadrupolar interaction are discussed in terms of structural considerations with the help of a simple point charge model. Finally, the ECM analysis is shown to be relevant for studying the distribution of CSA tensor parameters and gives new insight into the structural characterization of disordered systems by solid-state NMR.

Extended Czjzek model applied to NMR parameter distributions in sodium metaphosphate glass.

PubMed

Vasconcelos, Filipe; Cristol, Sylvain; Paul, Jean-François; Delevoye, Laurent; Mauri, Francesco; Charpentier, Thibault; Le Caër, Gérard

2013-06-26

The extended Czjzek model (ECM) is applied to the distribution of NMR parameters of a simple glass model (sodium metaphosphate, NaPO3) obtained by molecular dynamics (MD) simulations. Accurate NMR tensors, electric field gradient (EFG) and chemical shift anisotropy (CSA) are calculated from density functional theory (DFT) within the well-established PAW/GIPAW framework. The theoretical results are compared to experimental high-resolution solid-state NMR data and are used to validate the considered structural model. The distributions of the calculated coupling constant C(Q) is proportional to |V(zz)| and the asymmetry parameter η(Q) that characterize the quadrupolar interaction are discussed in terms of structural considerations with the help of a simple point charge model. Finally, the ECM analysis is shown to be relevant for studying the distribution of CSA tensor parameters and gives new insight into the structural characterization of disordered systems by solid-state NMR.

δ M formalism: a new approach to cosmological perturbation theory in anisotropic inflation

NASA Astrophysics Data System (ADS)

Talebian-Ashkezari, A.; Ahmadi, N.; Abolhasani, A. A.

2018-03-01

We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the δ M formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in almost the same way that the so-called δ N formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twin formula, δ N, this new method can substantially reduce the amount of calculations related to the evolution of tensor modes. However, it is not as general as δ N it is a "perturbative" formula and solves the shear only to linear order. In other words, it is restricted to weak shear limit.

The Spectrum of Scalar Indices of Agyrotropy

NASA Astrophysics Data System (ADS)

Scudder, J. D.; Daughton, W. S.

2017-12-01

Quantitative scalar measures of departures from gyrotropy will be contrasted using 3D-PIC guide field simulations of a reconnection layer. Of interest are the sensitivity of 4 different proposed methods for inventorying the occurrence of needed signatures of demagnetization for identification of reconnection sites. Visual maps will be presented using the originally formulated diagnostic A0e for agyrotropy and three relatively recent attempts to generalize it. These visuals highlight the essentially common information contained in these approaches. The ``flavor'' distinctions between these techniques will be organized in terms of the types of deformations of the eVDF required for their distinctions to be present/significant. The first class of disturbances are those that explicitly cause the eVDF to depend on gyro phase in addition to pitch angle, while the second class requires a strong coordinated deformation of the eVDF in both polar angles. In the first class the magnetic field remains as an eigenvector of the deformed pressure tensor as in the originally proposed diagnostic A0e; in the second class NO eigenvector is aligned with the magnetic field and accompanies a more violent disruption of magnetization than the first class. The 3D VPIC guide simulation will be used as a data base to show the relative frequency of occurrence of these two types of disruptions in regions with non-zero agyrotropy. As far as identifying whether a region has demagnetization or not all techniques are virtually interchangeable and are shown to be statistically strongly correlated using billions of estimates. Accordingly, extensive early surveys using A0e to survey PIC reconnection geometries for signatures of demagnetization are not supplanted by the existence of alternate recipes for quantifying the geometry of the pressure tensor that get slightly larger values in relatively esoteric circumstances. Of the two types of deformation of the eVDF required to produce different ``flavors'' of agyrotropy, the gyro phase only modulations resolved completely by A0e are statistically the more common instances of demagnetization in 3D-PIC simulations.

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

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

Cui, T; Huang, Q; Miller, W

2014-06-15

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

Quantifying deformation in North Borneo with GPS

NASA Astrophysics Data System (ADS)

Mustafar, Mohamad Asrul; Simons, Wim J. F.; Tongkul, Felix; Satirapod, Chalermchon; Omar, Kamaludin Mohd; Visser, Pieter N. A. M.

2017-10-01

The existence of intra-plate deformation of the Sundaland platelet along its eastern edge in North Borneo, South-East Asia, makes it an interesting area that still is relatively understudied. In addition, the motion of the coastal area of North-West Borneo is directed toward a frontal fold-and-thrust belt and has been fueling a long debate on the possible geophysical sources behind it. At present this fold-and-thrust belt is not generating significant seismic activity and may also not be entirely active due to a decreasing shelfal extension from south to north. Two sets of Global Positioning System (GPS) data have been used in this study; the first covering a time period from 1999 until 2004 (ending just before the Giant Sumatra-Andaman earthquake) to determine the continuous Sundaland tectonic plate motion, and the second from 2009 until 2011 to investigate the current deformations of North Borneo. Both absolute and relative positioning methods were carried out to investigate horizontal and vertical displacements. Analysis of the GPS results indicates a clear trend of extension along coastal regions of Sarawak and Brunei in North Borneo. On the contrary strain rate tensors in Sabah reveal that only insignificant and inconsistent extension and compression occurs throughout North-West Borneo. Moreover, station velocities and rotation rate tensors on the northern part of North Borneo suggest a clockwise (micro-block) rotation. The first analysis of vertical displacements recorded by GPS in North-West Borneo points to low subsidence rates along the western coastal regions of Sabah and inconsistent trends between the Crocker and Trusmadi mountain ranges. These results have not been able to either confirm or reject the hypothesis that gravity sliding is the main driving force behind the local motions in North Borneo. The ongoing Sundaland-Philippine Sea plate convergence may also still play an active role in the present-day deformation (crustal shortening) in North Borneo and the possible clockwise rotation of the northern part of North Borneo as a micro-block. However, more observations need to be collected to determine if the northern part of North Borneo indeed is (slowly) moving independently.

Observations of Quasi-Love Waves in Tibet Indicates Coherent Deformation of the Crust and Upper Mantle

NASA Astrophysics Data System (ADS)

Chen, X.; Park, J. J.

