Tensor Minkowski Functionals for random fields on the sphere

NASA Astrophysics Data System (ADS)

Chingangbam, Pravabati; Yogendran, K. P.; Joby, P. K.; Ganesan, Vidhya; Appleby, Stephen; Park, Changbom

2017-12-01

We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random field on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh fields. The results hold on flat as well as any curved space with affine connection. We elucidate the way in which the matrix elements encode information about the Gaussian nature and statistical isotropy (or departure from isotropy) of the field. Finally, we apply the method to maps of the Galactic foreground emissions from the 2015 PLANCK data and demonstrate their high level of statistical anisotropy and departure from Gaussianity.

Dielectric permeability tensor and linear waves in spin-1/2 quantum kinetics with non-trivial equilibrium spin-distribution functions

NASA Astrophysics Data System (ADS)

Andreev, Pavel A.; Kuz'menkov, L. S.

2017-11-01

A consideration of waves propagating parallel to the external magnetic field is presented. The dielectric permeability tensor is derived from the quantum kinetic equations with non-trivial equilibrium spin-distribution functions in the linear approximation on the amplitude of wave perturbations. It is possible to consider the equilibrium spin-distribution functions with nonzero z-projection proportional to the difference of the Fermi steps of electrons with the chosen spin direction, while x- and y-projections are equal to zero. It is called the trivial equilibrium spin-distribution functions. In the general case, x- and y-projections of the spin-distribution functions are nonzero which is called the non-trivial regime. A corresponding equilibrium solution is found in Andreev [Phys. Plasmas 23, 062103 (2016)]. The contribution of the nontrivial part of the spin-distribution function appears in the dielectric permeability tensor in the additive form. It is explicitly found here. A corresponding modification in the dispersion equation for the transverse waves is derived. The contribution of the nontrivial part of the spin-distribution function in the spectrum of transverse waves is calculated numerically. It is found that the term caused by the nontrivial part of the spin-distribution function can be comparable with the classic terms for the relatively small wave vectors and frequencies above the cyclotron frequency. In a majority of regimes, the extra spin caused term dominates over the spin term found earlier, except the small frequency regime, where their contributions in the whistler spectrum are comparable. A decrease of the left-hand circularly polarized wave frequency, an increase of the high-frequency right-hand circularly polarized wave frequency, and a decrease of frequency changing by an increase of frequency at the growth of the wave vector for the whistler are found. A considerable decrease of the spin wave frequency is found either. It results in an increase of module of the negative group velocity of the spin wave. The found dispersion equations are used for obtaining of an effective quantum hydrodynamics reproducing these results. This generalization requires the introduction of the corresponding equation of state for the thermal part of the spin current in the spin evolution equation.

Tensor-based dynamic reconstruction method for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Tensor 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.

A fast and robust method for moment tensor and depth determination of shallow seismic events in CTBT related studies.

NASA Astrophysics Data System (ADS)

Baker, Ben; Stachnik, Joshua; Rozhkov, Mikhail

2017-04-01

International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event according to the protocol to the Protocol to the Comprehensive Nuclear Test Ban Treaty. Determination of seismic event source mechanism and its depth is closely related to these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. In this presentation we demonstrate preliminary results obtained with the latter approach from an improved software design. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Posterior distributions of moment tensor parameters show narrow peaks where a significant number of reliable surface wave observations are available. For earthquake examples, fault orientation (strike, dip, and rake) posterior distributions also provide results consistent with published catalogues. Inclusion of observations on horizontal components will provide further constraints. In addition, the calculation of teleseismic P wave Green's Functions are improved through prior analysis to determine an appropriate attenuation parameter for each source-receiver path. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis/AXISEM full waveform synthetics added to a pre-computed GF archive. Along with traditional post processing analysis of waveform misfits through several objective functions and variance reduction, we follow a probabilistic approach to assess the robustness of moment tensor solution. In a course of this project full moment tensor and depth estimates are determined for DPRK events and shallow earthquakes using a new implementation of teleseismic P waves waveform fitting. A full grid search over the entire moment tensor space is used to appropriately sample all possible solutions. A recent method by Tape & Tape (2012) to discretize the complete moment tensor space from a geometric perspective is used. Probabilistic uncertainty estimates on the moment tensor parameters provide robustness to solution.

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

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

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Stuchlík, Zdeněk

2018-05-01

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

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.

Volume in moment tensor space in terms of distance

NASA Astrophysics Data System (ADS)

Tape, Walter; Tape, Carl

2017-07-01

Suppose that we want to assess the extent to which some large collection of moment tensors is concentrated near a fixed moment tensor m. We are naturally led to consider the distribution of the distances of the moment tensors from m. This distribution, however, can only be judged in conjunction with the distribution of distances from m for randomly chosen moment tensors. In cumulative form, the latter distribution is the same as the fractional volume \\hat{V}(ω ) of the set of all moment tensors that are within distance ω of m. This definition of \\hat{V}(ω ) assumes that a reasonable universe {M} of moment tensors has been specified at the outset and that it includes the original collection as a subset. Our main goal in this article is to derive a formula for \\hat{V}(ω ) when {M} is the set [Λ]_{U} of all moment tensors having a specified eigenvalue triple Λ. We find that \\hat{V}(ω ) depends strongly on Λ, and we illustrate the dependence by plotting the derivative curves \\hat{V}^' }(ω ) for various seismologically relevant Λs. The exotic and unguessable shapes of these curves underscores the futility of interpreting the distribution of distances for the original moment tensors without knowing \\hat{V}(ω ) or \\hat{V}^' }(ω ). The derivation of the formula for \\hat{V}(ω ) relies on a certain ϕ σz coordinate system for [Λ]_{U}, which we treat in detail. Our underlying motivation for the paper is the estimation of uncertainties in moment tensor inversion.

Global QCD Analysis of the Nucleon Tensor Charge with Lattice QCD Constraints

NASA Astrophysics Data System (ADS)

Shows, Harvey, III; Melnitchouk, Wally; Sato, Nobuo

2017-09-01

By studying the parton distribution functions (PDFs) of a nucleon, we probe the partonic scale of nature, exploring what it means to be a nucleon. In this study, we are interested in the transversity PDF-the least studied of the three collinear PDFs. By conducting a global analysis on experimental data from semi-inclusive deep inelastic scattering (SIDIS), as well as single-inclusive e+e- annihilation (SIA), we extract the fit parameters needed to describe the transverse moment dependent (TMD) transversity PDF, as well as the Collins fragmentation function. Once the collinear transversity PDF is obtained by integrating the extracted TMD PDF, we wish to resolve discrepancies between lattice QCD calculations and phenomenological extractions of the tensor charge from data. Here we show our results for the transversity distribution and tensor charge. Using our method of iterative Monte Carlo, we now have a more robust understanding of the transversity PDF. With these results we are able to progress in our understanding of TMD PDFs, as well as testify to the efficacy of current lattice QCD calculations. This work is made possible through support from NSF award 1659177 to Old Dominion University.

Extended Czjzek model applied to NMR parameter distributions in sodium metaphosphate glass

NASA Astrophysics Data System (ADS)

Vasconcelos, Filipe; Cristol, Sylvain; Paul, Jean-François; Delevoye, Laurent; Mauri, Francesco; Charpentier, Thibault; Le Caër, Gérard

2013-06-01

The extended Czjzek model (ECM) is applied to the distribution of NMR parameters of a simple glass model (sodium metaphosphate, NaPO3) obtained by molecular dynamics (MD) simulations. Accurate NMR tensors, electric field gradient (EFG) and chemical shift anisotropy (CSA) are calculated from density functional theory (DFT) within the well-established PAW/GIPAW framework. The theoretical results are compared to experimental high-resolution solid-state NMR data and are used to validate the considered structural model. The distributions of the calculated coupling constant CQ ∝ |Vzz| and the asymmetry parameter ηQ that characterize the quadrupolar interaction are discussed in terms of structural considerations with the help of a simple point charge model. Finally, the ECM analysis is shown to be relevant for studying the distribution of CSA tensor parameters and gives new insight into the structural characterization of disordered systems by solid-state NMR.

Extended Czjzek model applied to NMR parameter distributions in sodium metaphosphate glass.

PubMed

Vasconcelos, Filipe; Cristol, Sylvain; Paul, Jean-François; Delevoye, Laurent; Mauri, Francesco; Charpentier, Thibault; Le Caër, Gérard

2013-06-26

The extended Czjzek model (ECM) is applied to the distribution of NMR parameters of a simple glass model (sodium metaphosphate, NaPO3) obtained by molecular dynamics (MD) simulations. Accurate NMR tensors, electric field gradient (EFG) and chemical shift anisotropy (CSA) are calculated from density functional theory (DFT) within the well-established PAW/GIPAW framework. The theoretical results are compared to experimental high-resolution solid-state NMR data and are used to validate the considered structural model. The distributions of the calculated coupling constant C(Q) is proportional to |V(zz)| and the asymmetry parameter η(Q) that characterize the quadrupolar interaction are discussed in terms of structural considerations with the help of a simple point charge model. Finally, the ECM analysis is shown to be relevant for studying the distribution of CSA tensor parameters and gives new insight into the structural characterization of disordered systems by solid-state NMR.

Pseudoscalar Meson Electroproduction and Transversity

NASA Astrophysics Data System (ADS)

Goldstein, Gary R.; Liuti, Simonetta

2011-02-01

Exclusive meson leptoproduction from nucleons in the deeply virtual exchanged boson limit can be described by generalized parton distributions (GPDs). Including spin dependence in the description requires 8 independent quark-parton and gluon-parton functions. The chiral even subset of 4 quark-nucleon GPDs are related to nucleon form factors and to parton distribution functions. The chiral odd set of 4 quark-nucleon GPDs are related to transversity, the tensor charge, and other quantities related to transversity. Different meson or photon production processes access different combinations of GPDs. This is analyzed in terms of t-channel exchange quantum numbers, JPC and it is shown that pseudoscalar production can isolate chiral odd GPDs. There is a sensitive dependence in various cross sections and asymmetries on the tensor charge of the nucleon and other transversity parameters. In a second section, analyticity and completeness are shown to limit the partonic interpret ation of the GPDs in the ERBL region.

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.

