Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous, Anisotropic Media

NASA Astrophysics Data System (ADS)

Zhou, Bing; Greenhalgh, S. A.

2011-10-01

2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity of the seismograms to changes in the model parameters. This paper applies two methods, called `the perturbation method' and `the matrix method', to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green's function vectors and their gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The two Green's function vectors are the responses of the displacement vector to the two directed unit vectors located at the source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green's function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic (TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen parameters) plus one angle defining the symmetry axis.

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.

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.

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

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.

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.

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

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

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.

Gradient Augmented Level Set Method for Two Phase Flow Simulations with Phase Change

NASA Astrophysics Data System (ADS)

Anumolu, C. R. Lakshman; Trujillo, Mario F.

2016-11-01

A sharp interface capturing approach is presented for two-phase flow simulations with phase change. The Gradient Augmented Levelset method is coupled with the two-phase momentum and energy equations to advect the liquid-gas interface and predict heat transfer with phase change. The Ghost Fluid Method (GFM) is adopted for velocity to discretize the advection and diffusion terms in the interfacial region. Furthermore, the GFM is employed to treat the discontinuity in the stress tensor, velocity, and temperature gradient yielding an accurate treatment in handling jump conditions. Thermal convection and diffusion terms are approximated by explicitly identifying the interface location, resulting in a sharp treatment for the energy solution. This sharp treatment is extended to estimate the interfacial mass transfer rate. At the computational cell, a d-cubic Hermite interpolating polynomial is employed to describe the interface location, which is locally fourth-order accurate. This extent of subgrid level description provides an accurate methodology for treating various interfacial processes with a high degree of sharpness. The ability to predict the interface and temperature evolutions accurately is illustrated by comparing numerical results with existing 1D to 3D analytical solutions.

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.

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

NASA Astrophysics Data System (ADS)

Wang, Tai-Han; Huang, Da-Nian; Ma, Guo-Qing; Meng, Zhao-Hai; Li, Ye

2017-06-01

With the continuous development of full tensor gradiometer (FTG) measurement techniques, three-dimensional (3D) inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit (GPU) and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation (SSOR) technique and the incomplete Choleksy decomposition conjugate gradient algorithm (ICCG). Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noisecontaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit (CPU). Real airborne gravity-gradiometry data from Vinton salt dome (southwest Louisiana, USA) are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

NASA Technical Reports Server (NTRS)

Leone, Frank A., Jr.

2015-01-01

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

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.

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.

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.

Inference of segmented color and texture description by tensor voting.

PubMed

Jia, Jiaya; Tang, Chi-Keung

2004-06-01

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

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.

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.

Gradient optimization of finite projected entangled pair states

NASA Astrophysics Data System (ADS)

Liu, Wen-Yuan; Dong, Shao-Jun; Han, Yong-Jian; Guo, Guang-Can; He, Lixin

2017-05-01

Projected entangled pair states (PEPS) methods have been proven to be powerful tools to solve strongly correlated quantum many-body problems in two dimensions. However, due to the high computational scaling with the virtual bond dimension D , in a practical application, PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, frustrated systems. Optimization of the ground state using the imaginary time evolution method with a simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that by combining the imaginary time evolution method with a simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking advantage of massive parallel computing, we can study quantum systems with larger bond dimensions up to D =10 without resorting to any symmetry. Benchmark tests of the method on the J1-J2 model give impressive accuracy compared with exact results.

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

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

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

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

Insights into the Lurking Structures and Related Intraplate Earthquakes in the Region of Bay of Bengal Using Gravity and Full Gravity Gradient Tensor

NASA Astrophysics Data System (ADS)

Dubey, C. P.; Tiwari, V. M.; Rao, P. R.

2017-12-01

Comprehension of subsurface structures buried under thick sediments in the region of Bay of Bengal is vital as structural features are the key parameters that influence or are caused by the subsurface deformation and tectonic events like earthquakes. Here, we address this issue using the integrated analysis and interpretation of gravity and full gravity gradient tensor with few seismic profiles available in the poorly known region. A 2D model of the deep earth crust-mantle is constructed and interpreted with gravity gradients and seismic profiles, which made it possible to obtain a visual image of a deep seated fault below the basement associated with thick sediments strata. Gravity modelling along a NE-SW profile crossing the hypocentre of the earthquake of 21 May 2014 ( M w 6.0) in the northern Bay of Bengal suggests that the location of intraplate normal dip fault earthquake in the upper mantle is at the boundary of density anomalies, which is probably connected to the crustal fault. We also report an enhanced structural trend of two major ridges, the 85°E and the 90°E ridges hidden under the sedimentary cover from the computed full gravity gradients tensor components.

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.

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.

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

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

PubMed

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

2018-04-01

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

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.

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

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

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

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

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.

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

PubMed Central

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

2010-01-01

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

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.

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.

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

PubMed

Jia, Chengcheng; Fu, Yun

2016-07-09

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

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

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.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

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.

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).

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.

Inversion of airborne tensor VLF data using integral equations

NASA Astrophysics Data System (ADS)

Kamm, Jochen; Pedersen, Laust B.

2014-08-01

The Geological Survey of Sweden has been collecting airborne tensor very low frequency data (VLF) over several decades, covering large parts of the country. The data has been an invaluable source of information for identifying conductive structures that can among other things be related to water-filled fault zones, wet sediments that fill valleys or ore mineralizations. Because the method only uses two differently polarized plane waves of very similar frequency, vertical resolution is low and interpretation is in most cases limited to maps that are directly derived from the data. Occasionally, 2-D inversion is carried out along selected profiles. In this paper, we present for the first time a 3-D inversion for tensor VLF data in order to further increase the usefulness of the data set. The inversion is performed using a non-linear conjugate gradient scheme (Polak-Ribière) with an inexact line-search. The gradient is obtained by an algebraic adjoint method that requires one additional forward calculation involving the adjoint system matrix. The forward modelling is based on integral equations with an analytic formulation of the half-space Green's tensor. It avoids typically required Hankel transforms and is particularly amenable to singularity removal prior to the numerical integration over the volume elements. The system is solved iteratively, thus avoiding construction and storage of the dense system matrix. By using fast 3-D Fourier transforms on nested grids, subsequently farther away interactions are represented with less detail and therefore with less computational effort, enabling us to bridge the gap between the relatively short wavelengths of the fields (tens of metres) and the large model dimensions (several square kilometres). We find that the approximation of the fields can be off by several per cent, yet the transfer functions in the air are practically unaffected. We verify our code using synthetic calculations from well-established 2-D methods, and trade modelling accuracy off against computational effort in order to keep the inversion feasible in both respects. Our compromise is to limit the permissible resistivity to not fall below 100 Ωm to maintain computational domains as large as 10 × 10 km2 and computation times on the order of a few hours on standard PCs. We investigate the effect of possible local violations of these limits. Even though the conductivity magnitude can then not be recovered correctly, we do not observe any structural artefacts related to this in our tests. We invert a data set from northern Sweden, where we find an excellent agreement of known geological features, such as contacts or fault zones, with elongated conductive structures, while high resistivity is encountered in probably less disturbed geology, often related to topographic highs, which have survived predominantly glacial erosion processes. As expected from synthetic studies, the resolution is laterally high, but vertically limited down to the top of conductive structures.

Robotic Online Path Planning on Point Cloud.

PubMed

Liu, Ming

2016-05-01

This paper deals with the path-planning problem for mobile wheeled- or tracked-robot which drive in 2.5-D environments, where the traversable surface is usually considered as a 2-D-manifold embedded in a 3-D ambient space. Specially, we aim at solving the 2.5-D navigation problem using raw point cloud as input. The proposed method is independent of traditional surface parametrization or reconstruction methods, such as a meshing process, which generally has high-computational complexity. Instead, we utilize the output of 3-D tensor voting framework on the raw point clouds. The computation of tensor voting is accelerated by optimized implementation on graphics computation unit. Based on the tensor voting results, a novel local Riemannian metric is defined using the saliency components, which helps the modeling of the latent traversable surface. Using the proposed metric, we prove that the geodesic in the 3-D tensor space leads to rational path-planning results by experiments. Compared to traditional methods, the results reveal the advantages of the proposed method in terms of smoothing the robot maneuver while considering the minimum travel distance.

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.

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

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.

Full moment tensor and source location inversion based on full waveform adjoint method

NASA Astrophysics Data System (ADS)

Morency, C.

2012-12-01

The development of high-performance computing and numerical techniques enabled global and regional tomography to reach high levels of precision, and seismic adjoint tomography has become a state-of-the-art tomographic technique. The method was successfully used for crustal tomography of Southern California (Tape et al., 2009) and Europe (Zhu et al., 2012). Here, I will focus on the determination of source parameters (full moment tensor and location) based on the same approach (Kim et al, 2011). The method relies on full wave simulations and takes advantage of the misfit between observed and synthetic seismograms. An adjoint wavefield is calculated by back-propagating the difference between observed and synthetics from the receivers to the source. The interaction between this adjoint wavefield and the regular forward wavefield helps define Frechet derivatives of the source parameters, that is, the sensitivity of the misfit with respect to the source parameters. Source parameters are then recovered by minimizing the misfit based on a conjugate gradient algorithm using the Frechet derivatives. First, I will demonstrate the method on synthetic cases before tackling events recorded at the Geysers. The velocity model used at the Geysers is based on the USGS 3D velocity model. Waveform datasets come from the Northern California Earthquake Data Center. Finally, I will discuss strategies to ultimately use this method to characterize smaller events for microseismic and induced seismicity monitoring. References: - Tape, C., Q. Liu, A. Maggi, and J. Tromp, 2009, Adjoint tomography of the Southern California crust: Science, 325, 988992. - Zhu, H., Bozdag, E., Peter, D., and Tromp, J., 2012, Structure of the European upper mantle revealed by adjoint method: Nature Geoscience, 5, 493-498. - Kim, Y., Q. Liu, and J. Tromp, 2011, Adjoint centroid-moment tensor inversions: Geophys. J. Int., 186, 264278. Prepared by LLNL under Contract DE-AC52-07NA27344.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

The 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.

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

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.

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

NASA Astrophysics Data System (ADS)

Khoromskaia, Venera; Khoromskij, Boris N.

2014-12-01

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

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.

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

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.

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

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.

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.

Video denoising using low rank tensor decomposition

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Ab initio and DFT studies of the spin-orbit and spin-spin contributions to the zero-field splitting tensors of triplet nitrenes with aryl scaffolds.

PubMed

Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji

2011-04-21

Spin-orbit and spin-spin contributions to the zero-field splitting (ZFS) tensors (D tensors) of spin-triplet phenyl-, naphthyl-, and anthryl-nitrenes in their ground state are investigated by quantum chemical calculations, focusing on the effects of the ring size and substituted position of nitrene on the D tensor. A hybrid CASSCF/MRMP2 approach to the spin-orbit term of the D tensor (D(SO) tensor), which was recently proposed by us, has shown that the spin-orbit contribution to the entire D value, termed the ZFS parameter or fine-structure constant, is about 10% in all the arylnitrenes under study and less depends on the size and connectivity of the aryl groups. Order of the absolute values for D(SO) can be explained by the perturbation on the energy level and spatial distributions of π-SOMO through the orbital interaction between SOMO of the nitrene moiety and frontier orbitals of the aryl scaffolds. Spin-spin contribution to the D tensor (D(SS) tensor) has been calculated in terms of the McWeeny-Mizuno equation with the DFT/EPR-II spin densities. The D(SS) value calculated with the RO-B3LYP spin density agrees well with the D(Exptl) -D(SO) reference value in phenylnitrene, but agreement with the reference value gradually becomes worse as the D value decreases. Exchange-correlation functional dependence on the D(SS) tensor has been explored with standard 23 exchange-correlation functionals in both RO- and U-DFT methodologies, and the RO-HCTH/407 method gives the best agreement with the D(Exptl) -D(SO) reference value. Significant exchange-correlation functional dependence is observed in spin-delocalized systems such as 9-anthrylnitrene (6). By employing the hybrid CASSCF/MRMP2 approach and the McWeeny-Mizuno equation combined with the RO-HCTH/407/EPR-II//U-HCTH/407/6-31G* spin densities for D(SO) and D(SS), respectively, a quantitative agreement with the experiment is achieved with errors less than 10% in all the arylnitrenes under study. Guidelines to the putative approaches to D(SS) tensor calculations are given.

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.

The Topology of Three-Dimensional Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

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

An ab initio MO study of heavy atom effects on the zero-field splitting tensors of high-spin nitrenes: how the spin-orbit contributions are affected.

PubMed

Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji

2014-05-21

The CASSCF and the hybrid CASSCF-MRMP2 methods are applied to the calculations of spin-spin and spin-orbit contributions to the zero-field splitting tensors (D tensors) of the halogen-substituted spin-septet 2,4,6-trinitrenopyridines, focusing on the heavy atom effects on the spin-orbit term of the D tensors (D(SO) tensors). The calculations reproduced experimentally determined |D| values within an error of 15%. Halogen substitutions at the 3,5-positions are less influential in the spin-spin dipolar (D(SS)) term of 2,4,6-trinitrenopyridines, although the D(SO) terms are strongly affected by the introduction of heavier halogens. The absolute sign of the D(SO) value (D = D(ZZ) - (D(XX) + D(YY))/2) of 3,5-dibromo derivative 3 is predicted to be negative, which contradicts the Pederson-Khanna (PK) DFT result previously reported. The large negative contributions to the D(SO) value of 3 arise from the excited spin-septet states ascribed mainly to the excitations of in-plane lone pair of bromine atoms → SOMO of π nature. The importance of the excited states involving electron transitions from the lone pair orbital of the halogen atom is also confirmed in the D(SO) tensors of halogen-substituted para-phenylnitrenes. A new scheme based on the orbital region partitioning is proposed for the analysis of the D(SO) tensors as calculated by means of the PK-DFT approach.

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

3D joint inversion of gravity-gradient and borehole gravity data

NASA Astrophysics Data System (ADS)

Geng, Meixia; Yang, Qingjie; Huang, Danian

2017-12-01

Borehole gravity is increasingly used in mineral exploration due to the advent of slim-hole gravimeters. Given the full-tensor gradiometry data available nowadays, joint inversion of surface and borehole data is a logical next step. Here, we base our inversions on cokriging, which is a geostatistical method of estimation where the error variance is minimised by applying cross-correlation between several variables. In this study, the density estimates are derived using gravity-gradient data, borehole gravity and known densities along the borehole as a secondary variable and the density as the primary variable. Cokriging is non-iterative and therefore is computationally efficient. In addition, cokriging inversion provides estimates of the error variance for each model, which allows direct assessment of the inverse model. Examples are shown involving data from a single borehole, from multiple boreholes, and combinations of borehole gravity and gravity-gradient data. The results clearly show that the depth resolution of gravity-gradient inversion can be improved significantly by including borehole data in addition to gravity-gradient data. However, the resolution of borehole data falls off rapidly as the distance between the borehole and the feature of interest increases. In the case where the borehole is far away from the target of interest, the inverted result can be improved by incorporating gravity-gradient data, especially all five independent components for inversion.

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

From progressive to finite deformation, and back: the universal deformation matrix

NASA Astrophysics Data System (ADS)

Provost, A.; Buisson, C.; Merle, O.

2003-04-01

It is widely accepted that any finite strain recorded in the field may be interpreted in terms of the simultaneous combination of a pure shear component with one or several simple shear components. To predict strain in geological structures, approximate solutions may be obtained by multiplying successive small increments of each elementary strain component. A more rigorous method consists in achieving the simultaneous combination in the velocity gradient tensor but solutions already proposed in the literature are valid for special cases only and cannot be used, e.g., for the general combination of a pure shear component and six elementary simple shear components. In this paper, we show that the combination of any strain components is as simple as a mouse click, both analytically and numerically. The finite deformation matrix is given by L=exp(L.Δt) where L.Δt is the time-integrated velocity gradient tensor. This method makes it possible to predict finite strain for any combination of strain components. Reciprocally, L.Δt=ln(D) , which allows to unravel the simplest deformation history that might be liable for a given finite deformation. Given the strain ellipsoid only, it is still possible to constrain the range of compatible deformation matrices and thus the range of strain component combinations. Interestingly, certain deformation matrices, though geologically sensible, have no real logarithm so cannot be explained by a deformation history implying strain rate components with constant proportions, what implies significant changes of the stress field during the history of deformation. The study as a whole opens the possibility for further investigations on deformation analysis in general, the method could be used wathever the configuration is.

Behaviour of DFT-based approaches to the spin-orbit term of zero-field splitting tensors: a case study of metallocomplexes, MIII(acac)3 (M = V, Cr, Mn, Fe and Mo).

PubMed

Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji

2017-11-15

Spin-orbit contributions to the zero-field splitting (ZFS) tensor (D SO tensor) of M III (acac) 3 complexes (M = V, Cr, Mn, Fe and Mo; acac = acetylacetonate anion) are evaluated by means of ab initio (a hybrid CASSCF/MRMP2) and DFT (Pederson-Khanna (PK) and natural orbital-based Pederson-Khanna (NOB-PK)) methods, focusing on the behaviour of DFT-based approaches to the D SO tensors against the valence d-electron configurations of the transition metal ions in octahedral coordination. Both the DFT-based approaches reproduce trends in the D tensors. Significantly, the differences between the theoretical and experimental D (D = D ZZ - (D XX + D YY )/2) values are smaller in NOB-PK than in PK, emphasising the usefulness of the natural orbital-based approach to the D tensor calculations of transition metal ion complexes. In the case of d 2 and d 4 electronic configurations, the D SO (NOB-PK) values are considerably underestimated in the absolute magnitude, compared with the experimental ones. The D SO tensor analysis based on the orbital region partitioning technique (ORPT) revealed that the D SO contributions attributed to excitations from the singly occupied region (SOR) to the unoccupied region (UOR) are significantly underestimated in the DFT-based approaches to all the complexes under study. In the case of d 3 and d 5 configurations, the (SOR → UOR) excitations contribute in a nearly isotropic manner, which causes fortuitous error cancellations in the DFT-based D SO values. These results indicate that more efforts to develop DFT frameworks should be directed towards the reproduction of quantitative D SO tensors of transition metal complexes with various electronic configurations and local symmetries around metal ions.

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.

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

PubMed

Papadopoulo, Théo; Ghosh, Aurobrata; Deriche, Rachid

2014-01-01

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

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

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.

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

NASA Astrophysics Data System (ADS)

Kopriva, Ivica; Peršin, Antun

2010-03-01

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

A 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

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.

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.

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).

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.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Shape-from-focus by tensor voting.

PubMed

Hariharan, R; Rajagopalan, A N

2012-07-01

In this correspondence, we address the task of recovering shape-from-focus (SFF) as a perceptual organization problem in 3-D. Using tensor voting, depth hypotheses from different focus operators are validated based on their likelihood to be part of a coherent 3-D surface, thereby exploiting scene geometry and focus information to generate reliable depth estimates. The proposed method is fast and yields significantly better results compared with existing SFF methods.

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

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

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.

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.

Tensor body: real-time reconstruction of the human body and avatar synthesis from RGB-D.

PubMed

Barmpoutis, Angelos

2013-10-01

Real-time 3-D reconstruction of the human body has many applications in anthropometry, telecommunications, gaming, fashion, and other areas of human-computer interaction. In this paper, a novel framework is presented for reconstructing the 3-D model of the human body from a sequence of RGB-D frames. The reconstruction is performed in real time while the human subject moves arbitrarily in front of the camera. The method employs a novel parameterization of cylindrical-type objects using Cartesian tensor and b-spline bases along the radial and longitudinal dimension respectively. The proposed model, dubbed tensor body, is fitted to the input data using a multistep framework that involves segmentation of the different body regions, robust filtering of the data via a dynamic histogram, and energy-based optimization with positive-definite constraints. A Riemannian metric on the space of positive-definite tensor splines is analytically defined and employed in this framework. The efficacy of the presented methods is demonstrated in several real-data experiments using the Microsoft Kinect sensor.

Magnetoresistance in relativistic hydrodynamics without anomalies

DOE PAGES

Baumgartner, Andrew; Karch, Andreas; Lucas, Andrew

2017-06-12

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. Wemore » 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.« less

Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

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

Stevens, Andrew J.; Pu, Yunchen; Sun, Yannan

We introduce new dictionary learning methods for tensor-variate data of any order. We represent each data item as a sum of Kruskal decomposed dictionary atoms within the framework of beta-process factor analysis (BPFA). Our model is nonparametric and can infer the tensor-rank of each dictionary atom. This Kruskal-Factor Analysis (KFA) is a natural generalization of BPFA. We also extend KFA to a deep convolutional setting and develop online learning methods. We test our approach on image processing and classification tasks achieving state of the art results for 2D & 3D inpainting and Caltech 101. The experiments also show that atom-rankmore » impacts both overcompleteness and sparsity.« less

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

NASA Technical Reports Server (NTRS)

Avis, L. M.

1976-01-01

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

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.

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.

Mean template for tensor-based morphometry using deformation tensors.

PubMed

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

2007-01-01

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

Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Pazner, Will; Persson, Per-Olof

2018-02-01

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

Determining the depth of certain gravity sources without a priori specification of their structural index

NASA Astrophysics Data System (ADS)

Zhou, Shuai; Huang, Danian

2015-11-01

We have developed a new method for the interpretation of gravity tensor data based on the generalized Tilt-depth method. Cooper (2011, 2012) extended the magnetic Tilt-depth method to gravity data. We take the gradient-ratio method of Cooper (2011, 2012) and modify it so that the source type does not need to be specified a priori. We develop the new method by generalizing the Tilt-depth method for depth estimation for different types of source bodies. The new technique uses only the three vertical tensor components of the full gravity tensor data observed or calculated at different height plane to estimate the depth of the buried bodies without a priori specification of their structural index. For severely noise-corrupted data, our method utilizes different upward continuation height data, which can effectively reduce the influence of noise. Theoretical simulations of the gravity source model with and without noise illustrate the ability of the method to provide source depth information. Additionally, the simulations demonstrate that the new method is simple, computationally fast and accurate. Finally, we apply the method using the gravity data acquired over the Humble Salt Dome in the USA as an example. The results show a good correspondence to the previous drilling and seismic interpretation results.

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).

Orientationally invariant metrics of apparent compartment eccentricity from double pulsed field gradient diffusion experiments.

PubMed

Jespersen, Sune Nørhøj; Lundell, Henrik; Sønderby, Casper Kaae; Dyrby, Tim B

2013-12-01

Pulsed field gradient diffusion sequences (PFG) with multiple diffusion encoding blocks have been indicated to offer new microstructural tissue information, such as the ability to detect nonspherical compartment shapes in macroscopically isotropic samples, i.e. samples with negligible directional signal dependence on diffusion gradients in standard diffusion experiments. However, current acquisition schemes are not rotationally invariant in the sense that the derived metrics depend on the orientation of the sample, and are affected by the interplay of sampling directions and compartment orientation dispersion when applied to macroscopically anisotropic systems. Here we propose a new framework, the d-PFG 5-design, to enable rotationally invariant estimation of double wave vector diffusion metrics (d-PFG). The method is based on the idea that an appropriate orientational average of the signal emulates the signal from a powder preparation of the same sample, where macroscopic anisotropy is absent by construction. Our approach exploits the theory of exact numerical integration (quadrature) of polynomials on the rotation group, and we exemplify the general procedure with a set consisting of 60 pairs of diffusion wave vectors (the d-PFG 5-design) facilitating a theoretically exact determination of the fourth order Taylor or cumulant expansion of the orientationally averaged signal. The d-PFG 5-design is evaluated with numerical simulations and ex vivo high field diffusion MRI experiments in a nonhuman primate brain. Specifically, we demonstrate rotational invariance when estimating compartment eccentricity, which we show offers new microstructural information, complementary to that of fractional anisotropy (FA) from diffusion tensor imaging (DTI). The imaging observations are supported by a new theoretical result, directly relating compartment eccentricity to FA of individual pores. Copyright © 2013 John Wiley & Sons, Ltd.

HYPGEO - A collaboration between geophysics and remote sensing for mineral exploration

NASA Astrophysics Data System (ADS)

Meyer, Uwe; Frei, Michaela; Petersen, Hauke; Papenfuß, Anne; Ibs-von Seht, Malte; Stolz, Ronny; Queitsch, Matthias; Buchholz, Peter; Siemon, Bernhard

2017-04-01

The German Federal Institute for Geosciences and Natural Resources (BGR) aims to promote and design application oriented, generic techniques for the detection and 3D-characterisation of mineral deposits. Most newly developed mineral mining structures are still exploiting near surface sources. Since exploration and exploitation of mineral resources are increasingly under public review concerning environmental issues and social acceptance, non-invasive methods using satellites, fixed-wing aircraft, helicopters or unmanned aerial vehicles are preferred techniques within this investigation. Therefore, a data combination of helicopter-borne gamma ray spectrometry, hyperspectral imagery and full tensor gradient magnetometry is being evaluated. Test areas are open pit mining structures in Aznalcollar and Tharsis within the Pyrite Belt of southern Spain. First test flights using gamma-ray spectrometry and gradient magnetometry using SQUID-based sensors have been performed. Hyperspectral imagery has been applied on ground. Rock and core samples from the mines have been taken or investigated for further analysis. The basic idea is to combine surface triggered signals from gamma-ray spectrometry and hyperspectral imagery to enhance the detection of shallow mineralisation structures. In order to investigate whether these structures are connected with near-surface ore veins, gradient magnetometry was applied to model subsurface formations. To verify that good correlations between the applied methods are given, open pit mining structures were chosen, where the mineral content and the local to regional geology is well known.

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.

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2017-04-27

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

Centroid moment tensor catalogue using a 3-D continental scale Earth model: Application to earthquakes in Papua New Guinea and the Solomon Islands

NASA Astrophysics Data System (ADS)

Hejrani, Babak; Tkalčić, Hrvoje; Fichtner, Andreas

2017-07-01

Although both earthquake mechanism and 3-D Earth structure contribute to the seismic wavefield, the latter is usually assumed to be layered in source studies, which may limit the quality of the source estimate. To overcome this limitation, we implement a method that takes advantage of a 3-D heterogeneous Earth model, recently developed for the Australasian region. We calculate centroid moment tensors (CMTs) for earthquakes in Papua New Guinea (PNG) and the Solomon Islands. Our method is based on a library of Green's functions for each source-station pair for selected Geoscience Australia and Global Seismic Network stations in the region, and distributed on a 3-D grid covering the seismicity down to 50 km depth. For the calculation of Green's functions, we utilize a spectral-element method for the solution of the seismic wave equation. Seismic moment tensors were calculated using least squares inversion, and the 3-D location of the centroid is found by grid search. Through several synthetic tests, we confirm a trade-off between the location and the correct input moment tensor components when using a 1-D Earth model to invert synthetics produced in a 3-D heterogeneous Earth. Our CMT catalogue for PNG in comparison to the global CMT shows a meaningful increase in the double-couple percentage (up to 70%). Another significant difference that we observe is in the mechanism of events with depth shallower then 15 km and Mw < 6, which contributes to accurate tectonic interpretation of the region.

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

DTIC Science & Technology

2012-08-01

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

3D electromagnetic modelling of a TTI medium and TTI effects in inversion

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil; de la Kethulle de Ryhove, Sébastien

2016-04-01

We present a numerical algorithm for 3D electromagnetic (EM) forward modelling in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For simulation data corresponding to a 3D model with a TTI anticlinal structure, a standard vertical transverse isotropic inversion is not able to image a resistor, while for a 3D model with a TTI synclinal structure the inversion produces a false resistive anomaly. If inversion uses the proposed forward solver that can handle TTI anisotropy, it produces resistivity images consistent with the true models.

Visualization of 3-D tensor fields

NASA Technical Reports Server (NTRS)

Hesselink, L.

1996-01-01

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

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).

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Hou, Tingjun; McCammon, J. Andrew

2005-08-01

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM.

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.

On-Time 3D Time-Domain EMI and Tensor Magnetic Gradiometry for UXO Detection and Discrimination

DTIC Science & Technology

2008-06-04

three-axis fluxgate magnetometers mounted on a tetrahedral structure as shown in figure 5.1.3.1. TMGS was intended to measure gradients of vector...manufacturer of the fluxgate magnetometers supplied specifications for each of the triaxial sensors (figure 5.3.2.25). Figure 5.3.2.25...Manufacturer’s specifications for the four triaxial fluxgate magnetometers used in the TMGS planar array. As shown previously in figure 5.3.2.4

Anomalous Polarized Raman Scattering and Large Circular Intensity Differential in Layered Triclinic ReS2.

PubMed

Zhang, Shishu; Mao, Nannan; Zhang, Na; Wu, Juanxia; Tong, Lianming; Zhang, Jin

2017-10-24

The Raman tensor of a crystal is the derivative of its polarizability tensor and is dependent on the symmetries of the crystal and the Raman-active vibrational mode. The intensity of a particular mode is determined by the Raman selection rule, which involves the Raman tensor and the polarization configurations. For anisotropic two-dimensional (2D) layered crystals, polarized Raman scattering has been used to reveal the crystalline orientations. However, due to its complicated Raman tensors and optical birefringence, the polarized Raman scattering of triclinic 2D crystals has not been well studied yet. Herein, we report the anomalous polarized Raman scattering of 2D layered triclinic rhenium disulfide (ReS 2 ) and show a large circular intensity differential (CID) of Raman scattering in ReS 2 of different thicknesses. The origin of CID and the anomalous behavior in polarized Raman scattering were attributed to the appearance of nonzero off-diagonal Raman tensor elements and the phase factor owing to optical birefringence. This can provide a method to identify the vertical orientation of triclinic layered materials. These findings may help to further understand the Raman scattering process in 2D materials of low symmetry and may indicate important applications in chiral recognition by using 2D materials.

Mapping Earth's electromagnetic dimensionality

NASA Astrophysics Data System (ADS)

Love, J. J.; Kelbert, A.; Bedrosian, P.

2017-12-01

The form of a magnetotelluric impedance tensor, obtained for a given geographic site through simultaneous measurement of geomagnetic and geoelectric field variation, is affected by electrical conductivity structure beneath the measurement site. Building on existing methods for characterizing the symmetry of magnetotelluric impedance tensors, a simple scalar measure is developed for measuring the (frequency dependent) proportion of the impedance tensor that is not just a one-dimensional (1D) function of depth ("non-1D-ness"). These measures are applied to nearly 1000 impedance tensors obtained during magnetotelluric surveys, those for the continental United States and obtained principally through the National Science Foundation's EarthScope project. Across geomagnetic/geoelectric variational periods ranging from 30 s to 3,000 s, corresponding to crustal and upper mantle depths, it is shown that local Earth structure is very often not simply 1D-depth-dependent - often less than 50% of magnetotelluric impedance is 1D. For selected variational frequencies, non-1D-ness is mapped and the relationship between electromagnetic dimensionality and known geological and tectonic structures is discussed. The importance of using realistic surface impedances to accurately evaluate magnetic-storm geoelectric hazards is emphasized.