2012-12-01

The high uplift of the Tibet area is caused by the continental collision between the Indian plate and the Eurasian plate. The style of deformation along with the collision is still being debated, particularly whether the deformation is vertically coherent or not, i.e., whether the upper mantle deforms coherently with the crust. In this work, we have used quasi-Love (QL) waves to constrain the anisotropy pattern around the Tibet region. The existence of anisotropy gradients has been identified with the observations of QL waves, which is a converted Rayleigh-wave motion that follows the arrival of the Love wave. Further, the locations of the anisotropy gradients have been pinned with the delay time between the Love wave and the QL wave, which is determined from cross-correlation. Our results show that the frequency content of Tibetan QL wave is centered around 10 mHz, indicating the depth range of anisotropy should be in the asthenosphere. Most of the scatterers of QL wave that we can detect lie outside the Tibet Plateau. Their distribution correlates well with the boundary of the Persia-Tibet- Burma orogeny, which has been identified from surface geologic data. This correlation, between surface geology and upper mantle anisotropy inferred from QL observations at the orogenic boundary, suggests that the crust and upper mantle of the orogeny are deforming coherently. Other scatterers that are off the Persia-Tibet-Burma orogenic boundary mostly cluster in two locations, the Tarim Basin, and the Bangong-Nujiang Suture, where there could exist contrasting anisotropy patterns in the upper mantle. The deformation in the Tibet region is complicated, yet our research suggests a vertically coherent deformation style of the upper mantle in Tibet.

Deformation behavior and mechanical analysis of vertically aligned carbon nanotube (VACNT) bundles

NASA Astrophysics Data System (ADS)

Hutchens, Shelby B.

Vertically aligned carbon nanotubes (VACNTs) serve as integral components in a variety of applications including MEMS devices, energy absorbing materials, dry adhesives, light absorbing coatings, and electron emitters, all of which require structural robustness. It is only through an understanding of VACNT's structural mechanical response and local constitutive stress-strain relationship that future advancements through rational design may take place. Even for applications in which the structural response is not central to device performance, VACNTs must be sufficiently robust and therefore knowledge of their microstructure-property relationship is essential. This thesis first describes the results of in situ uniaxial compression experiments of 50 micron diameter cylindrical bundles of these complex, hierarchical materials as they undergo unusual deformation behavior. Most notably they deform via a series of localized folding events, originating near the bundle base, which propagate laterally and collapse sequentially from bottom to top. This deformation mechanism accompanies an overall foam-like stress-strain response having elastic, plateau, and densification regimes with the addition of undulations in the stress throughout the plateau regime that correspond to the sequential folding events. Microstructural observations indicate the presence of a strength gradient, due to a gradient in both tube density and alignment along the bundle height, which is found to play a key role in both the sequential deformation process and the overall stress-strain response. Using the complicated structural response as both motivation and confirmation, a finite element model based on a viscoplastic solid is proposed. This model is characterized by a flow stress relation that contains an initial peak followed by strong softening and successive hardening. Analysis of this constitutive relation results in capture of the sequential buckling phenomenon and a strength gradient effect. This combination of experimental and modeling approaches motivates discussion of the particular microstructural mechanisms and local material behavior that govern the non-trivial energy absorption via sequential, localized buckle formation in the VACNT bundles.

High angular resolution diffusion imaging with stimulated echoes: compensation and correction in experiment design and analysis.

PubMed

Lundell, Henrik; Alexander, Daniel C; Dyrby, Tim B

2014-08-01

Stimulated echo acquisition mode (STEAM) diffusion MRI can be advantageous over pulsed-gradient spin-echo (PGSE) for diffusion times that are long compared with T2 . It therefore has potential for biomedical diffusion imaging applications at 7T and above where T2 is short. However, gradient pulses other than the diffusion gradients in the STEAM sequence contribute much greater diffusion weighting than in PGSE and lead to a disrupted experimental design. Here, we introduce a simple compensation to the STEAM acquisition that avoids the orientational bias and disrupted experiment design that these gradient pulses can otherwise produce. The compensation is simple to implement by adjusting the gradient vectors in the diffusion pulses of the STEAM sequence, so that the net effective gradient vector including contributions from diffusion and other gradient pulses is as the experiment intends. High angular resolution diffusion imaging (HARDI) data were acquired with and without the proposed compensation. The data were processed to derive standard diffusion tensor imaging (DTI) maps, which highlight the need for the compensation. Ignoring the other gradient pulses, a bias in DTI parameters from STEAM acquisition is found, due both to confounds in the analysis and the experiment design. Retrospectively correcting the analysis with a calculation of the full B matrix can partly correct for these confounds, but an acquisition that is compensated as proposed is needed to remove the effect entirely. © 2014 The Authors. NMR in Biomedicine published by John Wiley & Sons, Ltd.

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Strain rate dependent activation of slip systems in calcite marbles from Syros (Cyclades, Greece)

NASA Astrophysics Data System (ADS)

Rogowitz, Anna; Grasemann, Bernhard; Morales, Luiz F. G.; Huet, Benjamin; White, Joseph C.

2017-04-01

The activation of certain slip systems in calcite has been experimentally proven to be highly temperature dependent, but also the strain rate plays an important role on the activation of the dominant slip system. In this study, observations from a flanking structure (i.e. shear zone) that developed under lower greenschist-facies conditions, in an almost pure calcite marble (Syros Island, Greece) are presented. The shear zone is characterized by a strain gradient from the slightly deformed tips (γ ˜ 50) to the highly strained centre (γ up to 1000) while the host rock is moderately deformed (γ ˜ 3). During the shear zone development, the strain gradient coincided with a strain rate gradient with strain rate varying from 10-13 to 10-9 s-1. The studied outcrop thus represents the final state of a natural experiment and gives us a great opportunity to get natural constraints on strain rate dependent mechanical behaviour in a calcite marble. Detailed microstructural analyses have been performed via optical microscopy, electron microscopy, electron backscatter diffraction mapping and transmission electron microscopy, on samples from the highly strained shear zone and the host rock. The analyses show that the calcite microfabric varies depending on position within the shear zone, indicating activation of different deformation, recrystallization mechanisms and slip systems at different strain rates. Up to strain rates of ˜10-10 s-1 the marble deformed exclusively within the dislocation creep field, showing a change in recrystallization mechanism and dominant active slip system. While the marble preferentially recrystallized by grain boundary migration at relatively low strain rates (˜10-13 s-1), subgrain rotation recrystallization seems to be the dominant mechanism at higher strain rates (˜10-12 to 10-10 s-1). At higher strain rates (˜10-9 s-1), the recrystallization mechanism is bulging, resulting in the development of an extremely fine grained ultramylonite (average grain size ˜3 μm) accompanied by a switch in deformation mechanism from dislocation creep to a combined deformation by grain boundary sliding and dislocation activity. Constraints on dominant active slip system depending on deformation strain rate have been made by a combination of misorientation analyses and viscoplastic self-consistent modelling.