Evolution of axis ratios from phase space dynamics of triaxial collapse

NASA Astrophysics Data System (ADS)

Nadkarni-Ghosh, Sharvari; Arya, Bhaskar

2018-04-01

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

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

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

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Dispersion characteristics of anisotropic unmagnetized ultra-relativistic transverse plasma wave with arbitrary electron degeneracy

NASA Astrophysics Data System (ADS)

Sarfraz, M.; Farooq, H.; Abbas, G.; Noureen, S.; Iqbal, Z.; Rasheed, A.

2018-03-01

Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (T/e TF e ≈1 ) comprising arbitrary electron degeneracy, where Te and TF e, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.

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).

Geometric multiaxial representation of N -qubit mixed symmetric separable states

NASA Astrophysics Data System (ADS)

SP, Suma; Sirsi, Swarnamala; Hegde, Subramanya; Bharath, Karthik

2017-08-01

The study of N -qubit mixed symmetric separable states is a longstanding challenging problem as no unique separability criterion exists. In this regard, we take up the N -qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer an elegant mathematical analysis since the dimension of the Hilbert space is reduced from 2N to N +1 . Since there exists a one-to-one correspondence between the spin-j system and an N -qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of the spin-density matrix. Further, we use a geometric multiaxial representation (MAR) of the density matrix to characterize the mixed symmetric separable states. Since the separability problem is NP-hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P -distribution function λ (θ ,ϕ ) . We show that the N -qubit mixed symmetric separable states can be visualized as a uniaxial system if the distribution function is independent of θ and ϕ . We further choose a distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N -qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two-qubit mixed symmetric separable state. We also observe that there exists a correspondence between the separability and classicality of states.

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

NASA Astrophysics Data System (ADS)

Wang, Xin; Szalay, Alex

2016-03-01

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

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

Wang, Xin; Szalay, Alex, E-mail: xwang@cita.utoronto.ca

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differentialmore » equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.« less

3D glasma initial state for relativistic heavy ion collisions

DOE PAGES

Schenke, Björn; Schlichting, Sören

2016-10-13

We extend the impact-parameter-dependent Glasma model to three dimensions using explicit small-x evolution of the two incoming nuclear gluon distributions. We compute rapidity distributions of produced gluons and the early-time energy momentum tensor as a function of space-time rapidity and transverse coordinates. Finally, we study rapidity correlations and fluctuations of the initial geometry and multiplicity distributions and make comparisons to existing models for the three-dimensional initial state.

Monitoring the refinement of crystal structures with {sup 15}N solid-state NMR shift tensor data

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

Kalakewich, Keyton; Eloranta, Harriet; Harper, James K.

The {sup 15}N chemical shift tensor is shown to be extremely sensitive to lattice structure and a powerful metric for monitoring density functional theory refinements of crystal structures. These refinements include lattice effects and are applied here to five crystal structures. All structures improve based on a better agreement between experimental and calculated {sup 15}N tensors, with an average improvement of 47.0 ppm. Structural improvement is further indicated by a decrease in forces on the atoms by 2–3 orders of magnitude and a greater similarity in atom positions to neutron diffraction structures. These refinements change bond lengths by more thanmore » the diffraction errors including adjustments to X–Y and X–H bonds (X, Y = C, N, and O) of 0.028 ± 0.002 Å and 0.144 ± 0.036 Å, respectively. The acquisition of {sup 15}N tensors at natural abundance is challenging and this limitation is overcome by improved {sup 1}H decoupling in the FIREMAT method. This decoupling dramatically narrows linewidths, improves signal-to-noise by up to 317%, and significantly improves the accuracy of measured tensors. A total of 39 tensors are measured with shifts distributed over a range of more than 400 ppm. Overall, experimental {sup 15}N tensors are at least 5 times more sensitive to crystal structure than {sup 13}C tensors due to nitrogen’s greater polarizability and larger range of chemical shifts.« less

Spatially Resolved Measurement of the Stress Tensor in Thin Membranes Using Bending Waves

NASA Astrophysics Data System (ADS)

Waitz, Reimar; Lutz, Carolin; Nößner, Stephan; Hertkorn, Michael; Scheer, Elke

2015-04-01

The mode shape of bending waves in thin silicon and silicon-carbide membranes is measured as a function of space and time, using a phase-shift interferometer with stroboscopic light. The mode shapes hold information about all the relevant mechanical parameters of the samples, including the spatial distribution of static prestress. We present a simple algorithm to obtain a map of the lateral tensor components of the prestress, with a spatial resolution much better than the wavelength of the bending waves. The method is not limited to measuring the stress of bending waves. It is applicable in almost any situation, where the fields determining the state of the system can be measured as a function of space and time.

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

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

Levashov, V. A.

2016-03-07

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

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

PubMed

Levashov, V A

2016-03-07

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

One-loop gravitational wave spectrum in de Sitter spacetime

NASA Astrophysics Data System (ADS)

Fröb, Markus B.; Roura, Albert; Verdaguer, Enric

2012-08-01

The two-point function for tensor metric perturbations around de Sitter spacetime including one-loop corrections from massless conformally coupled scalar fields is calculated exactly. We work in the Poincaré patch (with spatially flat sections) and employ dimensional regularization for the renormalization process. Unlike previous studies we obtain the result for arbitrary time separations rather than just equal times. Moreover, in contrast to existing results for tensor perturbations, ours is manifestly invariant with respect to the subgroup of de Sitter isometries corresponding to a simultaneous time translation and rescaling of the spatial coordinates. Having selected the right initial state for the interacting theory via an appropriate iepsilon prescription is crucial for that. Finally, we show that although the two-point function is a well-defined spacetime distribution, the equal-time limit of its spatial Fourier transform is divergent. Therefore, contrary to the well-defined distribution for arbitrary time separations, the power spectrum is strictly speaking ill-defined when loop corrections are included.

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

Jensen, Jens H; Helpern, Joseph A; Tabesh, Ali

2014-02-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. 2013 John Wiley & Sons, Ltd.

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

Jensen, Jens H.; Helpern, Joseph A.; Tabesh, Ali

2014-01-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed out of the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves upon the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. PMID:24738143

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

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

Modeling the evolution of lithium-ion particle contact distributions using a fabric tensor approach

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

Stershic, A. J.; Simunovic, S.; Nanda, J.

2015-08-25

Electrode microstructure and processing can strongly influence lithium-ion battery performance such as capacity retention, power, and rate. Battery electrodes are multi-phase composite structures wherein conductive diluents and binder bond active material to a current collector. The structure and response of this composite network during repeated electrochemical cycling directly affects battery performance characteristics. We propose the fabric tensor formalism for describing the structure and evolution of the electrode microstructure. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Fabric tensor analysis is applied to experimental data-sets for positivemore » electrode made of lithium nickel manganese cobalt oxide, captured by X-ray tomography for several compositions and consolidation pressures. We show that fabric tensors capture the evolution of inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode. The fabric tensor analysis is also applied to Discrete Element Method (DEM) simulations of electrode microstructures using spherical particles with size distributions from the tomography. Furthermore, these results do not follow the experimental trends, which indicates that the particle size distribution alone is not a sufficient measure for the electrode microstructures in DEM simulations.« less

Revisiting ignited-quenched transition and the non-Newtonian rheology of a sheared dilute gas-solid suspension

NASA Astrophysics Data System (ADS)

Saha, Saikat; Alam, Meheboob

2017-12-01

The hydrodynamics and rheology of a sheared dilute gas-solid suspension, consisting of inelastic hard-spheres suspended in a gas, are analysed using anisotropic Maxwellian as the single particle distribution function. The closed-form solutions for granular temperature and three invariants of the second-moment tensor are obtained as functions of the Stokes number ($St$), the mean density ($\

An Integrated Tensorial Approach for Quantifying Porous, Fractured Rocks

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Director Field Analysis (DFA): Exploring Local White Matter Geometric Structure in Diffusion MRI.

PubMed

Cheng, Jian; Basser, Peter J

2018-01-01

In Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI), a tensor field or a spherical function field (e.g., an orientation distribution function field), can be estimated from measured diffusion weighted images. In this paper, inspired by the microscopic theoretical treatment of phases in liquid crystals, we introduce a novel mathematical framework, called Director Field Analysis (DFA), to study local geometric structural information of white matter based on the reconstructed tensor field or spherical function field: (1) We propose a set of mathematical tools to process general director data, which consists of dyadic tensors that have orientations but no direction. (2) We propose Orientational Order (OO) and Orientational Dispersion (OD) indices to describe the degree of alignment and dispersion of a spherical function in a single voxel or in a region, respectively; (3) We also show how to construct a local orthogonal coordinate frame in each voxel exhibiting anisotropic diffusion; (4) Finally, we define three indices to describe three types of orientational distortion (splay, bend, and twist) in a local spatial neighborhood, and a total distortion index to describe distortions of all three types. To our knowledge, this is the first work to quantitatively describe orientational distortion (splay, bend, and twist) in general spherical function fields from DTI or HARDI data. The proposed DFA and its related mathematical tools can be used to process not only diffusion MRI data but also general director field data, and the proposed scalar indices are useful for detecting local geometric changes of white matter for voxel-based or tract-based analysis in both DTI and HARDI acquisitions. The related codes and a tutorial for DFA will be released in DMRITool. Copyright © 2017 Elsevier B.V. All rights reserved.

Cerebral White Matter Integrity and Cognitive Aging: Contributions from Diffusion Tensor Imaging

PubMed Central

Madden, David J.; Bennett, Ilana J.; Song, Allen W.

2009-01-01

The integrity of cerebral white matter is critical for efficient cognitive functioning, but little is known regarding the role of white matter integrity in age-related differences in cognition. Diffusion tensor imaging (DTI) measures the directional displacement of molecular water and as a result can characterize the properties of white matter that combine to restrict diffusivity in a spatially coherent manner. This review considers DTI studies of aging and their implications for understanding adult age differences in cognitive performance. Decline in white matter integrity contributes to a disconnection among distributed neural systems, with a consistent effect on perceptual speed and executive functioning. The relation between white matter integrity and cognition varies across brain regions, with some evidence suggesting that age-related effects exhibit an anterior-posterior gradient. With continued improvements in spatial resolution and integration with functional brain imaging, DTI holds considerable promise, both for theories of cognitive aging and for translational application. PMID:19705281

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.

Spinors: A Mathematica package for doing spinor calculus in General Relativity

NASA Astrophysics Data System (ADS)

Gómez-Lobo, Alfonso García-Parrado; Martín-García, José M.