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

Non-classical continuum theory for fluids incorporating internal and Cosserat rotation rates

NASA Astrophysics Data System (ADS)

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

2017-11-01

This paper presents a non-classical continuum theory for fluent continua in which the conservation and balance laws are derived by incorporating both internal rotation rates arising from the velocity gradient tensor and the rotation rates of the Cosserats. Specifically, in this non-classical continuum theory we have (1) the usual velocities (\\bar{ ±b {\\varvec{v }}}), (2) the three internal rotation rates ({}_i^t\\bar{ ±b {\\varvec{Θ }}}) about the axes of a fixed triad whose axes are parallel to the x-frame arising from the velocity gradient tensor (\\bar{ ±b {\\varvec{L }}}) that are completely defined by the antisymmetric part of the velocity gradient tensor, and (3) three additional rotation rates ({}_e^t\\bar{ ±b {\\varvec{Θ }}}) about the axes of the same triad located at each material point as additional three unknown degrees of freedom, referred to as Cosserat rotation rates. This gives rise to \\bar{ ±b {\\varvec{v }}} and {}_e^t\\bar{ ±b {\\varvec{Θ }}} as six degrees of freedom at a material point. The internal rotation rates {}_i^t\\bar{ ±b {\\varvec{Θ }}}, often neglected in classical fluid mechanics, exist in all deforming fluent continua as these are due to velocity gradient tensor. When the internal rotation rates {}_i^t\\bar{ ±b {\\varvec{Θ }}} are resisted by deforming fluent continua, conjugate moment tensor arises that together with {}_i^t\\bar{ ±b {\\varvec{Θ }}} may result in energy storage and/or dissipation, which must be considered in the conservation and balance laws. The Cosserat rotation rations {}_e^t\\bar{ ±b {\\varvec{Θ }}} also result in conjugate moment tensor that together with {}_e^t\\bar{ ±b {\\varvec{Θ }}} may also result in energy storage and/or dissipation. The main focus of this paper is a consistent derivation of conservation and balance laws for fluent continua that incorporate the aforementioned physics and associated constitutive theories for thermofluids using the conditions resulting from the entropy inequality. The material coefficients derived in the constitutive theories are clearly defined and discussed.

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.

Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations.

PubMed

Peng, Bo; Kowalski, Karol

2017-09-12

The representation and storage of two-electron integral tensors are vital in large-scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this work, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of the atomic basis set, N b , ranging from ∼100 up to ∼2,000, the observed numerical scaling of our implementation shows [Formula: see text] versus [Formula: see text] cost of performing single CD on the two-electron integral tensor in most of the other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic orbital (AO) two-electron integral tensor from [Formula: see text] to [Formula: see text] with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled cluster formalism employing single and double excitations (CCSD) on several benchmark systems including the C 60 molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10 -4 to 10 -3 to give acceptable compromise between efficiency and accuracy.

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.

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.

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.

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

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.

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

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

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

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

Accurate computation of gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

We developed an accurate method to compute the gravitational field of a tesseroid. The method numerically integrates a surface integral representation of the gravitational potential of the tesseroid by conditionally splitting its line integration intervals and by using the double exponential quadrature rule. Then, it evaluates the gravitational acceleration vector and the gravity gradient tensor by numerically differentiating the numerically integrated potential. The numerical differentiation is conducted by appropriately switching the central and the single-sided second-order difference formulas with a suitable choice of the test argument displacement. If necessary, the new method is extended to the case of a general tesseroid with the variable density profile, the variable surface height functions, and/or the variable intervals in longitude or in latitude. The new method is capable of computing the gravitational field of the tesseroid independently on the location of the evaluation point, namely whether outside, near the surface of, on the surface of, or inside the tesseroid. The achievable precision is 14-15 digits for the potential, 9-11 digits for the acceleration vector, and 6-8 digits for the gradient tensor in the double precision environment. The correct digits are roughly doubled if employing the quadruple precision computation. The new method provides a reliable procedure to compute the topographic gravitational field, especially that near, on, and below the surface. Also, it could potentially serve as a sure reference to complement and elaborate the existing approaches using the Gauss-Legendre quadrature or other standard methods of numerical integration.

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.

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.

Analytical Energy Gradients for Excited-State Coupled-Cluster Methods

NASA Astrophysics Data System (ADS)

Wladyslawski, Mark; Nooijen, Marcel

The equation-of-motion coupled-cluster (EOM-CC) and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the paper is the derivation of analytical energy gradients for such non-variational electronic structure approaches, with an ultimate focus on obtaining their detailed algebraic working equations. A general theoretical framework using Lagrange's method of undetermined multipliers is presented, and the method is applied to formulate the EOM-CC and STEOM-CC gradients in abstract operator terms, following the previous work in [P.G. Szalay, Int. J. Quantum Chem. 55 (1995) 151] and [S.R. Gwaltney, R.J. Bartlett, M. Nooijen, J. Chem. Phys. 111 (1999) 58]. Moreover, the systematics of the Lagrange multiplier approach is suitable for automation by computer, enabling the derivation of the detailed derivative equations through a standardized and direct procedure. To this end, we have developed the SMART (Symbolic Manipulation and Regrouping of Tensors) package of automated symbolic algebra routines, written in the Mathematica programming language. The SMART toolkit provides the means to expand, differentiate, and simplify equations by manipulation of the detailed algebraic tensor expressions directly. The Lagrangian multiplier formulation establishes a uniform strategy to perform the automated derivation in a standardized manner: A Lagrange multiplier functional is constructed from the explicit algebraic equations that define the energy in the electronic method; the energy functional is then made fully variational with respect to all of its parameters, and the symbolic differentiations directly yield the explicit equations for the wavefunction amplitudes, the Lagrange multipliers, and the analytical gradient via the perturbation-independent generalized Hellmann-Feynman effective density matrix. This systematic automated derivation procedure is applied to obtain the detailed gradient equations for the excitation energy (EE-), double ionization potential (DIP-), and double electron affinity (DEA-) similarity transformed equation-of-motion coupled-cluster singles-and-doubles (STEOM-CCSD) methods. In addition, the derivatives of the closed-shell-reference excitation energy (EE-), ionization potential (IP-), and electron affinity (EA-) equation-of-motion coupled-cluster singles-and-doubles (EOM-CCSD) methods are derived. Furthermore, the perturbative EOM-PT and STEOM-PT gradients are obtained. The algebraic derivative expressions for these dozen methods are all derived here uniformly through the automated Lagrange multiplier process and are expressed compactly in a chain-rule/intermediate-density formulation, which facilitates a unified modular implementation of analytic energy gradients for CCSD/PT-based electronic methods. The working equations for these analytical gradients are presented in full detail, and their factorization and implementation into an efficient computer code are discussed.

Vessel Enhancement and Segmentation of 4D CT Lung Image Using Stick Tensor Voting

NASA Astrophysics Data System (ADS)

Cong, Tan; Hao, Yang; Jingli, Shi; Xuan, Yang

2016-12-01

Vessel enhancement and segmentation plays a significant role in medical image analysis. This paper proposes a novel vessel enhancement and segmentation method for 4D CT lung image using stick tensor voting algorithm, which focuses on addressing the vessel distortion issue of vessel enhancement diffusion (VED) method. Furthermore, the enhanced results are easily segmented using level-set segmentation. In our method, firstly, vessels are filtered using Frangi's filter to reduce intrapulmonary noises and extract rough blood vessels. Secondly, stick tensor voting algorithm is employed to estimate the correct direction along the vessel. Then the estimated direction along the vessel is used as the anisotropic diffusion direction of vessel in VED algorithm, which makes the intensity diffusion of points locating at the vessel wall be consistent with the directions of vessels and enhance the tubular features of vessels. Finally, vessels can be extracted from the enhanced image by applying level-set segmentation method. A number of experiments results show that our method outperforms traditional VED method in vessel enhancement and results in satisfied segmented vessels.

Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil V.; de la Kethulle de Ryhove, Sébastien; Bratteland, Tarjei

2016-12-01

We present a numerical algorithm for 3-D electromagnetic (EM) simulations in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3-D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For synthetic data corresponding to a 3-D model with a TTI anticlinal structure, a standard vertical transverse isotropic (VTI) inversion is not able to image a resistor, while for a 3-D model with a TTI synclinal structure it produces a false resistive anomaly. However, if the VTI forward solver used in the inversion is replaced by the proposed TTI solver with perfect knowledge of the strike and dip of the dipping structures, the resulting resistivity images become consistent with the true models.

Universal instability of hairy black holes in Lovelock-Galileon theories in D dimensions

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Suyama, Teruaki; Kobayashi, Tsutomu

2016-03-01

We analyze spherically symmetric black hole solutions with time-dependent scalar hair in a class of Lovelock-Galileon theories, which are the scalar-tensor theories with second-order field equations in arbitrary dimensions. We first show that known black hole solutions in five dimensions are always plagued by the ghost/gradient instability in the vicinity of the horizon. We then generalize such black hole solutions to higher dimensions and show that the same instability found in five dimensions appears universally in any number of dimensions.

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

PubMed Central

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

2008-01-01

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

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)}.

Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations

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

Peng, Bo; Kowalski, Karol

The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition ofmore » the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^{-4} to 10^{-3} to give acceptable compromise between efficiency and accuracy.« less

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.

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.

Method to compute the stress-energy tensor for a quantum field outside a black hole that forms from collapse

NASA Astrophysics Data System (ADS)

Anderson, Paul; Evans, Charles

2017-01-01

A method to compute the stress-energy tensor for a quantized massless minimally coupled scalar field outside the event horizon of a 4-D black hole that forms from the collapse of a spherically symmetric null shell is given. The method is illustrated in the corresponding 2-D case which is mathematically similar but is simple enough that the calculations can be done analytically. The approach to the Unruh state at late times is discussed. National Science Foundation Grant No. PHY-1505875 to Wake Forest University and National Science Foundation Grant No. PHY-1506182 to the University of North Carolina, Chapel Hill

Velocity model calibration as a tool to improve regional wave moment tensors: Application to the Basin and Range Province

NASA Astrophysics Data System (ADS)

Ichinose, G. A.

2006-12-01

Many scientific issues for the Basin and Range Province (BRP) remain unsettled including structural evolution, strain rates, slip partitioning and earthquake source physics. A catalog of earthquake source parameters including locations and moment tensors is the basis for tectonic and geophysical study. New instrumentation from the Advance National Seismic System, EarthScope Plate Boundary Observatory, Bigfoot and US-Array brings the opportunity for high quality research; therefore, a catalog is an underlying foundation for examining the BRP. We are continuing to generate a moment tensor catalog for the BRP (Mw<3.5) using long-period regional waves spanning back to 1990. Iterative waveform inversion method (e.g., Nolet et al., 1986, Randell, 1994) is used to calibrate the BRP velocity and density structure using two northern and southern BRP earthquakes. The calibrated models generate realistic synthetics for (f<0.5Hz) with ~50-80% variance reduction. We averaged all path specific models to construct a 1-D BRP community background model. The crust is relatively simple between 5-20km (~6.12km/s) and there is a strong velocity gradient in the upper 5- km. There are lower velocities in the upper crust but higher velocities in the mid-crust for the Sierra Nevada paths relative to BRP. There is also a lower crust high-velocity anomaly near Battle Mountain and Elko that is faster by ~5% and may indicate a wider area of under-plating by basaltic magmas. There are significant low velocity zones in the upper and mid crust mainly across the Walker Lane Belt that may indicate the presence of fluids. We are continuing to work on assessing the performance of these newly calibrated models in improving the estimation of moment tensors down to lower magnitudes and mapping out holes in the seismic network which can be filled to improve moment tensor catalog. We also are looking at how these models work at locating earthquakes and comparing synthetics with those computed from models constrained from different data including refraction, surface wave dispersion, and travel-time tomography.

Comparison of bootstrap approaches for estimation of uncertainties of DTI parameters.

PubMed

Chung, SungWon; Lu, Ying; Henry, Roland G

2006-11-01

Bootstrap is an empirical non-parametric statistical technique based on data resampling that has been used to quantify uncertainties of diffusion tensor MRI (DTI) parameters, useful in tractography and in assessing DTI methods. The current bootstrap method (repetition bootstrap) used for DTI analysis performs resampling within the data sharing common diffusion gradients, requiring multiple acquisitions for each diffusion gradient. Recently, wild bootstrap was proposed that can be applied without multiple acquisitions. In this paper, two new approaches are introduced called residual bootstrap and repetition bootknife. We show that repetition bootknife corrects for the large bias present in the repetition bootstrap method and, therefore, better estimates the standard errors. Like wild bootstrap, residual bootstrap is applicable to single acquisition scheme, and both are based on regression residuals (called model-based resampling). Residual bootstrap is based on the assumption that non-constant variance of measured diffusion-attenuated signals can be modeled, which is actually the assumption behind the widely used weighted least squares solution of diffusion tensor. The performances of these bootstrap approaches were compared in terms of bias, variance, and overall error of bootstrap-estimated standard error by Monte Carlo simulation. We demonstrate that residual bootstrap has smaller biases and overall errors, which enables estimation of uncertainties with higher accuracy. Understanding the properties of these bootstrap procedures will help us to choose the optimal approach for estimating uncertainties that can benefit hypothesis testing based on DTI parameters, probabilistic fiber tracking, and optimizing DTI methods.

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.

The method of planes pressure tensor for a spherical subvolume

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

Heyes, D. M., E-mail: d.heyes@imperial.ac.uk; Smith, E. R., E-mail: edward.smith05@imperial.ac.uk; Dini, D., E-mail: d.dini@imperial.ac.uk

2014-02-07

Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emergemore » naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.« less

Reduced acoustic noise in diffusion tensor imaging on a compact MRI system.

PubMed

Tan, Ek T; Hardy, Christopher J; Shu, Yunhong; In, Myung-Ho; Guidon, Arnaud; Huston, John; Bernstein, Matt A; K F Foo, Thomas

2018-06-01

To investigate the feasibility of substantially reducing acoustic noise while performing diffusion tensor imaging (DTI) on a compact 3T (C3T) MRI scanner equipped with a 42-cm inner-diameter asymmetric gradient. A-weighted acoustic measurements were made using 10 mT/m-amplitude sinusoidal waveforms, corresponding to echo-planar imaging (EPI) echo spacing of 0.25 to 5.0 ms, on a conventional, whole-body 3T MRI and on the C3T. Acoustic measurements of DTI with trapezoidal EPI waveforms were then made at peak gradient performance on the C3T (80 mT/m amplitude, 700 T/m/s slew rate) and at derated performance (33 mT/m, 10 to 50 T/m/s) for acoustic noise reduction. DTI was acquired in two different phantoms and in seven human subjects, with and without gradient-derating corresponding to multi- and single-shot acquisitions, respectively. Sinusoidal waveforms on the C3T were quieter by 8.5 to 15.6 A-weighted decibels (dBA) on average as compared to the whole-body MRI. The derated multishot DTI acquisition noise level was only 8.7 dBA (at 13 T/m/s slew rate) above ambient, and was quieter than non-derated, single-shot DTI by 22.3 dBA; however, the scan time was almost quadrupled. Although derating resulted in negligible diffusivity differences in the phantoms, small biases in diffusivity measurements were observed in human subjects (apparent diffusion coefficient = +9.3 ± 8.8%, fractional anisotropy = +3.2 ± 11.2%, radial diffusivity = +9.4 ± 16.8%, parallel diffusivity = +10.3 ± 8.4%). The feasibility of achieving reduced acoustic noise levels with whole-brain DTI on the C3T MRI was demonstrated. Magn Reson Med 79:2902-2911, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Simultaneous two-view epipolar geometry estimation and motion segmentation by 4D tensor voting.

PubMed

Tong, Wai-Shun; Tang, Chi-Keung; Medioni, Gérard

2004-09-01

We address the problem of simultaneous two-view epipolar geometry estimation and motion segmentation from nonstatic scenes. Given a set of noisy image pairs containing matches of n objects, we propose an unconventional, efficient, and robust method, 4D tensor voting, for estimating the unknown n epipolar geometries, and segmenting the static and motion matching pairs into n independent motions. By considering the 4D isotropic and orthogonal joint image space, only two tensor voting passes are needed, and a very high noise to signal ratio (up to five) can be tolerated. Epipolar geometries corresponding to multiple, rigid motions are extracted in succession. Only two uncalibrated frames are needed, and no simplifying assumption (such as affine camera model or homographic model between images) other than the pin-hole camera model is made. Our novel approach consists of propagating a local geometric smoothness constraint in the 4D joint image space, followed by global consistency enforcement for extracting the fundamental matrices corresponding to independent motions. We have performed extensive experiments to compare our method with some representative algorithms to show that better performance on nonstatic scenes are achieved. Results on challenging data sets are presented.

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.

Tensor network simulation of QED on infinite lattices: Learning from (1 +1 ) d , and prospects for (2 +1 ) d

NASA Astrophysics Data System (ADS)

Zapp, Kai; Orús, Román

2017-06-01

The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful. The vision is that such methods will, eventually, be used to simulate theories in (3 +1 ) dimensions in regimes difficult for other methods. So far, however, TN methods have mostly simulated lattice gauge theories in (1 +1 ) dimensions. The aim of this paper is to explore the simulation of quantum electrodynamics (QED) on infinite lattices with TNs, i.e., fermionic matter fields coupled to a U (1 ) gauge field, directly in the thermodynamic limit. With this idea in mind we first consider a gauge-invariant infinite density matrix renormalization group simulation of the Schwinger model—i.e., QED in (1 +1 ) d . After giving a precise description of the numerical method, we benchmark our simulations by computing the subtracted chiral condensate in the continuum, in good agreement with other approaches. Our simulations of the Schwinger model allow us to build intuition about how a simulation should proceed in (2 +1 ) dimensions. Based on this, we propose a variational ansatz using infinite projected entangled pair states (PEPS) to describe the ground state of (2 +1 ) d QED. The ansatz includes U (1 ) gauge symmetry at the level of the tensors, as well as fermionic (matter) and bosonic (gauge) degrees of freedom both at the physical and virtual levels. We argue that all the necessary ingredients for the simulation of (2 +1 ) d QED are, a priori, already in place, paving the way for future upcoming results.

An artificial nonlinear diffusivity method for supersonic reacting flows with shocks

NASA Astrophysics Data System (ADS)

Fiorina, B.; Lele, S. K.

2007-03-01

A computational approach for modeling interactions between shocks waves, contact discontinuities and reactions zones with a high-order compact scheme is investigated. To prevent the formation of spurious oscillations around shocks, artificial nonlinear viscosity [A.W. Cook, W.H. Cabot, A high-wavenumber viscosity for high resolution numerical method, J. Comput. Phys. 195 (2004) 594-601] based on high-order derivative of the strain rate tensor is used. To capture temperature and species discontinuities a nonlinear diffusivity based on the entropy gradient is added. It is shown that the damping of 'wiggles' is controlled by the model constants and is largely independent of the mesh size and the shock strength. The same holds for the numerical shock thickness and allows a determination of the L2 error. In the shock tube problem, with fluids of different initial entropy separated by the diaphragm, an artificial diffusivity is required to accurately capture the contact surface. Finally, the method is applied to a shock wave propagating into a medium with non-uniform density/entropy and to a CJ detonation wave. Multi-dimensional formulation of the model is presented and is illustrated by a 2D oblique wave reflection from an inviscid wall, by a 2D supersonic blunt body flow and by a Mach reflection problem.

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.

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.

The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2018-06-01

It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

Obtaining orthotropic elasticity tensor using entries zeroing method.

NASA Astrophysics Data System (ADS)

Gierlach, Bartosz; Danek, Tomasz

2017-04-01

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

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.

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.

Gap filling of 3-D microvascular networks by tensor voting.

PubMed

Risser, L; Plouraboue, F; Descombes, X

2008-05-01

We present a new algorithm which merges discontinuities in 3-D images of tubular structures presenting undesirable gaps. The application of the proposed method is mainly associated to large 3-D images of microvascular networks. In order to recover the real network topology, we need to fill the gaps between the closest discontinuous vessels. The algorithm presented in this paper aims at achieving this goal. This algorithm is based on the skeletonization of the segmented network followed by a tensor voting method. It permits to merge the most common kinds of discontinuities found in microvascular networks. It is robust, easy to use, and relatively fast. The microvascular network images were obtained using synchrotron tomography imaging at the European Synchrotron Radiation Facility. These images exhibit samples of intracortical networks. Representative results are illustrated.

Motion-induced phase error estimation and correction in 3D diffusion tensor imaging.

PubMed

Van, Anh T; Hernando, Diego; Sutton, Bradley P

2011-11-01

A multishot data acquisition strategy is one way to mitigate B0 distortion and T2∗ blurring for high-resolution diffusion-weighted magnetic resonance imaging experiments. However, different object motions that take place during different shots cause phase inconsistencies in the data, leading to significant image artifacts. This work proposes a maximum likelihood estimation and k-space correction of motion-induced phase errors in 3D multishot diffusion tensor imaging. The proposed error estimation is robust, unbiased, and approaches the Cramer-Rao lower bound. For rigid body motion, the proposed correction effectively removes motion-induced phase errors regardless of the k-space trajectory used and gives comparable performance to the more computationally expensive 3D iterative nonlinear phase error correction method. The method has been extended to handle multichannel data collected using phased-array coils. Simulation and in vivo data are shown to demonstrate the performance of the method.

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.

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

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.

Local nematic susceptibility in stressed BaFe 2 As 2 from NMR electric field gradient measurements

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

Kissikov, T.; Sarkar, R.; Lawson, M.

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 BaFe 2As 2. 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. In conclusion,more » our work establishes an alternative method to extract the nematic susceptibility which, in contrast to transport methods, can be extended inside the superconducting state.« less

Local nematic susceptibility in stressed BaFe 2 As 2 from NMR electric field gradient measurements

DOE PAGES

Kissikov, T.; Sarkar, R.; Lawson, M.; ...

2017-12-15

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 BaFe 2As 2. 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. In conclusion,more » our work establishes an alternative method to extract the nematic susceptibility which, in contrast to transport methods, can be extended inside the superconducting state.« less

Tensor manifold-based extreme learning machine for 2.5-D face recognition

NASA Astrophysics Data System (ADS)

Chong, Lee Ying; Ong, Thian Song; Teoh, Andrew Beng Jin

2018-01-01

We explore the use of the Gabor regional covariance matrix (GRCM), a flexible matrix-based descriptor that embeds the Gabor features in the covariance matrix, as a 2.5-D facial descriptor and an effective means of feature fusion for 2.5-D face recognition problems. Despite its promise, matching is not a trivial problem for GRCM since it is a special instance of a symmetric positive definite (SPD) matrix that resides in non-Euclidean space as a tensor manifold. This implies that GRCM is incompatible with the existing vector-based classifiers and distance matchers. Therefore, we bridge the gap of the GRCM and extreme learning machine (ELM), a vector-based classifier for the 2.5-D face recognition problem. We put forward a tensor manifold-compliant ELM and its two variants by embedding the SPD matrix randomly into reproducing kernel Hilbert space (RKHS) via tensor kernel functions. To preserve the pair-wise distance of the embedded data, we orthogonalize the random-embedded SPD matrix. Hence, classification can be done using a simple ridge regressor, an integrated component of ELM, on the random orthogonal RKHS. Experimental results show that our proposed method is able to improve the recognition performance and further enhance the computational efficiency.

Finsler geometry of nonlinear elastic solids with internal structure

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

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

On deformation of complex continuum immersed in a plane space

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

Evaluation of Optimal Formulas for Gravitational Tensors up to Gravitational Curvatures of a Tesseroid

NASA Astrophysics Data System (ADS)

Deng, Xiao-Le; Shen, Wen-Bin

2018-01-01

The forward modeling of the topographic effects of the gravitational parameters in the gravity field is a fundamental topic in geodesy and geophysics. Since the gravitational effects, including for instance the gravitational potential (GP), the gravity vector (GV) and the gravity gradient tensor (GGT), of the topographic (or isostatic) mass reduction have been expanded by adding the gravitational curvatures (GC) in geoscience, it is crucial to find efficient numerical approaches to evaluate these effects. In this paper, the GC formulas of a tesseroid in Cartesian integral kernels are derived in 3D/2D forms. Three generally used numerical approaches for computing the topographic effects (e.g., GP, GV, GGT, GC) of a tesseroid are studied, including the Taylor Series Expansion (TSE), Gauss-Legendre Quadrature (GLQ) and Newton-Cotes Quadrature (NCQ) approaches. Numerical investigations show that the GC formulas in Cartesian integral kernels are more efficient if compared to the previously given GC formulas in spherical integral kernels: by exploiting the 3D TSE second-order formulas, the computational burden associated with the former is 46%, as an average, of that associated with the latter. The GLQ behaves better than the 3D/2D TSE and NCQ in terms of accuracy and computational time. In addition, the effects of a spherical shell's thickness and large-scale geocentric distance on the GP, GV, GGT and GC functionals have been studied with the 3D TSE second-order formulas as well. The relative approximation errors of the GC functionals are larger with the thicker spherical shell, which are the same as those of the GP, GV and GGT. Finally, the very-near-area problem and polar singularity problem have been considered by the numerical methods of the 3D TSE, GLQ and NCQ. The relative approximation errors of the GC components are larger than those of the GP, GV and GGT, especially at the very near area. Compared to the GC formulas in spherical integral kernels, these new GC formulas can avoid the polar singularity problem.

Correction of geometric distortion in Propeller echo planar imaging using a modified reversed gradient approach

PubMed Central

Chang, Hing-Chiu; Chuang, Tzu-Chao; Wang, Fu-Nien; Huang, Teng-Yi; Chung, Hsiao-Wen

2013-01-01

Objective This study investigates the application of a modified reversed gradient algorithm to the Propeller-EPI imaging method (periodically rotated overlapping parallel lines with enhanced reconstruction based on echo-planar imaging readout) for corrections of geometric distortions due to the EPI readout. Materials and methods Propeller-EPI acquisition was executed with 360-degree rotational coverage of the k-space, from which the image pairs with opposite phase-encoding gradient polarities were extracted for reversed gradient geometric and intensity corrections. The spatial displacements obtained on a pixel-by-pixel basis were fitted using a two-dimensional polynomial followed by low-pass filtering to assure correction reliability in low-signal regions. Single-shot EPI images were obtained on a phantom, whereas high spatial resolution T2-weighted and diffusion tensor Propeller-EPI data were acquired in vivo from healthy subjects at 3.0 Tesla, to demonstrate the effectiveness of the proposed algorithm. Results Phantom images show success of the smoothed displacement map concept in providing improvements of the geometric corrections at low-signal regions. Human brain images demonstrate prominently superior reconstruction quality of Propeller-EPI images with modified reversed gradient corrections as compared with those obtained without corrections, as evidenced from verification against the distortion-free fast spin-echo images at the same level. Conclusions The modified reversed gradient method is an effective approach to obtain high-resolution Propeller-EPI images with substantially reduced artifacts. PMID:23630654

A novel dipolar dephasing method for the slow magic angle turning experiment.

PubMed

Hu, J Z; Taylor, C M; Pugmire, R J; Grant, D M

2001-09-01

Complete suppression of the resonances from protonated carbons in a slow magic angle spinning experiment can be achieved using five dipolar dephasing (Five-DD) periods distributed in one rotor period. This produces a spectrum containing only the spinning sidebands (SSB) from the nonprotonated carbons. It is shown that the SSB patterns corresponding to the nonprotonated carbons are not distorted over a wide range of dipolar dephasing times. Hence, this method can be used to obtain reliable principal values of the chemical shift tensors for each nonprotonated carbon. The Five-DD method can be readily incorporated into isotropic-anisotropic 2D experiments such as FIREMAT and 2D-PASS to facilitate the measurement of the (13)C chemical shift tensors in complex systems. Copyright 2001 Academic Press.

The behavior of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient. Ph.D. Thesis - Washington Univ., Seattle, Aug. 1972

NASA Technical Reports Server (NTRS)

Rose, W. C.

1973-01-01

The results of an experimental investigation of the mean- and fluctuating-flow properties of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient are presented. The turbulent boundary layer developed on the wall of an axially symmetric nozzle and test section whose nominal free-stream Mach number and boundary-layer thickness Reynolds number were 4 and 100,000, respectively. The adverse pressure gradient was induced by an externally generated conical shock wave. Mean and time-averaged fluctuating-flow data, including the complete experimental Reynolds stress tensor and experimental turbulent mass- and heat-transfer rates are presented for the boundary layer and external flow, upstream, within and downstream of the pressure gradient. The mean-flow data include distributions of total temperature throughout the region of interest. The turbulent mixing properties of the flow were determined experimentally with a hot-wire anemometer. The calibration of the wires and the interpretation of the data are discussed. From the results of the investigation, it is concluded that the shock-wave - boundary-layer interaction significantly alters the turbulent mixing characteristics of the boundary layer.

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

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.

Multivariate Tensor-based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS

PubMed Central

Wang, Yalin; Zhang, Jie; Gutman, Boris; Chan, Tony F.; Becker, James T.; Aizenstein, Howard J.; Lopez, Oscar L.; Tamburo, Robert J.; Toga, Arthur W.; Thompson, Paul M.

2010-01-01

Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics - these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain. PMID:19900560

Polyhedral shape model for terrain correction of gravity and gravity gradient data based on an adaptive mesh

NASA Astrophysics Data System (ADS)

Guo, Zhikui; Chen, Chao; Tao, Chunhui

2016-04-01

Since 2007, there are four China Da yang cruises (CDCs), which have been carried out to investigate polymetallic sulfides in the southwest Indian ridge (SWIR) and have acquired both gravity data and bathymetry data on the corresponding survey lines(Tao et al., 2014). Sandwell et al. (2014) published a new global marine gravity model including the free air gravity data and its first order vertical gradient (Vzz). Gravity data and its gradient can be used to extract unknown density structure information(e.g. crust thickness) under surface of the earth, but they contain all the mass effect under the observation point. Therefore, how to get accurate gravity and its gradient effect of the existing density structure (e.g. terrain) has been a key issue. Using the bathymetry data or ETOPO1 (http://www.ngdc.noaa.gov/mgg/global/global.html) model at a full resolution to calculate the terrain effect could spend too much computation time. We expect to develop an effective method that takes less time but can still yield the desired accuracy. In this study, a constant-density polyhedral model is used to calculate the gravity field and its vertical gradient, which is based on the work of Tsoulis (2012). According to gravity field attenuation with distance and variance of bathymetry, we present an adaptive mesh refinement and coarsening strategies to merge both global topography data and multi-beam bathymetry data. The local coarsening or size of mesh depends on user-defined accuracy and terrain variation (Davis et al., 2011). To depict terrain better, triangular surface element and rectangular surface element are used in fine and coarse mesh respectively. This strategy can also be applied to spherical coordinate in large region and global scale. Finally, we applied this method to calculate Bouguer gravity anomaly (BGA), mantle Bouguer anomaly(MBA) and their vertical gradient in SWIR. Further, we compared the result with previous results in the literature. Both synthetic model tests and field applications indicate that the adaptive terrain correction method can be adopted as a rapid and accurate tool of marine gravity data processing. References Davis, K. &Kass, M.A. & Li, Y., 2011. Rapid gravity and gravity gradiometry terrain corrections via an adaptive quadtree mesh discretization, EXPLOR GEOPHYS, 42, 88-97. Sandwell, D.T., Müller, R.D., Smith, W.H., Garcia, E. & Francis, R., 2014. New global marine gravity model from CryoSat-2 and Jason-1 reveals buried tectonic structure, SCIENCE, 346, 65-67. Tao, C., Li, H., Jin, X., Zhou, J., Wu, T., He, Y., Deng, X., Gu, C., Zhang, G. & Liu, W., 2014. Seafloor hydrothermal activity and polymetallic sulfide exploration on the southwest Indian ridge, CHINESE SCI BULL, 59, 2266-2276. Tsoulis, D., 2012. Analytical computation of the full gravity tensor of a homogeneous arbitrarily shaped polyhedral source using line integrals, GEOPHYSICS, 77, F1-F11.

3D Representative Volume Element Reconstruction of Fiber Composites via Orientation Tensor and Substructure Features

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

Li, Yi; Chen, Wei; Xu, Hongyi

To provide a seamless integration of manufacturing processing simulation and fiber microstructure modeling, two new stochastic 3D microstructure reconstruction methods are proposed for two types of random fiber composites: random short fiber composites, and Sheet Molding Compounds (SMC) chopped fiber composites. A Random Sequential Adsorption (RSA) algorithm is first developed to embed statistical orientation information into 3D RVE reconstruction of random short fiber composites. For the SMC composites, an optimized Voronoi diagram based approach is developed for capturing the substructure features of SMC chopped fiber composites. The proposed methods are distinguished from other reconstruction works by providing a way ofmore » integrating statistical information (fiber orientation tensor) obtained from material processing simulation, as well as capturing the multiscale substructures of the SMC composites.« less

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.

Correction of geometric distortion in Propeller echo planar imaging using a modified reversed gradient approach.