Single molecule studies of flexible polymers under shear and mixed flows

NASA Astrophysics Data System (ADS)

Teixeira, Rodrigo Esquivel

We combine manipulation and single molecule visualization of flexible DNA polymers with the generation of controlled simple shear and planar mixed flows for the investigation of polymer flow physics. With the ability to observe polymer conformation directly and follow its evolution in both dilute and entangled regimes we provide a direct test for molecular models. The coil-stretch transition of polymer extension was investigated in planar mixed flows approaching simple shear. Visualization of individual molecules revealed a sharp coil-stretch transition in the steady-state length of the polymer with increasing strain rate in flows slightly more straining than rotational. In slightly more rotational flows significant transient polymer deformation was observed. Next, dilute polymers were visualized in the flow-gradient plane of a steady shear flow. By exploiting the linear proportionality between polymer mass and image intensity, the radius of gyration tensor elements ( Gij) were measured over time. Then, the Giesekus stress tensor was used to obtain the bulk shear viscosity and first normal stress coefficient, thus performing rheology measurements from single molecule conformations. End-over-end tumbling was discovered for the first time, confirming a long-standing prediction and numerous single-chain computer simulation studies. The tumbling frequency followed Wi0.62, and an equation derived from simple advection and diffusion arguments was able to reproduce these observations. Power spectral densities of chain orientation trajectories were found to be single-peaked around the tumbling frequency, thus suggesting a periodic character for polymer dynamics. Finally, we investigated well-entangled polymer solutions. Identical preparations were used in both rheological characterizations and single molecule observations under a variety of shear flow histories. Polymer extension relaxations after the cessation of a fast shear flow revealed two intrinsic characteristic times. The fast one was insensitive to concentration and at least an order of magnitude larger than the Rouse time presupposed by theoretical treatments. The slow timescale grew steeply with concentration, in qualitative agreement with theory. Transient and steady shear flows showed vastly different conformations even among identical molecules subjected to identical flow histories. This "molecular individualism" of well-entangled solutions and its broad conformational distributions calls into question the validity of preaveraging approximations made in molecular-level theories.

The anelastic Ericksen problem: universal eigenstrains and deformations in compressible isotropic elastic solids.

PubMed

Yavari, Arash; Goriely, Alain

2016-12-01

The elastic Ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is, we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains. In a nonlinear solid, these eigenstrains can be modelled by a Riemannian material manifold whose metric depends on their distribution. In this framework, we show that the natural generalization of the concept of homogeneous deformations is the notion of covariantly homogeneous deformations -deformations with covariantly constant deformation gradients. We prove that these deformations are the only universal deformations and that they put severe restrictions on possible universal eigenstrains . We show that, in a simply-connected body, for any distribution of universal eigenstrains the material manifold is a symmetric Riemannian manifold and that in dimensions 2 and 3 the universal eigenstrains are zero-stress.

Photothermal Nanocomposite Hydrogel Actuator with Electric-Field-Induced Gradient and Oriented Structure.

PubMed

Yang, Yang; Tan, Yun; Wang, Xionglei; An, Wenli; Xu, Shimei; Liao, Wang; Wang, Yuzhong

2018-03-07

Recent research of hydrogel actuators is still not sophisticated enough to meet the requirement of fast, reversible, complex, and robust reconfiguration. Here, we present a new kind of poly( N-isopropylacrylamide)/graphene oxide gradient hydrogel by utilizing direct current electric field to induce gradient and oriented distribution of graphene oxide into poly( N-isopropylacrylamide) hydrogel. Upon near-infrared light irradiation, the hydrogel exhibited excellent comprehensive actuation performance as a result of directional bending deformation, promising great potential in the application of soft actuators and optomechanical system.

A preliminary compressible second-order closure model for high speed flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu

1989-01-01

A preliminary version of a compressible second-order closure model that was developed in connection with the National Aero-Space Plane Project is presented. The model requires the solution of transport equations for the Favre-averaged Reynolds stress tensor and dissipation rate. Gradient transport hypotheses are used for the Reynolds heat flux, mass flux, and turbulent diffusion terms. Some brief remarks are made about the direction of future research to generalize the model.

Effect of interface deformability on thermocapillary motion of a drop in a tube

NASA Astrophysics Data System (ADS)

Mahesri, S.; Haj-Hariri, H.; Borhan, A.

2014-03-01

The effect of an externally imposed axial temperature gradient on the mobility and deformation of a drop in an otherwise stagnant liquid within an insulated cylindrical tube is investigated. In the absence of bulk transport of momentum and energy, the boundary integral technique is used to obtain the flow and temperature fields inside and outside the deformable drop. The steady drop shapes and the corresponding migration velocities are examined over a wide range of the dimensionless parameters. The steady drop shape is nearly spherical for dimensionless drop sizes <0.5, but becomes slightly elongated in the axial direction for drop sizes comparable to tube diameter. The adverse effect of drop deformation on the effective temperature gradient driving the motion is slightly more pronounced than its favorable effect of reducing drag, thereby leading to a slight reduction in drop mobility with increasing drop deformation. Increasing the viscosity ratio reduces drop deformation and leads to a slight enhancement in the relative mobility (with respect to free thermocapillary motion) of confined drops. When the drop fluid has a lower thermal conductivity than the exterior phase, the presence of the thermally-insulating wall increases the thermal driving force for drop motion (compared to that for the same drop in unbounded domain) by causing more pronounced bending of the isotherms toward the drop. However, the favorable thermal effect of the confining wall is overwhelmed by its retarding hydrodynamic effect, causing the confined drop to always move slower than its unbounded counterpart regardless of the value of the thermal conductivity ratio.