2012-10-01

The Spinors software is a Mathematica package which implements 2-component spinor calculus as devised by Penrose for General Relativity in dimension 3+1. The Spinors software is part of the xAct system, which is a collection of Mathematica packages to do tensor analysis by computer. In this paper we give a thorough description of Spinors and present practical examples of use. Program summary Program title: Spinors Catalogue identifier: AEMQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 117039 No. of bytes in distributed program, including test data, etc.: 300404 Distribution format: tar.gz Programming language: Mathematica. Computer: Any computer running Mathematica 7.0 or higher. Operating system: Any operating system compatible with Mathematica 7.0 or higher. RAM: 94Mb in Mathematica 8.0. Classification: 1.5. External routines: Mathematica packages xCore, xPerm and xTensor which are part of the xAct system. These can be obtained at http://www.xact.es. Nature of problem: Manipulation and simplification of spinor expressions in General Relativity. Solution method: Adaptation of the tensor functionality of the xAct system for the specific situation of spinor calculus in four dimensional Lorentzian geometry. Restrictions: The software only works on 4-dimensional Lorentzian space-times with metric of signature (1, -1, -1, -1). There is no direct support for Dirac spinors. Unusual features: Easy rules to transform tensor expressions into spinor ones and back. Seamless integration of abstract index manipulation of spinor expressions with component computations. Running time: Under one second to handle and canonicalize standard spinorial expressions with a few dozen indices. (These expressions arise naturally in the transformation of a spinor expression into a tensor one or vice versa.)

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images

ERIC Educational Resources Information Center

Barmpoutis, Angelos

2009-01-01

Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…

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

Decentralized Dimensionality Reduction for Distributed Tensor Data Across Sensor Networks.

PubMed

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

2016-11-01

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

Gradients estimation from random points with volumetric tensor in turbulence

NASA Astrophysics Data System (ADS)

Watanabe, Tomoaki; Nagata, Koji

2017-12-01

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

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

The light-front gauge-invariant energy-momentum tensor

DOE PAGES

Lorce, Cedric

2015-08-11

In this study, we provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor, generalizing therefore former works on the symmetric, local and gauge-invariant kinetic energy-momentum tensor also known as the Belinfante-Rosenfeld energy-momentum tensor. We discuss in detail the various constraints imposed by non-locality, linear and angular momentum conservation. We also derive the relations with two-parton generalized and transverse-momentum dependent distributions, clarifying what can be learned from the latter. In particular, we show explicitly that two-parton transverse-momentum dependent distributions cannot provide any model-independent information about the parton orbitalmore » angular momentum. On the way, we recover the Burkardt sum rule and obtain similar new sum rules for higher-twist distributions.« less

Strain distribution and band structure of InAs/GaAs quantum ring superlattice

NASA Astrophysics Data System (ADS)

Mughnetsyan, Vram; Kirakosyan, Albert

2017-12-01

The elastic strain distribution and the band structure of InAs/GaAs one-layer quantum ring superlattice with square symmetry has been considered in this work. The Green's function formalism based on the method of inclusions has been implied to calculate the components of the strain tensor, while the combination of Green's function method with the Fourier transformation to momentum space in Pikus-Bir Hamiltonian has been used for obtaining the miniband energy dispersion surfaces via the exact diagonalization procedure. The dependencies of the strain tensor components on spatial coordinates are compared with ones for single quantum ring and are in good agreement with previously obtained results for cylindrical quantum disks. It is shown that strain significantly affects the miniband structure of the superlattice and has contribution to the degeneracy lifting effect due to heavy hole-light hole coupling. The demonstrated method is simple and provides reasonable results for comparatively small Hamiltonian matrix. The obtained results may be useful for further investigation and construction of novel devices based on quantum ring superlattices.

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

NASA Astrophysics Data System (ADS)

Hashlamoun, Kotaybah; Grillo, Alfio; Federico, Salvatore

2016-10-01

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

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.

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

Statistics of the detection rates for tensor and scalar gravitational waves from the Local Galaxy universe

NASA Astrophysics Data System (ADS)

Baryshev, Yu. V.; Paturel, G.

2001-05-01

We use data on the local 3-dimensional galaxy distribution for studying the statistics of the detection rates of gravitational waves (GW) coming from supernova explosions. We consider both tensor and scalar gravitational waves which are possible in a wide range of relativistic and quantum gravity theories. We show that statistics of GW events as a function of sidereal time can be used for distinction between scalar and tensor gravitational waves because of the anisotropy of spatial galaxy distribution. For calculation of the expected amplitudes of GW signals we use the values of the released GW energy, frequency and duration of GW pulse which are consistent with existing scenarios of SN core collapse. The amplitudes of the signals produced by Virgo and the Great Attractor clusters of galaxies is expressed as a function of the sidereal time for resonant bar detectors operating now (IGEC) and for forthcoming laser interferometric detectors (VIRGO). Then, we calculate the expected number of GW events as a function of sidereal time produced by all the galaxies within 100 Mpc. In the case of axisymmetric rotational core collapse which radiates a GW energy of 10-9Msunc2, only the closest explosions can be detected. However, in the case of nonaxisymmetric supernova explosion, due to such phenomena as centrifugal hangup, bar and lump formation, the GW radiation could be as strong as that from a coalescing neutron-star binary. For radiated GW energy higher than 10-6Msunc2 and sensitivity of detectors at the level h ~ 10-23 it is possible to detect Virgo cluster and Great Attractor, and hence to use the statistics of GW events for testing gravity theories.

Experimental evaluation of electrical conductivity imaging of anisotropic brain tissues using a combination of diffusion tensor imaging and magnetic resonance electrical impedance tomography

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

Sajib, Saurav Z. K.; Jeong, Woo Chul; Oh, Tong In

Anisotropy of biological tissues is a low-frequency phenomenon that is associated with the function and structure of cell membranes. Imaging of anisotropic conductivity has potential for the analysis of interactions between electromagnetic fields and biological systems, such as the prediction of current pathways in electrical stimulation therapy. To improve application to the clinical environment, precise approaches are required to understand the exact responses inside the human body subjected to the stimulated currents. In this study, we experimentally evaluate the anisotropic conductivity tensor distribution of canine brain tissues, using a recently developed diffusion tensor-magnetic resonance electrical impedance tomography method. At lowmore » frequency, electrical conductivity of the biological tissues can be expressed as a product of the mobility and concentration of ions in the extracellular space. From diffusion tensor images of the brain, we can obtain directional information on diffusive movements of water molecules, which correspond to the mobility of ions. The position dependent scale factor, which provides information on ion concentration, was successfully calculated from the magnetic flux density, to obtain the equivalent conductivity tensor. By combining the information from both techniques, we can finally reconstruct the anisotropic conductivity tensor images of brain tissues. The reconstructed conductivity images better demonstrate the enhanced signal intensity in strongly anisotropic brain regions, compared with those resulting from previous methods using a global scale factor.« less

Analytic non-Maxwellian electron velocity distribution function in a Hall discharge plasma

NASA Astrophysics Data System (ADS)

Shagayda, Andrey; Tarasov, Alexey

2017-10-01

The electron velocity distribution function in the low-pressure discharges with the crossed electric and magnetic fields, which occur in magnetrons, plasma accelerators, and Hall thrusters with a closed electron drift, is not Maxwellian. A deviation from equilibrium is caused by a large electron mean free path relative to the Larmor radius and the size of the discharge channel. In this study, we derived in the relaxation approximation the analytical expression of the electron velocity distribution function in a weakly ionized Lorentz plasma with the crossed electric and magnetic fields in the presence of the electron density and temperature gradients in the direction of the electric field. The solution was obtained in the stationary approximation far from boundary surfaces, when diffusion and mobility are determined by the classical effective collision frequency of electrons with ions and atoms. The moments of the distribution function including the average velocity, the stress tensor, and the heat flux were calculated and compared with the classical hydrodynamic expressions. It was shown that a kinetic correction to the drift velocity stems from a contribution of the off-diagonal component of the stress tensor. This correction becomes essential if the drift velocity in the crossed electric and magnetic fields would be comparable to the thermal velocity of electrons. The electron temperature has three different components at a nonzero effective collision frequency and two different components in the limit when the collision frequency tends to zero. It is shown that, in the presence of ionization collisions, the components of the heat flux have additives that are not related to the temperature gradient, and arise because of the electron drift.

The Invar tensor package: Differential invariants of Riemann

NASA Astrophysics Data System (ADS)

Martín-García, J. M.; Yllanes, D.; Portugal, R.

2008-10-01

The long standing problem of the relations among the scalar invariants of the Riemann tensor is computationally solved for all 6ṡ10 objects with up to 12 derivatives of the metric. This covers cases ranging from products of up to 6 undifferentiated Riemann tensors to cases with up to 10 covariant derivatives of a single Riemann. We extend our computer algebra system Invar to produce within seconds a canonical form for any of those objects in terms of a basis. The process is as follows: (1) an invariant is converted in real time into a canonical form with respect to the permutation symmetries of the Riemann tensor; (2) Invar reads a database of more than 6ṡ10 relations and applies those coming from the cyclic symmetry of the Riemann tensor; (3) then applies the relations coming from the Bianchi identity, (4) the relations coming from commutations of covariant derivatives, (5) the dimensionally-dependent identities for dimension 4, and finally (6) simplifies invariants that can be expressed as product of dual invariants. Invar runs on top of the tensor computer algebra systems xTensor (for Mathematica) and Canon (for Maple). Program summaryProgram title:Invar Tensor Package v2.0 Catalogue identifier:ADZK_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_v2_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:3 243 249 No. of bytes in distributed program, including test data, etc.:939 Distribution format:tar.gz Programming language:Mathematica and Maple Computer:Any computer running Mathematica versions 5.0 to 6.0 or Maple versions 9 and 11 Operating system:Linux, Unix, Windows XP, MacOS RAM:100 Mb Word size:64 or 32 bits Supplementary material:The new database of relations is much larger than that for the previous version and therefore has not been included in the distribution. To obtain the Mathematica and Maple database files click on this link. Classification:1.5, 5 Does the new version supersede the previous version?:Yes. The previous version (1.0) only handled algebraic invariants. The current version (2.0) has been extended to cover differential invariants as well. Nature of problem:Manipulation and simplification of scalar polynomial expressions formed from the Riemann tensor and its covariant derivatives. Solution method:Algorithms of computational group theory to simplify expressions with tensors that obey permutation symmetries. Tables of syzygies of the scalar invariants of the Riemann tensor. Reasons for new version:With this new version, the user can manipulate differential invariants of the Riemann tensor. Differential invariants are required in many physical problems in classical and quantum gravity. Summary of revisions:The database of syzygies has been expanded by a factor of 30. New commands were added in order to deal with the enlarged database and to manipulate the covariant derivative. Restrictions:The present version only handles scalars, and not expressions with free indices. Additional comments:The distribution file for this program is over 53 Mbytes and therefore is not delivered directly when download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. Running time:One second to fully reduce any monomial of the Riemann tensor up to degree 7 or order 10 in terms of independent invariants. The Mathematica notebook included in the distribution takes approximately 5 minutes to run.