PubMed

Chang, Hing-Chiu; Chuang, Tzu-Chao; Lin, Yi-Ru; Wang, Fu-Nien; Huang, Teng-Yi; Chung, Hsiao-Wen

2013-04-01

This study investigates the application of a modified reversed gradient algorithm to the Propeller-EPI imaging method (periodically rotated overlapping parallel lines with enhanced reconstruction based on echo-planar imaging readout) for corrections of geometric distortions due to the EPI readout. Propeller-EPI acquisition was executed with 360-degree rotational coverage of the k-space, from which the image pairs with opposite phase-encoding gradient polarities were extracted for reversed gradient geometric and intensity corrections. The spatial displacements obtained on a pixel-by-pixel basis were fitted using a two-dimensional polynomial followed by low-pass filtering to assure correction reliability in low-signal regions. Single-shot EPI images were obtained on a phantom, whereas high spatial resolution T2-weighted and diffusion tensor Propeller-EPI data were acquired in vivo from healthy subjects at 3.0 Tesla, to demonstrate the effectiveness of the proposed algorithm. Phantom images show success of the smoothed displacement map concept in providing improvements of the geometric corrections at low-signal regions. Human brain images demonstrate prominently superior reconstruction quality of Propeller-EPI images with modified reversed gradient corrections as compared with those obtained without corrections, as evidenced from verification against the distortion-free fast spin-echo images at the same level. The modified reversed gradient method is an effective approach to obtain high-resolution Propeller-EPI images with substantially reduced artifacts.

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

NASA Astrophysics Data System (ADS)

Basak, Anup; Levitas, Valery I.

2018-04-01

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

GOCE gravity gradient data for lithospheric modeling - From well surveyed to frontier areas

NASA Astrophysics Data System (ADS)

Bouman, J.; Ebbing, J.; Gradmann, S.; Fuchs, M.; Fattah, R. Abdul; Meekes, S.; Schmidt, M.; Lieb, V.; Haagmans, R.

2012-04-01

We explore how GOCE gravity gradient data can improve modeling of the Earth's lithosphere and thereby contribute to a better understanding of the Earth's dynamic processes. The idea is to invert satellite gravity gradients and terrestrial gravity data in the well explored and understood North-East Atlantic Margin and to compare the results of this inversion, providing improved information about the lithosphere and upper mantle, with results obtained by means of models based upon other sources like seismics and magnetic field information. Transfer of the obtained knowledge to the less explored Rub' al Khali desert is foreseen. We present a case study for the North-East Atlantic margin, where we analyze the use of satellite gravity gradients by comparison with a well-constrained 3D density model that provides a detailed picture from the upper mantle to the top basement (base of sediments). The latter horizon is well resolved from gravity and especially magnetic data, whereas sedimentary layers are mainly constrained from seismic studies, but do in general not show a prominent effect in the gravity and magnetic field. We analyze how gravity gradients can increase confidence in the modeled structures by calculating a sensitivity matrix for the existing 3D model. This sensitivity matrix describes the relation between calculated gravity gradient data and geological structures with respect to their depth, extent and relative density contrast. As the sensitivity of the modeled bodies varies for different tensor components, we can use this matrix for a weighted inversion of gradient data to optimize the model. This sensitivity analysis will be used as input to study the Rub' al Khali desert in Saudi Arabia. In terms of modeling and data availability this is a frontier area. Here gravity gradient data will be used to better identify the extent of anomalous structures within the basin, with the goal to improve the modeling for hydrocarbon exploration purposes.

A simple test for spacetime symmetry

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Yasui, Yukinori

2015-03-01

This paper presents a simple method for investigating spacetime symmetry for a given metric. The method makes use of the curvature conditions that are obtained from the Killing equations. We use the solutions of the curvature conditions to compute an upper bound on the number of Killing vector fields, as well as Killing-Yano (KY) tensors and closed conformal KY tensors. We also use them in the integration of the Killing equations. By means of the method, we thoroughly investigate KY symmetry of type D vacuum solutions such as the Kerr metric in four dimensions. The method is also applied to a large variety of physical metrics in four and five dimensions.

Separation of variables in Maxwell equations in Plebański-Demiański spacetime

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.; Krtouš, Pavel; KubizÅák, David

2018-05-01

A new method for separating variables in the Maxwell equations in four- and higher-dimensional Kerr-(A)dS spacetimes proposed recently by Lunin is generalized to any off-shell metric that admits a principal Killing-Yano tensor. The key observation is that Lunin's ansatz for the vector potential can be formulated in a covariant form—in terms of the principal tensor. In particular, focusing on the four-dimensional case we demonstrate separability of Maxwell's equations in the Kerr-NUT-(A)dS and the Plebański-Demiański family of spacetimes. The new method of separation of variables is quite different from the standard approach based on the Newman-Penrose formalism.

Modeling Seismic Anisotropy From the Top to the Bottom of the Mantle

NASA Astrophysics Data System (ADS)

Ribe, N. M.; Castelnau, O.

2011-12-01

Understanding the origin of seismic anisotropy in the mantle requires quantifying the link between the strain history experienced by a rock and the evolving orientation distribution of its constituent crystals (`crystal preferred orientation' or CPO). The fundamental quantity of interest in any model of CPO is the vector spin ω(g, d) of the crystallographic axes of each crystal, which depends on the crystal's orientation g and on the velocity gradient tensor d of the aggregate-scale deformation. Existing methods for determining ω(g, d) rely on unwieldy discrete representations of the crystal orientation distribution in terms of 103-104 individual grains. We propose a new method based on (1) an analytical expression for ω(g, d) and (2) a representation of CPO in terms of a small number (N≤4) of continuous functions of g (`structured basis functions' or SBFs) each of which satisfies the hyperbolic partial differential equation governing the evolution of CPO when only a single slip system is active. The SBFs are then combined via an appropriate weighting scheme to represent a realistic CPO produced by the simultaneous activity of several slip systems.The approach yields a set of N coupled ordinary differential equations for the temporal evolution of the coefficients of the SBFs, which can be solved numerically for an arbitrary strain history at a computational cost ≈10-6 that of homogenization methods such as VPSC. Example calculations will be shown for model mineralogies and strain histories appropriate for the uppermost and lowermost mantles.

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

NASA Technical Reports Server (NTRS)

Ristorcelli, J. R.

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Axial, scalar, and tensor charges of the nucleon from 2 + 1 + 1 -flavor lattice QCD

DOE PAGES

Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Cohen, Saul D.; ...

2016-09-19

Here, we present results for the isovector axial, scalar, and tensor charges g u–d A, g u–d S, and g u–d T of the nucleon needed to probe the Standard Model and novel physics. The axial charge is a fundamental parameter describing the weak interactions of nucleons. The scalar and tensor charges probe novel interactions at the TeV scale in neutron and nuclear β-decays, and the flavor-diagonal tensor charges g u T, g d T, and g s T are needed to quantify the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice-QCD calculations weremore » done using nine ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quarks action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06,0.09, and 0.12 fm and light-quark masses corresponding to the pion masses M π ≈ 135, 225, and 315 MeV. High-statistics estimates on five ensembles using the all-mode-averaging method allow us to quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume, and light-quark masses for the connected contributions. Our final estimates, in the ¯MS scheme at 2 GeV, of the isovector charges are g u–d A = 1.195(33)(20), g u–d S = 0.97(12)(6), and g u–d T = 0.987(51)(20). The first error includes statistical and all systematic uncertainties except that due to the extrapolation Ansatz, which is given by the second error estimate. Combining our estimate for gu–dS with the difference of light quarks masses (m d–m u) QCD = 2.67(35) MeV given by the Flavor Lattice Average Group, we obtain (M N – M P) QCD = 2.59(49) MeV. Estimates of the connected part of the flavor-diagonal tensor charges of the proton are g u T = 0.792(42) and g d T = –0.194(14). Combining our new estimates with precision low-energy experiments, we present updated constraints on novel scalar and tensor interactions, ε S,T, at the TeV scale.« less

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

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).

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

Light-cone distribution amplitudes of light JPC = 2- tensor mesons in QCD

NASA Astrophysics Data System (ADS)

Aliev, T. M.; Bilmis, S.; Yang, Kwei-Chou

2018-06-01

We present a study for two-quark light-cone distribution amplitudes for the 13D2 light tensor meson states with quantum number JPC =2-. Because of the G-parity, the chiral-even two-quark light-cone distribution amplitudes of this tensor meson are antisymmetric under the interchange of momentum fractions of the quark and antiquark in the SU(3) limit, while the chiral-odd ones are symmetric. The asymptotic leading-twist LCDAs with the strange quark mass correction are shown. We estimate the relevant parameters, the decay constants fT and fT⊥, and first Gegenbauer moment a1⊥ , by using the QCD sum rule method. These parameters play a central role in the investigation of B meson decaying into the 2- tensor mesons.

The complex-scaled multiconfigurational spin-tensor electron propagator method for low-lying shape resonances in Be-, Mg- and Ca-

NASA Astrophysics Data System (ADS)

Tsogbayar, Tsednee; Yeager, Danny L.

2017-01-01

We further apply the complex scaled multiconfigurational spin-tensor electron propagator method (CMCSTEP) for the theoretical determination of resonance parameters with electron-atom systems including open-shell and highly correlated (non-dynamical correlation) atoms and molecules. The multiconfigurational spin-tensor electron propagator method (MCSTEP) developed and implemented by Yeager and his coworkers for real space gives very accurate and reliable ionization potentials and electron affinities. CMCSTEP uses a complex scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. CMCSTEP is designed for determining resonances. We apply CMCSTEP to get the lowest 2P (Be-, Mg-) and 2D (Mg-, Ca-) shape resonances using several different basis sets each with several complete active spaces. Many of these basis sets we employ have been used by others with different methods. Hence, we can directly compare results with different methods but using the same basis sets.

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

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

Finite Moment Tensors of Southern California Earthquakes

NASA Astrophysics Data System (ADS)

Jordan, T. H.; Chen, P.; Zhao, L.

2003-12-01

We have developed procedures for inverting broadband waveforms for the finite moment tensors (FMTs) of regional earthquakes. The FMT is defined in terms of second-order polynomial moments of the source space-time function and provides the lowest order representation of a finite fault rupture; it removes the fault-plane ambiguity of the centroid moment tensor (CMT) and yields several additional parameters of seismological interest: the characteristic length L{c}, width W{c}, and duration T{c} of the faulting, as well as the directivity vector {v}{d} of the fault slip. To formulate the inverse problem, we follow and extend the methods of McGuire et al. [2001, 2002], who have successfully recovered the second-order moments of large earthquakes using low-frequency teleseismic data. We express the Fourier spectra of a synthetic point-source waveform in its exponential (Rytov) form and represent the observed waveform relative to the synthetic in terms two frequency-dependent differential times, a phase delay δ τ {p}(ω ) and an amplitude-reduction time δ τ {q}(ω ), which we measure using Gee and Jordan's [1992] isolation-filter technique. We numerically calculate the FMT partial derivatives in terms of second-order spatiotemporal gradients, which allows us to use 3D finite-difference seismograms as our isolation filters. We have applied our methodology to a set of small to medium-sized earthquakes in Southern California. The errors in anelastic structure introduced perturbations larger than the signal level caused by finite source effect. We have therefore employed a joint inversion technique that recovers the CMT parameters of the aftershocks, as well as the CMT and FMT parameters of the mainshock, under the assumption that the source finiteness of the aftershocks can be ignored. The joint system of equations relating the δ τ {p} and δ τ {q} data to the source parameters of the mainshock-aftershock cluster is denuisanced for path anomalies in both observables; this projection operation effectively corrects the mainshock data for path-related amplitude anomalies in a way similar to, but more flexible than, empirical Green function (EGF) techniques.

Finite-Difference Numerical Simulation of Seismic Gradiometry

NASA Astrophysics Data System (ADS)

Aldridge, D. F.; Symons, N. P.; Haney, M. M.

2006-12-01

We use the phrase seismic gradiometry to refer to the developing research area involving measurement, modeling, analysis, and interpretation of spatial derivatives (or differences) of a seismic wavefield. In analogy with gradiometric methods used in gravity and magnetic exploration, seismic gradiometry offers the potential for enhancing resolution, and revealing new (or hitherto obscure) information about the subsurface. For example, measurement of pressure and rotation enables the decomposition of recorded seismic data into compressional (P) and shear (S) components. Additionally, a complete observation of the total seismic wavefield at a single receiver (including both rectilinear and rotational motions) offers the possibility of inferring the type, speed, and direction of an incident seismic wave. Spatially extended receiver arrays, conventionally used for such directional and phase speed determinations, may be dispensed with. Seismic wave propagation algorithms based on the explicit, time-domain, finite-difference (FD) numerical method are well-suited for investigating gradiometric effects. We have implemented in our acoustic, elastic, and poroelastic algorithms a point receiver that records the 9 components of the particle velocity gradient tensor. Pressure and particle rotation are obtained by forming particular linear combinations of these tensor components, and integrating with respect to time. All algorithms entail 3D O(2,4) FD solutions of coupled, first- order systems of partial differential equations on uniformly-spaced staggered spatial and temporal grids. Numerical tests with a 1D model composed of homogeneous and isotropic elastic layers show isolation of P, SV, and SH phases recorded in a multiple borehole configuration, even in the case of interfering events. Synthetic traces recorded by geophones and rotation receivers in a shallow crosswell geometry with randomly heterogeneous poroelastic models also illustrate clear P (fast and slow) and S separation. Finally, numerical tests of the "point seismic array" concept are oriented toward understanding its potential and limitations. Sandia National Laboratories is a multiprogram science and engineering facility operated by Sandia Corporation, a Lockheed-Martin company, for the United States Department of Energy under contract DE- AC04-94AL85000.

Diffusion MRI and its role in neuropsychology

PubMed Central

Mueller, Bryon A; Lim, Kelvin O; Hemmy, Laura; Camchong, Jazmin

2015-01-01

Diffusion Magnetic Resonance Imaging (dMRI) is a popular method used by neuroscientists to uncover unique information about the structural connections within the brain. dMRI is a non-invasive imaging methodology in which image contrast is based on the diffusion of water molecules in tissue. While applicable to many tissues in the body, this review focuses exclusively on the use of dMRI to examine white matter in the brain. In this review, we begin with a definition of diffusion and how diffusion is measured with MRI. Next we introduce the diffusion tensor model, the predominant model used in dMRI. We then describe acquisition issues related to acquisition parameters and scanner hardware and software. Sources of artifacts are then discussed, followed by a brief review of analysis approaches. We provide an overview of the limitations of the traditional diffusion tensor model, and highlight several more sophisticated non-tensor models that better describe the complex architecture of the brain’s white matter. We then touch on reliability and validity issues of diffusion measurements. Finally, we describe examples of ways in which dMRI has been applied to studies of brain disorders and how identified alterations relate to symptomatology and cognition. PMID:26255305

Multiple Echo Diffusion Tensor Acquisition Technique (MEDITATE) on a 3T clinical scanner

PubMed Central

Baete, Steven H.; Cho, Gene; Sigmund, Eric E.

2013-01-01

This paper describes the concepts and implementation of an MRI method, Multiple Echo Diffusion Tensor Acquisition Technique (MEDITATE), which is capable of acquiring apparent diffusion tensor maps in two scans on a 3T clinical scanner. In each MEDITATE scan, a set of RF-pulses generates multiple echoes whose amplitudes are diffusion-weighted in both magnitude and direction by a pattern of diffusion gradients. As a result, two scans acquired with different diffusion weighting strengths suffice for accurate estimation of diffusion tensor imaging (DTI)-parameters. The MEDITATE variation presented here expands previous MEDITATE approaches to adapt to the clinical scanner platform, such as exploiting longitudinal magnetization storage to reduce T2-weighting. Fully segmented multi-shot Cartesian encoding is used for image encoding. MEDITATE was tested on isotropic (agar gel), anisotropic diffusion phantoms (asparagus), and in vivo skeletal muscle in healthy volunteers with cardiac-gating. Comparisons of accuracy were performed with standard twice-refocused spin echo (TRSE) DTI in each case and good quantitative agreement was found between diffusion eigenvalues, mean diffusivity, and fractional anisotropy derived from TRSE-DTI and from the MEDITATE sequence. Orientation patterns were correctly reproduced in both isotropic and anisotropic phantoms, and approximately so for in vivo imaging. This illustrates that the MEDITATE method of compressed diffusion encoding is feasible on the clinical scanner platform. With future development and employment of appropriate view-sharing image encoding this technique may be used in clinical applications requiring time-sensitive acquisition of DTI parameters such as dynamical DTI in muscle. PMID:23828606

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

PubMed

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

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

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.

High-Resolution Multi-Shot Spiral Diffusion Tensor Imaging with Inherent Correction of Motion-Induced Phase Errors

PubMed Central

Truong, Trong-Kha; Guidon, Arnaud

2014-01-01

Purpose To develop and compare three novel reconstruction methods designed to inherently correct for motion-induced phase errors in multi-shot spiral diffusion tensor imaging (DTI) without requiring a variable-density spiral trajectory or a navigator echo. Theory and Methods The first method simply averages magnitude images reconstructed with sensitivity encoding (SENSE) from each shot, whereas the second and third methods rely on SENSE to estimate the motion-induced phase error for each shot, and subsequently use either a direct phase subtraction or an iterative conjugate gradient (CG) algorithm, respectively, to correct for the resulting artifacts. Numerical simulations and in vivo experiments on healthy volunteers were performed to assess the performance of these methods. Results The first two methods suffer from a low signal-to-noise ratio (SNR) or from residual artifacts in the reconstructed diffusion-weighted images and fractional anisotropy maps. In contrast, the third method provides high-quality, high-resolution DTI results, revealing fine anatomical details such as a radial diffusion anisotropy in cortical gray matter. Conclusion The proposed SENSE+CG method can inherently and effectively correct for phase errors, signal loss, and aliasing artifacts caused by both rigid and nonrigid motion in multi-shot spiral DTI, without increasing the scan time or reducing the SNR. PMID:23450457

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.

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

PubMed

Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J

2017-01-01

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D , observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄ . When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model.

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments*

PubMed Central

Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J.

2017-01-01

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model. PMID:28989561

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

NASA Astrophysics Data System (ADS)

Levi, Adam; Ori, Amos

2015-05-01

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

Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations

NASA Astrophysics Data System (ADS)

Katkar, L. N.

2015-03-01

In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ∗ is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ∗ on a form of any degree is not zero.

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.

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

Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Cohen, Saul D.

Here, we present results for the isovector axial, scalar, and tensor charges g u–d A, g u–d S, and g u–d T of the nucleon needed to probe the Standard Model and novel physics. The axial charge is a fundamental parameter describing the weak interactions of nucleons. The scalar and tensor charges probe novel interactions at the TeV scale in neutron and nuclear β-decays, and the flavor-diagonal tensor charges g u T, g d T, and g s T are needed to quantify the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice-QCD calculations weremore » done using nine ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quarks action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06,0.09, and 0.12 fm and light-quark masses corresponding to the pion masses M π ≈ 135, 225, and 315 MeV. High-statistics estimates on five ensembles using the all-mode-averaging method allow us to quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume, and light-quark masses for the connected contributions. Our final estimates, in the ¯MS scheme at 2 GeV, of the isovector charges are g u–d A = 1.195(33)(20), g u–d S = 0.97(12)(6), and g u–d T = 0.987(51)(20). The first error includes statistical and all systematic uncertainties except that due to the extrapolation Ansatz, which is given by the second error estimate. Combining our estimate for gu–dS with the difference of light quarks masses (m d–m u) QCD = 2.67(35) MeV given by the Flavor Lattice Average Group, we obtain (M N – M P) QCD = 2.59(49) MeV. Estimates of the connected part of the flavor-diagonal tensor charges of the proton are g u T = 0.792(42) and g d T = –0.194(14). Combining our new estimates with precision low-energy experiments, we present updated constraints on novel scalar and tensor interactions, ε S,T, at the TeV scale.« less

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

DOE PAGES

Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Cohen, Saul D.; ...

2015-11-01

Here, we present results for the isovector and flavor diagonal tensor charges g u–d T, g u T, g d T, and g s T needed to probe novel tensor interactions at the TeV scale in neutron and nuclear β-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06, 0.09 and 0.12 fm and three quark masses corresponding to the pionmore » masses M π ≈ 130, 220 and 310 MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the isovector combination is g u–d T = 1.020(76) in the MS¯ scheme at 2 GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find g u T = 0.774(66), g d T = –0.233(28) and g u+d T = 0.541(67). The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio m s/m u,d, is g s T = 0.008(9) in the continuum limit.« less

Crustal wavespeed structure of North Texas and Oklahoma based on ambient noise cross-correlation functions and adjoint tomography

NASA Astrophysics Data System (ADS)

Zhu, H.

2017-12-01

Recently, seismologists observed increasing seismicity in North Texas and Oklahoma. Based on seismic observations and other geophysical measurements, some studies suggested possible links between the increasing seismicity and wastewater injection during unconventional oil and gas exploration. To better monitor seismic events and investigate their mechanisms, we need an accurate 3D crustal wavespeed model for North Texas and Oklahoma. Considering the uneven distribution of earthquakes in this region, seismic tomography with local earthquake records have difficulties to achieve good illumination. To overcome this limitation, in this study, ambient noise cross-correlation functions are used to constrain subsurface variations in wavespeeds. I use adjoint tomography to iteratively fit frequency-dependent phase differences between observed and predicted band-limited Green's functions. The spectral-element method is used to numerically calculate the band-limited Green's functions and the adjoint method is used to calculate misfit gradients with respect to wavespeeds. 25 preconditioned conjugate gradient iterations are used to update model parameters and minimize data misfits. Features in the new crustal model M25 correlates with geological units in the study region, including the Llano uplift, the Anadarko basin and the Ouachita orogenic front. In addition, these seismic anomalies correlate with gravity and magnetic observations. This new model can be used to better constrain earthquake source parameters in North Texas and Oklahoma, such as epicenter location and moment tensor solutions, which are important for investigating potential relations between seismicity and unconventional oil and gas exploration.

Conformal and Nearly Conformal Theories at Large N

NASA Astrophysics Data System (ADS)

Tarnoplskiy, Grigory M.

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

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.

Nongyrotropic Electrons in Guide Field Reconnection

NASA Technical Reports Server (NTRS)

Wendel, D. E.; Hesse, M.; Bessho, N.; Adrian, M. L.; Kuznetsova, M.

2016-01-01

We apply a scalar measure of nongyrotropy to the electron pressure tensor in a 2D particle-in-cell simulation of guide field reconnection and assess the corresponding electron distributions and the forces that account for the nongyrotropy. The scalar measure reveals that the nongyrotropy lies in bands that straddle the electron diffusion region and the separatrices, in the same regions where there are parallel electric fields. Analysis of electron distributions and fields shows that the nongyrotropy along the inflow and outflow separatrices emerges as a result of multiple populations of electrons influenced differently by large and small-scale parallel electric fields and by gradients in the electric field. The relevant parallel electric fields include large-scale potential ramps emanating from the x-line and sub-ion inertial scale bipolar electron holes. Gradients in the perpendicular electric field modify electrons differently depending on their phase, thus producing nongyrotropy. Magnetic flux violation occurs along portions of the separatrices that coincide with the parallel electric fields. An inductive electric field in the electron EB drift frame thus develops, which has the effect of enhancing nongyrotropies already produced by other mechanisms and under certain conditions producing their own nongyrotropy. Particle tracing of electrons from nongyrotropic populations along the inflows and outflows shows that the striated structure of nongyrotropy corresponds to electrons arriving from different source regions. We also show that the relevant parallel electric fields receive important contributions not only from the nongyrotropic portion of the electron pressure tensor but from electron spatial and temporal inertial terms as well.

Mathematical modeling of sample stacking methods in microfluidic systems

NASA Astrophysics Data System (ADS)

Horek, Jon

Gradient focusing methods are a general class of experimental techniques used to simultaneously separate and increase the cross-sectionally averaged concentration of charged particle mixtures. In comparison, Field Amplified Sample Stacking (FASS) techniques first concentrate the collection of molecules before separating them. Together, we denote gradient focusing and FASS methods "sample stacking" and study the dynamics of a specific method, Temperature Gradient Focusing (TGF), in which an axial temperature gradient is applied along a channel filled with weak buffer. Gradients in electroosmotic fluid flow and electrophoretic species velocity create the simultaneous separating and concentrating mechanism mentioned above. In this thesis, we begin with the observation that very little has been done to model the dynamics of gradient focusing, and proceed to solve the fundamental equations of fluid mechanics and scalar transport, assuming the existence of slow axial variations and the Taylor-Aris dispersion coefficient. In doing so, asymptotic methods reduce the equations from 3D to 1D, and we arrive at a simple 1D model which can be used to predict the transient evolution of the cross-sectionally averaged analyte concentration. In the second half of this thesis, we run several numerical focusing experiments with a 3D finite volume code. Comparison of the 1D theory and 3D simulations illustrates not only that the asymptotic theory converges as a certain parameter tends to zero, but also that fairly large axial slip velocity gradients lead to quite small errors in predicted steady variance. Additionally, we observe that the axial asymmetry of the electrophoretic velocity model leads to asymmetric peak shapes, a violation of the symmetric Gaussians predicted by the 1D theory. We conclude with some observations on the effect of Peclet number and gradient strength on the performance of focusing experiments, and describe a method for experimental optimization. Such knowledge is useful for design of lab-on-a-chip devices.

Voxel-Wise Comparisons of the Morphology of Diffusion Tensors Across Groups of Experimental Subjects

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Plessen, Kerstin J.; Xu, Dongrong; Royal, Jason; Peterson, Bradley S.

2007-01-01

Water molecules in the brain diffuse preferentially along the fiber tracts within white matter, which form the anatomical connections across spatially distant brain regions. A diffusion tensor (DT) is a probabilistic ellipsoid composed of 3 orthogonal vectors, each having a direction and an associated scalar magnitude, that represent the probability of water molecules diffusing in each of those directions. The 3D morphologies of DTs can be compared across groups of subjects to reveal disruptions in structural organization and neuroanatomical connectivity of the brains of persons with various neuropsychiatric illnesses. Comparisons of tensor morphology across groups have typically been performed on scalar measures of diffusivity, such as Fractional Anisotropy (FA), rather than directly on the complex 3D morphologies of DTs. Scalar measures, however, are related in nonlinear ways to the eigenvalues and eigenvectors that create the 3D morphologies of DTs. We present a mathematical framework that permits the direct comparison across groups of mean eigenvalues and eigenvectors of individual DTs. We show that group-mean eigenvalues and eigenvectors are multivariate Gaussian distributed, and we use the Delta method to compute their approximate covariance matrices. Our results show that the theoretically computed Mean Tensor (MT) eigenvectors and eigenvalues match well with their respective true values. Furthermore, a comparison of synthetically generated groups of DTs highlights the limitations of using FA to detect group differences. Finally, analyses of in vivo DT data using our method reveal significant between-group differences in diffusivity along fiber tracts within white matter, whereas analyses based on FA values failed to detect some of these differences. PMID:18006284

Determination of reversed-phase high performance liquid chromatography based octanol-water partition coefficients for neutral and ionizable compounds: Methodology evaluation.

PubMed

Liang, Chao; Qiao, Jun-Qin; Lian, Hong-Zhen

2017-12-15

Reversed-phase liquid chromatography (RPLC) based octanol-water partition coefficient (logP) or distribution coefficient (logD) determination methods were revisited and assessed comprehensively. Classic isocratic and some gradient RPLC methods were conducted and evaluated for neutral, weak acid and basic compounds. Different lipophilicity indexes in logP or logD determination were discussed in detail, including the retention factor logk w corresponding to neat water as mobile phase extrapolated via linear solvent strength (LSS) model from isocratic runs and calculated with software from gradient runs, the chromatographic hydrophobicity index (CHI), apparent gradient capacity factor (k g ') and gradient retention time (t g ). Among the lipophilicity indexes discussed, logk w from whether isocratic or gradient elution methods best correlated with logP or logD. Therefore logk w is recommended as the preferred lipophilicity index for logP or logD determination. logk w easily calculated from methanol gradient runs might be the main candidate to replace logk w calculated from classic isocratic run as the ideal lipophilicity index. These revisited RPLC methods were not applicable for strongly ionized compounds that are hardly ion-suppressed. A previously reported imperfect ion-pair RPLC method was attempted and further explored for studying distribution coefficients (logD) of sulfonic acids that totally ionized in the mobile phase. Notably, experimental logD values of sulfonic acids were given for the first time. The IP-RPLC method provided a distinct way to explore logD values of ionized compounds. Copyright © 2017 Elsevier B.V. All rights reserved.

Investigating source processes of isotropic events

NASA Astrophysics Data System (ADS)

Chiang, Andrea

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

Moment Tensor Inversion with 3D sensor configuration of Mining Induced Seismicity (Kiruna mine, Sweden)

NASA Astrophysics Data System (ADS)

Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian

2018-03-01

Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). Stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double couple and full moment tensor with high frequency data is very challenging. Moreover, the application to underground mining system requires accounting for the 3D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to 8 events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip, rake configurations of the double couple term were obtained. The orientations of the nodal planes of the double-couple component in most cases vary from NNW to NNE with a dip along the ore body or in the opposite direction.

The magnetotelluric phase tensor analysis of the Sembalun-Propok area, West Nusa Tenggara, Indonesia

NASA Astrophysics Data System (ADS)

Febriani, F.; Widarto, D. S.; Gaffar, E.; Nasution, A.; Grandis, H.

2017-04-01

The subsurface structure of the Sembalun-Propok area, NTB, Indonesia, has been investigated using magnetotelluric method (MT). To obtain the information of the dimensionality of the regional structure and determine the regional strike of the study area, the phase tensor analysis has been performed in this study. The results show that most of the skew angle values (β) are distributed within ± 5°. It indicates that the regional structure of the study area can be assumed as two dimensional. In addition, to determine the regional strike of the study area, we also calculated the major axes of the phase tensor. The result presents that the regional strike of the study area is about N330°E. According to the results of the phase tensor analysis, we rotated the impedance tensor to N330°E and performed 2-D inversion modeling. The result presents that the substructure model suits with the geological background of the study area.

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.

3D Printed Programmable Release Capsules.

PubMed

Gupta, Maneesh K; Meng, Fanben; Johnson, Blake N; Kong, Yong Lin; Tian, Limei; Yeh, Yao-Wen; Masters, Nina; Singamaneni, Srikanth; McAlpine, Michael C

2015-08-12

The development of methods for achieving precise spatiotemporal control over chemical and biomolecular gradients could enable significant advances in areas such as synthetic tissue engineering, biotic-abiotic interfaces, and bionanotechnology. Living organisms guide tissue development through highly orchestrated gradients of biomolecules that direct cell growth, migration, and differentiation. While numerous methods have been developed to manipulate and implement biomolecular gradients, integrating gradients into multiplexed, three-dimensional (3D) matrices remains a critical challenge. Here we present a method to 3D print stimuli-responsive core/shell capsules for programmable release of multiplexed gradients within hydrogel matrices. These capsules are composed of an aqueous core, which can be formulated to maintain the activity of payload biomolecules, and a poly(lactic-co-glycolic) acid (PLGA, an FDA approved polymer) shell. Importantly, the shell can be loaded with plasmonic gold nanorods (AuNRs), which permits selective rupturing of the capsule when irradiated with a laser wavelength specifically determined by the lengths of the nanorods. This precise control over space, time, and selectivity allows for the ability to pattern 2D and 3D multiplexed arrays of enzyme-loaded capsules along with tunable laser-triggered rupture and release of active enzymes into a hydrogel ambient. The advantages of this 3D printing-based method include (1) highly monodisperse capsules, (2) efficient encapsulation of biomolecular payloads, (3) precise spatial patterning of capsule arrays, (4) "on the fly" programmable reconfiguration of gradients, and (5) versatility for incorporation in hierarchical architectures. Indeed, 3D printing of programmable release capsules may represent a powerful new tool to enable spatiotemporal control over biomolecular gradients.