Characterization of a Dynamic String Method for the Construction of Transition Pathways in Molecular Reactions

PubMed Central

Johnson, Margaret E.; Hummer, Gerhard

2012-01-01

We explore the theoretical foundation of different string methods used to find dominant reaction pathways in high-dimensional configuration spaces. Pathways are assessed by the amount of reactive flux they carry and by their orientation relative to the committor function. By examining the effects of transforming between different collective coordinates that span the same underlying space, we unmask artificial coordinate dependences in strings optimized to follow the free energy gradient. In contrast, strings optimized to follow the drift vector produce reaction pathways that are significantly less sensitive to reparameterizations of the collective coordinates. The differences in these paths arise because the drift vector depends on both the free energy gradient and the diffusion tensor of the coarse collective variables. Anisotropy and position dependence of diffusion tensors arise commonly in spaces of coarse variables, whose generally slow dynamics are obtained by nonlinear projections of the strongly coupled atomic motions. We show here that transition paths constructed to account for dynamics by following the drift vector will (to a close approximation) carry the maximum reactive flux both in systems with isotropic position dependent diffusion, and in systems with constant but anisotropic diffusion. We derive a simple method for calculating the committor function along paths that follow the reactive flux. Lastly, we provide guidance for the practical implementation of the dynamic string method. PMID:22616575

Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames

NASA Astrophysics Data System (ADS)

Wacks, Daniel; Konstantinou, Ilias; Chakraborty, Nilanjan

2018-04-01

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar-turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable.

Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames

PubMed Central

Konstantinou, Ilias; Chakraborty, Nilanjan

2018-01-01

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar--turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable. PMID:29740257

Registration of PET and CT images based on multiresolution gradient of mutual information demons algorithm for positioning esophageal cancer patients.

PubMed

Jin, Shuo; Li, Dengwang; Wang, Hongjun; Yin, Yong

2013-01-07

Accurate registration of 18F-FDG PET (positron emission tomography) and CT (computed tomography) images has important clinical significance in radiation oncology. PET and CT images are acquired from (18)F-FDG PET/CT scanner, but the two acquisition processes are separate and take a long time. As a result, there are position errors in global and deformable errors in local caused by respiratory movement or organ peristalsis. The purpose of this work was to implement and validate a deformable CT to PET image registration method in esophageal cancer to eventually facilitate accurate positioning the tumor target on CT, and improve the accuracy of radiation therapy. Global registration was firstly utilized to preprocess position errors between PET and CT images, achieving the purpose of aligning these two images on the whole. Demons algorithm, based on optical flow field, has the features of fast process speed and high accuracy, and the gradient of mutual information-based demons (GMI demons) algorithm adds an additional external force based on the gradient of mutual information (GMI) between two images, which is suitable for multimodality images registration. In this paper, GMI demons algorithm was used to achieve local deformable registration of PET and CT images, which can effectively reduce errors between internal organs. In addition, to speed up the registration process, maintain its robustness, and avoid the local extremum, multiresolution image pyramid structure was used before deformable registration. By quantitatively and qualitatively analyzing cases with esophageal cancer, the registration scheme proposed in this paper can improve registration accuracy and speed, which is helpful for precisely positioning tumor target and developing the radiation treatment planning in clinical radiation therapy application.

Registration of PET and CT images based on multiresolution gradient of mutual information demons algorithm for positioning esophageal cancer patients

PubMed Central

Jin, Shuo; Li, Dengwang; Yin, Yong

2013-01-01

Accurate registration of  18F−FDG PET (positron emission tomography) and CT (computed tomography) images has important clinical significance in radiation oncology. PET and CT images are acquired from  18F−FDG PET/CT scanner, but the two acquisition processes are separate and take a long time. As a result, there are position errors in global and deformable errors in local caused by respiratory movement or organ peristalsis. The purpose of this work was to implement and validate a deformable CT to PET image registration method in esophageal cancer to eventually facilitate accurate positioning the tumor target on CT, and improve the accuracy of radiation therapy. Global registration was firstly utilized to preprocess position errors between PET and CT images, achieving the purpose of aligning these two images on the whole. Demons algorithm, based on optical flow field, has the features of fast process speed and high accuracy, and the gradient of mutual information‐based demons (GMI demons) algorithm adds an additional external force based on the gradient of mutual information (GMI) between two images, which is suitable for multimodality images registration. In this paper, GMI demons algorithm was used to achieve local deformable registration of PET and CT images, which can effectively reduce errors between internal organs. In addition, to speed up the registration process, maintain its robustness, and avoid the local extremum, multiresolution image pyramid structure was used before deformable registration. By quantitatively and qualitatively analyzing cases with esophageal cancer, the registration scheme proposed in this paper can improve registration accuracy and speed, which is helpful for precisely positioning tumor target and developing the radiation treatment planning in clinical radiation therapy application. PACS numbers: 87.57.nj, 87.57.Q‐, 87.57.uk PMID:23318381

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Multiscale framework for predicting the coupling between deformation and fluid diffusion in porous rocks

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

Andrade, José E; Rudnicki, John W

2012-12-14

In this project, a predictive multiscale framework will be developed to simulate the strong coupling between solid deformations and fluid diffusion in porous rocks. We intend to improve macroscale modeling by incorporating fundamental physical modeling at the microscale in a computationally efficient way. This is an essential step toward further developments in multiphysics modeling, linking hydraulic, thermal, chemical, and geomechanical processes. This research will focus on areas where severe deformations are observed, such as deformation bands, where classical phenomenology breaks down. Multiscale geometric complexities and key geomechanical and hydraulic attributes of deformation bands (e.g., grain sliding and crushing, and poremore » collapse, causing interstitial fluid expulsion under saturated conditions), can significantly affect the constitutive response of the skeleton and the intrinsic permeability. Discrete mechanics (DEM) and the lattice Boltzmann method (LBM) will be used to probe the microstructure---under the current state---to extract the evolution of macroscopic constitutive parameters and the permeability tensor. These evolving macroscopic constitutive parameters are then directly used in continuum scale predictions using the finite element method (FEM) accounting for the coupled solid deformation and fluid diffusion. A particularly valuable aspect of this research is the thorough quantitative verification and validation program at different scales. The multiscale homogenization framework will be validated using X-ray computed tomography and 3D digital image correlation in situ at the Advanced Photon Source in Argonne National Laboratories. Also, the hierarchical computations at the specimen level will be validated using the aforementioned techniques in samples of sandstone undergoing deformation bands.« less