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.

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).

Elastic field of a spherical inclusion with non-uniform eigenfields in second strain gradient elasticity

NASA Astrophysics Data System (ADS)

Delfani, M. R.; Latifi Shahandashti, M.

2017-09-01

In this paper, within the complete form of Mindlin's second strain gradient theory, the elastic field of an isolated spherical inclusion embedded in an infinitely extended homogeneous isotropic medium due to a non-uniform distribution of eigenfields is determined. These eigenfields, in addition to eigenstrain, comprise eigen double and eigen triple strains. After the derivation of a closed-form expression for Green's function associated with the problem, two different cases of non-uniform distribution of the eigenfields are considered as follows: (i) radial distribution, i.e. the distributions of the eigenfields are functions of only the radial distance of points from the centre of inclusion, and (ii) polynomial distribution, i.e. the distributions of the eigenfields are polynomial functions in the Cartesian coordinates of points. While the obtained solution for the elastic field of the latter case takes the form of an infinite series, the solution to the former case is represented in a closed form. Moreover, Eshelby's tensors associated with the two mentioned cases are obtained.

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

PubMed

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

2013-08-07

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

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.

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.

Electrical impedance tomography in anisotropic media with known eigenvectors

NASA Astrophysics Data System (ADS)

Abascal, Juan-Felipe P. J.; Lionheart, William R. B.; Arridge, Simon R.; Schweiger, Martin; Atkinson, David; Holder, David S.

2011-06-01

Electrical impedance tomography is an imaging method, with which volumetric images of conductivity are produced by injecting electrical current and measuring boundary voltages. It has the potential to become a portable non-invasive medical imaging technique. Until now, most implementations have neglected anisotropy even though human tissues like bone, muscle and brain white matter are markedly anisotropic. The recovery of an anisotropic conductivity tensor is uniquely determined by boundary measurements only up to a diffeomorphism that fixes the boundary. Nevertheless, uniqueness can be restored by providing information about the diffeomorphism. There are uniqueness results for two constraints: one eigenvalue and a multiple scalar of a general tensor. A useable constraint for medical applications is when the eigenvectors of the underlying tissue are known, which can be approximated from MRI or estimated from DT-MRI, although the eigenvalues are unknown. However there is no known theoretical result guaranteeing uniqueness for this constraint. In fact, only a few previous inversion studies have attempted to recover one or more eigenvalues assuming certain symmetries while ignoring nonuniqueness. In this work, the aim was to undertake a numerical study of the feasibility of the recovery of a piecewise linear finite element conductivity tensor in anisotropic media with known eigenvectors from the complete boundary data. The work suggests that uniqueness holds for this constraint, in addition to proposing a methodology for the incorporation of this prior for general conductivity tensors. This was carried out by performing an analysis of the Jacobian rank and by reconstructing four conductivity distributions: two diagonal tensors whose eigenvalues were linear and sinusoidal functions, and two general tensors whose eigenvectors resembled physiological tissue, one with eigenvectors spherically orientated like a spherical layered structure, and a sample of DT-MRI data of brain white matter. The Jacobian with respect to three eigenvalues was full-rank and it was possible to recover three eigenvalues for the four simulated distributions. This encourages further theoretical study of the uniqueness for this constraint and supports the use of this as a relevant usable method for medical applications.

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.

Differential invariants and exact solutions of the Einstein equations

NASA Astrophysics Data System (ADS)

Lychagin, Valentin; Yumaguzhin, Valeriy

2017-06-01

In this paper (cf. Lychagin and Yumaguzhin, in Anal Math Phys, 2016) a class of totally geodesics solutions for the vacuum Einstein equations is introduced. It consists of Einstein metrics of signature (1,3) such that 2-dimensional distributions, defined by the Weyl tensor, are completely integrable and totally geodesic. The complete and explicit description of metrics from these class is given. It is shown that these metrics depend on two functions in one variable and one harmonic function.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2006-01-01

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

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

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.

Finite temperature behavior of the CPT-even and parity-even electrodynamics of the standard model extension

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

Casana, Rodolfo; Ferreira, Manoel M. Jr; Rodrigues, Josberg S.

2009-10-15

In this work, we examine the finite temperature properties of the CPT-even and Lorentz-invariance-violating (LIV) electrodynamics of the standard model extension, represented by the term W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}F{sup {alpha}}{sup {nu}}F{sup {rho}}{sup {phi}}. We begin analyzing the Hamiltonian structure following the Dirac's procedure for constrained systems and construct a well-defined and gauge invariant partition function in the functional integral formalism. Next, we specialize for the nonbirefringent coefficients of the tensor W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}. In the sequel, the partition function is explicitly carried out for the parity-even sector of the tensor W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}. The modifiedmore » partition function is a power of the Maxwell's partition function. It is observed that the LIV coefficients induce an anisotropy in the black body angular energy density distribution. The Planck's radiation law, however, retains its frequency dependence and the Stefan-Boltzmann law keeps the usual form, except for a change in the Stefan-Boltzmann constant by a factor containing the LIV contributions.« less

Crossing Fibers Detection with an Analytical High Order Tensor Decomposition

PubMed Central

Megherbi, T.; Kachouane, M.; Oulebsir-Boumghar, F.; Deriche, R.

2014-01-01

Diffusion magnetic resonance imaging (dMRI) is the only technique to probe in vivo and noninvasively the fiber structure of human brain white matter. Detecting the crossing of neuronal fibers remains an exciting challenge with an important impact in tractography. In this work, we tackle this challenging problem and propose an original and efficient technique to extract all crossing fibers from diffusion signals. To this end, we start by estimating, from the dMRI signal, the so-called Cartesian tensor fiber orientation distribution (CT-FOD) function, whose maxima correspond exactly to the orientations of the fibers. The fourth order symmetric positive definite tensor that represents the CT-FOD is then analytically decomposed via the application of a new theoretical approach and this decomposition is used to accurately extract all the fibers orientations. Our proposed high order tensor decomposition based approach is minimal and allows recovering the whole crossing fibers without any a priori information on the total number of fibers. Various experiments performed on noisy synthetic data, on phantom diffusion, data and on human brain data validate our approach and clearly demonstrate that it is efficient, robust to noise and performs favorably in terms of angular resolution and accuracy when compared to some classical and state-of-the-art approaches. PMID:25246940

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.

Anisotropy and phonon modes from analysis of the dielectric function tensor and the inverse dielectric function tensor of monoclinic yttrium orthosilicate

NASA Astrophysics Data System (ADS)

Mock, A.; Korlacki, R.; Knight, S.; Schubert, M.

2018-04-01

We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y2SiO5 using generalized spectroscopic ellipsometry from 40-1200 cm-1. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017), 10.1103/PhysRevB.95.165202], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain an excellent match between all measured and model-calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 Au and 22 Bu symmetry long-wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 Au symmetry and 22 Bu transverse and longitudinal optical mode parameters and their orientation within the monoclinic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys Rev. Lett. 117, 215502 (2016), 10.1103/PhysRevLett.117.215502].

Tensor Algebra Library for NVidia Graphics Processing Units

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

Liakh, Dmitry

This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion of the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor operation are assumed to be stored in local RAMmore » of a node or GPU RAM. The main research area where this library can be utilized is the quantum many-body theory (e.g., in electronic structure theory).« less

Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

DOE PAGES

Gorelenkov, Nikolai N.; Zakharov, Leonid E.

2018-04-27

Here, we formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed spacial dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Consideredmore » effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem.« less

Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

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

Gorelenkov, Nikolai N.; Zakharov, Leonid E.

Here, we formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed spacial dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Consideredmore » effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem.« less

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).

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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.

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

DOE PAGES

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

2015-05-18

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

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

Tensor modes on the string theory landscape

NASA Astrophysics Data System (ADS)

Westphal, Alexander

2013-04-01

We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.

Electromagnetic van Kampen waves

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

Ignatov, A. M., E-mail: aign@fpl.gpi.ru

2017-01-15

The theory of van Kampen waves in plasma with an arbitrary anisotropic distribution function is developed. The obtained solutions are explicitly expressed in terms of the permittivity tensor. There are three types of perturbations, one of which is characterized by the frequency dependence on the wave vector, while for the other two, the dispersion relation is lacking. Solutions to the conjugate equations allowing one to solve the initial value problem are analyzed.

Mechanical behaviour of the human atria.

PubMed

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

2013-07-01

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

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

PubMed Central

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

2009-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

Tensor-driven extraction of developmental features from varying paediatric EEG datasets.

PubMed

Kinney-Lang, Eli; Spyrou, Loukianos; Ebied, Ahmed; Chin, Richard Fm; Escudero, Javier

2018-05-21

Constant changes in developing children's brains can pose a challenge in EEG dependant technologies. Advancing signal processing methods to identify developmental differences in paediatric populations could help improve function and usability of such technologies. Taking advantage of the multi-dimensional structure of EEG data through tensor analysis may offer a framework for extracting relevant developmental features of paediatric datasets. A proof of concept is demonstrated through identifying latent developmental features in resting-state EEG. Approach. Three paediatric datasets (n = 50, 17, 44) were analyzed using a two-step constrained parallel factor (PARAFAC) tensor decomposition. Subject age was used as a proxy measure of development. Classification used support vector machines (SVM) to test if PARAFAC identified features could predict subject age. The results were cross-validated within each dataset. Classification analysis was complemented by visualization of the high-dimensional feature structures using t-distributed Stochastic Neighbour Embedding (t-SNE) maps. Main Results. Development-related features were successfully identified for the developmental conditions of each dataset. SVM classification showed the identified features could accurately predict subject at a significant level above chance for both healthy and impaired populations. t-SNE maps revealed suitable tensor factorization was key in extracting the developmental features. Significance. The described methods are a promising tool for identifying latent developmental features occurring throughout childhood EEG. © 2018 IOP Publishing Ltd.

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

NASA Astrophysics Data System (ADS)

Alvizuri, Celso R.