Efficient gradient calibration based on diffusion MRI

PubMed Central

Teh, Irvin; Maguire, Mahon L.

2016-01-01

Purpose To propose a method for calibrating gradient systems and correcting gradient nonlinearities based on diffusion MRI measurements. Methods The gradient scaling in x, y, and z were first offset by up to 5% from precalibrated values to simulate a poorly calibrated system. Diffusion MRI data were acquired in a phantom filled with cyclooctane, and corrections for gradient scaling errors and nonlinearity were determined. The calibration was assessed with diffusion tensor imaging and independently validated with high resolution anatomical MRI of a second structured phantom. Results The errors in apparent diffusion coefficients along orthogonal axes ranged from −9.2% ± 0.4% to + 8.8% ± 0.7% before calibration and −0.5% ± 0.4% to + 0.8% ± 0.3% after calibration. Concurrently, fractional anisotropy decreased from 0.14 ± 0.03 to 0.03 ± 0.01. Errors in geometric measurements in x, y and z ranged from −5.5% to + 4.5% precalibration and were likewise reduced to −0.97% to + 0.23% postcalibration. Image distortions from gradient nonlinearity were markedly reduced. Conclusion Periodic gradient calibration is an integral part of quality assurance in MRI. The proposed approach is both accurate and efficient, can be setup with readily available materials, and improves accuracy in both anatomical and diffusion MRI to within ±1%. Magn Reson Med 77:170–179, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. PMID:26749277

Seismic moment tensor inversion using 3D velocity model and its application to the 2013 Lushan earthquake sequence

NASA Astrophysics Data System (ADS)

Zhu, Lupei; Zhou, Xiaofeng

2016-10-01

Source inversion of small-magnitude events such as aftershocks or mine collapses requires use of relatively high frequency seismic waveforms which are strongly affected by small-scale heterogeneities in the crust. In this study, we developed a new inversion method called gCAP3D for determining general moment tensor of a seismic source using Green's functions of 3D models. It inherits the advantageous features of the ;Cut-and-Paste; (CAP) method to break a full seismogram into the Pnl and surface-wave segments and to allow time shift between observed and predicted waveforms. It uses grid search for 5 source parameters (relative strengths of the isotropic and compensated-linear-vector-dipole components and the strike, dip, and rake of the double-couple component) that minimize the waveform misfit. The scalar moment is estimated using the ratio of L2 norms of the data and synthetics. Focal depth can also be determined by repeating the inversion at different depths. We applied gCAP3D to the 2013 Ms 7.0 Lushan earthquake and its aftershocks using a 3D crustal-upper mantle velocity model derived from ambient noise tomography in the region. We first relocated the events using the double-difference method. We then used the finite-differences method and reciprocity principle to calculate Green's functions of the 3D model for 20 permanent broadband seismic stations within 200 km from the source region. We obtained moment tensors of the mainshock and 74 aftershocks ranging from Mw 5.2 to 3.4. The results show that the Lushan earthquake is a reverse faulting at a depth of 13-15 km on a plane dipping 40-47° to N46° W. Most of the aftershocks occurred off the main rupture plane and have similar focal mechanisms to the mainshock's, except in the proximity of the mainshock where the aftershocks' focal mechanisms display some variations.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

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

2018-03-01

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

Diffusion tensor imaging in evaluation of human skeletal muscle injury.

PubMed

Zaraiskaya, Tatiana; Kumbhare, Dinesh; Noseworthy, Michael D

2006-08-01

To explore the capability and reliability of diffusion tensor magnetic resonance imaging (DTI) in the evaluation of human skeletal muscle injury. DTI of four patients with gastrocnemius and soleus muscles injuries was compared to eight healthy controls. Imaging was performed using a GE 3.0T short-bore scanner. A diffusion-weighted 2D spin echo echo-planar imaging (EPI) pulse sequence optimized for skeletal muscle was used. From a series of axially acquired diffusion tensor images the diffusion tensor eigenparameters (eigenvalues and eigenvectors), fractional anisotropy (FA), and apparent diffusion coefficient (ADC) were calculated and compared for injured and healthy calf muscles. Two dimensional (2D) projection maps of the principal eigenvectors were plotted to visualize the healthy and pathologic muscle fiber architectures. Clear differences in FA and ADC were observed in injured skeletal muscle, compared to healthy controls. Mean control FA was 0.23 +/- 0.02 for medial and lateral gastrocnemius (mg and lg) muscles, and 0.20 +/- 0.02 for soleus (sol) muscles. In all patients FA values were reduced compared to controls, to as low as 0.08 +/- 0.02. The ADC in controls ranged from 1.41 to 1.31 x 10(-9) m(2)/second, while in patients this was consistently higher. The 2D projection maps revealed muscle fiber disorder in injured calves, while in healthy controls the 2D projection maps show a well organized (ordered) fiber structure. DTI is a suitable method to assess human calf muscle injury.

Moment Tensor Inversion of the 1998 Aiquile Earthquake Using Long-period surface waves

NASA Astrophysics Data System (ADS)

Wang, H.

2016-12-01

On 22nd May 1998 at 04:49(GMT), an earthquake of magnitude Mw = 6.6 struck the Aiquile region of Bolivia, causing 105 deaths and significant damage to the nearby towns of Hoyadas and Pampa Grande. This was the largest shallow earthquake (15 km depth) in Bolivia in over 50 years, and was felt as far Sucre, approximately 100 km away. In this report, a centroid moment tensor (CMT) inversion is carried using body waves and surface waves from 1998 Aiquile earthquake with 1-D and 3-D earth models to obtain the source model parameters and moment tensor, which are the values will be subsequently compared against the Global Centroid Moment Tensor Catalog(GCMT). Also, the excitation kernels could be gained and synthetic data can be created with different earth models. The two method for calculating synthetic seismograms are SPECFEM3D Globe which is based on shear wave mantle model S40RTS and crustal model CRUST 2.0, and AxiSEM which is based on PREM 1-D earth Model. Within the report, the theory behind the CMT inversion was explained and the source parameters gained from the inversion can be used to reveal the tectonics of the source of this earthquake, these information could be helpful in assessing seismic hazard and overall tectonic regime of this region. Furthermore, results of synthetic seismograms and the solution of inversion are going to be used to assess two models.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

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

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.

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

DTIC Science & Technology

2010-01-31

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

Individual spectral densities and molecular motion in polycrystalline hexamethylbenzene-d18

NASA Astrophysics Data System (ADS)

Hoatson, Gina L.; Vold, Robert L.; Tse, Tak Y.

1994-04-01

Methods are described for obtaining the orientation dependence of individual motional spectral densities, J1(ω0) and J2(2ω0), from deuterium spin relaxation experiments on polycrystalline materials. Spectral density measurements provide detailed information in a motional regime too fast to be studied by the two-dimensional (2D) exchange method. Their potential as a source of detailed kinetic and geometric information is illustrated for hexamethylbenzene-d18 (HMB). The relaxation behavior of HMB cannot be explained exclusively by six-site jumps around the C6v axis. Agreement between the experimentally determined spectral densities and simulations is improved if the methyl rotation is explicitly included. At ambient temperature the experimental data are best fitted with the simultaneous jump rates, k6=3.85×108 s-1 and k3=5.0×1011 s-1. This is significantly different from the rate determined using a simple six-site jump model, k6=3.9×109 s-1. Geometric distortions of the methyl rotation axes can account for the observed motionally averaged electric field gradient tensor. When these distortions are included in analysis of the spectral density data, there is a small, but significant, improvement in the fit. k3 is unchanged and the best fit k6 is reduced to 2.2×108 s-1, with distortions out of plane by δ=2.5° and in plane ɛ=ɛ'=1.202.

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.

Moment tensor clustering: a tool to monitor mining induced seismicity

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

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.

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.

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

NASA Astrophysics Data System (ADS)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

Fast and accurate 3D tensor calculation of the Fock operator in a general basis

NASA Astrophysics Data System (ADS)

Khoromskaia, V.; Andrae, D.; Khoromskij, B. N.

2012-11-01

The present paper contributes to the construction of a “black-box” 3D solver for the Hartree-Fock equation by the grid-based tensor-structured methods. It focuses on the calculation of the Galerkin matrices for the Laplace and the nuclear potential operators by tensor operations using the generic set of basis functions with low separation rank, discretized on a fine N×N×N Cartesian grid. We prove the Ch2 error estimate in terms of mesh parameter, h=O(1/N), that allows to gain a guaranteed accuracy of the core Hamiltonian part in the Fock operator as h→0. However, the commonly used problem adapted basis functions have low regularity yielding a considerable increase of the constant C, hence, demanding a rather large grid-size N of about several tens of thousands to ensure the high resolution. Modern tensor-formatted arithmetics of complexity O(N), or even O(logN), practically relaxes the limitations on the grid-size. Our tensor-based approach allows to improve significantly the standard basis sets in quantum chemistry by including simple combinations of Slater-type, local finite element and other basis functions. Numerical experiments for moderate size organic molecules show efficiency and accuracy of grid-based calculations to the core Hamiltonian in the range of grid parameter N3˜1015.

A New View of the Dynamics of Reynolds Stress Generation in Turbulent Boundary Layers

NASA Technical Reports Server (NTRS)

Cantwell, Brian J.; Chacin, Juan M.

1998-01-01

The structure of a numerically simulated turbulent boundary layer over a flat plate at Re(theta) = 670 was studied using the invariants of the velocity gradient tensor (Q and R) and a related scalar quantity, the cubic discriminant (D = 27R(exp 2)/4 + Q(exp 3)). These invariants have previously been used to study the properties of the small-scale motions responsible for the dissipation of turbulent kinetic energy. In addition, these scalar quantities allow the local flow patterns to be unambiguously classified according to the terminology proposed by Chong et al. The use of the discriminant as a marker of coherent motions reveals complex, large-scale flow structures that are shown to be associated with the generation of Reynolds shear stress -u'v'(bar). These motions are characterized by high spatial gradients of the discriminant and are believed to be an important part of the mechanism that sustains turbulence in the near-wall region.

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.

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.

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

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.

A Mo-95 and C-13 Solid-state NMR and Relativistic DFT Investigation of Mesitylenetricarbonylmolybdenum(0) -a Typical Transition Metal Piano-stool Complex

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

Bryce, David L.; Wasylishen, Roderick E.

2002-06-21

The chemical shift (CS) and electric field gradient (EFG) tensors in the piano-stool compound mesitylenetricarbonylmolybdenum(0), 1, have been investigated via {sup 95}Mo and {sup 13}C solid-state magic-angle spinning (MAS) NMR as well as relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) calculations. Molybdenum-95 (I = 5/2) MAS NMR spectra acquired at 18.8 T are dominated by the anisotropic chemical shift interaction ({Omega} = 775 {+-} 30 ppm) rather than the 2nd-order quadrupolar interaction (C{sub Q} = -0.96 {+-} 0.15 MHz), an unusual situation for a quadrupolar nucleus. ZORA-DFT calculations of the {sup 95}Mo EFG and CS tensors are in agreementmore » with the experimental data. Mixing of appropriate occupied and virtual d-orbital dominated MOs in the region of the HOMO-LUMO gap are shown to be responsible for the large chemical shift anisotropy. The small, but non-negligible, {sup 95}Mo quadrupolar interaction is discussed in terms of the geometry about Mo. Carbon-13 CPMAS spectra acquired at 4.7 T demonstrate the crystallographic and magnetic nonequivalence of the twelve {sup 13}C nuclei in 1, despite the chemical equivalence of some of these nuclei in isotropic solutions. The principal components of the carbon CS tensors are determined via a Herzfeld-Berger analysis, and indicate that motion of the mesitylene ring is slow compared to a rate which would influence the carbon CS tensors (i.e. tens of {micro}s). ZORA-DFT calculations reproduce the experimental carbon CS tensors accurately. Oxygen-17 EFG and CS tensors for 1 are also calculated and discussed in terms of existing experimental data for related molybdenum carbonyl compounds. This work provides an example of the information available from combined multi-field solid-state multinuclear magnetic resonance and computational investigations of transition metal compounds, in particular the direct study of quadrupolar transition metal nuclei with relatively small magnetic moments.« less

Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

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

Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele,more » Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.« less

Spacetime encodings. IV. The relationship between Weyl curvature and Killing tensors in stationary axisymmetric vacuum spacetimes

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

Brink, Jeandrew

The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst potential is considered. The coupling between the nonlocal curvature content of the spacetime as encoded in the Weyl tensor, and the existence of a Killing tensor is explored and a constructive, algebraic test for a fourth-order Killing tensor suggested. The approach used exploits the variables defined for the Baecklund transformations to clarify the relationship between Weyl curvature, constants of geodesic motion, expressed as Killing tensors, and the solution-generation techniques. A new symmetricmore » noncovariant formulation of the Killing equations is given. This formulation transforms the problem of looking for fourth-order Killing tensors in 4D into one of looking for four interlocking two-manifolds admitting fourth-order Killing tensors in 2D.« less

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

A moment-tensor catalog for intermediate magnitude earthquakes in Mexico

NASA Astrophysics Data System (ADS)

Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Martínez-Peláez, Liliana; Franco, Sara; Iglesias Mendoza, Arturo

2016-04-01

Located among five tectonic plates, Mexico is one of the world's most seismically active regions. The earthquake focal mechanisms provide important information on the active tectonics. A widespread technique for estimating the earthquake magnitud and focal mechanism is the inversion for the moment tensor, obtained by minimizing a misfit function that estimates the difference between synthetic and observed seismograms. An important element in the estimation of the moment tensor is an appropriate velocity model, which allows for the calculation of accurate Green's Functions so that the differences between observed and synthetics seismograms are due to the source of the earthquake rather than the velocity model. However, calculating accurate synthetic seismograms gets progressively more difficult as the magnitude of the earthquakes decreases. Large earthquakes (M>5.0) excite waves of longer periods that interact weakly with lateral heterogeneities in the crust. For these events, using 1D velocity models to compute Greens functions works well and they are well characterized by seismic moment tensors reported in global catalogs (eg. USGS fast moment tensor solutions and GCMT). The opposite occurs for small and intermediate sized events, where the relatively shorter periods excited interact strongly with lateral heterogeneities in the crust and upper mantle. To accurately model the Green's functions for the smaller events in a large heterogeneous area, requires 3D or regionalized 1D models. To obtain a rapid estimate of earthquake magnitude, the National Seismological Survey in Mexico (Servicio Sismológico Nacional, SSN) automatically calculates seismic moment tensors for events in the Mexican Territory (Franco et al., 2002; Nolasco-Carteño, 2006). However, for intermediate-magnitude and small earthquakes the signal-to-noise ratio could is low for many of the seismic stations, and without careful selection and filtering of the data, obtaining a stable focal mechanism is difficult. The selection of data windows and filter parameters is tedious without a tool that allows easy viewing of the data prior to the inversion. Therefore, we developed a graphical user interface (GUI), based on Python and the python library ObsPy, that processes in a iterative and interactive way observed and synthetic seismograms prior to the inversion. The processing includes filtering, choosing and discarding traces and manual adjustment of time windows in which synthetics and observed seismograms will be compared. We calculate the Green Functions using the SPECFEM3D_GLOBE algorithm (Komatitsch et al.,2004) which employs a velocity model that is composed of a mantle and a crustal model, S362ANI (Kustowski et al., 2008) and CRUST2.0 (Bassin et al., 2000), respectively. We invert the observed seismograms for the seismic moment tensor using a method developed for earthquakes in California (Liu et al., 2004) and implemented for earthquakes in Mexico (De la Vega, 2014). In this work, we introduce the GUI, the inversion method and the results from the moment-tensor inversions obtained for intermediate-magnitude earthquakes (4.5

Three dimensional topography correction applied to magnetotelluric data from Sikkim Himalayas

NASA Astrophysics Data System (ADS)

Kumar, Sushil; Patro, Prasanta K.; Chaudhary, B. S.

2018-06-01

Magnetotelluric (MT) method is one of the powerful tools to investigate the deep crustal image of mountainous regions such as Himalayas. Topographic variations due to irregular surface terrain distort the resistivity curves and hence may not give accurate interpretation of magnetotelluric data. The two-dimensional (2-D) topographic effects in Transverse Magnetic (TM) mode is only galvanic whereas inductive in Transverse Electric (TE) mode, thus TM mode responses is much more important than TE mode responses in 2-D. In three-dimensional (3-D), the topography effect is both galvanic and inductive in each element of impedance tensor and hence the interpretation is complicated. In the present work, we investigate the effects of three-dimensional (3-D) topography for a hill model. This paper presents the impedance tensor correction algorithm to reduce the topographic effects in MT data. The distortion caused by surface topography effectively decreases by using homogeneous background resistivity in impedance correction method. In this study, we analyze the response of ramp, distance from topographic edges, conductive and resistive dykes. The new correction method is applied to the real data from Sikkim Himalayas, which brought out the true nature of the basement in this region.

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.

Advanced Magnetic Resonance Imaging techniques to probe muscle structure and function

NASA Astrophysics Data System (ADS)

Malis, Vadim

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

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

NASA Astrophysics Data System (ADS)

Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

2017-08-01

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

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.

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

PubMed

Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

2018-07-04

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

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

NASA Astrophysics Data System (ADS)

Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

2018-07-01

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

Counting conformal correlators

NASA Astrophysics Data System (ADS)

Kravchuk, Petr; Simmons-Duffin, David

2018-02-01

We introduce simple group-theoretic techniques for classifying conformallyinvariant tensor structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and n ≥ 4-point functions of general conserved currents, with or without permutation symmetries, and in any spacetime dimension d. Our techniques are useful for bootstrap applications. The rules we derive simultaneously count tensor structures for flat-space scattering amplitudes in d + 1 dimensions.

Crustal wavespeed structure of North Texas and Oklahoma based on ambient noise cross-correlation functions and adjoint tomography

NASA Astrophysics Data System (ADS)

Zhu, Hejun

2018-04-01

Recently, seismologists observed increasing seismicity in North Texas and Oklahoma. Based on seismic observations and other geophysical measurements, numerous studies suggested links between the increasing seismicity and wastewater injection during unconventional oil and gas exploration. To better monitor seismic events and investigate their triggering mechanisms, we need an accurate 3D crustal wavespeed model for the study region. Considering the uneven distribution of earthquakes in this area, seismic tomography with local earthquake records have difficulties achieving even illumination. To overcome this limitation, in this study, ambient noise cross-correlation functions are used to constrain subsurface variations in wavespeeds. I use adjoint tomography to iteratively fit frequency-dependent phase differences between observed and predicted band-limited Green's functions. The spectral-element method is used to numerically calculate the band-limited Green's functions and the adjoint method is used to calculate misfit gradients with respect to wavespeeds. Twenty five preconditioned conjugate gradient iterations are used to update model parameters and minimize data misfits. Features in the new crustal model TO25 correlates well with geological provinces in the study region, including the Llano uplift, the Anadarko basin and the Ouachita orogenic front, etc. In addition, there are relatively good correlations between seismic results with gravity and magnetic observations. This new crustal model can be used to better constrain earthquake source parameters in North Texas and Oklahoma, such as epicenter location as well as moment tensor solutions, which are important for investigating triggering mechanisms between these induced earthquakes and unconventional oil and gas exploration activities.

AUTOMATED CELL SEGMENTATION WITH 3D FLUORESCENCE MICROSCOPY IMAGES.

PubMed

Kong, Jun; Wang, Fusheng; Teodoro, George; Liang, Yanhui; Zhu, Yangyang; Tucker-Burden, Carol; Brat, Daniel J

2015-04-01

A large number of cell-oriented cancer investigations require an effective and reliable cell segmentation method on three dimensional (3D) fluorescence microscopic images for quantitative analysis of cell biological properties. In this paper, we present a fully automated cell segmentation method that can detect cells from 3D fluorescence microscopic images. Enlightened by fluorescence imaging techniques, we regulated the image gradient field by gradient vector flow (GVF) with interpolated and smoothed data volume, and grouped voxels based on gradient modes identified by tracking GVF field. Adaptive thresholding was then applied to voxels associated with the same gradient mode where voxel intensities were enhanced by a multiscale cell filter. We applied the method to a large volume of 3D fluorescence imaging data of human brain tumor cells with (1) small cell false detection and missing rates for individual cells; and (2) trivial over and under segmentation incidences for clustered cells. Additionally, the concordance of cell morphometry structure between automated and manual segmentation was encouraging. These results suggest a promising 3D cell segmentation method applicable to cancer studies.

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2017-04-01

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

Resistivity Image from 2D Inversion of Magnetotelluric Data in the Northern Cascadia Subduction Zone (United States)

NASA Astrophysics Data System (ADS)

Gultom, F. B.; Niasari, S. W.; Hartantyo, E.

2018-04-01

Cascadia Subduction Zone (CSZ) lies between Pacific margin and North America plate. The purpose of this research is to identify the CSZ along Oregon, Idaho, Wyoming from conductivity (σ) contrast in the subsurface by using the magnetotelluric (MT) method. MT is an electromagnetic method that use frequency between 10-4 Hz and 104 Hz. We obtained the MT data from the EarthScope USArray in the form of EDI-File (five components of the electromagnetic field). We analyzed the MT data using phase tensor and modeled the data using 2D inversion. From the phase tensor analysis, the 3D data dominated the eastern regions. Global data misfit is 6,88, where WYI18 (close to Yellowstone) contributes misfit of 29,3. This means that the model response does not fit the data, which implies the data is not fully 2D. The 2D inversion results are found high resistivity anomalies (more than 500 ohm.m) at shallow depth beneath Oregon and Wyoming, which coresspond to high density anomalies. This high resistivity anomalies might correspond to the north American plate. Thus, it can be concluded that 2D inversion model can be used for most 3D MT data to illustrate the resistivity distribution in the Cascadia Subduction Zone.

H?, D? and HD adsorption upon the metal-organic framework [Cu?Zn?(btc)?]? studied by pulsed ENDOR and HYSCORE spectroscopy

NASA Astrophysics Data System (ADS)

Jee, Bettina; Hartmann, Martin; Pöppl, Andreas

2013-10-01

The adsorption of hydrogen has become interesting in terms of gas separation as well as safe and reversible storage of hydrogen as an energy carrier. In this regard, metal-organic framework compounds are potential candidates. The metal-organic framework [Cu?Zn?(btc)?]? as a partially Zn-substituted analogue of the well known compound HKUST-1 is well suited for studying adsorption geometries at cupric ions by electron paramagnetic resonance (EPR) methods due to the formation of few mixed Cu/Zn paddle wheel units with isolated S = 1/2 electron spins. The adsorption of hydrogen (H2) as well as the deuterium (D2) and HD molecules were investigated by continuous wave EPR and pulsed ENDOR and HYSCORE spectroscopy. The principal values of the proton and deuterium hyperfine coupling tensors ? and ? were determined by spectral simulations as well as of the deuterium nuclear quadrupole tensor ? for adsorbed HD and D2. The results show a side-on coordination of HD and D2 with identical Cu-H and Cu-D distances rCuX = 2.8 Å with the tensors ? and ? aligned parallel to the C4 symmetry axis of the paddle wheel unit. A thermodynamic non-equilibrium state with J = 1, mJ = ±1 is indicated by the experimental data with ? and ? averaged by rotation around C4.

Determining transport coefficients for a microscopic simulation of a hadron gas

NASA Astrophysics Data System (ADS)

Pratt, Scott; Baez, Alexander; Kim, Jane

2017-02-01

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

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

PubMed

Raju, Suvrat

2011-03-04

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

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.

Sparse alignment for robust tensor learning.

PubMed

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

2014-10-01

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

First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints

DOE PAGES

Lin, Huey-Wen; Melnitchouk, Wally; Prokudin, Alexei; ...

2018-04-11

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new Monte Carlo method based on nested sampling and constraints on the isovector tensor chargemore » $$g_T$$ from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with $$g_T$$ values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller $$g_T$$ values. The contributions to the nucleon tensor charge from $u$ and $d$ quarks are found to be $$\\delta u = 0.3(2)$$ and $$\\delta d = -0.7(2)$$ at a scale $Q^2 = 2$ GeV$^2$.« less

First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints

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

Lin, Huey-Wen; Melnitchouk, Wally; Prokudin, Alexei

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new Monte Carlo method based on nested sampling and constraints on the isovector tensor chargemore » $$g_T$$ from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with $$g_T$$ values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller $$g_T$$ values. The contributions to the nucleon tensor charge from $u$ and $d$ quarks are found to be $$\\delta u = 0.3(2)$$ and $$\\delta d = -0.7(2)$$ at a scale $Q^2 = 2$ GeV$^2$.« less

First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints.

PubMed

Lin, H-W; Melnitchouk, W; Prokudin, A; Sato, N; Shows, H

2018-04-13

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new Monte Carlo method based on nested sampling and constraints on the isovector tensor charge g_{T} from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with g_{T} values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller g_{T} values. The contributions to the nucleon tensor charge from u and d quarks are found to be δu=0.3(2) and δd=-0.7(2) at a scale Q^{2}=2  GeV^{2}.

First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints

NASA Astrophysics Data System (ADS)

Lin, H.-W.; Melnitchouk, W.; Prokudin, A.; Sato, N.; Shows, H.; Jefferson Lab Angular Momentum JAM Collaboration

2018-04-01

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new Monte Carlo method based on nested sampling and constraints on the isovector tensor charge gT from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with gT values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller gT values. The contributions to the nucleon tensor charge from u and d quarks are found to be δ u =0.3 (2 ) and δ d =-0.7 (2 ) at a scale Q2=2 GeV2.

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

Theoretical study of diaquamalonatozinc(II) single crystal for applications in non-linear optical devices

NASA Astrophysics Data System (ADS)

Chakraborty, Mitesh; Rai, Vineet Kumar

2017-12-01

The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM) with the microscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. g-tensor and D-tensor, has been determined by using the ORCA program package developed by F Neese et al. The unrestricted Kohn-Sham orbitals-based Pederson-Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin-orbit tensor (D^{SO}) of the axial ZFS parameter D. The effects of spin-spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin-spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson-Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn-Sham-based natural orbital with Pederson-Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of Mn^{2+} ion in the host matrix.

Monoplane 3D-2D registration of cerebral angiograms based on multi-objective stratified optimization

NASA Astrophysics Data System (ADS)

Aksoy, T.; Špiclin, Ž.; Pernuš, F.; Unal, G.

2017-12-01

Registration of 3D pre-interventional to 2D intra-interventional medical images has an increasingly important role in surgical planning, navigation and treatment, because it enables the physician to co-locate depth information given by pre-interventional 3D images with the live information in intra-interventional 2D images such as x-ray. Most tasks during image-guided interventions are carried out under a monoplane x-ray, which is a highly ill-posed problem for state-of-the-art 3D to 2D registration methods. To address the problem of rigid 3D-2D monoplane registration we propose a novel multi-objective stratified parameter optimization, wherein a small set of high-magnitude intensity gradients are matched between the 3D and 2D images. The stratified parameter optimization matches rotation templates to depth templates, first sampled from projected 3D gradients and second from the 2D image gradients, so as to recover 3D rigid-body rotations and out-of-plane translation. The objective for matching was the gradient magnitude correlation coefficient, which is invariant to in-plane translation. The in-plane translations are then found by locating the maximum of the gradient phase correlation between the best matching pair of rotation and depth templates. On twenty pairs of 3D and 2D images of ten patients undergoing cerebral endovascular image-guided intervention the 3D to monoplane 2D registration experiments were setup with a rather high range of initial mean target registration error from 0 to 100 mm. The proposed method effectively reduced the registration error to below 2 mm, which was further refined by a fast iterative method and resulted in a high final registration accuracy (0.40 mm) and high success rate (> 96%). Taking into account a fast execution time below 10 s, the observed performance of the proposed method shows a high potential for application into clinical image-guidance systems.

Tensor voting for image correction by global and local intensity alignment.

PubMed

Jia, Jiaya; Tang, Chi-Keung

2005-01-01

This paper presents a voting method to perform image correction by global and local intensity alignment. The key to our modeless approach is the estimation of global and local replacement functions by reducing the complex estimation problem to the robust 2D tensor voting in the corresponding voting spaces. No complicated model for replacement function (curve) is assumed. Subject to the monotonic constraint only, we vote for an optimal replacement function by propagating the curve smoothness constraint using a dense tensor field. Our method effectively infers missing curve segments and rejects image outliers. Applications using our tensor voting approach are proposed and described. The first application consists of image mosaicking of static scenes, where the voted replacement functions are used in our iterative registration algorithm for computing the best warping matrix. In the presence of occlusion, our replacement function can be employed to construct a visually acceptable mosaic by detecting occlusion which has large and piecewise constant color. Furthermore, by the simultaneous consideration of color matches and spatial constraints in the voting space, we perform image intensity compensation and high contrast image correction using our voting framework, when only two defective input images are given.

A Guided Tour of Mathematical Methods

NASA Astrophysics Data System (ADS)

Snieder, Roel

2009-04-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical co-ordinates; 5. The gradient; 6. The divergence of a vector field; 7. The curl of a vector field; 8. The theorem of Gauss; 9. The theorem of Stokes; 10. The Laplacian; 11. Conservation laws; 12. Scale analysis; 13. Linear algebra; 14. The Dirac delta function; 15. Fourier analysis; 16. Analytic functions; 17. Complex integration; 18. Green's functions: principles; 19. Green's functions: examples; 20. Normal modes; 21. Potential theory; 22. Cartesian tensors; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Variational calculus; 26. Epilogue, on power and knowledge; References.

Documentation for the “XT3D” option in the Node Property Flow (NPF) Package of MODFLOW 6

USGS Publications Warehouse

Provost, Alden M.; Langevin, Christian D.; Hughes, Joseph D.

2017-08-10

This report describes the “XT3D” option in the Node Property Flow (NPF) Package of MODFLOW 6. The XT3D option extends the capabilities of MODFLOW by enabling simulation of fully three-dimensional anisotropy on regular or irregular grids in a way that properly takes into account the full, three-dimensional conductivity tensor. It can also improve the accuracy of groundwater-flow simulations in cases in which the model grid violates certain geometric requirements. Three example problems demonstrate the use of the XT3D option to simulate groundwater flow on irregular grids and through three-dimensional porous media with anisotropic hydraulic conductivity.Conceptually, the XT3D method of estimating flow between two MODFLOW 6 model cells can be viewed in terms of three main mathematical steps: construction of head-gradient estimates by interpolation; construction of fluid-flux estimates by application of the full, three-dimensional form of Darcy’s Law, in which the conductivity tensor can be heterogeneous and anisotropic; and construction of the flow expression by enforcement of continuity of flow across the cell interface. The resulting XT3D flow expression, which relates the flow across the cell interface to the values of heads computed at neighboring nodes, is the sum of terms in which conductance-like coefficients multiply head differences, as in the conductance-based flow expression the NPF Package uses by default. However, the XT3D flow expression contains terms that involve “neighbors of neighbors” of the two cells for which the flow is being calculated. These additional terms have no analog in the conductance-based formulation. When assembled into matrix form, the XT3D formulation results in a larger stencil than the conductance-based formulation; that is, each row of the coefficient matrix generally contains more nonzero elements. The “RHS” suboption can be used to avoid expanding the stencil by placing the additional terms on the right-hand side of the matrix equation and evaluating them at the previous iteration or time step.The XT3D option can be an alternative to the Ghost-Node Correction (GNC) Package. However, the XT3D formulation is typically more computationally intensive than the conductance-based formulation the NPF Package uses by default, either with or without ghost nodes. Before deciding whether to use the GNC Package or XT3D option for production runs, the user should consider whether the conductance-based formulation alone can provide acceptable accuracy for the particular problem being solved.

First-principles calculations of finite temperature Sc and O NMR parameters in Pb(Sc2/3W1/3)O3

NASA Astrophysics Data System (ADS)

Krakauer, Henry; Walter, Eric J.; Ellden, Jeremy; Hoatson, Gina L.; Vold, Robert L.