Resonant Raman spectra of diindenoperylene thin films

NASA Astrophysics Data System (ADS)

Scholz, R.; Gisslén, L.; Schuster, B.-E.; Casu, M. B.; Chassé, T.; Heinemeyer, U.; Schreiber, F.

2011-01-01

Resonant and preresonant Raman spectra obtained on diindenoperylene (DIP) thin films are interpreted with calculations of the deformation of a relaxed excited molecule with density functional theory (DFT). The comparison of excited state geometries based on time-dependent DFT or on a constrained DFT scheme with observed absorption spectra of dissolved DIP reveals that the deformation pattern deduced from constrained DFT is more reliable. Most observed Raman peaks can be assigned to calculated A_g-symmetric breathing modes of DIP or their combinations. As the position of one of the laser lines used falls into a highly structured absorption band, we have carefully analyzed the Raman excitation profile arising from the frequency dependence of the dielectric tensor. This procedure gives Raman cross sections in good agreement with the observed relative intensities, both in the fully resonant and in the preresonant case.

Resonant Raman spectra of diindenoperylene thin films.

PubMed

Scholz, R; Gisslén, L; Schuster, B-E; Casu, M B; Chassé, T; Heinemeyer, U; Schreiber, F

2011-01-07

Resonant and preresonant Raman spectra obtained on diindenoperylene (DIP) thin films are interpreted with calculations of the deformation of a relaxed excited molecule with density functional theory (DFT). The comparison of excited state geometries based on time-dependent DFT or on a constrained DFT scheme with observed absorption spectra of dissolved DIP reveals that the deformation pattern deduced from constrained DFT is more reliable. Most observed Raman peaks can be assigned to calculated A(g)-symmetric breathing modes of DIP or their combinations. As the position of one of the laser lines used falls into a highly structured absorption band, we have carefully analyzed the Raman excitation profile arising from the frequency dependence of the dielectric tensor. This procedure gives Raman cross sections in good agreement with the observed relative intensities, both in the fully resonant and in the preresonant case.

Methods for determining remanent and total magnetisations of magnetic sources - a review

NASA Astrophysics Data System (ADS)

Clark, David A.

2014-07-01

Assuming without evidence that magnetic sources are magnetised parallel to the geomagnetic field can seriously mislead interpretation and can result in drill holes missing their targets. This article reviews methods that are available for estimating, directly or indirectly, the natural remanent magnetisation (NRM) and total magnetisation of magnetic sources, noting the strengths and weaknesses of each approach. These methods are: (i) magnetic property measurements of samples; (ii) borehole magnetic measurements; (iii) inference of properties from petrographic/petrological information, supplemented by palaeomagnetic databases; (iv) constrained modelling/inversion of magnetic sources; (v) direct inversions of measured or calculated vector and gradient tensor data for simple sources; (vi) retrospective inference of magnetisation of a mined deposit by comparing magnetic data acquired pre- and post-mining; (vii) combined analysis of magnetic and gravity anomalies using Poisson's theorem; (viii) using a controlled magnetic source to probe the susceptibility distribution of the subsurface; (ix) Helbig-type analysis of gridded vector components, gradient tensor elements, and tensor invariants; (x) methods based on reduction to the pole and related transforms; and (xi) remote in situ determination of NRM direction, total magnetisation direction and Koenigsberger ratio by deploying dual vector magnetometers or a single combined gradiometer/magnetometer to monitor local perturbation of natural geomagnetic variations, operating in base station mode within a magnetic anomaly of interest. Characterising the total and remanent magnetisations of sources is important for several reasons. Knowledge of total magnetisation is often critical for accurate determination of source geometry and position. Knowledge of magnetic properties such as magnetisation intensity and Koenigsberger ratio constrains the likely magnetic mineralogy (composition and grain size) of a source, which gives an indication of its geological nature. Determining the direction of a stable ancient remanence gives an indication of the age of magnetisation, which provides useful information about the geological history of the source and its environs.

Atomistic determination of flexoelectric properties of crystalline dielectrics

NASA Astrophysics Data System (ADS)

Maranganti, R.; Sharma, P.

2009-08-01

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

Dynamics of Deformable Active Particles under External Flow Field

NASA Astrophysics Data System (ADS)

Tarama, Mitsusuke

2017-10-01

In most practical situations, active particles are affected by their environment, for example, by a chemical concentration gradient, light intensity, gravity, or confinement. In particular, the effect of an external flow field is important for particles swimming in a solvent fluid. For deformable active particles such as self-propelled liquid droplets and active vesicles, as well as microorganisms such as euglenas and neutrophils, a general description has been developed by focusing on shape deformation. In this review, we present our recent studies concerning the dynamics of a single active deformable particle under an external flow field. First, a set of model equations of active deformable particles including the effect of a general external flow is introduced. Then, the dynamics under two specific flow profiles is discussed: a linear shear flow, as the simplest example, and a swirl flow. In the latter case, the scattering dynamics of the active deformable particles by the swirl flow is also considered.

Improving Functional MRI Registration Using Whole-Brain Functional Correlation Tensors.