We present a catalog of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broadband stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the six-dimensional space of moment tensors. For each event we show the misfit function in eigenvalue space, represented by a lune. We identify three subsets of the catalog: (1) 6 isotropic events, (2) 5 tensional crack events, and (3) a swarm of 14 events southeast of the volcanic center that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model. Proper characterization of uncertainties for full moment tensors is critical for distinguishing among physical models of source processes. A seismic moment tensor is a 3x3 symmetric matrix that provides a compact representation of a seismic source. We develop an algorithm to estimate moment tensors and their uncertainties from observed seismic data. For a given event, the algorithm performs a grid search over the six-dimensional space of moment tensors by generating synthetic waveforms for each moment tensor and then evaluating a misfit function between the observed and synthetic waveforms. 'The' moment tensor M0 for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M0, we first convert the misfit function to a probability function. The uncertainty, or rather the confidence, is then given by the 'confidence curve' P( V), where P(V) is the probability that the true moment tensor for the event lies within the neighborhood of M that has fractional volume V. The area under the confidence curve provides a single, abbreviated 'confidence parameter' for M0. We apply the method to data from events in different regions and tectonic settings: 63 small (M w 4) earthquakes in the southern Alaska subduction zone, and 12 earthquakes and 17 nuclear explosions at the Nevada Test Site. Characterization of moment tensor uncertainties puts us in better position to discriminate among moment tensor source types and to assign physical processes to the events.

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

McCaskey, Alexander J.

There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.

A Riemannian framework for orientation distribution function computing.

PubMed

Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid

2009-01-01

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy H1/2 of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation.

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

PubMed

Greene, Samuel M; Batista, Victor S

2017-09-12

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

A 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.

Efficient calculation of nuclear spin-rotation constants from auxiliary density functional theory.

PubMed

Zuniga-Gutierrez, Bernardo; Camacho-Gonzalez, Monica; Bendana-Castillo, Alfonso; Simon-Bastida, Patricia; Calaminici, Patrizia; Köster, Andreas M

2015-09-14

The computation of the spin-rotation tensor within the framework of auxiliary density functional theory (ADFT) in combination with the gauge including atomic orbital (GIAO) scheme, to treat the gauge origin problem, is presented. For the spin-rotation tensor, the calculation of the magnetic shielding tensor represents the most demanding computational task. Employing the ADFT-GIAO methodology, the central processing unit time for the magnetic shielding tensor calculation can be dramatically reduced. In this work, the quality of spin-rotation constants obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-cluster level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good and very similar to the ones obtained by the coupled-cluster single-doubles-perturbative triples-GIAO methodology. With the improved computational performance achieved, the computation of the spin-rotation tensors of large systems or along Born-Oppenheimer molecular dynamics trajectories becomes feasible in reasonable times. Three models of carbon fullerenes containing hundreds of atoms and thousands of basis functions are used for benchmarking the performance. Furthermore, a theoretical study of temperature effects on the structure and spin-rotation tensor of the H(12)C-(12)CH-DF complex is presented. Here, the temperature dependency of the spin-rotation tensor of the fluorine nucleus can be used to identify experimentally the so far unknown bent isomer of this complex. To the best of our knowledge this is the first time that temperature effects on the spin-rotation tensor are investigated.

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

PubMed

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

2009-12-21

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

Second-order Boltzmann equation: gauge dependence and gauge invariance

NASA Astrophysics Data System (ADS)

Naruko, Atsushi; Pitrou, Cyril; Koyama, Kazuya; Sasaki, Misao

2013-08-01

In the context of cosmological perturbation theory, we derive the second-order Boltzmann equation describing the evolution of the distribution function of radiation without a specific gauge choice. The essential steps in deriving the Boltzmann equation are revisited and extended given this more general framework: (i) the polarization of light is incorporated in this formalism by using a tensor-valued distribution function; (ii) the importance of a choice of the tetrad field to define the local inertial frame in the description of the distribution function is emphasized; (iii) we perform a separation between temperature and spectral distortion, both for the intensity and polarization for the first time; (iv) the gauge dependence of all perturbed quantities that enter the Boltzmann equation is derived, and this enables us to check the correctness of the perturbed Boltzmann equation by explicitly showing its gauge-invariance for both intensity and polarization. We finally discuss several implications of the gauge dependence for the observed temperature.

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

PubMed

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

2014-11-20

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

Estimation of Uncertainties of Full Moment Tensors

DTIC Science & Technology

2017-10-06

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

The distribution of hot spots

NASA Technical Reports Server (NTRS)

Stefanick, M.; Jurdy, D. M.

1984-01-01

Statistical analyses are compared for two published hot spot data sets, one minimal set of 42 and another larger set of 117, using three different approaches. First, the earths surface is divided into 16 equal-area fractions and the observed distribution of hot spots among them is analyzed using chi-square tests. Second, cumulative distributions about the principal axes of the hot spot inertia tensor are used to describe hot spot distribution. Finally, a hot spot density function is constructed for each of the two hot spot data sets. The methods all indicate that hot spots have a nonuniform distribution, even when statistical fluctuations are considered. To the first order, hot spots are concentrated on one half of of the earth's surface area; within that portion, the distribution is consistent with a uniform distribution. The observed hot spot densities for neither data set are explained solely by plate speed.

Entangled scalar and tensor fluctuations during inflation

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

Collins, Hael; Vardanyan, Tereza

2016-11-29

We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with amore » simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.« less

Computer simulation of ledge formation and ledge interaction for the silicon (111) free surface

NASA Technical Reports Server (NTRS)

Balamane, H.; Halicioglu, T.; Tiller, W. A.

1987-01-01

Both strip and triangular clusters, composed of 2 -1 -1 line ledges, have been simulated on the Si (111) surface. The long-range ledge-ledge interaction and the surface stress tensor distribution have been evaluated for these two pill-box geometries using a semiempirical potential-energy function that incorporates both two-body and three-body contributions. The consequences of the ledge-ledge interaction on two-dimensional nucleation for Si (111) has been evaluated as a function of Si adatom supersaturation and shown to differ significantly from conventional theory, where such interaction is neglected.

Navigating the Functional Landscape of Transcription Factors via Non-Negative Tensor Factorization Analysis of MEDLINE Abstracts

PubMed Central

Roy, Sujoy; Yun, Daqing; Madahian, Behrouz; Berry, Michael W.; Deng, Lih-Yuan; Goldowitz, Daniel; Homayouni, Ramin

2017-01-01

In this study, we developed and evaluated a novel text-mining approach, using non-negative tensor factorization (NTF), to simultaneously extract and functionally annotate transcriptional modules consisting of sets of genes, transcription factors (TFs), and terms from MEDLINE abstracts. A sparse 3-mode term × gene × TF tensor was constructed that contained weighted frequencies of 106,895 terms in 26,781 abstracts shared among 7,695 genes and 994 TFs. The tensor was decomposed into sub-tensors using non-negative tensor factorization (NTF) across 16 different approximation ranks. Dominant entries of each of 2,861 sub-tensors were extracted to form term–gene–TF annotated transcriptional modules (ATMs). More than 94% of the ATMs were found to be enriched in at least one KEGG pathway or GO category, suggesting that the ATMs are functionally relevant. One advantage of this method is that it can discover potentially new gene–TF associations from the literature. Using a set of microarray and ChIP-Seq datasets as gold standard, we show that the precision of our method for predicting gene–TF associations is significantly higher than chance. In addition, we demonstrate that the terms in each ATM can be used to suggest new GO classifications to genes and TFs. Taken together, our results indicate that NTF is useful for simultaneous extraction and functional annotation of transcriptional regulatory networks from unstructured text, as well as for literature based discovery. A web tool called Transcriptional Regulatory Modules Extracted from Literature (TREMEL), available at http://binf1.memphis.edu/tremel, was built to enable browsing and searching of ATMs. PMID:28894735

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.

Orientation of cosmic web filaments with respect to the underlying velocity field

NASA Astrophysics Data System (ADS)

Tempel, E.; Libeskind, N. I.; Hoffman, Y.; Liivamägi, L. J.; Tamm, A.

2014-01-01

The large-scale structure of the Universe is characterized by a web-like structure made of voids, sheets, filaments and knots. The structure of this so-called cosmic web is dictated by the local velocity shear tensor. In particular, the local direction of a filament should be strongly aligned with hat{e}_3, the eigenvector associated with the smallest eigenvalue of the tensor. That conjecture is tested here on the basis of a cosmological simulation. The cosmic web delineated by the halo distribution is probed by a marked point process with interactions (the Bisous model), detecting filaments directly from the halo distribution (P-web). The detected P-web filaments are found to be strongly aligned with the local hat{e}_3: the alignment is within 30° for ˜80 per cent of the elements. This indicates that large-scale filaments defined purely from the distribution of haloes carry more than just morphological information, although the Bisous model does not make any prior assumption on the underlying shear tensor. The P-web filaments are also compared to the structure revealed from the velocity shear tensor itself (V-web). In the densest regions, the P- and V-web filaments overlap well (90 per cent), whereas in lower density regions, the P-web filaments preferentially mark sheets in the V-web.

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

NASA Astrophysics Data System (ADS)

Suzuki, Atsushi; Oku, Takeo

2016-02-01

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

Large deformation analysis of axisymmetric inhomogeneities including coupled elastic and plastic anisotropy

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

Brannon, R.M.

1996-12-31

A mathematical framework is developed for the study of materials containing axisymmetric inclusions or flaws such as ellipsoidal voids, penny-shaped cracks, or fibers of circular cross-section. The general case of nonuniform statistical distributions of such heterogeneities is attacked by first considering a spatially uniform distribution of flaws that are all oriented in the same direction. Assuming an isotropic substrate, the macroscopic material properties of this simpler microstructure naturally should be transversely isotropic. An orthogonal basis for the linear subspace consisting of all double-symmetric transversely-isotropic fourth-order tensors associated with a given material vector is applied to deduce the explicit functional dependencemore » of the material properties of these aligned materials on the shared symmetry axis. The aligned and uniform microstructure seems geometrically simple enough that the macroscopic transversely isotropic properties could be derived in closed form. Since the resulting properties are transversely isotropic, the analyst must therefore be able to identify the appropriate coefficients of the transverse basis. Once these functions are identified, a principle of superposition of strain rates ay be applied to define an expectation integral for the composite properties of a material containing arbitrary anisotropic distributions of axisymmetric inhomogeneities. A proposal for coupling plastic anisotropy to the elastic anisotropy is presented in which the composite yield surface is interpreted as a distortion of the isotropic substrate yield surface; the distortion directions are coupled to the elastic anisotropy directions. Finally, some commonly assumed properties (such as major symmetry) of the Cauchy tangent stiffness tensor are shown to be inappropriate for large distortions of anisotropic materials.« less

Brain white matter fiber estimation and tractography using Q-ball imaging and Bayesian MODEL.