2012-02-01

Understanding the dynamics of complex relaxor ferroelectrics is important to characterizing their large electromechanical coupling. Preliminary NMR measurements of Sc electric-field-gradients (EFG) in Pb(Sc2/3W1/3)O3 (PSW) show a strong temperature dependence in the range T = 250 - 330 K. To understand this behavior, we use the first-principles GIPAWootnotetextC. J. Pickard and F. Mauri, Phys. Rev. B 63, 245101 (2001); method within the Quantum Espresso (QE) packageootnotetextP. Giannozzi et al., Journal of Physics: Condensed Matter 21, 395502 (2009) to calculate ^45Sc and ^17O chemical-shifts and EFG tensors. To study finite temperature effects, we incorporate the thermal expansion of the lattice and sample thermal disorder, using the phonon degrees of freedom. As in our previous studies of perovksites,ootnotetextD. L. Pechkis, E. J. Walter, and H. Krakauer. J. Chem. Phys. 135, 114507 (2011); ibid. 131, 184511 (2009) we show that the ^17O chemical shifts in PSW also exhibit a linear correlation with the nearest-neighbor B-O bond length.

Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order

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

Gu Zhengcheng; Wen Xiaogang

2009-10-15

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors T{sub inv} plus the symmetry group G{sub sym} of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, asmore » illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (G{sub sym},T{sub inv}) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (G{sub sym},T{sub inv}) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.« less

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

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

Quantum quenches in two spatial dimensions using chain array matrix product states

DOE PAGES

A. J. A. James; Konik, R.

2015-10-15

We describe a method for simulating the real time evolution of extended quantum systems in two dimensions (2D). The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular, it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum [(2+1)-dimensional] Ising model. As a result, in quenches that cross a phase boundary we find that the return probability shows nonanalyticities in time.

Progress towards a space-borne quantum gravity gradiometer

NASA Technical Reports Server (NTRS)

Yu, Nan; Kohel, James M.; Ramerez-Serrano, Jaime; Kellogg, James R.; Lim, Lawrence; Maleki, Lute

2004-01-01

Quantum interferometer gravity gradiometer for 3D mapping is a project for developing the technology of atom interferometer-based gravity sensor in space. The atom interferometer utilizes atomic particles as free fall test masses to measure inertial forces with unprecedented sensitivity and precision. It also allows measurements of the gravity gradient tensor components for 3D mapping of subsurface mass distribution. The overall approach is based on recent advances of laser cooling and manipulation of atoms in atomic and optical physics. Atom interferometers have been demonstrated in research laboratories for gravity and gravity gradient measurements. In this approach, atoms are first laser cooled to micro-kelvin temperatures. Then they are allowed to freefall in vacuum as true drag-free test masses. During the free fall, a sequence of laser pulses is used to split and recombine the atom waves to realize the interferometric measurements. We have demonstrated atom interferometer operation in the Phase I period, and we are implementing the second generation for a complete gradiometer demonstration unit in the laboratory. Along with this development, we are developing technologies at component levels that will be more suited for realization of a space instrument. We will present an update of these developments and discuss the future directions of the quantum gravity gradiometer project.

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

NASA Astrophysics Data System (ADS)

Kugo, T.; Ohashi, K.

2002-12-01

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

Simulations of molecular diffusion in lattices of cells: insights for NMR of red blood cells.

PubMed Central

Regan, David G; Kuchel, Philip W

2002-01-01

The pulsed field-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) experiment, conducted on a suspension of red blood cells (RBC) in a strong magnetic field yields a q-space plot consisting of a series of maxima and minima. This is mathematically analogous to a classical optical diffraction pattern. The method provides a noninvasive and novel means of characterizing cell suspensions that is sensitive to changes in cell shape and packing density. The positions of the features in a q-space plot characterize the rate of exchange across the membrane, cell dimensions, and packing density. A diffusion tensor, containing information regarding the diffusion anisotropy of the system, can also be derived from the PGSE NMR data. In this study, we carried out Monte Carlo simulations of diffusion in suspensions of "virtual" cells that had either biconcave disc (as in RBC) or oblate spheroid geometry. The simulations were performed in a PGSE NMR context thus enabling predictions of q-space and diffusion tensor data. The simulated data were compared with those from real PGSE NMR diffusion experiments on RBC suspensions that had a range of hematocrit values. Methods that facilitate the processing of q-space data were also developed. PMID:12080109

Simulations of molecular diffusion in lattices of cells: insights for NMR of red blood cells.

PubMed

Regan, David G; Kuchel, Philip W

2002-07-01

The pulsed field-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) experiment, conducted on a suspension of red blood cells (RBC) in a strong magnetic field yields a q-space plot consisting of a series of maxima and minima. This is mathematically analogous to a classical optical diffraction pattern. The method provides a noninvasive and novel means of characterizing cell suspensions that is sensitive to changes in cell shape and packing density. The positions of the features in a q-space plot characterize the rate of exchange across the membrane, cell dimensions, and packing density. A diffusion tensor, containing information regarding the diffusion anisotropy of the system, can also be derived from the PGSE NMR data. In this study, we carried out Monte Carlo simulations of diffusion in suspensions of "virtual" cells that had either biconcave disc (as in RBC) or oblate spheroid geometry. The simulations were performed in a PGSE NMR context thus enabling predictions of q-space and diffusion tensor data. The simulated data were compared with those from real PGSE NMR diffusion experiments on RBC suspensions that had a range of hematocrit values. Methods that facilitate the processing of q-space data were also developed.

MULTISCALE TENSOR ANISOTROPIC FILTERING OF FLUORESCENCE MICROSCOPY FOR DENOISING MICROVASCULATURE.

PubMed

Prasath, V B S; Pelapur, R; Glinskii, O V; Glinsky, V V; Huxley, V H; Palaniappan, K

2015-04-01

Fluorescence microscopy images are contaminated by noise and improving image quality without blurring vascular structures by filtering is an important step in automatic image analysis. The application of interest here is to automatically extract the structural components of the microvascular system with accuracy from images acquired by fluorescence microscopy. A robust denoising process is necessary in order to extract accurate vascular morphology information. For this purpose, we propose a multiscale tensor with anisotropic diffusion model which progressively and adaptively updates the amount of smoothing while preserving vessel boundaries accurately. Based on a coherency enhancing flow with planar confidence measure and fused 3D structure information, our method integrates multiple scales for microvasculature preservation and noise removal membrane structures. Experimental results on simulated synthetic images and epifluorescence images show the advantage of our improvement over other related diffusion filters. We further show that the proposed multiscale integration approach improves denoising accuracy of different tensor diffusion methods to obtain better microvasculature segmentation.

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

NASA Astrophysics Data System (ADS)

Chen, Y.; Huang, L.

2017-12-01

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

Automatic deformable diffusion tensor registration for fiber population analysis.

PubMed

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

2008-01-01

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

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.

Theory of liquid crystal elastomers and polymer networks : Connection between neoclassical theory and differential geometry.

PubMed

Nguyen, Thanh-Son; Selinger, Jonathan V

2017-09-01

In liquid crystal elastomers and polymer networks, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymers. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation gradient tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geometry respond to a change of temperature.

Moment tensor inversion with three-dimensional sensor configuration of mining induced seismicity (Kiruna mine, Sweden)

NASA Astrophysics Data System (ADS)

Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian

2018-06-01

Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). A stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double-couple and full moment tensor with high frequency data, is very challenging. Moreover, the application to underground mining system requires accounting for the 3-D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3-D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in the presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to eight events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double-couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip and rake configurations of the double-couple term were obtained. The orientations of the nodal planes of the double-couple component in most cases vary from NNW to NNE with a dip along the ore body or in the opposite direction.

Rotation covariant image processing for biomedical applications.

PubMed

Skibbe, Henrik; Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences.

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

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

NASA Astrophysics Data System (ADS)

Hori, Takayuki; Ohya, Jun; Kurumisawa, Jun

2009-02-01

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

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.

Using the ratio of the magnetic field to the analytic signal of the magnetic gradient tensor in determining the position of simple shaped magnetic anomalies

NASA Astrophysics Data System (ADS)

Karimi, Kurosh; Shirzaditabar, Farzad

2017-08-01

The analytic signal of magnitude of the magnetic field’s components and its first derivatives have been employed for locating magnetic structures, which can be considered as point-dipoles or line of dipoles. Although similar methods have been used for locating such magnetic anomalies, they cannot estimate the positions of anomalies in noisy states with an acceptable accuracy. The methods are also inexact in determining the depth of deep anomalies. In noisy cases and in places other than poles, the maximum points of the magnitude of the magnetic vector components and Az are not located exactly above 3D bodies. Consequently, the horizontal location estimates of bodies are accompanied by errors. Here, the previous methods are altered and generalized to locate deeper models in the presence of noise even at lower magnetic latitudes. In addition, a statistical technique is presented for working in noisy areas and a new method, which is resistant to noise by using a ‘depths mean’ method, is made. Reduction to the pole transformation is also used to find the most possible actual horizontal body location. Deep models are also well estimated. The method is tested on real magnetic data over an urban gas pipeline in the vicinity of Kermanshah province, Iran. The estimated location of the pipeline is accurate in accordance with the result of the half-width method.

Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition

NASA Astrophysics Data System (ADS)

Li, Jin; Liu, Zilong

2017-12-01

Nonnegative tensor Tucker decomposition (NTD) in a transform domain (e.g., 2D-DWT, etc) has been used in the compression of hyper-spectral images because it can remove redundancies between spectrum bands and also exploit spatial correlations of each band. However, the use of a NTD has a very high computational cost. In this paper, we propose a low complexity NTD-based compression method of hyper-spectral images. This method is based on a pair-wise multilevel grouping approach for the NTD to overcome its high computational cost. The proposed method has a low complexity under a slight decrease of the coding performance compared to conventional NTD. We experimentally confirm this method, which indicates that this method has the less processing time and keeps a better coding performance than the case that the NTD is not used. The proposed approach has a potential application in the loss compression of hyper-spectral or multi-spectral images

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

BLIPPED (BLIpped Pure Phase EncoDing) high resolution MRI with low amplitude gradients

NASA Astrophysics Data System (ADS)

Xiao, Dan; Balcom, Bruce J.

2017-12-01

MRI image resolution is proportional to the maximum k-space value, i.e. the temporal integral of the magnetic field gradient. High resolution imaging usually requires high gradient amplitudes and/or long spatial encoding times. Special gradient hardware is often required for high amplitudes and fast switching. We propose a high resolution imaging sequence that employs low amplitude gradients. This method was inspired by the previously proposed PEPI (π Echo Planar Imaging) sequence, which replaced EPI gradient reversals with multiple RF refocusing pulses. It has been shown that when the refocusing RF pulse is of high quality, i.e. sufficiently close to 180°, the magnetization phase introduced by the spatial encoding magnetic field gradient can be preserved and transferred to the following echo signal without phase rewinding. This phase encoding scheme requires blipped gradients that are identical for each echo, with low and constant amplitude, providing opportunities for high resolution imaging. We now extend the sequence to 3D pure phase encoding with low amplitude gradients. The method is compared with the Hybrid-SESPI (Spin Echo Single Point Imaging) technique to demonstrate the advantages in terms of low gradient duty cycle, compensation of concomitant magnetic field effects and minimal echo spacing, which lead to superior image quality and high resolution. The 3D imaging method was then applied with a parallel plate resonator RF probe, achieving a nominal spatial resolution of 17 μm in one dimension in the 3D image, requiring a maximum gradient amplitude of only 5.8 Gauss/cm.

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

NASA Astrophysics Data System (ADS)

Garfinkle, David; Glass, E. N.

2013-03-01

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

Monte Carlo Volcano Seismic Moment Tensors

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Studying microstructure and microstructural changes in plant tissues by advanced diffusion magnetic resonance imaging techniques

PubMed Central

Morozov, Darya; Tal, Iris; Pisanty, Odelia; Shani, Eilon

2017-01-01

Abstract As sessile organisms, plants must respond to the environment by adjusting their growth and development. Most of the plant body is formed post-embryonically by continuous activity of apical and lateral meristems. The development of lateral adventitious roots is a complex process, and therefore the development of methods that can visualize, non-invasively, the plant microstructure and organ initiation that occur during growth and development is of paramount importance. In this study, relaxation-based and advanced diffusion magnetic resonance imaging (MRI) methods including diffusion tensor (DTI), q-space diffusion imaging (QSI), and double-pulsed-field-gradient (d-PFG) MRI, at 14.1 T, were used to characterize the hypocotyl microstructure and the microstructural changes that occurred during the development of lateral adventitious roots in tomato. Better contrast was observed in relaxation-based MRI using higher in-plane resolution but this also resulted in a significant reduction in the signal-to-noise ratio of the T2-weighted MR images. Diffusion MRI revealed that water diffusion is highly anisotropic in the vascular cylinder. QSI and d-PGSE MRI showed that in the vascular cylinder some of the cells have sizes in the range of 6–10 μm. The MR images captured cell reorganization during adventitious root formation in the periphery of the primary vascular bundles, adjacent to the xylem pole that broke through the cortex and epidermis layers. This study demonstrates that MRI and diffusion MRI methods allow the non-invasive study of microstructural features of plants, and enable microstructural changes associated with adventitious root formation to be followed. PMID:28398563

Symmetric Topological Phases and Tensor Network States

NASA Astrophysics Data System (ADS)

Jiang, Shenghan

Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.

Using Perturbation Theory to Reduce Noise in Diffusion Tensor Fields

PubMed Central

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

2009-01-01

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

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

Application of multigrid methods to the solution of liquid crystal equations on a SIMD computer

NASA Technical Reports Server (NTRS)

Farrell, Paul A.; Ruttan, Arden; Zeller, Reinhardt R.

1993-01-01

We will describe a finite difference code for computing the equilibrium configurations of the order-parameter tensor field for nematic liquid crystals in rectangular regions by minimization of the Landau-de Gennes Free Energy functional. The implementation of the free energy functional described here includes magnetic fields, quadratic gradient terms, and scalar bulk terms through the fourth order. Boundary conditions include the effects of strong surface anchoring. The target architectures for our implementation are SIMD machines, with interconnection networks which can be configured as 2 or 3 dimensional grids, such as the Wavetracer DTC. We also discuss the relative efficiency of a number of iterative methods for the solution of the linear systems arising from this discretization on such architectures.

Generalized Higher Order Orthogonal Iteration for Tensor Learning and Decomposition.

PubMed

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

2016-12-01

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

A complex fermionic tensor model in d dimensions

NASA Astrophysics Data System (ADS)

Prakash, Shiroman; Sinha, Ritam

2018-02-01

In this note, we study a melonic tensor model in d dimensions based on three-index Dirac fermions with a four-fermion interaction. Summing the melonic diagrams at strong coupling allows one to define a formal large- N saddle point in arbitrary d and calculate the spectrum of scalar bilinear singlet operators. For d = 2 - ɛ the theory is an infrared fixed point, which we find has a purely real spectrum that we determine numerically for arbitrary d < 2, and analytically as a power series in ɛ. The theory appears to be weakly interacting when ɛ is small, suggesting that fermionic tensor models in 1-dimension can be studied in an ɛ expansion. For d > 2, the spectrum can still be calculated using the saddle point equations, which may define a formal large- N ultraviolet fixed point analogous to the Gross-Neveu model in d > 2. For 2 < d < 6, we find that the spectrum contains at least one complex scalar eigenvalue (similar to the complex eigenvalue present in the bosonic tensor model recently studied by Giombi, Klebanov and Tarnopolsky) which indicates that the theory is unstable. We also find that the fixed point is weakly-interacting when d = 6 (or more generally d = 4 n + 2) and has a real spectrum for 6 < d < 6 .14 which we present as a power series in ɛ in 6 + ɛ dimensions.

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.

Tensor-based Dictionary Learning for Spectral CT Reconstruction

PubMed Central

Zhang, Yanbo; Wang, Ge

2016-01-01

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

Simulations of Ground Motion in Southern California based upon the Spectral-Element Method

NASA Astrophysics Data System (ADS)

Tromp, J.; Komatitsch, D.; Liu, Q.

2003-12-01

We use the spectral-element method to simulate ground motion generated by recent well-recorded small earthquakes in Southern California. Simulations are performed using a new sedimentary basin model that is constrained by hundreds of petroleum industry well logs and more than twenty thousand kilometers of seismic reflection profiles. The numerical simulations account for 3D variations of seismic wave speeds and density, topography and bathymetry, and attenuation. Simulations for several small recent events demonstrate that the combination of a detailed sedimentary basin model and an accurate numerical technique facilitates the simulation of ground motion at periods of 2 seconds and longer inside the Los Angeles basin and 6 seconds and longer elsewhere. Peak ground displacement, velocity and acceleration maps illustrate that significant amplification occurs in the basin. Centroid-Moment Tensor mechanisms are obtained based upon Pnl and surface waveforms and numerically calculated 3D Frechet derivatives. We use a combination of waveform and waveform-envelope misfit criteria, and facilitate pure double-couple or zero-trace moment-tensor inversions.

2D-3D registration using gradient-based MI for image guided surgery systems

NASA Astrophysics Data System (ADS)

Yim, Yeny; Chen, Xuanyi; Wakid, Mike; Bielamowicz, Steve; Hahn, James

2011-03-01

Registration of preoperative CT data to intra-operative video images is necessary not only to compare the outcome of the vocal fold after surgery with the preplanned shape but also to provide the image guidance for fusion of all imaging modalities. We propose a 2D-3D registration method using gradient-based mutual information. The 3D CT scan is aligned to 2D endoscopic images by finding the corresponding viewpoint between the real camera for endoscopic images and the virtual camera for CT scans. Even though mutual information has been successfully used to register different imaging modalities, it is difficult to robustly register the CT rendered image to the endoscopic image due to varying light patterns and shape of the vocal fold. The proposed method calculates the mutual information in the gradient images as well as original images, assigning more weight to the high gradient regions. The proposed method can emphasize the effect of vocal fold and allow a robust matching regardless of the surface illumination. To find the viewpoint with maximum mutual information, a downhill simplex method is applied in a conditional multi-resolution scheme which leads to a less-sensitive result to local maxima. To validate the registration accuracy, we evaluated the sensitivity to initial viewpoint of preoperative CT. Experimental results showed that gradient-based mutual information provided robust matching not only for two identical images with different viewpoints but also for different images acquired before and after surgery. The results also showed that conditional multi-resolution scheme led to a more accurate registration than single-resolution.

Algorithms for tensor network renormalization

NASA Astrophysics Data System (ADS)

Evenbly, G.

2017-01-01

We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. First, we recall established techniques for how the partition function of a 2 D classical many-body system or the Euclidean path integral of a 1 D quantum system can be represented as a network of tensors, before describing how TNR can be implemented to efficiently contract the network via a sequence of coarse-graining transformations. The efficacy of the TNR approach is then benchmarked for the 2 D classical statistical and 1 D quantum Ising models; in particular the ability of TNR to maintain a high level of accuracy over sustained coarse-graining transformations, even at a critical point, is demonstrated.

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.

A Guided Tour of Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Snieder, Roel; van Wijk, Kasper

2015-05-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical coordinates; 5. Gradient; 6. Divergence of a vector field; 7. Curl of a vector field; 8. Theorem of Gauss; 9. Theorem of Stokes; 10. The Laplacian; 11. Scale analysis; 12. Linear algebra; 13. Dirac delta function; 14. Fourier analysis; 15. Analytic functions; 16. Complex integration; 17. Green's functions: principles; 18. Green's functions: examples; 19. Normal modes; 20. Potential-field theory; 21. Probability and statistics; 22. Inverse problems; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Conservation laws; 26. Cartesian tensors; 27. Variational calculus; 28. Epilogue on power and knowledge.

Efficient gradient calibration based on diffusion MRI.

PubMed

Teh, Irvin; Maguire, Mahon L; Schneider, Jürgen E

2017-01-01

To propose a method for calibrating gradient systems and correcting gradient nonlinearities based on diffusion MRI measurements. The gradient scaling in x, y, and z were first offset by up to 5% from precalibrated values to simulate a poorly calibrated system. Diffusion MRI data were acquired in a phantom filled with cyclooctane, and corrections for gradient scaling errors and nonlinearity were determined. The calibration was assessed with diffusion tensor imaging and independently validated with high resolution anatomical MRI of a second structured phantom. The errors in apparent diffusion coefficients along orthogonal axes ranged from -9.2% ± 0.4% to + 8.8% ± 0.7% before calibration and -0.5% ± 0.4% to + 0.8% ± 0.3% after calibration. Concurrently, fractional anisotropy decreased from 0.14 ± 0.03 to 0.03 ± 0.01. Errors in geometric measurements in x, y and z ranged from -5.5% to + 4.5% precalibration and were likewise reduced to -0.97% to + 0.23% postcalibration. Image distortions from gradient nonlinearity were markedly reduced. Periodic gradient calibration is an integral part of quality assurance in MRI. The proposed approach is both accurate and efficient, can be setup with readily available materials, and improves accuracy in both anatomical and diffusion MRI to within ±1%. Magn Reson Med 77:170-179, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. © 2016 Wiley Periodicals, Inc.

Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.

NASA Astrophysics Data System (ADS)

Lubicz, Vittorio; Riggio, Lorenzo; Salerno, Giorgio; Simula, Silvano; Tarantino, Cecilia

2018-03-01

We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.

A real-time moment-tensor inversion system (GRiD-MT-3D) using 3-D Green's functions

NASA Astrophysics Data System (ADS)

Nagao, A.; Furumura, T.; Tsuruoka, H.

2016-12-01

We developed a real-time moment-tensor inversion system using 3-D Green's functions (GRiD-MT-3D) by improving the current system (GRiD-MT; Tsuruoka et al., 2009), which uses 1-D Green's functions for longer periods than 20 s. Our moment-tensor inversion is applied to the real-time monitoring of earthquakes occurring beneath Kanto basin area. The basin, which is constituted of thick sediment layers, lies on the complex subduction of the Philippine-Sea Plate and the Pacific Plate that can significantly affect the seismic wave propagation. We compute 3-D Green's functions using finite-difference-method (FDM) simulations considering a 3-D velocity model, which is based on the Japan Integrated Velocity Structure Model (Koketsu et al., 2012), that includes crust, mantle, and subducting plates. The 3-D FDM simulations are computed over a volume of 468 km by 432 km by 120 km in the EW, NS, and depth directions, respectively, that is discretized into 0.25 km grids. Considering that the minimum S wave velocity of the sedimentary layer is 0.5 km/s, simulations can compute seismograms up to 0.5 Hz. We calculate Green's functions between 24,700 sources, which are distributed every 0.1° in the horizontal direction and every 9 km in depth direction, and 13 F-net stations. To compute this large number of Green's functions, we used the EIC parallel computer of ERI. The reciprocity theory, which switches the source and station positions, is used to reduce total computation costs. It took 156 hours to compute all the Green's functions. Results show that at long-periods (T>15 s), only small differences are observed between the 3-D and 1-D Green's functions as indicated by high correlation coefficients of 0.9 between the waveforms. However, at shorter periods (T<10 s), the differences become larger and the correlation coefficients drop to 0.5. The effect of the 3-D heterogeneous structure especially affects the Green's functions for the ray paths that across complex geological structures, such as the sedimentary basin or the subducting plates. After incorporation of the 3-D Green's functions in the GRiD-MT-3D system, we compare the results to the former GRiD-MT system to demonstrate the effectiveness of the new system in terms of variance reduction and accuracy of the moment-tensor estimation for much smaller events than the current one.

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.

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.

Potentials for transverse trace-free tensors

NASA Astrophysics Data System (ADS)

Conboye, Rory; Murchadha, Niall Ó.

2014-04-01

In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space.

Electronic structures and magnetic/optical properties of metal phthalocyanine complexes

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

Baba, Shintaro; Suzuki, Atsushi, E-mail: suzuki@mat.usp.ac.jp; Oku, Takeo

2016-02-01

Electronic structures and magnetic / optical properties of metal phthalocyanine complexes were studied by quantum calculations using density functional theory. Effects of central metal and expansion of π orbital on aromatic ring as conjugation system on the electronic structures, magnetic, optical properties and vibration modes of infrared and Raman spectra of metal phthalocyanines were investigated. Electron and charge density distribution and energy levels near frontier orbital and excited states were influenced by the deformed structures varied with central metal and charge. The magnetic parameters of chemical shifts in {sup 13}C-nuclear magnetic resonance ({sup 13}C-NMR), principle g-tensor, A-tensor, V-tensor of electricmore » field gradient and asymmetry parameters derived from the deformed structures with magnetic interaction of nuclear quadruple interaction based on electron and charge density distribution with a bias of charge near ligand under crystal field.« less

Temporary Hearing Threshold Shift in Healthy Volunteers with Hearing Protection Caused by Acoustic Noise Exposure during 3-T Multisequence MR Neuroimaging.

PubMed

Jin, Chao; Li, Huan; Li, Xianjun; Wang, Miaomiao; Liu, Congcong; Guo, Jianxin; Yang, Jian

2018-02-01

Purpose To determine whether a single 51-minute exposure to acoustic noise during 3-T multisequence magnetic resonance (MR) neuroimaging could affect the hearing threshold of healthy adults with earplugs and sponge mats as hearing protection. Materials and Methods With earplugs and motion-refraining sponge mats as hearing protection, 26 healthy young adults underwent 3-T MR neuroimaging imaging that included T1-weighted three-dimensional gradient-echo sequence, T2-weighted fast spin-echo sequence, diffusion-tensor imaging, diffusion-kurtosis imaging, T2*-weighted three-dimensional multiecho gradient-echo sequence, and blood oxygen level-dependent imaging. Automated auditory brainstem response (ABR) was used to measure the hearing thresholds within 24 hours before, within 20 minutes after, and 25 days after the MR examination. One-way repeated-measure analysis of variance with Bonferroni adjustment was used to compare automated ABR results among the three tests and partial η 2 (η p 2 ) was reported as a measure of effect size. Results Automated ABR results showed significantly increased mean threshold shift of 5.0 dB ± 8.1 (standard deviation) (left ear: 4.8 dB ± 9.2 [95% confidence interval: 1.09, 8.53], η p 2 = 0.221, P = .013; right ear: 5.2 dB ± 6.9 [95% confidence interval: 2.36, 8.02], η p 2 = 0.364, P = .001) immediately after the MR examination compared with the baseline study. This shift is below the temporary threshold shift of 40-50 dB that is associated with cochlea nerve changes. Automated ABR obtained at day 25 after MR imaging showed no significant differences from baseline (left ear: -2.3 dB ± 8.6 [95% confidence interval: -5.79, 1.78], η p 2 = 0.069, P = .185; right ear: 0.4 dB ± 7.3 [95% confidence interval: -3.35, 2.58], η p 2 = 0.003, P = .791). Conclusion A 3-T MR neuroimaging examination with the acoustic noise at equivalent sound pressure level of 103.5-111.3 dBA lasting 51 minutes can cause temporary hearing threshold shift in healthy volunteers with hearing protection. © RSNA, 2017.

From 6D superconformal field theories to dynamic gauged linear sigma models

NASA Astrophysics Data System (ADS)

Apruzzi, Fabio; Hassler, Falk; Heckman, Jonathan J.; Melnikov, Ilarion V.

2017-09-01

Compactifications of six-dimensional (6D) superconformal field theories (SCFTs) on four- manifolds generate a large class of novel two-dimensional (2D) quantum field theories. We consider in detail the case of the rank-one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kähler surfaces, we present evidence that this provides a method to realize 2D SCFTs with N =(0 ,2 ) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2D fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a "dynamic GLSM" (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the antichiral two-form of the 6D theory. These extra sectors include both chiral and antichiral currents, as well as spacetime filling noncritical strings of the 6D theory. For each candidate 2D SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.

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

PubMed

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

2017-05-01

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

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

NASA Astrophysics Data System (ADS)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

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

The Stroh Formalism for Anisotropic Elasticity with Applications to Composite Materials

DTIC Science & Technology

1991-10-07

572 (1989). [4] Changsong Dongye and T. C. T. Ting, "Explicit expressions of Barnett-Lothe tensors and their associated tensors for orthotropic...SCIENTIFIC PERSONNEL ON THE PROJECT Chyanbin Hwu, Ph. D. Qianqian Li, Ph. D. Changsong Dongye, Visiting Scholar, from Dalien Railway Institute, Dalien

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

Preliminary diffusion tensor imaging studies in limb-girdle muscular dystrophies

NASA Astrophysics Data System (ADS)

Hidalgo-Tobon, S.; Hernandez-Salazar, G.; Vargas-Cañas, S.; Marrufo-Melendez, O.; Solis-Najera, S.; Taboada-Barajas, J.; Rodriguez, A. O.; Delgado-Hernandez, R.

2012-10-01

Limb-girdle muscular dystrophies (LGMD) are a group of autosomal dominantly or recessively inherited muscular dystrophies that also present with primary proximal (limb-girdle) muscle weakness. This type of dystrophy involves the shoulder and pelvic girdles, distinct phenotypic or clinical characteristics are recognized. Imaging experiments were conducted on a 1.5T GE scanner (General Electric Medical Systems. Milwaukee. USA), using a combination of two eight-channel coil array. Diffusion Tensor Imaging (DTI) data were acquired using a SE-EPI sequence, diffusion weighted gradients were applied along 30 non-collinear directions with a b-value=550 s/mm2. The connective tissue content does not appear to have a significant effect on the directionality of the diffusion, as assessed by fractional anisotropy. The fibers of the Sartorius muscle and gracilis showed decreased number of tracts, secondary to fatty infiltration and replacement of connective tissue and muscle mass loss characteristic of the underlying pathology. Our results demonstrated the utility of non-invasive MRI techniques to characterize the muscle pathology, through quantitative and qualitative methods such as the FA values and tractrography.

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

Determination of focal mechanisms of intermediate-magnitude earthquakes in Mexico, based on Greens functions calculated for a 3D Earth model

NASA Astrophysics Data System (ADS)

Rodrigo Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala

2015-04-01

One important ingredient in the study of the complex active tectonics in Mexico is the analysis of earthquake focal mechanisms, or the seismic moment tensor. They can be determined trough the calculation of Green functions and subsequent inversion for moment-tensor parameters. However, this calculation is gets progressively more difficult as the magnitude of the earthquakes decreases. Large earthquakes excite waves of longer periods that interact weakly with laterally heterogeneities in the crust. For these earthquakes, using 1D velocity models to compute the Greens fucntions works well. The opposite occurs for smaller and intermediate sized events, where the relatively shorter periods excited interact strongly with lateral heterogeneities in the crust and upper mantle and requires more specific or regional 3D models. In this study, we calculate Greens functions for earthquakes in Mexico using a laterally heterogeneous seismic wave speed model, comprised of mantle model S362ANI (Kustowski et al 2008) and crustal model CRUST 2.0 (Bassin et al 1990). Subsequently, we invert the observed seismograms for the seismic moment tensor using a method developed by Liu et al (2004) an implemented by Óscar de La Vega (2014) for earthquakes in Mexico. By following a brute force approach, in which we include all observed Rayleigh and Love waves of the Mexican National Seismic Network (Servicio Sismológico Naciona, SSN), we obtain reliable focal mechanisms for events that excite a considerable amount of low frequency waves (Mw > 4.8). However, we are not able to consistently estimate focal mechanisms for smaller events using this method, due to high noise levels in many of the records. Excluding the noisy records, or noisy parts of the records manually, requires interactive edition of the data, using an efficient tool for the editing. Therefore, we developed a graphical user interface (GUI), based on python and the python library ObsPy, that allows the edition of observed and synthetic seismograms data such as signal filtering, choosing and disregarding traces and manual adjustment of time windows, to only include segments where the noise are excluded as much as possible. Subsequently, we invert for the seismic moment tensor of events of variable magnitude in the Mexican territory and compare the results to those obtained by other methods. In this presentation we introduce the software and present the results from the moment-tensor inversions.

Influence of solvent and salt concentration on the alignment properties of acrylamide copolymer gels for the measurement of RDC.