PubMed

Zhou, Yujia; Yap, Pew-Thian; Zhang, Han; Zhang, Lichi; Feng, Qianjin; Shen, Dinggang

2017-09-01

Population studies of brain function with resting-state functional magnetic resonance imaging (rs-fMRI) largely rely on the accurate inter-subject registration of functional areas. This is typically achieved through registration of the corresponding T1-weighted MR images with more structural details. However, accumulating evidence has suggested that such strategy cannot well-align functional regions which are not necessarily confined by the anatomical boundaries defined by the T1-weighted MR images. To mitigate this problem, various registration algorithms based directly on rs-fMRI data have been developed, most of which have utilized functional connectivity (FC) as features for registration. However, most of the FC-based registration methods usually extract the functional features only from the thin and highly curved cortical grey matter (GM), posing a great challenge in accurately estimating the whole-brain deformation field. In this paper, we demonstrate that the additional useful functional features can be extracted from brain regions beyond the GM, particularly, white-matter (WM) based on rs-fMRI, for improving the overall functional registration. Specifically, we quantify the local anisotropic correlation patterns of the blood oxygenation level-dependent (BOLD) signals, modeled by functional correlation tensors (FCTs), in both GM and WM. Functional registration is then performed based on multiple components of the whole-brain FCTs using a multichannel Large Deformation Diffeomorphic Metric Mapping (mLDDMM) algorithm. Experimental results show that our proposed method achieves superior functional registration performance, compared with other conventional registration methods.

White matter reorganization after surgical resection of brain tumors and vascular malformations.

PubMed

Lazar, M; Alexander, A L; Thottakara, P J; Badie, B; Field, A S

2006-01-01

Diffusion tensor imaging (DTI) and white matter tractography (WMT) are promising techniques for estimating the course, extent, and connectivity patterns of the white matter (WM) structures in the human brain. In this study, DTI and WMT were used to evaluate WM tract reorganization after the surgical resection of brain tumors and vascular malformations. Pre- and postoperative DTI data were obtained in 6 patients undergoing surgical resection of brain lesions. WMT using a tensor deflection algorithm was used to reconstruct WM tracts adjacent to the lesions. Reconstructed tracts included corticospinal tracts, the corona radiata, superior longitudinal and inferior fronto-occipital fasciculi, cingulum bundles, and the corpus callosum. WMT revealed a series of tract alteration patterns including deviation, deformation, infiltration, and apparent tract interruption. In general, the organization of WM tracts appeared more similar to normal anatomy after resection, with either disappearance or reduction of the deviation, deformation, or infiltration present preoperatively. In patients whose lesions were associated with corticospinal tract involvement, the WMT reconstructions showed that the tract was preserved during surgery and improved in position and appearance, and this finding correlated with improvement or preservation of motor function as determined by clinical assessment. WMT is useful for appreciating the complex relationships between specific WM structures and the anatomic distortions created by brain lesions. Further studies with intraoperative correlation are necessary to confirm these initial findings and to determine WMT utility for presurgical planning and evaluation of surgical treatments.

General models for the distributions of electric field gradients in disordered solids

NASA Astrophysics Data System (ADS)

LeCaër, G.; Brand, R. A.

1998-11-01

Hyperfine studies of disordered materials often yield the distribution of the electric field gradient (EFG) or related quadrupole splitting (QS). The question of the structural information that may be extracted from such distributions has been considered for more than fifteen years. Experimentally most studies have been performed using Mössbauer spectroscopy, especially on 0953-8984/10/47/020/img5. However, NMR, NQR, EPR and PAC methods have also received some attention. The EFG distribution for a random distribution of electric charges was for instance first investigated by Czjzek et al [1] and a general functional form was derived for the joint (bivariate) distribution of the principal EFG tensor component 0953-8984/10/47/020/img6 and the asymmetry parameter 0953-8984/10/47/020/img7. The importance of the Gauss distribution for such rotationally invariant structural models was thus evidenced. Extensions of that model which are based on degenerate multivariate Gauss distributions for the elements of the EFG tensor were proposed by Czjzek. The latter extensions have been used since that time, more particularly in Mössbauer spectroscopy, under the name `shell models'. The mathematical foundations of all the previous models are presented and critically discussed as they are evidenced by simple calculations in the case of the EFG tensor. The present article only focuses on those aspects of the EFG distribution in disordered solids which can be discussed without explicitly looking at particular physical mechanisms. We present studies of three different model systems. A reference model directly related to the first model of Czjzek, called the Gaussian isotropic model (GIM), is shown to be the limiting case for many different models with a large number of independent contributions to the EFG tensor and not restricted to a point-charge model. The extended validity of the marginal distribution of 0953-8984/10/47/020/img7 in the GIM model is discussed. It is also shown that the second model based on degenerate multivariate normal distributions for the EFG components yields questionable results and has been exaggeratedly used in experimental studies. The latter models are further discussed in the light of new results. The problems raised by these extensions are due to the fact that the consequences of the statistical invariance by rotation of the EFG tensor have not been sufficiently taken into account. Further difficulties arise because the structural degrees of freedom of the disordered solid under consideration have been confused with the degrees of freedom of QS distributions. The relations which are derived and discussed are further illustrated by the case of the EFG tensor distribution created at the centre of a sphere by m charges randomly distributed on its surface. The third model, a simple extension of the GIM, considers the case of an EFG tensor which is the sum of a fixed part and of a random part with variable weights. The bivariate distribution 0953-8984/10/47/020/img9 is calculated exactly in the most symmetric case and the effect of the random part is investigated as a function of its weight. The various models are more particularly discussed in connection with short-range order in disordered solids. An ambiguity problem which arises in the evaluation of bivariate distributions of centre lineshift (isomer shift) and quadrupole splitting from 0953-8984/10/47/020/img10 Mössbauer spectra is finally quantitatively considered.