PubMed

Lu, Meng

2015-01-01

Diffusion tensor imaging allows for the non-invasive in vivo mapping of the brain tractography. However, fiber bundles have complex structures such as fiber crossings, fiber branchings and fibers with large curvatures that tensor imaging (DTI) cannot accurately handle. This study presents a novel brain white matter tractography method using Q-ball imaging as the data source instead of DTI, because QBI can provide accurate information about multiple fiber crossings and branchings in a single voxel using an orientation distribution function (ODF). The presented method also uses graph theory to construct the Bayesian model-based graph, so that the fiber tracking between two voxels can be represented as the shortest path in a graph. Our experiment showed that our new method can accurately handle brain white matter fiber crossings and branchings, and reconstruct brain tractograhpy both in phantom data and real brain data.

Sum-Frequency Generation from a Thin Cylindrical Layer

NASA Astrophysics Data System (ADS)

Shamyna, A. A.; Kapshai, V. N.

2018-01-01

In the Rayleigh-Gans-Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation

PubMed Central

Duarte-Carvajalino, Julio M.; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis. PMID:23596381

Quantifying the effect of non-Larmor motion of electrons on the pressure tensor

NASA Astrophysics Data System (ADS)

Che, H.; Schiff, C.; Le, G.; Dorelli, J. C.; Giles, B. L.; Moore, T. E.

2018-03-01

In space plasma, various effects of magnetic reconnection and turbulence cause the electron motion to significantly deviate from their Larmor orbits. Collectively these orbits affect the electron velocity distribution function and lead to the appearance of the "non-gyrotropic" elements in the pressure tensor. Quantification of this effect has important applications in space and laboratory plasma, one of which is tracing the electron diffusion region (EDR) of magnetic reconnection in space observations. Three different measures of agyrotropy of pressure tensor have previously been proposed, namely, A ∅ e , Dng, and Q. The multitude of contradictory measures has caused confusion within the community. We revisit the problem by considering the basic properties an agyrotropy measure should have. We show that A ∅ e , Dng, and Q are all defined based on the sum of the principle minors (i.e., the rotation invariant I2) of the pressure tensor. We discuss in detail the problems of I2-based measures and explain why they may produce ambiguous and biased results. We introduce a new measure AG constructed based on the determinant of the pressure tensor (i.e., the rotation invariant I3) which does not suffer from the problems of I2-based measures. We compare AG with other measures in 2- and 3-dimension particle-in-cell magnetic reconnection simulations and show that AG effectively trace the EDR of reconnection in both Harris and force-free current sheets. On the other hand, A ∅ e does not show prominent peaks in the EDR and part of the separatrix in the force-free reconnection simulations, demonstrating that A ∅ e does not measure all the non-gyrotropic effects in this case and is not suitable for studying magnetic reconnection in more general situations other than Harris sheet reconnection.

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation.

PubMed

Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

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

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

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

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

Affine theory of gravitation

NASA Astrophysics Data System (ADS)

Popławski, Nikodem

2014-01-01

We propose a theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct a simple dynamical Lagrangian density that is entirely composed from the connection, via its curvature and torsion, and is a polynomial function of its derivatives. It is given by the contraction of the Ricci tensor with a tensor which is inverse to the symmetric, contracted square of the torsion tensor, . We vary the total action for the gravitational field and matter with respect to the affine connection, assuming that the matter fields couple to the connection only through . We derive the resulting field equations and show that they are identical with the Einstein equations of general relativity with a nonzero cosmological constant if the tensor is regarded as proportional to the metric tensor. The cosmological constant is simply a constant of proportionality between the two tensors, which together with and provides a natural system of units in gravitational physics. This theory therefore provides a physical construction of the metric as a polynomial function of the connection, and explains dark energy as an intrinsic property of spacetime.

Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method

NASA Astrophysics Data System (ADS)

Hayata, Tomoya; Hidaka, Yoshimasa; Noumi, Toshifumi; Hongo, Masaru

2015-09-01

We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.

Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities.

PubMed

Frelat, Romain; Lindegren, Martin; Denker, Tim Spaanheden; Floeter, Jens; Fock, Heino O; Sguotti, Camilla; Stäbler, Moritz; Otto, Saskia A; Möllmann, Christian

2017-01-01

Understanding spatio-temporal dynamics of biotic communities containing large numbers of species is crucial to guide ecosystem management and conservation efforts. However, traditional approaches usually focus on studying community dynamics either in space or in time, often failing to fully account for interlinked spatio-temporal changes. In this study, we demonstrate and promote the use of tensor decomposition for disentangling spatio-temporal community dynamics in long-term monitoring data. Tensor decomposition builds on traditional multivariate statistics (e.g. Principal Component Analysis) but extends it to multiple dimensions. This extension allows for the synchronized study of multiple ecological variables measured repeatedly in time and space. We applied this comprehensive approach to explore the spatio-temporal dynamics of 65 demersal fish species in the North Sea, a marine ecosystem strongly altered by human activities and climate change. Our case study demonstrates how tensor decomposition can successfully (i) characterize the main spatio-temporal patterns and trends in species abundances, (ii) identify sub-communities of species that share similar spatial distribution and temporal dynamics, and (iii) reveal external drivers of change. Our results revealed a strong spatial structure in fish assemblages persistent over time and linked to differences in depth, primary production and seasonality. Furthermore, we simultaneously characterized important temporal distribution changes related to the low frequency temperature variability inherent in the Atlantic Multidecadal Oscillation. Finally, we identified six major sub-communities composed of species sharing similar spatial distribution patterns and temporal dynamics. Our case study demonstrates the application and benefits of using tensor decomposition for studying complex community data sets usually derived from large-scale monitoring programs.

Inflationary tensor fossils in large-scale structure

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

Dimastrogiovanni, Emanuela; Fasiello, Matteo; Jeong, Donghui

Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to bemore » satisfied. We then consider several examples of inflation models, such as non-attractor and solid-inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.« less

The competition of particle-vibration coupling and tensor interaction in spherical nuclei

NASA Astrophysics Data System (ADS)

Afanasjev, Anatoli; Litvinova, Elena

2014-09-01

The search for missing terms in the energy density functionals (EDF) is one of the leading directions in the development of nuclear density functional theory (DFT). Tensor force is one of possible candidates. However, despite extensive studies the questions about its effective strength and unambiguous signals still remain open. One of the main experimental benchmarks for the studies of tensor interaction is provided by the data on the single-particle states in the N = 82 and Z = 50 isotopes. The energy splittings of the proton h11 / 2 and g7 / 2 states in the Z = 50 isotopes and neutron 1i13 / 2 and 1h9 / 2 states in the N = 82 isotones are used in the definition of tensor force in the Skyrme DFT. However, in experiment these states are not ``mean-field'' states because of coupling with vibrations. Employing relativistic particle-vibration coupling (PVC) model we show that many features of these splittings can be reproduced when PVC is taken into account. This suggests the competition of PVC and tensor interaction and that tensor interaction should be weaker as compared with previous estimates. The search for missing terms in the energy density functionals (EDF) is one of the leading directions in the development of nuclear density functional theory (DFT). Tensor force is one of possible candidates. However, despite extensive studies the questions about its effective strength and unambiguous signals still remain open. One of the main experimental benchmarks for the studies of tensor interaction is provided by the data on the single-particle states in the N = 82 and Z = 50 isotopes. The energy splittings of the proton h11 / 2 and g7 / 2 states in the Z = 50 isotopes and neutron 1i13 / 2 and 1h9 / 2 states in the N = 82 isotones are used in the definition of tensor force in the Skyrme DFT. However, in experiment these states are not ``mean-field'' states because of coupling with vibrations. Employing relativistic particle-vibration coupling (PVC) model we show that many features of these splittings can be reproduced when PVC is taken into account. This suggests the competition of PVC and tensor interaction and that tensor interaction should be weaker as compared with previous estimates. This work has been supported by the U.S. Department of Energy under the Grant DE-FG02-07ER41459 and National Science Foundation Award PHY-1204486.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

Subcortical pathways serving cortical language sites: initial experience with diffusion tensor imaging fiber tracking combined with intraoperative language mapping.

PubMed

Henry, Roland G; Berman, Jeffrey I; Nagarajan, Srikantan S; Mukherjee, Pratik; Berger, Mitchel S

2004-02-01

The combination of mapping functional cortical neurons by intraoperative cortical stimulation and axonal architecture by diffusion tensor MRI fiber tracking can be used to delineate the pathways between functional regions. In this study the authors investigated the feasibility of combining these techniques to yield connectivity associated with motor speech and naming. Diffusion tensor MRI fiber tracking provides maps of axonal bundles and was combined with intraoperative mapping of eloquent cortex for a patient undergoing brain tumor surgery. Tracks from eight stimulated sites in the inferior frontal cortex including mouth motor, speech arrest, and anomia were generated from the diffusion tensor MRI data. The regions connected by the fiber tracking were compared to foci from previous functional imaging reports on language tasks. Connections were found between speech arrest, mouth motor, and anomia sites and the SMA proper and cerebral peduncle. The speech arrest and a mouth motor site were also seen to connect to the putamen via the external capsule. This is the first demonstration of delineation of subcortical pathways using diffusion tensor MRI fiber tracking with intraoperative cortical stimulation. The combined techniques may provide improved preservation of eloquent regions during neurological surgery, and may provide access to direct connectivity information between functional regions of the brain.

Subcortical pathways serving cortical language sites: initial experience with diffusion tensor imaging fiber tracking combined with intraoperative language mapping

PubMed Central

Henry, Roland G.; Berman, Jeffrey I.; Nagarajan, Srikantan S.; Mukherjee, Pratik; Berger, Mitchel S.