PubMed

Trigo-Mouriño, Pablo; Navarro-Vázquez, Armando; Sánchez-Pedregal, Víctor M

2012-12-01

The dependence of molecular alignment with solvent nature and salt concentration has been investigated for mechanically stretched polyacrylamide copolymer gels. Residual dipolar couplings (RDCs) were recorded for D(2)O, DMSO-d(6), and DMSO-d(6)/D(2)O solutions containing different proportions of the solvents and different sodium chloride concentrations. Alignment tensors were determined by fitting the experimental RDCs to the DFT-computed structure of N-methylcodeinium ion. Analysis of the tensors shows that the degree of alignment decreases with the proportion of DMSO-d(6) as well as with the concentration of sodium chloride, most likely due to enhanced ion-pair aggregation. Furthermore, rotation of the alignment tensor is observed when increasing the salt concentration. Copyright © 2012 John Wiley & Sons, Ltd.

Eckart frame vibration-rotation Hamiltonians: Contravariant metric tensor

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

Pesonen, Janne, E-mail: janne.pesonen@helsinki.fi

2014-02-21

Eckart frame is a unique embedding in the theory of molecular vibrations and rotations. It is defined by the condition that the Coriolis coupling of the reference structure of the molecule is zero for every choice of the shape coordinates. It is far from trivial to set up Eckart kinetic energy operators (KEOs), when the shape of the molecule is described by curvilinear coordinates. In order to obtain the KEO, one needs to set up the corresponding contravariant metric tensor. Here, I derive explicitly the Eckart frame rotational measuring vectors. Their inner products with themselves give the rotational elements, andmore » their inner products with the vibrational measuring vectors (which, in the absence of constraints, are the mass-weighted gradients of the shape coordinates) give the Coriolis elements of the contravariant metric tensor. The vibrational elements are given as the inner products of the vibrational measuring vectors with themselves, and these elements do not depend on the choice of the body-frame. The present approach has the advantage that it does not depend on any particular choice of the shape coordinates, but it can be used in conjunction with all shape coordinates. Furthermore, it does not involve evaluation of covariant metric tensors, chain rules of derivation, or numerical differentiation, and it can be easily modified if there are constraints on the shape of the molecule. Both the planar and non-planar reference structures are accounted for. The present method is particular suitable for numerical work. Its computational implementation is outlined in an example, where I discuss how to evaluate vibration-rotation energies and eigenfunctions of a general N-atomic molecule, the shape of which is described by a set of local polyspherical coordinates.« less

Reverse ray tracing for transformation optics.

PubMed

Hu, Chia-Yu; Lin, Chun-Hung

2015-06-29

Ray tracing is an important technique for predicting optical system performance. In the field of transformation optics, the Hamiltonian equations of motion for ray tracing are well known. The numerical solutions to the Hamiltonian equations of motion are affected by the complexities of the inhomogeneous and anisotropic indices of the optical device. Based on our knowledge, no previous work has been conducted on ray tracing for transformation optics with extreme inhomogeneity and anisotropicity. In this study, we present the use of 3D reverse ray tracing in transformation optics. The reverse ray tracing is derived from Fermat's principle based on a sweeping method instead of finding the full solution to ordinary differential equations. The sweeping method is employed to obtain the eikonal function. The wave vectors are then obtained from the gradient of that eikonal function map in the transformed space to acquire the illuminance. Because only the rays in the points of interest have to be traced, the reverse ray tracing provides an efficient approach to investigate the illuminance of a system. This approach is useful in any form of transformation optics where the material property tensor is a symmetric positive definite matrix. The performance and analysis of three transformation optics with inhomogeneous and anisotropic indices are explored. The ray trajectories and illuminances in these demonstration cases are successfully solved by the proposed reverse ray tracing method.

2D joint inversion of CSAMT and magnetic data based on cross-gradient theory

NASA Astrophysics Data System (ADS)

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

2017-06-01

A two-dimensional forward and backward algorithm for the controlled-source audio-frequency magnetotelluric (CSAMT) method is developed to invert data in the entire region (near, transition, and far) and deal with the effects of artificial sources. First, a regularization factor is introduced in the 2D magnetic inversion, and the magnetic susceptibility is updated in logarithmic form so that the inversion magnetic susceptibility is always positive. Second, the joint inversion of the CSAMT and magnetic methods is completed with the introduction of the cross gradient. By searching for the weight of the cross-gradient term in the objective function, the mutual influence between two different physical properties at different locations are avoided. Model tests show that the joint inversion based on cross-gradient theory offers better results than the single-method inversion. The 2D forward and inverse algorithm for CSAMT with source can effectively deal with artificial sources and ensures the reliability of the final joint inversion algorithm.

Extended Applicability of the Spherical-Harmonic and Point-Mass Modeling of the Gravity Field,

DTIC Science & Technology

1980-02-01

the metric in spherical coordinates {X,F, rl reads ds2 = r2cos 2j dX2 + r 2d 2 + dr2 yielding the metric tensor and the associated metric tensor: {grs...leading to (3.52) would have required considerably more space if the tensor approach to this problem had been avoided, whether for pedagogical or other...useful, especially from the pedagogical point of view, since it addresses itself to large audiences and exposes the treated subject in great depth. On

Tensor network state correspondence and holography

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder

2018-01-01

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.

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.

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-02-25

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

Tensor-based spatiotemporal saliency detection

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

General tensor discriminant analysis and gabor features for gait recognition.

PubMed

Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

2007-10-01

The traditional image representations are not suited to conventional classification methods, such as the linear discriminant analysis (LDA), because of the under sample problem (USP): the dimensionality of the feature space is much higher than the number of training samples. Motivated by the successes of the two dimensional LDA (2DLDA) for face recognition, we develop a general tensor discriminant analysis (GTDA) as a preprocessing step for LDA. The benefits of GTDA compared with existing preprocessing methods, e.g., principal component analysis (PCA) and 2DLDA, include 1) the USP is reduced in subsequent classification by, for example, LDA; 2) the discriminative information in the training tensors is preserved; and 3) GTDA provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of GTDA converges, while that of 2DLDA does not. We use human gait recognition to validate the proposed GTDA. The averaged gait images are utilized for gait representation. Given the popularity of Gabor function based image decompositions for image understanding and object recognition, we develop three different Gabor function based image representations: 1) the GaborD representation is the sum of Gabor filter responses over directions, 2) GaborS is the sum of Gabor filter responses over scales, and 3) GaborSD is the sum of Gabor filter responses over scales and directions. The GaborD, GaborS and GaborSD representations are applied to the problem of recognizing people from their averaged gait images.A large number of experiments were carried out to evaluate the effectiveness (recognition rate) of gait recognition based on first obtaining a Gabor, GaborD, GaborS or GaborSD image representation, then using GDTA to extract features and finally using LDA for classification. The proposed methods achieved good performance for gait recognition based on image sequences from the USF HumanID Database. Experimental comparisons are made with nine state of the art classification methods in gait recognition.

Fault structures in the focal area of the 2016 Kumamoto earthquake revealed by derivatives and structure parameters of a gravity gradient tensor

NASA Astrophysics Data System (ADS)

Hiramatsu, Y.; Matsumoto, N.; Sawada, A.

2016-12-01

We analyze gravity anomalies in the focal area of the 2016 Kumamoto earthquake, evaluate the continuity, segmentation and faulting type of the active fault zones, and discuss relationships between those features and the aftershock distribution. We compile the gravity data published by the Gravity Research Group in Southwest Japan (2001), the Geographical Survey Institute (2006), Yamamoto et al. (2011), Honda et al. (2012), and the Geological Survey of Japan, AIST (2013). We apply terrain corrections with 10 m DEM and a low-pass filter, then remove a linear trend to obtain Bouguer anomalies. We calculate the first horizontal derivative (HD), the first vertical derivative (VD), the normalized total horizontal derivative (TDX) (Cooper and Cowan, 2006), the dimensionality index (Di) (Beki and Pedersen, 2010), and dip angle (β) (Beki, 2013) from a gravity gradient tensor. The HD, VD and TDX show the existence of the continuous fault structure along the Futagawa fault zone, extending from the Uto peninsula to the Beppu Bay except Mt. Aso area. Aftershocks are distributed along this structural boundary from the confluence of the Futagawa and the Hinagu fault zones to the east end of the Aso volcano. The distribution of dip angle β along the Futagawa fault zone implies a normal faulting, which corresponds to the coseismic faulting estimated geologically and geomorphologically. We observe the S-shaped distribution of the Bouguer anomalies around the southern part of the Hinagu segment, indicating a right lateral faulting. The VD and TDX support the existence of the fault structure along the segment but it is not so clear. We can recognize no clear structural boundaries along the Takano-Shirahata segment. TDX implies the existence of a structural boundary with a NW-SE trend around the boundary between the Hinagu and Takano-Shirahata segments. The Di shows that this boundary has a 3D-like structure rather than a 2D-like one, suggesting the discontinuity of 2D-like fault structure along the fault zone. A geological map indicates that this structure boundary corresponds to a boundary between the metamorphic rock and the sedimentary rock. The active area of the aftershocks does not extend to the south beyond this structure boundary, implying that the spatial extent of the source fault is controlled by this boundary.

Diffusion tensor imaging in children with tuberous sclerosis complex: tract-based spatial statistics assessment of brain microstructural changes.

PubMed

Zikou, Anastasia K; Xydis, Vasileios G; Astrakas, Loukas G; Nakou, Iliada; Tzarouchi, Loukia C; Tzoufi, Meropi; Argyropoulou, Maria I

2016-07-01

There is evidence of microstructural changes in normal-appearing white matter of patients with tuberous sclerosis complex. To evaluate major white matter tracts in children with tuberous sclerosis complex using tract-based spatial statistics diffusion tensor imaging (DTI) analysis. Eight children (mean age ± standard deviation: 8.5 ± 5.5 years) with an established diagnosis of tuberous sclerosis complex and 8 age-matched controls were studied. The imaging protocol consisted of T1-weighted high-resolution 3-D spoiled gradient-echo sequence and a spin-echo, echo-planar diffusion-weighted sequence. Differences in the diffusion indices were evaluated using tract-based spatial statistics. Tract-based spatial statistics showed increased axial diffusivity in the children with tuberous sclerosis complex in the superior and anterior corona radiata, the superior longitudinal fascicle, the inferior fronto-occipital fascicle, the uncinate fascicle and the anterior thalamic radiation. No significant differences were observed in fractional anisotropy, mean diffusivity and radial diffusivity between patients and control subjects. No difference was found in the diffusion indices between the baseline and follow-up examination in the patient group. Patients with tuberous sclerosis complex have increased axial diffusivity in major white matter tracts, probably related to reduced axonal integrity.

Rotation Covariant Image Processing for Biomedical Applications

PubMed Central

Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences. PMID:23710255

Myocardial strains from 3D displacement encoded magnetic resonance imaging

PubMed Central

2012-01-01

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

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.

Determination of mouse skeletal muscle architecture using three-dimensional diffusion tensor imaging.

PubMed

Heemskerk, Anneriet M; Strijkers, Gustav J; Vilanova, Anna; Drost, Maarten R; Nicolay, Klaas

2005-06-01

Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six mice, the hindlimb was imaged with a diffusion-weighted (DW) 3D fast spin-echo (FSE) sequence followed by the acquisition of an exercise-induced, T(2)-enhanced data set. The data showed the expected fiber organization, from which the physiological cross-sectional area (PCSA), fiber length, and pennation angle for the tibialis anterior (TA) were obtained. The values of these parameters ranged from 5.4-9.1 mm(2), 5.8-7.8 mm, and 21-24 degrees , respectively, which is in agreement with values obtained previously with the use of invasive methods. This study shows that 3D DT acquisition and fiber tracking is feasible for the skeletal muscle of mice, and thus enables the quantitative determination of muscle architecture.

On Lovelock analogs of the Riemann tensor

NASA Astrophysics Data System (ADS)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

Accurate Methods for Large Molecular Systems (Preprint)

DTIC Science & Technology

2009-01-06

tensor, EFP calculations are basis set dependent. The smallest recommended basis set is 6- 31++G( d , p )52 The dependence of the computational cost of...and second order perturbation theory (MP2) levels with the 6-31G( d , p ) basis set. Additional SFM tests are presented for a small set of alpha...helices using the 6-31++G( d , p ) basis set. The larger 6-311++G(3df,2p) basis set is employed for creating all EFPs used for non- bonded interactions, since

Conformal Yano-Killing Tensors in General Relativity

NASA Astrophysics Data System (ADS)

Jezierski, Jacek

2011-09-01

How CYK tensors appear in General Relativity? Geometric definition of the asymptotic flat spacetime: strong asymptotic flatness, which guarantees well defined total angular momentum [2, 3, 4] Conserved quantities - asymptotic charges (ℐ, 𝓲0) [2, 3, 4, 5, 6, 9] Quasi-local mass and "rotational energy" for Kerr black hole [5] Constants of motion along geodesics and symmetric Killing tensors [5, 6] Spacetimes possessing CYK tensor [10]: Minkowski (quadratic polynomials) [5] (Anti-)deSitter (natural construction) [7, 8, 9] Kerr (type D spacetime) [5] Taub-NUT (new symmetric conformal Killing tensors) [6] Other applications: Symmetries of Dirac operator Symmetries of Maxwell equations

Automated artifact detection and removal for improved tensor estimation in motion-corrupted DTI data sets using the combination of local binary patterns and 2D partial least squares.

PubMed

Zhou, Zhenyu; Liu, Wei; Cui, Jiali; Wang, Xunheng; Arias, Diana; Wen, Ying; Bansal, Ravi; Hao, Xuejun; Wang, Zhishun; Peterson, Bradley S; Xu, Dongrong

2011-02-01

Signal variation in diffusion-weighted images (DWIs) is influenced both by thermal noise and by spatially and temporally varying artifacts, such as rigid-body motion and cardiac pulsation. Motion artifacts are particularly prevalent when scanning difficult patient populations, such as human infants. Although some motion during data acquisition can be corrected using image coregistration procedures, frequently individual DWIs are corrupted beyond repair by sudden, large amplitude motion either within or outside of the imaging plane. We propose a novel approach to identify and reject outlier images automatically using local binary patterns (LBP) and 2D partial least square (2D-PLS) to estimate diffusion tensors robustly. This method uses an enhanced LBP algorithm to extract texture features from a local texture feature of the image matrix from the DWI data. Because the images have been transformed to local texture matrices, we are able to extract discriminating information that identifies outliers in the data set by extending a traditional one-dimensional PLS algorithm to a two-dimension operator. The class-membership matrix in this 2D-PLS algorithm is adapted to process samples that are image matrix, and the membership matrix thus represents varying degrees of importance of local information within the images. We also derive the analytic form of the generalized inverse of the class-membership matrix. We show that this method can effectively extract local features from brain images obtained from a large sample of human infants to identify images that are outliers in their textural features, permitting their exclusion from further processing when estimating tensors using the DWIs. This technique is shown to be superior in performance when compared with visual inspection and other common methods to address motion-related artifacts in DWI data. This technique is applicable to correct motion artifact in other magnetic resonance imaging (MRI) techniques (e.g., the bootstrapping estimation) that use univariate or multivariate regression methods to fit MRI data to a pre-specified model. Copyright © 2011 Elsevier Inc. All rights reserved.

Research on the forward modeling of controlled-source audio-frequency magnetotellurics in three-dimensional axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong

2017-11-01

Controlled-source audio-frequency magnetotellurics (CSAMT) has developed rapidly in recent years and are widely used in the area of mineral and oil resource exploration as well as other fields. The current theory, numerical simulation, and inversion research are based on the assumption that the underground media have resistivity isotropy. However a large number of rock and mineral physical property tests show the resistivity of underground media is generally anisotropic. With the increasing application of CSAMT, the demand for probe accuracy of practical exploration to complex targets continues to increase. The question of how to evaluate the influence of anisotropic resistivity to CSAMT response is becoming important. To meet the demand for CSAMT response research of resistivity anisotropic media, this paper examines the CSAMT electric equations, derives and realizes a three-dimensional (3D) staggered-grid finite difference numerical simulation method of CSAMT resistivity axial anisotropy. Through building a two-dimensional (2D) resistivity anisotropy geoelectric model, we validate the 3D computation result by comparing it to the result of controlled-source electromagnetic method (CSEM) resistivity anisotropy 2D finite element program. Through simulating a 3D resistivity axial anisotropy geoelectric model, we compare and analyze the responses of equatorial configuration, axial configuration, two oblique sources and tensor source. The research shows that the tensor source is suitable for CSAMT to recognize the anisotropic effect of underground structure.

Classification of trivial spin-1 tensor network states on a square lattice

NASA Astrophysics Data System (ADS)

Lee, Hyunyong; Han, Jung Hoon

2016-09-01

Classification of possible quantum spin liquid (QSL) states of interacting spin-1/2's in two dimensions has been a fascinating topic of condensed matter for decades, resulting in enormous progress in our understanding of low-dimensional quantum matter. By contrast, relatively little work exists on the identification, let alone classification, of QSL phases for spin-1 systems in dimensions higher than one. Employing the powerful ideas of tensor network theory and its classification, we develop general methods for writing QSL wave functions of spin-1 respecting all the lattice symmetries, spin rotation, and time reversal with trivial gauge structure on the square lattice. We find 25 distinct classes characterized by five binary quantum numbers. Several explicit constructions of such wave functions are given for bond dimensions D ranging from two to four, along with thorough numerical analyses to identify their physical characters. Both gapless and gapped states are found. The topological entanglement entropy of the gapped states is close to zero, indicative of topologically trivial states. In D =4 , several different tensors can be linearly combined to produce a family of states within the same symmetry class. A rich "phase diagram" can be worked out among the phases of these tensors, as well as the phase transitions among them. Among the states we identified in this putative phase diagram is the plaquette-ordered phase, gapped resonating valence bond phase, and a critical phase. A continuous transition separates the plaquette-ordered phase from the resonating valence bond phase.

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.

Tensor-based dynamic reconstruction method for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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

DTIC Science & Technology

2014-11-01

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

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.

Tensor Toolbox for MATLAB v. 3.0

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

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

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

Visualizing dispersive features in 2D image via minimum gradient method

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

He, Yu; Wang, Yan; Shen, Zhi -Xun

Here, we developed a minimum gradient based method to track ridge features in a 2D image plot, which is a typical data representation in many momentum resolved spectroscopy experiments. Through both analytic formulation and numerical simulation, we compare this new method with existing DC (distribution curve) based and higher order derivative based analyses. We find that the new method has good noise resilience and enhanced contrast especially for weak intensity features and meanwhile preserves the quantitative local maxima information from the raw image. An algorithm is proposed to extract 1D ridge dispersion from the 2D image plot, whose quantitative applicationmore » to angle-resolved photoemission spectroscopy measurements on high temperature superconductors is demonstrated.« less

Visualizing dispersive features in 2D image via minimum gradient method

DOE PAGES

He, Yu; Wang, Yan; Shen, Zhi -Xun

2017-07-24

Here, we developed a minimum gradient based method to track ridge features in a 2D image plot, which is a typical data representation in many momentum resolved spectroscopy experiments. Through both analytic formulation and numerical simulation, we compare this new method with existing DC (distribution curve) based and higher order derivative based analyses. We find that the new method has good noise resilience and enhanced contrast especially for weak intensity features and meanwhile preserves the quantitative local maxima information from the raw image. An algorithm is proposed to extract 1D ridge dispersion from the 2D image plot, whose quantitative applicationmore » to angle-resolved photoemission spectroscopy measurements on high temperature superconductors is demonstrated.« less

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

N = (2,0) self-dual non-Abelian tensor multiplet in D = 3 + 3 generates N = (1,1) self-dual systems in D = 2 + 2

NASA Astrophysics Data System (ADS)

Nishino, Hitoshi; Rajpoot, Subhash

2018-03-01

We formulate an N = (2 , 0) system in D = 3 + 3 dimensions consisting of a Yang-Mills (YM)-multiplet (ˆ μ ˆ IA, λˆI), a self-dual non-Abelian tensor multiplet (ˆ μ ˆ ν ˆ IB, χˆI ,φˆI), and an extra vector multiplet (C ˆ μ ˆ IC, ρˆI). We next perform the dimensional reductions of this system into D = 2 + 2, and obtain N = (1 , 1) systems with a self-dual YM-multiplet (AIμ ,λI), a self-dual tensor multiplet (BIμν , χI , φI), and an extra vector multiplet (CIμ , ρI). In D = 2 + 2, we reach two distinct theories: 'Theory-I' and 'Theory-II'. The former has the self-dual field-strength Hμν(+)I of CIμ already presented in our recent paper, while the latter has anti-self-dual field strength Hμν(-)I. As an application, we show that Theory-II actually generates supersymmetric-KdV equations in D = 1 + 1. Our result leads to a new conclusion that the D = 3 + 3 theory with non-Abelian tensor multiplet can be a 'Grand Master Theory' for self-dual multiplet and self-dual YM-multiplet in D = 2 + 2, that in turn has been conjectured to be the 'Master Theory' for all supersymmetric integrable theories in D ≤ 3.

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.

Abelian tensor hierarchy in 4D N = 1 conformal supergravity

NASA Astrophysics Data System (ADS)

Aoki, Shuntaro; Higaki, Tetsutaro; Yamada, Yusuke; Yokokura, Ryo

2016-09-01

We consider Abelian tensor hierarchy in four-dimensional N = 1 supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric tensor fields. We introduce p-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the super-forms. As a result, each of form fields is expressed by a single gauge invariant superfield. We also show the relation between the superspace formalism and the superconformal tensor calculus.

Killing-Yano forms and Killing tensors on a warped space

NASA Astrophysics Data System (ADS)

Krtouš, Pavel; KubizÅák, David; Kolář, Ivan

2016-01-01

We formulate several criteria under which the symmetries associated with the Killing and Killing-Yano tensors on the base space can be lifted to the symmetries of the full warped geometry. The procedure is explicitly illustrated on several examples, providing new prototypes of spacetimes admitting such tensors. In particular, we study a warped product of two Kerr-NUT-(A)dS spacetimes and show that it gives rise to a new class of highly symmetric vacuum (with a cosmological constant) black hole solutions that inherit many of the properties of the Kerr-NUT-(A)dS geometry.

Higher derivative extensions of 3 d Chern-Simons models: conservation laws and stability

NASA Astrophysics Data System (ADS)

Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.

2015-11-01

We consider the class of higher derivative 3 d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.

Conjugate gradient method for phase retrieval based on the Wirtinger derivative.

PubMed

Wei, Zhun; Chen, Wen; Qiu, Cheng-Wei; Chen, Xudong

2017-05-01

A conjugate gradient Wirtinger flow (CG-WF) algorithm for phase retrieval is proposed in this paper. It is shown that, compared with recently reported Wirtinger flow and its modified methods, the proposed CG-WF algorithm is able to dramatically accelerate the convergence rate while keeping the dominant computational cost of each iteration unchanged. We numerically illustrate the effectiveness of our method in recovering 1D Gaussian signals and 2D natural color images under both Gaussian and coded diffraction pattern models.

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

PubMed Central

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

2013-01-01

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

Generalized minimal principle for rotor filaments.

PubMed

Dierckx, Hans; Wellner, Marcel; Bernus, Olivier; Verschelde, Henri

2015-05-01

To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G=det(D)D(-1). The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes.

A non-statistical regularization approach and a tensor product decomposition method applied to complex flow data

NASA Astrophysics Data System (ADS)

von Larcher, Thomas; Blome, Therese; Klein, Rupert; Schneider, Reinhold; Wolf, Sebastian; Huber, Benjamin

2016-04-01

Handling high-dimensional data sets like they occur e.g. in turbulent flows or in multiscale behaviour of certain types in Geosciences are one of the big challenges in numerical analysis and scientific computing. A suitable solution is to represent those large data sets in an appropriate compact form. In this context, tensor product decomposition methods currently emerge as an important tool. One reason is that these methods often enable one to attack high-dimensional problems successfully, another that they allow for very compact representations of large data sets. We follow the novel Tensor-Train (TT) decomposition method to support the development of improved understanding of the multiscale behavior and the development of compact storage schemes for solutions of such problems. One long-term goal of the project is the construction of a self-consistent closure for Large Eddy Simulations (LES) of turbulent flows that explicitly exploits the tensor product approach's capability of capturing self-similar structures. Secondly, we focus on a mixed deterministic-stochastic subgrid scale modelling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Advanced methods of time series analysis for the databased construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory based on a modified Akaike information criterion and on the Bayesian information criterion for the model discrimination are used to construct surrogate models for the non-resolved flux fluctuations. Vector-valued auto-regressive models with external influences form the basis for the modelling approach [1], [2], [4]. Here, we present the reconstruction capabilities of the two modeling approaches tested against 3D turbulent channel flow data computed by direct numerical simulation (DNS) for an incompressible, isothermal fluid at Reynolds number Reτ = 590 (computed by [3]). References [1] I. Horenko. On identification of nonstationary factor models and its application to atmospherical data analysis. J. Atm. Sci., 67:1559-1574, 2010. [2] P. Metzner, L. Putzig and I. Horenko. Analysis of persistent non-stationary time series and applications. CAMCoS, 7:175-229, 2012. [3] M. Uhlmann. Generation of a temporally well-resolved sequence of snapshots of the flow-field in turbulent plane channel flow. URL: http://www-turbul.ifh.unikarlsruhe.de/uhlmann/reports/produce.pdf, 2000. [4] Th. von Larcher, A. Beck, R. Klein, I. Horenko, P. Metzner, M. Waidmann, D. Igdalov, G. Gassner and C.-D. Munz. Towards a Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation. Meteorol. Z., 24:313-342, 2015.

Rapid Gradient-Echo Imaging

PubMed Central

Hargreaves, Brian

2012-01-01

Gradient echo sequences are widely used in magnetic resonance imaging (MRI) for numerous applications ranging from angiography to perfusion to functional MRI. Compared with spin-echo techniques, the very short repetition times of gradient-echo methods enable very rapid 2D and 3D imaging, but also lead to complicated “steady states.” Signal and contrast behavior can be described graphically and mathematically, and depends strongly on the type of spoiling: fully balanced (no spoiling), gradient spoiling, or RF-spoiling. These spoiling options trade off between high signal and pure T1 contrast while the flip angle also affects image contrast in all cases, both of which can be demonstrated theoretically and in image examples. As with spin-echo sequences, magnetization preparation can be added to gradient-echo sequences to alter image contrast. Gradient echo sequences are widely used for numerous applications such as 3D perfusion imaging, functional MRI, cardiac imaging and MR angiography. PMID:23097185

Surface‐wave Green’s tensors in the near field

USGS Publications Warehouse

Haney, Matt; Nakahara, Hisashi

2014-01-01

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

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

PubMed

Greene, Samuel M; Batista, Victor S

2017-09-12

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

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.

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.

TNSPackage: A Fortran2003 library designed for tensor network state methods

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Electrophysiological Modeling of Cardiac Ventricular Function: From Cell to Organ

PubMed Central

Winslow, R. L.; Scollan, D. F.; Holmes, A.; Yung, C. K.; Zhang, J.; Jafri, M. S.

2005-01-01

Three topics of importance to modeling the integrative function of the heart are reviewed. The first is modeling of the ventricular myocyte. Emphasis is placed on excitation-contraction coupling and intracellular Ca2+ handling, and the interpretation of experimental data regarding interval-force relationships. Second, data on use of diffusion tensor magnetic resonance (DTMR) imaging for measuring the anatomical structure of the cardiac ventricles are presented. A method for the semi-automated reconstruction of the ventricles using a combination of gradient recalled acquisition in the steady state (GRASS) and DTMR images is described. Third, we describe how these anatomically and biophysically based models of the cardiac ventricles can be implemented on parallel computers. PMID:11701509

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.

A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

NASA Astrophysics Data System (ADS)

Sulyok, G.

2017-07-01

Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Uncertainty estimations for moment tensor inversions: the issue of the 2012 May 20 Emilia earthquake

NASA Astrophysics Data System (ADS)

Scognamiglio, Laura; Magnoni, Federica; Tinti, Elisa; Casarotti, Emanuele

2016-08-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Geoscientists ordinarily use moment tensor catalogues, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their analysis. The 2012 May 20 Emilia main shock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. A variability of ˜0.5 units in magnitude leads to a controversial knowledge of the real size of the event and reveals how the solutions could be poorly constrained. In this work, we investigate the stability of the moment tensor solution for this earthquake, studying the effect of five different 1-D velocity models, the number and the distribution of the stations used in the inversion procedure. We also introduce a 3-D velocity model to account for structural heterogeneity. We finally estimate the uncertainties associated to the computed focal planes and the obtained Mw. We conclude that our reliable source solutions provide a moment magnitude that ranges from 5.87, 1-D model, to 5.96, 3-D model, reducing the variability of the literature to ˜0.1. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, requires coming out with disclosed assumptions and explicit processing workflows. Finally and, probably more important, when moment tensor solution is used for secondary analyses it has to be combined with the same main boundary conditions (e.g. wave-velocity propagation model) to avoid conflicting results.

HOSVD-Based 3D Active Appearance Model: Segmentation of Lung Fields in CT Images.

PubMed

Wang, Qingzhu; Kang, Wanjun; Hu, Haihui; Wang, Bin

2016-07-01

An Active Appearance Model (AAM) is a computer vision model which can be used to effectively segment lung fields in CT images. However, the fitting result is often inadequate when the lungs are affected by high-density pathologies. To overcome this problem, we propose a Higher-order Singular Value Decomposition (HOSVD)-based Three-dimensional (3D) AAM. An evaluation was performed on 310 diseased lungs form the Lung Image Database Consortium Image Collection. Other contemporary AAMs operate directly on patterns represented by vectors, i.e., before applying the AAM to a 3D lung volume,it has to be vectorized first into a vector pattern by some technique like concatenation. However, some implicit structural or local contextual information may be lost in this transformation. According to the nature of the 3D lung volume, HOSVD is introduced to represent and process the lung in tensor space. Our method can not only directly operate on the original 3D tensor patterns, but also efficiently reduce the computer memory usage. The evaluation resulted in an average Dice coefficient of 97.0 % ± 0.59 %, a mean absolute surface distance error of 1.0403 ± 0.5716 mm, a mean border positioning errors of 0.9187 ± 0.5381 pixel, and a Hausdorff Distance of 20.4064 ± 4.3855, respectively. Experimental results showed that our methods delivered significant and better segmentation results, compared with the three other model-based lung segmentation approaches, namely 3D Snake, 3D ASM and 3D AAM.

On the accurate analysis of vibroacoustics in head insert gradient coils.

PubMed

Winkler, Simone A; Alejski, Andrew; Wade, Trevor; McKenzie, Charles A; Rutt, Brian K

2017-10-01

To accurately analyze vibroacoustics in MR head gradient coils. A detailed theoretical model for gradient coil vibroacoustics, including the first description and modeling of Lorentz damping, is introduced and implemented in a multiphysics software package. Numerical finite-element method simulations were used to establish a highly accurate vibroacoustic model in head gradient coils in detail, including the newly introduced Lorentz damping effect. Vibroacoustic coupling was examined through an additional modal analysis. Thorough experimental studies were used to validate simulations. Average experimental sound pressure levels (SPLs) and accelerations over the 0-3000 Hz frequency range were 97.6 dB, 98.7 dB, and 95.4 dB, as well as 20.6 g, 8.7 g, and 15.6 g for the X-, Y-, and Z-gradients, respectively. A reasonable agreement between simulations and measurements was achieved. Vibroacoustic coupling showed a coupled resonance at 2300 Hz for the Z-gradient that is responsible for a sharp peak and the highest SPL value in the acoustic spectrum. We have developed and used more realistic multiphysics simulation methods to gain novel insights into the underlying concepts for vibroacoustics in head gradient coils, which will permit improved analyses of existing gradient coils and novel SPL reduction strategies for future gradient coil designs. Magn Reson Med 78:1635-1645, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

One-loop corrections to light cone wave functions: The dipole picture DIS cross section

NASA Astrophysics Data System (ADS)

Hänninen, H.; Lappi, T.; Paatelainen, R.