A new formula of the Gravitational Curvature for the prism

NASA Astrophysics Data System (ADS)

Grazia D'Urso, Maria

2017-04-01

Gravitational Curvatures (GC) are the components of the third-order gravitational tensor and physically represent the rate of change of the gravity gradient. While scalar, vector and second-order tensor quantities of the Earth's gravitational field have extensively been studied and their properties have been well understood [1], the first successful terrestrial measurements of the third-order vertical gravitational gradients have been recently performed in [2] by atom interferometry sensors in laboratory environment. Possible benefits of the airborne third-order gravitational gradients for exploration geophysics are discussed in [3] while Brieden et al. (2010) [4] have proposed a new satellite mission called OPTical Interferometry for global Mass change detection from space (OPTIMA) sensing the third-order gravitational gradients in space. Moreover, exploitation of GC for modelling the Earth's gravitational field has been object of recent studies [5-7]. We extend the approach presented by the author in previous papers [8-10] by evaluating the algebraic expression of the third-order gravitational tensor for a prism. Comparisons with previous results [11-12] are also included. [1] Freeden W, Schreiner M (2009) Spherical functions of mathematical geosciences. A scalar, vectorial, and tensorial setup. In: Advances in geophysical and environmental mechanics and mathematics. Springer, Berlin [2] Rosi G, Cacciapuoti L, Sorrentino F, Menchetti M, Prevedelli M, Tino GM (2015) Measurements of the gravity-field curvature by atom interferometry. Phys Rev Lett 114:013001 [3] Di Francesco D, Meyer T, Christensen A, FitzGerald D (2009) Gravity gradiometry - today and tomorrow. In: 11th SAGA Biennial technical meeting and exhibition, 13-18 September 2009, Switzerland, pp 80-83 [4] Brieden P, Müller J, Flury J, Heinzel G (2010) The mission OPTIMA - novelties and benefit. In: Geotechnologien science report No. 17, Potsdam, pp 134-139 [5] Šprlák M, Novák P (2015) Integral formulas for computing a third-order gravitational tensor from volumetric mass density, disturbing gravitational potential, gravity anomaly and gravity disturbance. J Geod 89:141-157 [6] Šprlák M, Novák P (2016) Spherical gravitational curvature boundary-value problem. J Geod 90:727-739 [7] Hamáčková E, Šprlák M , Pitoňák M, Novák P (2016) Non-singular expressions for the spherical harmonic synthesis of gravitational curvatures in a local north-oriented reference frame. Comp & Geosc 88: 152-162 [8] D'Urso MG (2012) New expressions of the gravitational potential and its derivates for the prism. In Hotine-Marussi International Symposium on Mathematical Geodesy, 7rd. Sneeuw N, Novak P, Crespi M, Sansò F. Springer-Verlag, Berlin Heidelberg pp. 251-256 [9] D'Urso MG (2013) On the evaluation of the gravity effects of polyhedral bodies and a consistent treatment of related singularities. J Geod 87:239-252 [10] D'Urso MG (2014)Analytical computation of gravity effects for polyhedral bodies. J Geod 88:13-29 [11] Nagy D, Papp G, Benedek J (2000) The gravitational potential and its derivatives for the prism. J Geod 74:552-560 [12] Holstein H, Fitzgerald DJ, H. Stefanov H (2013) Gravimagnetic similarity for homogeneous rectangular prisms. 75th EAGE Conference & Exhibition, London

Global Existence Results for Viscoplasticity at Finite Strain

NASA Astrophysics Data System (ADS)

Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe

2018-01-01

We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant plastic rate, and thus depends on the plastic state variable. The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energy-dissipation-balance and energy-dissipation-inequality solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory.

The anelastic Ericksen problem: universal eigenstrains and deformations in compressible isotropic elastic solids

PubMed Central

2016-01-01

The elastic Ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is, we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains. In a nonlinear solid, these eigenstrains can be modelled by a Riemannian material manifold whose metric depends on their distribution. In this framework, we show that the natural generalization of the concept of homogeneous deformations is the notion of covariantly homogeneous deformations—deformations with covariantly constant deformation gradients. We prove that these deformations are the only universal deformations and that they put severe restrictions on possible universal eigenstrains. We show that, in a simply-connected body, for any distribution of universal eigenstrains the material manifold is a symmetric Riemannian manifold and that in dimensions 2 and 3 the universal eigenstrains are zero-stress. PMID:28119554

Warpage of Large Curved Composite Panels due to Manufacturing Anomalies

NASA Technical Reports Server (NTRS)

Starnes, James H., Jr. (Technical Monitor); Ambur, Damadar (Technical Monitor); Ochinero, T. T.; Hyer, M. W.

2002-01-01

This paper discusses the influences of a misaligned layer, a resin-rich slightly thicker layer, and a small thermal gradient on the thermally-induced deformations of large curved composite panels during cooldown from their cure temperature. The deformations represent warpage of the panels due to anomalies that occur during layup, consolidation, and cure. Two-dimensional finite element analyses are used The deformations are categorized as to their impact on circumferential and twist warpage metrics. The results are intended to highlight the sensitivity of manufactured panel shape to the various unwanted effects that can occur during manufacturing.

The electric field gradient in natural iron-doped chrysoberyl Al2BeO4 and sinhalite MgAlBO4 single crystals

NASA Astrophysics Data System (ADS)

Lottermoser, Werner; Redhammer, Günther J.; Weber, Sven-Ulf; Litterst, Fred Jochen; Tippelt, Gerold; Dlugosz, Stephen; Bank, Hermann; Amthauer, Georg; Grodzicki, Michael

2011-12-01

This work reports on the evaluation of the electric field gradient (EFG) in natural chrysoberyl Al2BeO4 and sinhalite MgAlBO4 using two different procedures: (1) experimental, with single crystal Mössbauer spectroscopy (SCMBS) on the three principal sections of each sample and (2) a "fully quantitative" method with cluster molecular orbital calculations based on the density functional theory. Whereas the experimental and theoretical results for the EFG tensor are in quantitative agreement, the calculated isomer shifts and optical d-d-transitions exhibit systematic deviations from the measured values. These deviations indicate that the substitution of Al and Mg with iron should be accompanied by considerable local expansion of the coordination octahedra.

Healthy imperfect dark matter from effective theory of mimetic cosmological perturbations

NASA Astrophysics Data System (ADS)

Hirano, Shin'ichi; Nishi, Sakine; Kobayashi, Tsutomu

2017-07-01

We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar perturbations. To seek for an instability-free extension of imperfect dark matter, we develop an effective theory of cosmological perturbations subject to the constraint on the scalar field's kinetic term. This is done by using the unifying framework of general scalar-tensor theories based on the ADM formalism. We demonstrate that it is indeed possible to construct a model of imperfect dark matter which is free from ghost and gradient instabilities. As a side remark, we also show that mimetic F(Script R) theory is plagued with the Ostrogradsky instability.