2014-01-01

The combination of mapping functional cortical neurons by intraoperative cortical stimulation and axonal architecture by diffusion tensor MRI fiber tracking can be used to delineate the pathways between functional regions. In this study the authors investigated the feasibility of combining these techniques to yield connectivity associated with motor speech and naming. Diffusion tensor MRI fiber tracking provides maps of axonal bundles and was combined with intraoperative mapping of eloquent cortex for a patient undergoing brain tumor surgery. Tracks from eight stimulated sites in the inferior frontal cortex including mouth motor, speech arrest, and anomia were generated from the diffusion tensor MRI data. The regions connected by the fiber tracking were compared to foci from previous functional imaging reports on language tasks. Connections were found between speech arrest, mouth motor, and anomia sites and the SMA proper and cerebral peduncle. The speech arrest and a mouth motor site were also seen to connect to the putamen via the external capsule. This is the first demonstration of delineation of subcortical pathways using diffusion tensor MRI fiber tracking with intraoperative cortical stimulation. The combined techniques may provide improved preservation of eloquent regions during neurological surgery, and may provide access to direct connectivity information between functional regions of the brain. PMID:14980564

Tensor tomography on Cartan–Hadamard manifolds

NASA Astrophysics Data System (ADS)

Lehtonen, Jere; Railo, Jesse; Salo, Mikko

2018-04-01

We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016 arXiv:1612.04800) to dimensions n ≥slant 3 and to the case of tensor fields of any order.

Nonguiding Center Motion and Substorm Effects in the Magnetotail

NASA Technical Reports Server (NTRS)

Kaufmann, Richard L.; Kontodinas, Ioannis D.; Ball, Bryan M.; Larson, Douglas J.

1997-01-01

Thick and thin models of the middle magnetotail were developed using a consistent orbit tracing technique. It was found that currents carried near the equator by groups of ions with anisotropic distribution functions are not well approximated by the guiding center expressions. The guiding center equations fail primarily because the calculated pressure tensor is not magnetic field aligned. The pressure tensor becomes field aligned as one moves away from the equator, but here there is a small region in which the guiding center equations remain inadequate because the two perpendicular components of the pressure tensor are unequal. The significance of nonguiding center motion to substorm processes then was examined. One mechanism that may disrupt a thin cross-tail current sheet involves field changes that cause ions to begin following chaotic orbits. The lowest-altitude chaotic region, characterized by an adiabaticity parameter kappa approx. equal to 0.8, is especially important. The average cross-tail particle drift is slow, and we were unable to generate a thin current sheet using such ions. Therefore, any process that tends to create a thin current sheet in a region with kappa approaching 0.8 may cause the cross-tail current to get so low that it becomes insufficient to support the lobes. A different limit may be important in resonant orbit regions of a thin current sheet because particles reach a maximum cross-tail drift velocity. If the number of ions per unit length decreases as the tail is stretched, this part of the plasma sheet also may become unable to carry the cross-tail current needed to support the lobes. Thin sheets are needed for both resonant and chaotic orbit mechanisms because the distribution function must be highly structured. A description of current continuity is included to show how field aligned currents can evolve during the transition from a two-dimensional (2-D) to a 3-D configuration.

Software Toolbox for Low-Frequency Conductivity and Current Density Imaging Using MRI.

PubMed

Sajib, Saurav Z K; Katoch, Nitish; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je

2017-11-01

Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes. Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes.

Decorated tensor network renormalization for lattice gauge theories and spin foam models

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian

2016-05-01

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.

Anomalous current from the covariant Wigner function

NASA Astrophysics Data System (ADS)

Prokhorov, George; Teryaev, Oleg

2018-04-01

We consider accelerated and rotating media of weakly interacting fermions in local thermodynamic equilibrium on the basis of kinetic approach. Kinetic properties of such media can be described by covariant Wigner function incorporating the relativistic distribution functions of particles with spin. We obtain the formulae for axial current by summation of the terms of all orders of thermal vorticity tensor, chemical potential, both for massive and massless particles. In the massless limit all the terms of fourth and higher orders of vorticity and third order of chemical potential and temperature equal zero. It is shown, that axial current gets a topological component along the 4-acceleration vector. The similarity between different approaches to baryon polarization is established.

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

Sun Dongsheng; Wang Hongcai; Ma Yinsheng

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

Sample-based synthesis of two-scale structures with anisotropy

DOE PAGES

Liu, Xingchen; Shapiro, Vadim

2017-05-19

A vast majority of natural or synthetic materials are characterized by their anisotropic properties, such as stiffness. Such anisotropy is effected by the spatial distribution of the fine-scale structure and/or anisotropy of the constituent phases at a finer scale. In design, proper control of the anisotropy may greatly enhance the efficiency and performance of synthesized structures. In this paper, we propose a sample-based two-scale structure synthesis approach that explicitly controls anisotropic effective material properties of the structure on the coarse scale by orienting sampled material neighborhoods at the fine scale. We first characterize the non-uniform orientations distribution of the samplemore » structure by showing that the principal axes of an orthotropic material may be determined by the eigenvalue decomposition of its effective stiffness tensor. Such effective stiffness tensors can be efficiently estimated based on the two-point correlation functions of the fine-scale structures. Then we synthesize the two-scale structure by rotating fine-scale structures from the sample to follow a given target orientation field. Finally, the effectiveness of the proposed approach is demonstrated through examples in both 2D and 3D.« less

Sample-based synthesis of two-scale structures with anisotropy

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

Liu, Xingchen; Shapiro, Vadim

A vast majority of natural or synthetic materials are characterized by their anisotropic properties, such as stiffness. Such anisotropy is effected by the spatial distribution of the fine-scale structure and/or anisotropy of the constituent phases at a finer scale. In design, proper control of the anisotropy may greatly enhance the efficiency and performance of synthesized structures. In this paper, we propose a sample-based two-scale structure synthesis approach that explicitly controls anisotropic effective material properties of the structure on the coarse scale by orienting sampled material neighborhoods at the fine scale. We first characterize the non-uniform orientations distribution of the samplemore » structure by showing that the principal axes of an orthotropic material may be determined by the eigenvalue decomposition of its effective stiffness tensor. Such effective stiffness tensors can be efficiently estimated based on the two-point correlation functions of the fine-scale structures. Then we synthesize the two-scale structure by rotating fine-scale structures from the sample to follow a given target orientation field. Finally, the effectiveness of the proposed approach is demonstrated through examples in both 2D and 3D.« less

Full moment tensors with uncertainties for the 2017 North Korea declared nuclear test and for a collocated, subsequent event

NASA Astrophysics Data System (ADS)

Alvizuri, C. R.; Tape, C.

2017-12-01

A seismic moment tensor is a 3×3 symmetric matrix that characterizes the far-field seismic radiation from a source, whether it be an earthquake, volcanic event, explosion. We estimate full moment tensors and their uncertainties for the North Korea declared nuclear test and for a collocated event that occurred eight minutes later. The nuclear test and the subsequent event occurred on September 3, 2017 at around 03:30 and 03:38 UTC time. We perform a grid search over the six-dimensional space of moment tensors, generating synthetic waveforms at each moment tensor grid point and then evaluating a misfit function between the observed and synthetic waveforms. The synthetic waveforms are computed using a 1-D structure model for the region; this approximation requires careful assessment of time shifts between data and synthetics, as well as careful choice of the bandpass for filtering. For each moment tensor we characterize its uncertainty in terms of waveform misfit, a probability function, and a confidence curve for the probability that the true moment tensor lies within the neighborhood of the optimal moment tensor. For each event we estimate its moment tensor using observed waveforms from all available seismic stations within a 2000-km radius. We use as much of the waveform as possible, including surface waves for all stations, and body waves above 1 Hz for some of the closest stations. Our preliminary magnitude estimates are Mw 5.1-5.3 for the first event and Mw 4.7 for the second event. Our results show a dominantly positive isotropic moment tensor for the first event, and a dominantly negative isotropic moment tensor for the subsequent event. As expected, the details of the probability density, waveform fit, and confidence curves are influenced by the structural model, the choice of filter frequencies, and the selection of stations.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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.

Einstein gravity 3-point functions from conformal field theory

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Evaluation of the Thermodynamic Consistency of Closure Approximations in Several Models Proposed for the Description of Liquid Crystalline Dynamics

NASA Astrophysics Data System (ADS)

Edwards, Brian J.

2002-05-01

Given the premise that a set of dynamical equations must possess a definite, underlying mathematical structure to ensure local and global thermodynamic stability, as has been well documented, several different models for describing liquid crystalline dynamics are examined with respect to said structure. These models, each derived during the past several years using a specific closure approximation for the fourth moment of the distribution function in Doi's rigid rod theory, are all shown to be inconsistent with this basic mathematical structure. The source of this inconsistency lies in Doi's expressions for the extra stress tensor and temporal evolution of the order parameter, which are rederived herein using a transformation that allows for internal compatibility with the underlying mathematical structure that is present on the distribution function level of description.

Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities

PubMed Central

Lindegren, Martin; Denker, Tim Spaanheden; Floeter, Jens; Fock, Heino O.; Sguotti, Camilla; Stäbler, Moritz; Otto, Saskia A.; Möllmann, Christian

2017-01-01

Understanding spatio-temporal dynamics of biotic communities containing large numbers of species is crucial to guide ecosystem management and conservation efforts. However, traditional approaches usually focus on studying community dynamics either in space or in time, often failing to fully account for interlinked spatio-temporal changes. In this study, we demonstrate and promote the use of tensor decomposition for disentangling spatio-temporal community dynamics in long-term monitoring data. Tensor decomposition builds on traditional multivariate statistics (e.g. Principal Component Analysis) but extends it to multiple dimensions. This extension allows for the synchronized study of multiple ecological variables measured repeatedly in time and space. We applied this comprehensive approach to explore the spatio-temporal dynamics of 65 demersal fish species in the North Sea, a marine ecosystem strongly altered by human activities and climate change. Our case study demonstrates how tensor decomposition can successfully (i) characterize the main spatio-temporal patterns and trends in species abundances, (ii) identify sub-communities of species that share similar spatial distribution and temporal dynamics, and (iii) reveal external drivers of change. Our results revealed a strong spatial structure in fish assemblages persistent over time and linked to differences in depth, primary production and seasonality. Furthermore, we simultaneously characterized important temporal distribution changes related to the low frequency temperature variability inherent in the Atlantic Multidecadal Oscillation. Finally, we identified six major sub-communities composed of species sharing similar spatial distribution patterns and temporal dynamics. Our case study demonstrates the application and benefits of using tensor decomposition for studying complex community data sets usually derived from large-scale monitoring programs. PMID:29136658

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.

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.

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.

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.

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

PubMed

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

2015-11-10

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

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.