2018-06-01

We develop methods to perform loop calculations in light cone perturbation theory using a helicity basis, refining the method introduced in our earlier work. In particular this includes implementing a consistent way to contract the four-dimensional tensor structures from the helicity vectors with d-dimensional tensors arising from loop integrals, in a way that can be fully automatized. We demonstrate this explicitly by calculating the one-loop correction to the virtual photon to quark-antiquark dipole light cone wave function. This allows us to calculate the deep inelastic scattering cross section in the dipole formalism to next-to-leading order accuracy. Our results, obtained using the four dimensional helicity scheme, agree with the recent calculation by Beuf using conventional dimensional regularization, confirming the regularization scheme independence of this cross section.

EPR and optical absorption study of Cu{sup 2+} doped lithium sulphate monohydrate (LSMH) single crystals

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

Sheela, K. Juliet; Subramanian, P., E-mail: psubramaniangri@gmail.com; Krishnan, S. Radha

2016-05-23

EPR study of Cu{sup 2+} doped NLO active Lithium Sulphate monohydrate (Li{sub 2}SO{sub 4.}H{sub 2}O) single crystals were grown successfully by slow evaporation method at room temperature. The principal values of g and A tensors indicate existence of orthorhombic symmetry around the Cu{sup 2+} ion. From the direction cosines of g and A tensors, the locations of Cu{sup 2+} in the lattice have been identified as interstitial site. Optical absorption confirms the rhombic symmetry and ground state wave function of the Cu{sup 2+} ion in a lattice as d{sub x2-y2}.

Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.

PubMed

Hoy, Erik P; Mazziotti, David A

2015-08-14

Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

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

Moment Tensor Analysis of Shallow Sources

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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

PubMed Central

Barmpoutis, Angelos

2010-01-01

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

Self-interaction corrected LDA + U investigations of BiFeO3 properties: plane-wave pseudopotential method

NASA Astrophysics Data System (ADS)

Yaakob, M. K.; Taib, M. F. M.; Lu, L.; Hassan, O. H.; Yahya, M. Z. A.

2015-11-01

The structural, electronic, elastic, and optical properties of BiFeO3 were investigated using the first-principles calculation based on the local density approximation plus U (LDA + U) method in the frame of plane-wave pseudopotential density functional theory. The application of self-interaction corrected LDA + U method improved the accuracy of the calculated properties. Results of structural, electronic, elastic, and optical properties of BiFeO3, calculated using the LDA + U method were in good agreement with other calculation and experimental data; the optimized choice of on-site Coulomb repulsion U was 3 eV for the treatment of strong electronic localized Fe 3d electrons. Based on the calculated band structure and density of states, the on-site Coulomb repulsion U had a significant effect on the hybridized O 2p and Fe 3d states at the valence and the conduction band. Moreover, the elastic stiffness tensor, the longitudinal and shear wave velocities, bulk modulus, Poisson’s ratio, and the Debye temperature were calculated for U = 0, 3, and 6 eV. The elastic stiffness tensor, bulk modulus, sound velocities, and Debye temperature of BiFeO3 consistently decreased with the increase of the U value.

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

NASA Astrophysics Data System (ADS)

Pascal, Christophe

2004-04-01

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

Robust membrane detection based on tensor voting for electron tomography.

PubMed

Martinez-Sanchez, Antonio; Garcia, Inmaculada; Asano, Shoh; Lucic, Vladan; Fernandez, Jose-Jesus

2014-04-01

Electron tomography enables three-dimensional (3D) visualization and analysis of the subcellular architecture at a resolution of a few nanometers. Segmentation of structural components present in 3D images (tomograms) is often necessary for their interpretation. However, it is severely hampered by a number of factors that are inherent to electron tomography (e.g. noise, low contrast, distortion). Thus, there is a need for new and improved computational methods to facilitate this challenging task. In this work, we present a new method for membrane segmentation that is based on anisotropic propagation of the local structural information using the tensor voting algorithm. The local structure at each voxel is then refined according to the information received from other voxels. Because voxels belonging to the same membrane have coherent structural information, the underlying global structure is strengthened. In this way, local information is easily integrated at a global scale to yield segmented structures. This method performs well under low signal-to-noise ratio typically found in tomograms of vitrified samples under cryo-tomography conditions and can bridge gaps present on membranes. The performance of the method is demonstrated by applications to tomograms of different biological samples and by quantitative comparison with standard template matching procedure. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

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.

A new formulation of the dispersion tensor in homogeneous porous media

NASA Astrophysics Data System (ADS)

Valdés-Parada, Francisco J.; Lasseux, Didier; Bellet, Fabien

2016-04-01

Dispersion is the result of two mass transport processes, namely molecular diffusion, which is a pure mixing effect and hydrodynamic dispersion, which combines mixing and spreading. The identification of each contribution is crucial and is often misinterpreted. Traditionally, under a volume averaging framework, a single closure problem is solved and the resulting fields are substituted into diffusive and dispersive filters. However the diffusive filter (that leads to the effective diffusivity) allows passing information from convection, which leads to an incorrect definition of the effective medium coefficients composing the total dispersion tensor. In this work, we revisit the definitions of the effective diffusivity and hydrodynamic dispersion tensors using the method of volume averaging. Our analysis shows that, in the context of laminar flow with or without inertial effects, two closure problems need to be computed in order to correctly define the corresponding effective medium coefficients. The first closure problem is associated to momentum transport and needs to be solved for a prescribed Reynolds number and flow orientation. The second closure problem is related to mass transport and it is solved first with a zero Péclet number and second with the required Péclet number and flow orientation. All the closure problems are written using closure variables only as required by the upscaling method. The total dispersion tensor is shown to depend on the microstructure, macroscopic flow angles, the cell (or pore) Péclet number and the cell (or pore) Reynolds number. It is non-symmetric in the general case. The condition for quasi-symmetry is highlighted. The functionality of the longitudinal and transverse components of this tensor with the flow angle is investigated for a 2D model porous structure obtaining consistent results with previous studies.

Performance of local optimization in single-plane fluoroscopic analysis for total knee arthroplasty.

PubMed

Prins, A H; Kaptein, B L; Stoel, B C; Lahaye, D J P; Valstar, E R

2015-11-05

Fluoroscopy-derived joint kinematics plays an important role in the evaluation of knee prostheses. Fluoroscopic analysis requires estimation of the 3D prosthesis pose from its 2D silhouette in the fluoroscopic image, by optimizing a dissimilarity measure. Currently, extensive user-interaction is needed, which makes analysis labor-intensive and operator-dependent. The aim of this study was to review five optimization methods for 3D pose estimation and to assess their performance in finding the correct solution. Two derivative-free optimizers (DHSAnn and IIPM) and three gradient-based optimizers (LevMar, DoNLP2 and IpOpt) were evaluated. For the latter three optimizers two different implementations were evaluated: one with a numerically approximated gradient and one with an analytically derived gradient for computational efficiency. On phantom data, all methods were able to find the 3D pose within 1mm and 1° in more than 85% of cases. IpOpt had the highest success-rate: 97%. On clinical data, the success rates were higher than 85% for the in-plane positions, but not for the rotations. IpOpt was the most expensive method and the application of an analytically derived gradients accelerated the gradient-based methods by a factor 3-4 without any differences in success rate. In conclusion, 85% of the frames can be analyzed automatically in clinical data and only 15% of the frames require manual supervision. The optimal success-rate on phantom data (97% with IpOpt) on phantom data indicates that even less supervision may become feasible. Copyright © 2015 Elsevier Ltd. All rights reserved.

Orthogonal bases of invariants in tensor models

NASA Astrophysics Data System (ADS)

Diaz, Pablo; Rey, Soo-Jong

2018-02-01

Representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry G d = U( N 1) ⊗ · · · ⊗ U( N d ) . We show that there are two natural ways of counting invariants, one for arbitrary G d and another valid for large rank of G d . We construct basis of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of G d diagonalizes two-point function. It is analogous to the restricted Schur basis used in matrix models. We comment on future directions for investigation.

The notion of a plastic material spin in atomistic simulations

NASA Astrophysics Data System (ADS)

Dickel, D.; Tenev, T. G.; Gullett, P.; Horstemeyer, M. F.

2016-12-01

A kinematic algorithm is proposed to extend existing constructions of strain tensors from atomistic data to decouple elastic and plastic contributions to the strain. Elastic and plastic deformation and ultimately the plastic spin, useful quantities in continuum mechanics and finite element simulations, are computed from the full, discrete deformation gradient and an algorithm for the local elastic deformation gradient. This elastic deformation gradient algorithm identifies a crystal type using bond angle analysis (Ackland and Jones 2006 Phys. Rev. B 73 054104) and further exploits the relationship between bond angles to determine the local deformation from an ideal crystal lattice. Full definitions of plastic deformation follow directly using a multiplicative decomposition of the deformation gradient. The results of molecular dynamics simulations of copper in simple shear and torsion are presented to demonstrate the ability of these new discrete measures to describe plastic material spin in atomistic simulation and to compare them with continuum theory.

High Resolution Magnetotelluric Imaging of the Nisyros Caldera and Geothermal Resource (Greece)

NASA Astrophysics Data System (ADS)

Tzanis, Andreas; Sakkas, Vassilis; Lagios, Evangelos

2017-04-01

This work reports the qualitative and quantitative re-examination of legacy magnetotelluric soundings data obtained in the caldera of Nisyros, a small island volcano at the eastern end of the Hellenic Volcanic Arc (HVA), Greece, in an attempt to explore the high temperature geothermal resource of the area. The data set comprises 39 single-site soundings and is re-examined with improved data processing methods, new hypothetical event analysis techniques to study the spatial configuration of the telluric field and two-dimensional inversion tools. Iteratively reweighted least squares have been implemented to compute stable and smooth Earth response functions, which were found to exhibit 2-D to weakly 3-D attributes as a result of induction in low-contrast local geoelectric inhomogeneities, superimposed on a dominantly 2-D background structure. The transfer functions appear to be free of coastal and island induction effects due to the low offshore/onshore resistivity contrast at, and below sea level. The spatial properties of the telluric field are studied with hypothetical event analysis based on 3-D decompositions of the impedance tensor [1]. The results indicate that convection and hydrothermal circulation is controlled by a system of antithetic NE-SW oriented active normal faults which form a graben-like structure and define the 2-D background, as well as a conjugate system of NNW-SSE normal faults which is particularly active at the SW quadrant of the island and define the main convection path. It was determined that under these conditions the data can be interpreted with 2-D inversion, which was carried out with [2]. The inversion has successfully reconstructed detailed images of the structural and functional elements of the hydrothermal system. The structural elements include a number of shallow hot water reservoirs in the argillic and phyllic alteration zones and a laterally extended deep (approx. 1km) circulation zone, all embedded in a low-resistivity matrix with very low lateral contrasts. The functional elements include images of the most important convection conduits created by the intersection of major fault planes. The results are corroborated by the logs of two deep exploration wells. Overall, on the basis of a carefully reworked data set, our analysis has provided detailed images of the volcano's interior and valuable insight into its structure, function and geothermal potential. References [1] Tzanis, A., 2014. The Characteristic States of the Magnetotelluric Impedance Tensor: Construction, analytic properties and utility in the analysis of general Earth conductivity distributions, arXiv:1404.1478 [physics.geo-ph]; last accessed, January 2017. [2] Rodi, W. and Mackie, R.L., 2001. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion, Geophysics, 66 (1), 174-187.

Collagen density gradient on three-dimensional printed poly(ε-caprolactone) scaffolds for interface tissue engineering.

PubMed

D'Amora, Ugo; D'Este, Matteo; Eglin, David; Safari, Fatemeh; Sprecher, Christoph M; Gloria, Antonio; De Santis, Roberto; Alini, Mauro; Ambrosio, Luigi

2018-02-01

The ability to engineer scaffolds that resemble the transition between tissues would be beneficial to improve repair of complex organs, but has yet to be achieved. In order to mimic tissue organization, such constructs should present continuous gradients of geometry, stiffness and biochemical composition. Although the introduction of rapid prototyping or additive manufacturing techniques allows deposition of heterogeneous layers and shape control, the creation of surface chemical gradients has not been explored on three-dimensional (3D) scaffolds obtained through fused deposition modelling technique. Thus, the goal of this study was to introduce a gradient functionalization method in which a poly(ε-caprolactone) surface was first aminolysed and subsequently covered with collagen via carbodiimide reaction. The 2D constructs were characterized for their amine and collagen contents, wettability, surface topography and biofunctionality. Finally, chemical gradients were created in 3D printed scaffolds with controlled geometry and porosity. The combination of additive manufacturing and surface modification is a viable tool for the fabrication of 3D constructs with controlled structural and chemical gradients. These constructs can be employed for mimicking continuous tissue gradients for interface tissue engineering. Copyright © 2017 John Wiley & Sons, Ltd.

O(d,d)-duality in string theory

NASA Astrophysics Data System (ADS)

Rennecke, Felix

2014-10-01

A new method for obtaining dual string theory backgrounds is presented. Preservation of the Hamiltonian density and the energy momentum tensor induced by O( d, d)-transformations leads to a relation between dual sets of coordinate one-forms accompanied by a redefinition of the background fields and a shift of the dilaton. The necessity of isometric directions arises as integrability condition for this map. The isometry algebra is studied in detail using generalised geometry. In particular, non-abelian dualities and β-transformations are contained in this approach. The latter are exemplified by the construction of a new approximate non-geometric background.

Application of a moment tensor inversion code developed for mining-induced seismicity to fracture monitoring of civil engineering materials

NASA Astrophysics Data System (ADS)

Linzer, Lindsay; Mhamdi, Lassaad; Schumacher, Thomas

2015-01-01

A moment tensor inversion (MTI) code originally developed to compute source mechanisms from mining-induced seismicity data is now being used in the laboratory in a civil engineering research environment. Quantitative seismology methods designed for geological environments are being tested with the aim of developing techniques to assess and monitor fracture processes in structural concrete members such as bridge girders. In this paper, we highlight aspects of the MTI_Toolbox programme that make it applicable to performing inversions on acoustic emission (AE) data recorded by networks of uniaxial sensors. The influence of the configuration of a seismic network on the conditioning of the least-squares system and subsequent moment tensor results for a real, 3-D network are compared to a hypothetical 2-D version of the same network. This comparative analysis is undertaken for different cases: for networks consisting entirely of triaxial or uniaxial sensors; for both P and S-waves, and for P-waves only. The aim is to guide the optimal design of sensor configurations where only uniaxial sensors can be installed. Finally, the findings of recent laboratory experiments where the MTI_Toolbox has been applied to a concrete beam test are presented and discussed.

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.

A Structure Design Method for Reduction of MRI Acoustic Noise.

PubMed

Nan, Jiaofen; Zong, Nannan; Chen, Qiqiang; Zhang, Liangliang; Zheng, Qian; Xia, Yongquan

2017-01-01

The acoustic problem of the split gradient coil is one challenge in a Magnetic Resonance Imaging and Linear Accelerator (MRI-LINAC) system. In this paper, we aimed to develop a scheme to reduce the acoustic noise of the split gradient coil. First, a split gradient assembly with an asymmetric configuration was designed to avoid vibration in same resonant modes for the two assembly cylinders. Next, the outer ends of the split main magnet were constructed using horn structures, which can distribute the acoustic field away from patient region. Finally, a finite element method (FEM) was used to quantitatively evaluate the effectiveness of the above acoustic noise reduction scheme. Simulation results found that the noise could be maximally reduced by 6.9 dB and 5.6 dB inside and outside the central gap of the split MRI system, respectively, by increasing the length of one gradient assembly cylinder by 20 cm. The optimized horn length was observed to be 55 cm, which could reduce noise by up to 7.4 dB and 5.4 dB inside and outside the central gap, respectively. The proposed design could effectively reduce the acoustic noise without any influence on the application of other noise reduction methods.

Influence of tensor interactions on masses and decay widths of dibaryons

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

Pang Hourong; Ping Jialun; Chen Lingzhi

The influence of gluon and Goldstone boson induced tensor interactions on the dibaryon masses and D-wave decay widths has been studied in the quark delocalization, color screening model. The effective S-D wave transition interactions induced by gluon and Goldstone boson exchanges decrease rapidly with increasing strangeness of the channel. The tensor contribution of K and {eta} mesons is negligible in this model. There is no six-quark state in the light flavor world studied so far that can become bound by means of these tensor interactions besides the deuteron. The partial D-wave decay widths of the IJ{sup p}=(1/2)2{sup +}N{omega} state tomore » spin 0 and 1 {lambda}{xi} final states are 12.0 and 21.9 keV, respectively. This is a very narrow dibaryon resonance that might be detectable in those production reactions with rich high strangeness particles through the reconstruction of the vertex mass of the decay product {lambda}{xi} by existing detectors at RHIC and COMPASS at CERN or at JHF in Japan and FAIR in Germany in the future.« less

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

PubMed

Ghose, R; Fushman, D; Cowburn, D

2001-04-01

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

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

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.

The ionic DTI model (iDTI) of dynamic diffusion tensor imaging (dDTI)

PubMed Central

Makris, Nikos; Gasic, Gregory P.; Garrido, Leoncio

2014-01-01

Measurements of water molecule diffusion along fiber tracts in CNS by diffusion tensor imaging (DTI) provides a static map of neural connections between brain centers, but does not capture the electrical activity along axons for these fiber tracts. Here, a modification of the DTI method is presented to enable the mapping of active fibers. It is termed dynamic diffusion tensor imaging (dDTI) and is based on a hypothesized “anisotropy reduction due to axonal excitation” (“AREX”). The potential changes in water mobility accompanying the movement of ions during the propagation of action potentials along axonal tracts are taken into account. Specifically, the proposed model, termed “ionic DTI model”, was formulated as follows.•First, based on theoretical calculations, we calculated the molecular water flow accompanying the ionic flow perpendicular to the principal axis of fiber tracts produced by electrical conduction along excited myelinated and non-myelinated axons.•Based on the changes in molecular water flow we estimated the signal changes as well as the changes in fractional anisotropy of axonal tracts while performing a functional task.•The variation of fractional anisotropy in axonal tracts could allow mapping the active fiber tracts during a functional task. Although technological advances are necessary to enable the robust and routine measurement of this electrical activity-dependent movement of water molecules perpendicular to axons, the proposed model of dDTI defines the vectorial parameters that will need to be measured to bring this much needed technique to fruition. PMID:25431757

Edge gradients evaluation for 2D hybrid finite volume method model

USDA-ARS?s Scientific Manuscript database

In this study, a two-dimensional depth-integrated hydrodynamic model was developed using FVM on a hybrid unstructured collocated mesh system. To alleviate the negative effects of mesh irregularity and non-uniformity, a conservative evaluation method for edge gradients based on the second-order Tayl...

Traffic speed data imputation method based on tensor completion.

PubMed

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

2015-01-01

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

Traffic Speed Data Imputation Method Based on Tensor Completion

PubMed Central

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

2015-01-01

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

Solid-state (185/187)Re NMR and GIPAW DFT study of perrhenates and Re2(CO)10: chemical shift anisotropy, NMR crystallography, and a metal-metal bond.

PubMed

Widdifield, Cory M; Perras, Frédéric A; Bryce, David L

2015-04-21

Advances in solid-state nuclear magnetic resonance (SSNMR) methods, such as dynamic nuclear polarization (DNP), intricate pulse sequences, and increased applied magnetic fields, allow for the study of systems which even very recently would be impractical. However, SSNMR methods using certain quadrupolar probe nuclei (i.e., I > 1/2), such as (185/187)Re remain far from fully developed due to the exceedingly strong interaction between the quadrupole moment of these nuclei and local electric field gradients (EFGs). We present a detailed high-field (B0 = 21.1 T) experimental SSNMR study on several perrhenates (KReO4, AgReO4, Ca(ReO4)2·2H2O), as well as ReO3 and Re2(CO)10. We propose solid ReO3 as a new rhenium SSNMR chemical shift standard due to its reproducible and sharp (185/187)Re NMR resonances. We show that for KReO4, previously poorly understood high-order quadrupole-induced effects (HOQIE) on the satellite transitions can be used to measure the EFG tensor asymmetry (i.e., ηQ) to nearly an order-of-magnitude greater precision than competing SSNMR and nuclear quadrupole resonance (NQR) approaches. Samples of AgReO4 and Ca(ReO4)2·2H2O enable us to comment on the effects of counter-ions and hydration upon Re(vii) chemical shifts. Calcium-43 and (185/187)Re NMR tensor parameters allow us to conclude that two proposed crystal structures for Ca(ReO4)2·2H2O, which would be considered as distinct, are in fact the same structure. Study of Re2(CO)10 provides insights into the effects of Re-Re bonding on the rhenium NMR tensor parameters and rhenium oxidation state on the Re chemical shift value. As overtone NQR experiments allowed us to precisely measure the (185/187)Re EFG tensor of Re2(CO)10, we were able to measure rhenium chemical shift anisotropy (CSA) for the first time in a powdered sample. Experimental observations are supported by gauge-including projector augmented-wave (GIPAW) density functional theory (DFT) calculations, with NMR tensor calculations also provided for NH4ReO4, NaReO4 and RbReO4. These calculations are able to reproduce many of the experimental trends in rhenium δiso values and EFG tensor magnitudes. Using KReO4 as a prototypical perrhenate-containing system, we establish a correlation between the tetrahedral shear strain parameter (|ψ|) and the nuclear electric quadrupolar coupling constant (CQ), which enables the refinement of the structure of ND4ReO4. Shortcomings in traditional DFT approaches, even when including relativistic effects via the zeroth-order regular approximation (ZORA), for calculating rhenium NMR tensor parameters are identified for Re2(CO)10.

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

PubMed Central

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

2017-01-01

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

New methods for the assessment of accommodative convergence.

PubMed

Asakawa, Ken; Ishikawa, Hitoshi; Shoji, Nobuyuki

2009-01-01

The authors introduced a new objective method for measuring horizontal eye movements based on the first Purkinje image with the use of infrared charge-coupled device (CCD) cameras and compared stimulus accommodative convergence to accommodation (AC/A) ratios as determined by a standard gradient method. The study included 20 patients, 5 to 9 years old, who had intermittent exotropia (10 eyes) and accommodative esotropia (10 eyes). Measurement of horizontal eye movements in millimeters (mm), based on the first Purkinje image, was obtained with a TriIRIS C9000 instrument (Hamamatsu Photonics K.K., Hamamatsu, Japan). The stimulus AC/A ratio was determined with the far gradient method. The average values of horizontal eye movements (mm) and eye deviation (Delta) (a) before and (b) after an accommodative stimulus of 3.00 diopters (D) were calculated with the following formula: horizontal eye movements (mm/D) and stimulus AC/A ratio (Delta/D) = (b - a)/3. The average values of the horizontal eye movements and the stimulus AC/A ratio were 0.5 mm/D and 3.8 Delta/D, respectively. Correlation analysis showed a strong positive correlation between these two parameters (r = 0.92). Moreover, horizontal eye movements are directly proportional to the AC/A ratio measured with the gradient method. The methods used in this study allow objective recordings of accommodative convergence to be obtained in many clinical situations. Copyright 2009, SLACK Incorporated.

On physical property tensors invariant under line groups.

PubMed

Litvin, Daniel B

2014-03-01

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

A demonstration of adjoint methods for multi-dimensional remote sensing of the atmosphere and surface

NASA Astrophysics Data System (ADS)

Martin, William G. K.; Hasekamp, Otto P.

2018-01-01

In previous work, we derived the adjoint method as a computationally efficient path to three-dimensional (3D) retrievals of clouds and aerosols. In this paper we will demonstrate the use of adjoint methods for retrieving two-dimensional (2D) fields of cloud extinction. The demonstration uses a new 2D radiative transfer solver (FSDOM). This radiation code was augmented with adjoint methods to allow efficient derivative calculations needed to retrieve cloud and surface properties from multi-angle reflectance measurements. The code was then used in three synthetic retrieval studies. Our retrieval algorithm adjusts the cloud extinction field and surface albedo to minimize the measurement misfit function with a gradient-based, quasi-Newton approach. At each step we compute the value of the misfit function and its gradient with two calls to the solver FSDOM. First we solve the forward radiative transfer equation to compute the residual misfit with measurements, and second we solve the adjoint radiative transfer equation to compute the gradient of the misfit function with respect to all unknowns. The synthetic retrieval studies verify that adjoint methods are scalable to retrieval problems with many measurements and unknowns. We can retrieve the vertically-integrated optical depth of moderately thick clouds as a function of the horizontal coordinate. It is also possible to retrieve the vertical profile of clouds that are separated by clear regions. The vertical profile retrievals improve for smaller cloud fractions. This leads to the conclusion that cloud edges actually increase the amount of information that is available for retrieving the vertical profile of clouds. However, to exploit this information one must retrieve the horizontally heterogeneous cloud properties with a 2D (or 3D) model. This prototype shows that adjoint methods can efficiently compute the gradient of the misfit function. This work paves the way for the application of similar methods to 3D remote sensing problems.

SU-G-BRC-15: The Potential Clinical Significance of Dose Mapping Error for Intra- Fraction Dose Mapping for Lung Cancer Patients

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

Sayah, N; Weiss, E; Watkins, W

Purpose: To evaluate the dose-mapping error (DME) inherent to conventional dose-mapping algorithms as a function of dose-matrix resolution. Methods: As DME has been reported to be greatest where dose-gradients overlap tissue-density gradients, non-clinical 66 Gy IMRT plans were generated for 11 lung patients with the target edge defined as the maximum 3D density gradient on the 0% (end of inhale) breathing phase. Post-optimization, Beams were copied to 9 breathing phases. Monte Carlo dose computed (with 2*2*2 mm{sup 3} resolution) on all 10 breathing phases was deformably mapped to phase 0% using the Monte Carlo energy-transfer method with congruent mass-mapping (EMCM);more » an externally implemented tri-linear interpolation method with voxel sub-division; Pinnacle’s internal (tri-linear) method; and a post-processing energy-mass voxel-warping method (dTransform). All methods used the same base displacement-vector-field (or it’s pseudo-inverse as appropriate) for the dose mapping. Mapping was also performed at 4*4*4 mm{sup 3} by merging adjacent dose voxels. Results: Using EMCM as the reference standard, no clinically significant (>1 Gy) DMEs were found for the mean lung dose (MLD), lung V20Gy, or esophagus dose-volume indices, although MLD and V20Gy were statistically different (2*2*2 mm{sup 3}). Pinnacle-to-EMCM target D98% DMEs of 4.4 and 1.2 Gy were observed ( 2*2*2 mm{sup 3}). However dTransform, which like EMCM conserves integral dose, had DME >1 Gy for one case. The root mean square RMS of the DME for the tri-linear-to- EMCM methods was lower for the smaller voxel volume for the tumor 4D-D98%, lung V20Gy, and cord D1%. Conclusion: When tissue gradients overlap with dose gradients, organs-at-risk DME was statistically significant but not clinically significant. Target-D98%-DME was deemed clinically significant for 2/11 patients (2*2*2 mm{sup 3}). Since tri-linear RMS-DME between EMCM and tri-linear was reduced at 2*2*2 mm{sup 3}, use of this resolution is recommended for dose mapping. Interpolative dose methods are sufficiently accurate for the majority of cases. J.V. Siebers receives funding support from Varian Medical Systems.« less

Comparative study of inversion methods of three-dimensional NMR and sensitivity to fluids

NASA Astrophysics Data System (ADS)

Tan, Maojin; Wang, Peng; Mao, Keyu

2014-04-01

Three-dimensional nuclear magnetic resonance (3D NMR) logging can simultaneously measure transverse relaxation time (T2), longitudinal relaxation time (T1), and diffusion coefficient (D). These parameters can be used to distinguish fluids in the porous reservoirs. For 3D NMR logging, the relaxation mechanism and mathematical model, Fredholm equation, are introduced, and the inversion methods including Singular Value Decomposition (SVD), Butler-Reeds-Dawson (BRD), and Global Inversion (GI) methods are studied in detail, respectively. During one simulation test, multi-echo CPMG sequence activation is designed firstly, echo trains of the ideal fluid models are synthesized, then an inversion algorithm is carried on these synthetic echo trains, and finally T2-T1-D map is built. Futhermore, SVD, BRD, and GI methods are respectively applied into a same fluid model, and the computing speed and inversion accuracy are compared and analyzed. When the optimal inversion method and matrix dimention are applied, the inversion results are in good aggreement with the supposed fluid model, which indicates that the inversion method of 3D NMR is applieable for fluid typing of oil and gas reservoirs. Additionally, the forward modeling and inversion tests are made in oil-water and gas-water models, respectively, the sensitivity to the fluids in different magnetic field gradients is also examined in detail. The effect of magnetic gradient on fluid typing in 3D NMR logging is stuied and the optimal manetic gradient is choosen.

The use of Stress Tensor Discriminator Faults in separating heterogeneous fault-slip data with best-fit stress inversion methods. II. Compressional stress regimes

NASA Astrophysics Data System (ADS)

Tranos, Markos D.

2018-02-01

Synthetic heterogeneous fault-slip data as driven by Andersonian compressional stress tensors were used to examine the efficiency of best-fit stress inversion methods in separating them. Heterogeneous fault-slip data are separated only if (a) they have been driven by stress tensors defining 'hybrid' compression (R < 0.375), and their σ1 axes differ in trend more than 30° (R = 0) or 50° (R = 0.25). Separation is not feasible if they have been driven by (b) 'real' (R ≥ 0.375) and 'hybrid' compressional tensors having their σ1 axes in similar trend, or (c) 'real' compressional tensors. In case (a), the Stress Tensor Discriminator Faults (STDF) exist in more than 50% of the activated fault slip data while in cases (b) and (c), they exist in percentages of much less than 50% or not at all. They constitute a necessary discriminatory tool for the establishment and comparison of two compressional stress tensors determined by a best-fit stress inversion method. The best-fit stress inversion methods are not able to determine more than one 'real' compressional stress tensor, as far as the thrust stacking in an orogeny is concerned. They can only possibly discern stress differences in the late-orogenic faulting processes, but not between the main- and late-orogenic stages.

Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

PubMed

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

2007-01-01

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

An improved two-dimensional depth-integrated flow equation for rough-walled fractures

NASA Astrophysics Data System (ADS)

Mallikamas, Wasin; Rajaram, Harihar

2010-08-01

We present the development of an improved 2-D flow equation for rough-walled fractures. Our improved equation accounts for the influence of midsurface tortuosity and the fact that the aperture normal to the midsurface is in general smaller than the vertical aperture. It thus improves upon the well-known Reynolds equation that is widely used for modeling flow in fractures. Unlike the Reynolds equation, our approach begins from the lubrication approximation applied in an inclined local coordinate system tangential to the fracture midsurface. The local flow equation thus obtained is rigorously transformed to an arbitrary global Cartesian coordinate system, invoking the concepts of covariant and contravariant transformations for vectors defined on surfaces. Unlike previously proposed improvements to the Reynolds equation, our improved flow equation accounts for tortuosity both along and perpendicular to a flow path. Our approach also leads to a well-defined anisotropic local transmissivity tensor relating the representations of the flux and head gradient vectors in a global Cartesian coordinate system. We show that the principal components of the transmissivity tensor and the orientation of its principal axes depend on the directional local midsurface slopes. In rough-walled fractures, the orientations of the principal axes of the local transmissivity tensor will vary from point to point. The local transmissivity tensor also incorporates the influence of the local normal aperture, which is uniquely defined at each point in the fracture. Our improved flow equation is a rigorous statement of mass conservation in any global Cartesian coordinate system. We present three examples of simple geometries to compare our flow equation to analytical solutions obtained using the exact Stokes equations: an inclined parallel plate, and circumferential and axial flows in an incomplete annulus. The effective transmissivities predicted by our flow equation agree very well with values obtained using the exact Stokes equations in all these cases. We discuss potential limitations of our depth-integrated equation, which include the neglect of convergence/divergence and the inaccuracies implicit in any depth-averaging process near sharp corners where the wall and midsurface curvatures are large.