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.

Electrokinetic Control of Viscous Fingering

NASA Astrophysics Data System (ADS)

Mirzadeh, Mohammad; Bazant, Martin Z.

2017-10-01

We present a theory of the interfacial stability of two immiscible electrolytes under the coupled action of pressure gradients and electric fields in a Hele-Shaw cell or porous medium. Mathematically, our theory describes a phenomenon of "vector Laplacian growth," in which the interface moves in response to the gradient of a vector-valued potential function through a generalized mobility tensor. Physically, we extend the classical Saffman-Taylor problem to electrolytes by incorporating electrokinetic (EK) phenomena. A surprising prediction is that viscous fingering can be controlled by varying the injection ratio of electric current to flow rate. Beyond a critical injection ratio, stability depends only upon the relative direction of flow and current, regardless of the viscosity ratio. Possible applications include porous materials processing, electrically enhanced oil recovery, and EK remediation of contaminated soils.

Magnetoresistance in relativistic hydrodynamics without anomalies

NASA Astrophysics Data System (ADS)

Baumgartner, Andrew; Karch, Andreas; Lucas, Andrew

2017-06-01

We present expressions for the magnetoconductivity and the magnetoresistance of a strongly interacting metal in 3 + 1 dimensions, derivable from relativistic hydrodynamics. Such an approach is suitable for ultraclean metals with emergent Lorentz invariance. When this relativistic fluid contains chiral anomalies, it is known to exhibit longitudinal negative magnetoresistance. We show that similar effects can arise in non-anomalous relativistic fluids due to the distinctive gradient expansion. In contrast with a Galilean-invariant fluid, the resistivity tensor of a dirty relativistic fluid exhibits similar angular dependence to negative magnetoresistance, even when the constitutive relations and momentum relaxation rate are isotropic. We further account for the effect of magnetic field-dependent corrections to the gradient expansion and the effects of long-wavelength impurities on magnetoresistance. We note that the holographic D3/D7 system exhibits negative magnetoresistance.

Enhancement of orientation gradients during simple shear deformation by application of simple compression

NASA Astrophysics Data System (ADS)

Jahedi, Mohammad; Ardeljan, Milan; Beyerlein, Irene J.; Paydar, Mohammad Hossein; Knezevic, Marko

2015-06-01

We use a multi-scale, polycrystal plasticity micromechanics model to study the development of orientation gradients within crystals deforming by slip. At the largest scale, the model is a full-field crystal plasticity finite element model with explicit 3D grain structures created by DREAM.3D, and at the finest scale, at each integration point, slip is governed by a dislocation density based hardening law. For deformed polycrystals, the model predicts intra-granular misorientation distributions that follow well the scaling law seen experimentally by Hughes et al., Acta Mater. 45(1), 105-112 (1997), independent of strain level and deformation mode. We reveal that the application of a simple compression step prior to simple shearing significantly enhances the development of intra-granular misorientations compared to simple shearing alone for the same amount of total strain. We rationalize that the changes in crystallographic orientation and shape evolution when going from simple compression to simple shearing increase the local heterogeneity in slip, leading to the boost in intra-granular misorientation development. In addition, the analysis finds that simple compression introduces additional crystal orientations that are prone to developing intra-granular misorientations, which also help to increase intra-granular misorientations. Many metal working techniques for refining grain sizes involve a preliminary or concurrent application of compression with severe simple shearing. Our finding reveals that a pre-compression deformation step can, in fact, serve as another processing variable for improving the rate of grain refinement during the simple shearing of polycrystalline metals.

Kinematics of red cell aspiration by fluorescence-imaged microdeformation.

PubMed

Discher, D E; Mohandas, N

1996-10-01

Maps of fluorescing red cell membrane components on a pipette-aspirated projection are quantitated in an effort to elucidate and unify the heterogeneous kinematics of deformation. Transient gradients of diffusing fluorescent lipid first demonstrate the fluidity of an otherwise uniform-density bilayer and corroborate a "universal" calibration scale for relative surface density. A steep but smooth and stable gradient in the densities of the skeleton components spectrin, actin, and protein 4.1 is used to estimate large elastic strains along the aspirated skeleton. The deformation fields are argued to be an unhindered response to loading in the surface normal direction. Density maps intermediate to those of the compressible skeleton and fluid bilayer are exhibited by particular transmembrane proteins (e.g., Band 3) and yield estimates for the skeleton-connected fractions. Such connected proteins appear to occupy a significant proportion of the undeformed membrane surface and can lead to steric exclusion of unconnected integral membrane proteins from regions of network condensation. Consistent with membrane repatterning kinematics in reversible deformation, final vesiculation of the projection tip produces a cell fragment concentrated in freely diffusing proteins but depleted of skeleton.

Bioinspired adaptive gradient refractive index distribution lens

NASA Astrophysics Data System (ADS)

Yin, Kezhen; Lai, Chuan-Yar; Wang, Jia; Ji, Shanzuo; Aldridge, James; Feng, Jingxing; Olah, Andrew; Baer, Eric; Ponting, Michael

2018-02-01

Inspired by the soft, deformable human eye lens, a synthetic polymer gradient refractive index distribution (GRIN) lens with an adaptive geometry and focal power has been demonstrated via multilayer coextrusion and thermoforming of nanolayered elastomeric polymer films. A set of 30 polymer nanolayered films comprised of two thermoplastic polyurethanes having a refractive index difference of 0.05 were coextruded via forced-assembly technique. The set of 30 nanolayered polymer films exhibited transmission near 90% with each film varying in refractive index by 0.0017. An adaptive GRIN lens was fabricated from a laminated stack of the variable refractive index films with a 0.05 spherical GRIN. This lens was subsequently deformed by mechanical ring compression of the lens. Variation in the optical properties of the deformable GRIN lens was determined, including 20% variation in focal length and reduced spherical aberration. These properties were measured and compared to simulated results by placido-cone topography and ANSYS methods. The demonstration of a solid-state, dynamic focal length, GRIN lens with improved aberration correction was discussed relative to the potential future use in implantable devices.