A Least Squares Collocation Approach with GOCE gravity gradients for regional Moho-estimation

NASA Astrophysics Data System (ADS)

Rieser, Daniel; Mayer-Guerr, Torsten

2014-05-01

The depth of the Moho discontinuity is commonly derived by either seismic observations, gravity measurements or combinations of both. In this study, we aim to use the gravity gradient measurements of the GOCE satellite mission in a Least Squares Collocation (LSC) approach for the estimation of the Moho depth on regional scale. Due to its mission configuration and measurement setup, GOCE is able to contribute valuable information in particular in the medium wavelengths of the gravity field spectrum, which is also of special interest for the crust-mantle boundary. In contrast to other studies we use the full information of the gradient tensor in all three dimensions. The problem outline is formulated as isostatically compensated topography according to the Airy-Heiskanen model. By using a topography model in spherical harmonics representation the topographic influences can be reduced from the gradient observations. Under the assumption of constant mantle and crustal densities, surface densities are directly derived by LSC on regional scale, which in turn are converted in Moho depths. First investigations proofed the ability of this method to resolve the gravity inversion problem already with a small amount of GOCE data and comparisons with other seismic and gravitmetric Moho models for the European region show promising results. With the recently reprocessed GOCE gradients, an improved data set shall be used for the derivation of the Moho depth. In this contribution the processing strategy will be introduced and the most recent developments and results using the currently available GOCE data shall be presented.

A novel technique for real-time estimation of edge pedestal density gradients via reflectometer time delay data

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

Zeng, L., E-mail: zeng@fusion.gat.com; Doyle, E. J.; Rhodes, T. L.

2016-11-15

A new model-based technique for fast estimation of the pedestal electron density gradient has been developed. The technique uses ordinary mode polarization profile reflectometer time delay data and does not require direct profile inversion. Because of its simple data processing, the technique can be readily implemented via a Field-Programmable Gate Array, so as to provide a real-time density gradient estimate, suitable for use in plasma control systems such as envisioned for ITER, and possibly for DIII-D and Experimental Advanced Superconducting Tokamak. The method is based on a simple edge plasma model with a linear pedestal density gradient and low scrape-off-layermore » density. By measuring reflectometer time delays for three adjacent frequencies, the pedestal density gradient can be estimated analytically via the new approach. Using existing DIII-D profile reflectometer data, the estimated density gradients obtained from the new technique are found to be in good agreement with the actual density gradients for a number of dynamic DIII-D plasma conditions.« less

Analysing seismic-source mechanisms by linear-programming methods.

USGS Publications Warehouse

Julian, B.R.

1986-01-01

Linear-programming methods are powerful and efficient tools for objectively analysing seismic focal mechanisms and are applicable to a wide range of problems, including tsunami warning and nuclear explosion identification. The source mechanism is represented as a point in the 6-D space of moment-tensor components. The present method can easily be extended to fit observed seismic-wave amplitudes (either signed or absolute) subject to polarity constraints, and to assess the range of mechanisms consistent with a set of measured amplitudes. -from Author

Entanglement branching operator

NASA Astrophysics Data System (ADS)

Harada, Kenji

2018-01-01

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

General theories of linear gravitational perturbations to a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena

2018-02-01

We use the covariant formulation proposed by Tattersall, Lagos, and Ferreira [Phys. Rev. D 96, 064011 (2017), 10.1103/PhysRevD.96.064011] to analyze the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasinormal modes of perturbed black holes may be affected by modifications to general relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyze odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

A rapid and robust gradient measurement technique using dynamic single-point imaging.

PubMed

Jang, Hyungseok; McMillan, Alan B

2017-09-01

We propose a new gradient measurement technique based on dynamic single-point imaging (SPI), which allows simple, rapid, and robust measurement of k-space trajectory. To enable gradient measurement, we utilize the variable field-of-view (FOV) property of dynamic SPI, which is dependent on gradient shape. First, one-dimensional (1D) dynamic SPI data are acquired from a targeted gradient axis, and then relative FOV scaling factors between 1D images or k-spaces at varying encoding times are found. These relative scaling factors are the relative k-space position that can be used for image reconstruction. The gradient measurement technique also can be used to estimate the gradient impulse response function for reproducible gradient estimation as a linear time invariant system. The proposed measurement technique was used to improve reconstructed image quality in 3D ultrashort echo, 2D spiral, and multi-echo bipolar gradient-echo imaging. In multi-echo bipolar gradient-echo imaging, measurement of the k-space trajectory allowed the use of a ramp-sampled trajectory for improved acquisition speed (approximately 30%) and more accurate quantitative fat and water separation in a phantom. The proposed dynamic SPI-based method allows fast k-space trajectory measurement with a simple implementation and no additional hardware for improved image quality. Magn Reson Med 78:950-962, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Open-Universe Theory for Bayesian Inference, Decision, and Sensing (OUTBIDS)

DTIC Science & Technology

2014-01-01

using a novel dynamic programming algorithm [6]. The second allows for tensor data, in which observations at a given time step exhibit...unlimited. 5 We developed a dynamical tensor model that gives far better estimation and system- identification results than the standard vectorization...inference. Third, unlike prior work that learns different pieces of the model independently, use matching between 3D models and 2D views and/or voting

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.

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.

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

On the magnetic polarizability tensor of US coinage

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Homogenized moment tensor and the effect of near-field heterogeneities on nonisotropic radiation in nuclear explosion

NASA Astrophysics Data System (ADS)

Burgos, Gaël.; Capdeville, Yann; Guillot, Laurent

2016-06-01

We investigate the effect of small-scale heterogeneities close to a seismic explosive source, at intermediate periods (20-50 s), with an emphasis on the resulting nonisotropic far-field radiation. First, using a direct numerical approach, we show that small-scale elastic heterogeneities located in the near-field of an explosive source, generate unexpected phases (i.e., long period S waves). We then demonstrate that the nonperiodic homogenization theory applied to 2-D and 3-D elastic models, with various pattern of small-scale heterogeneities near the source, leads to accurate waveforms at a reduced computational cost compared to direct modeling. Further, it gives an interpretation of how nearby small-scale features interact with the source at low frequencies, through an explicit correction to the seismic moment tensor. In 2-D simulations, we find a deviatoric contribution to the moment tensor, as high as 21% for near-source heterogeneities showing a 25% contrast of elastic values (relative to a homogeneous background medium). In 3-D this nonisotropic contribution reaches 27%. Second, we analyze intermediate-periods regional seismic waveforms associated with some underground nuclear explosions conducted at the Nevada National Security Site and invert for the full moment tensor, in order to quantify the relative contribution of the isotropic and deviatoric components of the tensor. The average value of the deviatoric part is about 35%. We conclude that the interactions between an explosive source and small-scale local heterogeneities of moderate amplitude may lead to a deviatoric contribution to the seismic moment, close to what is observed using regional data from nuclear test explosions.

Adaptive momentum management for large space structures

NASA Technical Reports Server (NTRS)

Hahn, E.

1987-01-01

Momentum management is discussed for a Large Space Structure (LSS) with the structure selected configuration being the Initial Orbital Configuration (IOC) of the dual keel space station. The external forces considered were gravity gradient and aerodynamic torques. The goal of the momentum management scheme developed is to remove the bias components of the external torques and center the cyclic components of the stored angular momentum. The scheme investigated is adaptive to uncertainties of the inertia tensor and requires only approximate knowledge of principle moments of inertia. Computational requirements are minimal and should present no implementation problem in a flight type computer and the method proposed is shown to be effective in the presence of attitude control bandwidths as low as .01 radian/sec.

Adaptive momentum management for the dual keel Space Station

NASA Technical Reports Server (NTRS)

Hopkins, M.; Hahn, E.

1987-01-01

The report discusses momentum management for a large space structure with the structure selected configuration being the Initial Orbital Configuration of the dual-keel Space Station. The external torques considered were gravity gradient and aerodynamic torques. The goal of the momentum management scheme developed is to remove the bias components of the external torques and center the cyclic components of the stored angular momentum. The scheme investigated is adaptive to uncertainties of the inertia tensor and requires only approximate knowledge of principal moments of inertia. Computational requirements are minimal and should present no implementation problem in a flight-type computer. The method proposed is shown to be effective in the presence of attitude control bandwidths as low as 0.01 radian/sec.

A framework for fast probabilistic centroid-moment-tensor determination—inversion of regional static displacement measurements

NASA Astrophysics Data System (ADS)

Käufl, Paul; Valentine, Andrew P.; O'Toole, Thomas B.; Trampert, Jeannot

2014-03-01

The determination of earthquake source parameters is an important task in seismology. For many applications, it is also valuable to understand the uncertainties associated with these determinations, and this is particularly true in the context of earthquake early warning (EEW) and hazard mitigation. In this paper, we develop a framework for probabilistic moment tensor point source inversions in near real time. Our methodology allows us to find an approximation to p(m|d), the conditional probability of source models (m) given observations (d). This is obtained by smoothly interpolating a set of random prior samples, using Mixture Density Networks (MDNs)-a class of neural networks which output the parameters of a Gaussian mixture model. By combining multiple networks as `committees', we are able to obtain a significant improvement in performance over that of a single MDN. Once a committee has been constructed, new observations can be inverted within milliseconds on a standard desktop computer. The method is therefore well suited for use in situations such as EEW, where inversions must be performed routinely and rapidly for a fixed station geometry. To demonstrate the method, we invert regional static GPS displacement data for the 2010 MW 7.2 El Mayor Cucapah earthquake in Baja California to obtain estimates of magnitude, centroid location and depth and focal mechanism. We investigate the extent to which we can constrain moment tensor point sources with static displacement observations under realistic conditions. Our inversion results agree well with published point source solutions for this event, once the uncertainty bounds of each are taken into account.

Low-dose 4D cone-beam CT via joint spatiotemporal regularization of tensor framelet and nonlocal total variation

NASA Astrophysics Data System (ADS)

Han, Hao; Gao, Hao; Xing, Lei

2017-08-01

Excessive radiation exposure is still a major concern in 4D cone-beam computed tomography (4D-CBCT) due to its prolonged scanning duration. Radiation dose can be effectively reduced by either under-sampling the x-ray projections or reducing the x-ray flux. However, 4D-CBCT reconstruction under such low-dose protocols is prone to image artifacts and noise. In this work, we propose a novel joint regularization-based iterative reconstruction method for low-dose 4D-CBCT. To tackle the under-sampling problem, we employ spatiotemporal tensor framelet (STF) regularization to take advantage of the spatiotemporal coherence of the patient anatomy in 4D images. To simultaneously suppress the image noise caused by photon starvation, we also incorporate spatiotemporal nonlocal total variation (SNTV) regularization to make use of the nonlocal self-recursiveness of anatomical structures in the spatial and temporal domains. Under the joint STF-SNTV regularization, the proposed iterative reconstruction approach is evaluated first using two digital phantoms and then using physical experiment data in the low-dose context of both under-sampled and noisy projections. Compared with existing approaches via either STF or SNTV regularization alone, the presented hybrid approach achieves improved image quality, and is particularly effective for the reconstruction of low-dose 4D-CBCT data that are not only sparse but noisy.

Design and fabrication of integrated micro/macrostructure for 3D functional gradient systems based on additive manufacturing

NASA Astrophysics Data System (ADS)

Yin, Ming; Xie, Luofeng; Jiang, Weifeng; Yin, Guofu

2018-05-01

Functional gradient systems have important applications in many areas. Although a 2D dielectric structure that serves as the gradient index medium for controlling electromagnetic waves is well established, it may not be suitable for application in 3D case. In this paper, we present a method to realize functional gradient systems with 3D integrated micro/macrostructure. The homogenization of the structure is studied in detail by conducting band diagram analysis. The analysis shows that the effective medium approximation is valid even when periodicity is comparable to wavelength. The condition to ensure the polarization-invariant, isotropic, and frequency-independent property is investigated. The scheme for the design and fabrication of 3D systems requiring spatial material property distribution is presented. By using the vat photopolymerization process, a large overall size of macrostructure at the system level and precise fine features of microstructure at the unit cell level are realized, thus demonstrating considerable scalability of the system for wave manipulation.

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

NASA Astrophysics Data System (ADS)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

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

The Twist Tensor Nuclear Norm for Video Completion.

PubMed

Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui

2017-12-01

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.

Analytical performance bounds for multi-tensor diffusion-MRI.

PubMed

Ahmed Sid, Farid; Abed-Meraim, Karim; Harba, Rachid; Oulebsir-Boumghar, Fatima

2017-02-01

To examine the effects of MR acquisition parameters on brain white matter fiber orientation estimation and parameter of clinical interest in crossing fiber areas based on the Multi-Tensor Model (MTM). We compute the Cramér-Rao Bound (CRB) for the MTM and the parameter of clinical interest such as the Fractional Anisotropy (FA) and the dominant fiber orientations, assuming that the diffusion MRI data are recorded by a multi-coil, multi-shell acquisition system. Considering the sum-of-squares method for the reconstructed magnitude image, we introduce an approximate closed-form formula for Fisher Information Matrix that has the simplicity and easy interpretation advantages. In addition, we propose to generalize the FA and the mean diffusivity to the multi-tensor model. We show the application of the CRB to reduce the scan time while preserving a good estimation precision. We provide results showing how the increase of the number of acquisition coils compensates the decrease of the number of diffusion gradient directions. We analyze the impact of the b-value and the Signal-to-Noise Ratio (SNR). The analysis shows that the estimation error variance decreases with a quadratic rate with the SNR, and that the optimum b-values are not unique but depend on the target parameter, the context, and eventually the target cost function. In this study we highlight the importance of choosing the appropriate acquisition parameters especially when dealing with crossing fiber areas. We also provide a methodology for the optimal tuning of these parameters using the CRB. Copyright © 2016 Elsevier Inc. All rights reserved.

[The Role of Imaging in Central Nervous System Infections].

PubMed

Yokota, Hajime; Tazoe, Jun; Yamada, Kei

2015-07-01

Many infections invade the central nervous system. Magnetic resonance imaging (MRI) is the main tool that is used to evaluate infectious lesions of the central nervous system. The useful sequences on MRI are dependent on the locations, such as intra-axial, extra-axial, and spinal cord. For intra-axial lesions, besides the fundamental sequences, including T1-weighted images, T2-weighted images, and fluid-attenuated inversion recovery (FLAIR) images, advanced sequences, such as diffusion-weighted imaging, diffusion tensor imaging, susceptibility-weighted imaging, and MR spectroscopy, can be applied. They are occasionally used as determinants for quick and correct diagnosis. For extra-axial lesions, understanding the differences among 2D-conventional T1-weighted images, 2D-fat-saturated T1-weighted images, 3D-Spin echo sequences, and 3D-Gradient echo sequence after the administration of gadolinium is required to avoid wrong interpretations. FLAIR plus gadolinium is a useful tool for revealing abnormal enhancement on the brain surface. For the spinal cord, the sequences are limited. Evaluating the distribution and time course of the spinal cord are essential for correct diagnoses. We summarize the role of imaging in central nervous system infections and show the pitfalls, key points, and latest information in them on clinical practices.

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

NASA Astrophysics Data System (ADS)

Ghose, Ranajeet; Fushman, David; Cowburn, David

2001-04-01

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

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.

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

PubMed

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

2017-08-01

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

Accurate determination of chemical shift tensor orientations of single-crystals by solid-state magic angle spinning NMR

NASA Astrophysics Data System (ADS)

Avadhut, Yamini S.; Weber, Johannes; Schmedt auf der Günne, Jörn

2017-09-01

An improved implementation of single-crystal magic-angle-spinning (MAS) NMR is presented which gives access to chemical shift tensors both in orientation (relative to the crystal axis system) and principal axis values. For mounting arbitrary crystals inside ordinary MAS rotors, a mounting tool is described which allows to relate the crystal orientation determined by diffraction techniques to the rotor coordinate system. The crystal is finally mounted into a MAS rotor equipped with a special insert which allows a defined reorientation of the single-crystal by 90°. The approach is based on the idea that the dispersive spectra, which are obtained when applying read-pulses at specific rotor-phases, not only yield the size of the eigenvalues but also encode the orientation of the different chemical shift (rank-2) tensors. For this purpose two 2D-data sets with orthogonal crystal orientation are fitted simultaneously. The presented analysis for chemical shift tensors is supported by an analytical formula which allows fast calculation of phase and amplitude of individual spinning side-bands and by a protocol which solves the problem of finding the correct reference phase of the spectrum. Different rotor-synchronized pulse-sequences are introduced for the same reason. Experiments are performed on L-alanine and O-phosphorylethanolamine and the observed errors are analyzed in detail. The experimental data are opposed to DFT-computed chemical shift tensors which have been obtained by the extended embedded ion method.

The Application of COMSOL Multiphysics Package on the Modelling of Complex 3-D Lithospheric Electrical Resistivity Structures - A Case Study from the Proterozoic Orogenic belt within the North China Craton

NASA Astrophysics Data System (ADS)

Guo, L.; Yin, Y.; Deng, M.; Guo, L.; Yan, J.

2017-12-01

At present, most magnetotelluric (MT) forward modelling and inversion codes are based on finite difference method. But its structured mesh gridding cannot be well adapted for the conditions with arbitrary topography or complex tectonic structures. By contrast, the finite element method is more accurate in calculating complex and irregular 3-D region and has lower requirement of function smoothness. However, the complexity of mesh gridding and limitation of computer capacity has been affecting its application. COMSOL Multiphysics is a cross-platform finite element analysis, solver and multiphysics full-coupling simulation software. It achieves highly accurate numerical simulations with high computational performance and outstanding multi-field bi-directional coupling analysis capability. In addition, its AC/DC and RF module can be used to easily calculate the electromagnetic responses of complex geological structures. Using the adaptive unstructured grid, the calculation is much faster. In order to improve the discretization technique of computing area, we use the combination of Matlab and COMSOL Multiphysics to establish a general procedure for calculating the MT responses for arbitrary resistivity models. The calculated responses include the surface electric and magnetic field components, impedance components, magnetic transfer functions and phase tensors. Then, the reliability of this procedure is certificated by 1-D, 2-D and 3-D and anisotropic forward modeling tests. Finally, we establish the 3-D lithospheric resistivity model for the Proterozoic Wutai-Hengshan Mts. within the North China Craton by fitting the real MT data collected there. The reliability of the model is also verified by induced vectors and phase tensors. Our model shows more details and better resolution, compared with the previously published 3-D model based on the finite difference method. In conclusion, COMSOL Multiphysics package is suitable for modeling the 3-D lithospheric resistivity structures under complex tectonic deformation backgrounds, which could be a good complement to the existing finite-difference inversion algorithms.

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE PAGES

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

2018-03-20

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

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

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

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

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

Spectral-Element Simulations of Wave Propagation in Porous Media: Finite-Frequency Sensitivity Kernels Based Upon Adjoint Methods

NASA Astrophysics Data System (ADS)

Morency, C.; Tromp, J.

2008-12-01

The mathematical formulation of wave propagation in porous media developed by Biot is based upon the principle of virtual work, ignoring processes at the microscopic level, and does not explicitly incorporate gradients in porosity. Based on recent studies focusing on averaging techniques, we derive the macroscopic porous medium equations from the microscale, with a particular emphasis on the effects of gradients in porosity. In doing so, we are able to naturally determine two key terms in the momentum equations and constitutive relationships, directly translating the coupling between the solid and fluid phases, namely a drag force and an interfacial strain tensor. In both terms, gradients in porosity arise. One remarkable result is that when we rewrite this set of equations in terms of the well known Biot variables us, w), terms involving gradients in porosity are naturally accommodated by gradients involving w, the fluid motion relative to the solid, and Biot's formulation is recovered, i.e., it remains valid in the presence of porosity gradients We have developed a numerical implementation of the Biot equations for two-dimensional problems based upon the spectral-element method (SEM) in the time domain. The SEM is a high-order variational method, which has the advantage of accommodating complex geometries like a finite-element method, while keeping the exponential convergence rate of (pseudo)spectral methods. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well-suited to simulations on parallel computers. Effects associated with physical dispersion & attenuation and frequency-dependent viscous resistance are addressed by using a memory variable approach. Various benchmarks involving poroelastic wave propagation in the high- and low-frequency regimes, and acoustic-poroelastic and poroelastic-poroelastic discontinuities have been successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach.

PubMed

Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir

2016-08-01

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

A distinguishing gravitational property for gravitational equation in higher dimensions

NASA Astrophysics Data System (ADS)

Dadhich, Naresh

2016-03-01

It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in the action) gravity for which the Nth order Lovelock-Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, d=2N+1, dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good distinguishing and guiding criterion for the gravitational equation in higher dimensions.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Evaluation of gravitational curvatures of a tesseroid in spherical integral kernels

NASA Astrophysics Data System (ADS)

Deng, Xiao-Le; Shen, Wen-Bin

2018-04-01

Proper understanding of how the Earth's mass distributions and redistributions influence the Earth's gravity field-related functionals is crucial for numerous applications in geodesy, geophysics and related geosciences. Calculations of the gravitational curvatures (GC) have been proposed in geodesy in recent years. In view of future satellite missions, the sixth-order developments of the gradients are becoming requisite. In this paper, a set of 3D integral GC formulas of a tesseroid mass body have been provided by spherical integral kernels in the spatial domain. Based on the Taylor series expansion approach, the numerical expressions of the 3D GC formulas are provided up to sixth order. Moreover, numerical experiments demonstrate the correctness of the 3D Taylor series approach for the GC formulas with order as high as sixth order. Analogous to other gravitational effects (e.g., gravitational potential, gravity vector, gravity gradient tensor), numerically it is found that there exist the very-near-area problem and polar singularity problem in the GC east-east-radial, north-north-radial and radial-radial-radial components in spatial domain, and compared to the other gravitational effects, the relative approximation errors of the GC components are larger due to not only the influence of the geocentric distance but also the influence of the latitude. This study shows that the magnitude of each term for the nonzero GC functionals by a grid resolution 15^' } } × 15^' }} at GOCE satellite height can reach of about 10^{-16} m^{-1} s2 for zero order, 10^{-24 } or 10^{-23} m^{-1} s2 for second order, 10^{-29} m^{-1} s2 for fourth order and 10^{-35} or 10^{-34} m^{-1} s2 for sixth order, respectively.

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

PubMed

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

2011-02-01

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

Quasinormal Frequencies of D-Dimensional Schwarzschild Black Holes: Evaluation via Continued Fraction Method

NASA Astrophysics Data System (ADS)

Rostworowski, A.

2007-01-01

We adopt Leaver's [E. Leaver, {ITALIC Proc. R. Soc. Lond.} {A402}, 285 (1985)] method to determine quasi normal frequencies of the Schwarzschild black hole in higher (D geq 10) dimensions. In D-dimensional Schwarzschild metric, when D increases, more and more singularities, spaced uniformly on the unit circle |r|=1, approach the horizon at r=rh=1. Thus, a solution satisfying the outgoing wave boundary condition at the horizon must be continued to some mid point and only then the continued fraction condition can be applied. This prescription is general and applies to all cases for which, due to regular singularities on the way from the point of interest to the irregular singularity, Leaver's method in its original setting breaks down. We illustrate the method calculating gravitational vector and tensor quasinormal frequencies of the Schwarzschild black hole in D=11 and D=10 dimensions. We also give the details for the D=9 case, considered in the work of P. Bizoz, T. Chmaj, A. Rostworowski, B.G. Schmidt and Z. Tabor {ITALIC Phys. Rev.}{D72}, 121502(R) (2005) .

WE-AB-BRA-01: 3D-2D Image Registration for Target Localization in Spine Surgery: Comparison of Similarity Metrics Against Robustness to Content Mismatch

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

De Silva, T; Ketcha, M; Siewerdsen, J H

Purpose: In image-guided spine surgery, mapping 3D preoperative images to 2D intraoperative images via 3D-2D registration can provide valuable assistance in target localization. However, the presence of surgical instrumentation, hardware implants, and soft-tissue resection/displacement causes mismatches in image content, confounding existing registration methods. Manual/semi-automatic methods to mask such extraneous content is time consuming, user-dependent, error prone, and disruptive to clinical workflow. We developed and evaluated 2 novel similarity metrics within a robust registration framework to overcome such challenges in target localization. Methods: An IRB-approved retrospective study in 19 spine surgery patients included 19 preoperative 3D CT images and 50 intraoperativemore » mobile radiographs in cervical, thoracic, and lumbar spine regions. A neuroradiologist provided truth definition of vertebral positions in CT and radiography. 3D-2D registration was performed using the CMA-ES optimizer with 4 gradient-based image similarity metrics: (1) gradient information (GI); (2) gradient correlation (GC); (3) a novel variant referred to as gradient orientation (GO); and (4) a second variant referred to as truncated gradient correlation (TGC). Registration accuracy was evaluated in terms of the projection distance error (PDE) of the vertebral levels. Results: Conventional similarity metrics were susceptible to gross registration error and failure modes associated with the presence of surgical instrumentation: for GI, the median PDE and interquartile range was 33.0±43.6 mm; similarly for GC, PDE = 23.0±92.6 mm respectively. The robust metrics GO and TGC, on the other hand, demonstrated major improvement in PDE (7.6 ±9.4 mm and 8.1± 18.1 mm, respectively) and elimination of gross failure modes. Conclusion: The proposed GO and TGC similarity measures improve registration accuracy and robustness to gross failure in the presence of strong image content mismatch. Such registration capability could offer valuable assistance in target localization without disruption of clinical workflow. G. Kleinszig and S. Vogt are employees of Siemens Healthcare.« less

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.

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

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2015-04-01

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

Free-breathing diffusion tensor imaging and tractography of the human heart in healthy volunteers using wavelet-based image fusion.

PubMed

Wei, Hongjiang; Viallon, Magalie; Delattre, Benedicte M A; Moulin, Kevin; Yang, Feng; Croisille, Pierre; Zhu, Yuemin

2015-01-01

Free-breathing cardiac diffusion tensor imaging (DTI) is a promising but challenging technique for the study of fiber structures of the human heart in vivo. This work proposes a clinically compatible and robust technique to provide three-dimensional (3-D) fiber architecture properties of the human heart. To this end, 10 short-axis slices were acquired across the entire heart using a multiple shifted trigger delay (TD) strategy under free breathing conditions. Interscan motion was first corrected automatically using a nonrigid registration method. Then, two post-processing schemes were optimized and compared: an algorithm based on principal component analysis (PCA) filtering and temporal maximum intensity projection (TMIP), and an algorithm that uses the wavelet-based image fusion (WIF) method. The two methods were applied to the registered diffusion-weighted (DW) images to cope with intrascan motion-induced signal loss. The tensor fields were finally calculated, from which fractional anisotropy (FA), mean diffusivity (MD), and 3-D fiber tracts were derived and compared. The results show that the comparison of the FA values (FA(PCATMIP) = 0.45 ±0.10, FA(WIF) = 0.42 ±0.05, P=0.06) showed no significant difference, while the MD values ( MD(PCATMIP)=0.83 ±0.12×10(-3) mm (2)/s, MD(WIF)=0.74±0.05×10(-3) mm (2)/s, P=0.028) were significantly different. Improved helix angle variations through the myocardium wall reflecting the rotation characteristic of cardiac fibers were observed with WIF. This study demonstrates that the combination of multiple shifted TD acquisitions and dedicated post-processing makes it feasible to retrieve in vivo cardiac tractographies from free-breathing DTI acquisitions. The substantial improvements were observed using the WIF method instead of the previously published PCATMIP technique.

Advanced Computational Techniques in Regional Wave Studies

DTIC Science & Technology

1990-01-03

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

Introduction to tractography-guided navigation: using 3-tesla magnetic resonance tractography in surgery for cerebral arteriovenous malformations.

PubMed

Kikuta, K; Takagi, Y; Nozaki, K; Hashimoto, N

2008-01-01

To examine the effectiveness of magnetic resonance (MR) tractography in surgery for cerebral arteriovenous malformations (AVMs). A preoperative evaluation of major neural tracts around the nidus was carried out with 3-tesla (3 T) MR tractography in 25 consecutive patients with cerebral AVMs. The patients were 12 men and 13 women ranging in age from 4 to 60 years of age (mean age: 31.2 +/- 14.1 years). Twelve presented with hemorrhage. Images were obtained with T2-weighted turbo spin echo sequences, axial T1-weighted three-dimensional magnetization-prepared rapid acquisition gradient-echo (MPRAGE) sequences, three-dimensional time-of-flight MR angiography (3D TOF MRA), and thin-section diffusion-tensor imaging (DTI). The AVMs were obliterated in 22 of the 25 patients. A postoperative study of the MR tractography was carried out in 24 patients. In 21 patients, tracts were preserved and no postoperative neurological worsening was observed. Disruption of the tracts was found in 3 patients, and postoperative worsening was observed in 2 patients. However, no deterioration occurred in 1 patient with cerebellar AVM. Notwithstanding the limitations of this method, MR tractography can be considered useful for confirming the integrity of deviated tracts, for localizing deviated tracts, and for evaluating surgical risk, especially in cases of non-hemorrhagic AVM.

PET and MRI image fusion based on combination of 2-D Hilbert transform and IHS method.

PubMed

Haddadpour, Mozhdeh; Daneshvar, Sabalan; Seyedarabi, Hadi

2017-08-01

The process of medical image fusion is combining two or more medical images such as Magnetic Resonance Image (MRI) and Positron Emission Tomography (PET) and mapping them to a single image as fused image. So purpose of our study is assisting physicians to diagnose and treat the diseases in the least of the time. We used Magnetic Resonance Image (MRI) and Positron Emission Tomography (PET) as input images, so fused them based on combination of two dimensional Hilbert transform (2-D HT) and Intensity Hue Saturation (IHS) method. Evaluation metrics that we apply are Discrepancy (D k ) as an assessing spectral features and Average Gradient (AG k ) as an evaluating spatial features and also Overall Performance (O.P) to verify properly of the proposed method. In this paper we used three common evaluation metrics like Average Gradient (AG k ) and the lowest Discrepancy (D k ) and Overall Performance (O.P) to evaluate the performance of our method. Simulated and numerical results represent the desired performance of proposed method. Since that the main purpose of medical image fusion is preserving both spatial and spectral features of input images, so based on numerical results of evaluation metrics such as Average Gradient (AG k ), Discrepancy (D k ) and Overall Performance (O.P) and also desired simulated results, it can be concluded that our proposed method can preserve both spatial and spectral features of input images. Copyright © 2017 Chang Gung University. Published by Elsevier B.V. All rights reserved.

Tensor sufficient dimension reduction

PubMed Central

Zhong, Wenxuan; Xing, Xin; Suslick, Kenneth

2015-01-01

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

Tensor renormalization group methods for spin and gauge models

NASA Astrophysics Data System (ADS)

Zou, Haiyuan

The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for Diffusion

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2009-01-01

We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.

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

Short-range correlation in high-momentum antisymmetrized molecular dynamics

NASA Astrophysics Data System (ADS)

Myo, Takayuki

2018-03-01

We propose a new variational method for treating short-range repulsion of bare nuclear force for nuclei in antisymmetrized molecular dynamics (AMD). In AMD, the short-range correlation is described in terms of large imaginary centroids of Gaussian wave packets of nucleon pairs in opposite signs, causing high-momentum components in the nucleon pairs. We superpose these AMD basis states and call this method "high-momentum AMD" (HM-AMD), which is capable of describing the strong tensor correlation [T. Myo et al., Prog. Theor. Exp. Phys., 2017, 111D01 (2017)]. In this letter, we extend HM-AMD by including up to two kinds of nucleon pairs in each AMD basis state utilizing the cluster expansion, which produces many-body correlations involving high-momentum components. We investigate how well HM-AMD describes the short-range correlation by showing the results for ^3H using the Argonne V4^' central potential. It is found that HM-AMD reproduces the results of few-body calculations and also the tensor-optimized AMD. This means that HM-AMD is a powerful approach to describe the short-range correlation in nuclei. In HM-AMD, the momentum directions of nucleon pairs isotropically contribute to the short-range correlation, which is different from the tensor correlation.