Self-consistent current sheet structures in the quiet-time magnetotail

NASA Technical Reports Server (NTRS)

Holland, Daniel L.; Chen, James

1993-01-01

The structure of the quiet-time magnetotail is studied using a test particle simulation. Vlasov equilibria are obtained in the regime where v(D) = E(y) c/B(z) is much less than the ion thermal velocity and are self-consistent in that the current and magnetic field satisfy Ampere's law. Force balance between the plasma and magnetic field is satisfied everywhere. The global structure of the current sheet is found to be critically dependent on the source distribution function. The pressure tensor is nondiagonal in the current sheet with anisotropic temperature. A kinetic mechanism is proposed whereby changes in the source distribution results in a thinning of the current sheet.

The Enskog Equation for Confined Elastic Hard Spheres

NASA Astrophysics Data System (ADS)

Maynar, P.; García de Soria, M. I.; Brey, J. Javier

2018-03-01

A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, H[f], is identified. For any solution of the kinetic equation, H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a density field consistent with equilibrium statistical mechanics.

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.

Parallel Tensor Compression for Large-Scale Scientific Data.

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

Kolda, Tamara G.; Ballard, Grey; Austin, Woody Nathan

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that tracks 64 variables per grid point for 128 time steps yields 8 TB of data. By viewing the data as a dense five way tensor, we can compute a Tucker decomposition to find inherent low-dimensional multilinear structure, achieving compression ratios of up to 10000 on real-world data sets with negligible loss in accuracy. So that we can operate on such massive data, we present the first-ever distributed memorymore » parallel implementation for the Tucker decomposition, whose key computations correspond to parallel linear algebra operations, albeit with nonstandard data layouts. Our approach specifies a data distribution for tensors that avoids any tensor data redistribution, either locally or in parallel. We provide accompanying analysis of the computation and communication costs of the algorithms. To demonstrate the compression and accuracy of the method, we apply our approach to real-world data sets from combustion science simulations. We also provide detailed performance results, including parallel performance in both weak and strong scaling experiments.« less

Registration of High Angular Resolution Diffusion MRI Images Using 4th Order Tensors⋆

PubMed Central

Barmpoutis, Angelos; Vemuri, Baba C.; Forder, John R.

2009-01-01

Registration of Diffusion Weighted (DW)-MRI datasets has been commonly achieved to date in literature by using either scalar or 2nd-order tensorial information. However, scalar or 2nd-order tensors fail to capture complex local tissue structures, such as fiber crossings, and therefore, datasets containing fiber-crossings cannot be registered accurately by using these techniques. In this paper we present a novel method for non-rigidly registering DW-MRI datasets that are represented by a field of 4th-order tensors. We use the Hellinger distance between the normalized 4th-order tensors represented as distributions, in order to achieve this registration. Hellinger distance is easy to compute, is scale and rotation invariant and hence allows for comparison of the true shape of distributions. Furthermore, we propose a novel 4th-order tensor re-transformation operator, which plays an essential role in the registration procedure and shows significantly better performance compared to the re-orientation operator used in literature for DTI registration. We validate and compare our technique with other existing scalar image and DTI registration methods using simulated diffusion MR data and real HARDI datasets. PMID:18051145

Dynamical analysis for a scalar-tensor model with kinetic and nonminimal couplings

NASA Astrophysics Data System (ADS)

Granda, L. N.; Jimenez, D. F.

We study the autonomous system for a scalar-tensor model of dark energy with nonminimal coupling to curvature and nonminimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential were considered: power-law and exponential functions of the scalar field. For power-law couplings, the restrictions on stable quintessence and phantom solutions lead to asymptotic freedom regime for the gravitational interaction. For the exponential functions, the stable quintessence, phantom or de Sitter solutions allow asymptotic behaviors where the effective Newtonian coupling can reach either the asymptotic freedom regime or constant value. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation dominated phases can also be described.

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

MHD Turbulence, div B = 0 and Lattice Boltzmann Simulations

NASA Astrophysics Data System (ADS)

Phillips, Nate; Keating, Brian; Vahala, George; Vahala, Linda

2006-10-01

The question of div B = 0 in MHD simulations is a crucial issue. Here we consider lattice Boltzmann simulations for MHD (LB-MHD). One introduces a scalar distribution function for the velocity field and a vector distribution function for the magnetic field. This asymmetry is due to the different symmetries in the tensors arising in the time evolution of these fields. The simple algorithm of streaming and local collisional relaxation is ideally parallelized and vectorized -- leading to the best sustained performance/PE of any code run on the Earth Simulator. By reformulating the BGK collision term, a simple implicit algorithm can be immediately transformed into an explicit algorithm that permits simulations at quite low viscosity and resistivity. However the div B is not an imposed constraint. Currently we are examining a new formulations of LB-MHD that impose the div B constraint -- either through an entropic like formulation or by introducing forcing terms into the momentum equations and permitting simpler forms of relaxation distributions.

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure.

PubMed

Özarslan, Evren; Koay, Cheng Guan; Shepherd, Timothy M; Komlosh, Michal E; İrfanoğlu, M Okan; Pierpaoli, Carlo; Basser, Peter J

2013-09-01

Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue. Copyright © 2013 Elsevier Inc. All rights reserved.

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

Zuniga-Gutierrez, Bernardo, E-mail: bzuniga.51@gmail.com; Camacho-Gonzalez, Monica; Bendana-Castillo, Alfonso

The computation of the spin-rotation tensor within the framework of auxiliary density functional theory (ADFT) in combination with the gauge including atomic orbital (GIAO) scheme, to treat the gauge origin problem, is presented. For the spin-rotation tensor, the calculation of the magnetic shielding tensor represents the most demanding computational task. Employing the ADFT-GIAO methodology, the central processing unit time for the magnetic shielding tensor calculation can be dramatically reduced. In this work, the quality of spin-rotation constants obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-clustermore » level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good and very similar to the ones obtained by the coupled-cluster single-doubles-perturbative triples-GIAO methodology. With the improved computational performance achieved, the computation of the spin-rotation tensors of large systems or along Born-Oppenheimer molecular dynamics trajectories becomes feasible in reasonable times. Three models of carbon fullerenes containing hundreds of atoms and thousands of basis functions are used for benchmarking the performance. Furthermore, a theoretical study of temperature effects on the structure and spin-rotation tensor of the H{sup 12}C–{sup 12}CH–DF complex is presented. Here, the temperature dependency of the spin-rotation tensor of the fluorine nucleus can be used to identify experimentally the so far unknown bent isomer of this complex. To the best of our knowledge this is the first time that temperature effects on the spin-rotation tensor are investigated.« less

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

PubMed

Muhlestein, Michael B; Haberman, Michael R

2016-08-01

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

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

PubMed Central

Haberman, Michael R.

2016-01-01

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

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

NASA Astrophysics Data System (ADS)

Muhlestein, Michael B.; Haberman, Michael R.

2016-08-01

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

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

NASA Astrophysics Data System (ADS)

Delvaux, Damien

2016-04-01

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

The Kummer tensor density in electrodynamics and in gravity

NASA Astrophysics Data System (ADS)

Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.

2014-10-01

Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T, which is antisymmetric in its first two and its last two indices: T=-T=-T. Thus, K∼T3, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R of a Riemann-Cartan spacetime, then K∼R3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3).

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE

PubMed Central

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

2017-01-01

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

Relativistic interpretation of the nature of the nuclear tensor force

NASA Astrophysics Data System (ADS)

Zong, Yao-Yao; Sun, Bao-Yuan

2018-02-01

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

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

PubMed

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

2017-05-01

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

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.

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

DOE PAGES

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

2015-09-30

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

MR Diffusion Tensor Imaging: A Window into White Matter Integrity of the Working Brain

PubMed Central

Chanraud, Sandra; Zahr, Natalie; Pfefferbaum, Adolf

2010-01-01

As Norman Geschwind asserted in 1965, syndromes resulting from white matter lesions could produce deficits in higher-order functions and “disconnexion” or the interruption of connection between gray matter regions could be as disruptive as trauma to those regions per se. The advent of in vivo diffusion tensor imaging, which allows quantitative characterization of white matter fiber integrity in health and disease, has served to strengthen Geschwind's proposal. Here we present an overview of the principles of diffusion tensor imaging (DTI) and its contribution to progress in our current understanding of normal and pathological brain function. PMID:20422451

Virtual photon emission from a quark-gluon plasma

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

Suryanarayana, S. V.

We present phenomenological formulas for virtual photon emission rates from a thermalized quark-gluon plasma (QGP) that include bremsstrahlung and annihilation with scattering (AWS) mechanisms along with the Landau-Pomeranchuk-Migdal (LPM) effects. For this purpose we follow the approach of generalized emission functions (GEF) for virtual photon emission, we showed earlier for a fixed temperature and strong coupling constant. In the present work, we extend the LPM calculations for several temperatures and strong coupling strengths, photon energies (q{sub 0}), photon mass (Q{sup 2}), and quark energies (p{sub 0}). We generalize the dynamical scaling variables, x{sub T},x{sub L}, for bremsstrahlung and AWS processesmore » that are now functions of variables p{sub 0},q{sub 0},Q{sup 2},T,{alpha}{sub s}. The GEF introduced earlier, g{sub T}{sup b},g{sub T}{sup a},g{sub L}{sup b},g{sub L}{sup a}, are also generalized for any temperatures and coupling strengths. From this, the imaginary part of the photon polarization tensor as a function of photon mass and energy has been calculated as a one-dimensional integral over these GEF and parton distribution functions in the plasma. By fitting these polarization tensors obtained from GEF method, we obtained a phenomenological formula for virtual photon emission rates as a function of (q{sub 0},Q{sup 2},T,{alpha}{sub s}) that includes bremsstrahlung and AWS mechanisms with LPM effects.« less

New algorithm for tensor contractions on multi-core CPUs, GPUs, and accelerators enables CCSD and EOM-CCSD calculations with over 1000 basis functions on a single compute node.

PubMed

Kaliman, Ilya A; Krylov, Anna I

2017-04-30

A new hardware-agnostic contraction algorithm for tensors of arbitrary symmetry and sparsity is presented. The algorithm is implemented as a stand-alone open-source code libxm. This code is also integrated with general tensor library libtensor and with the Q-Chem quantum-chemistry package. An overview of the algorithm, its implementation, and benchmarks are presented. Similarly to other tensor software, the algorithm exploits efficient matrix multiplication libraries and assumes that tensors are stored in a block-tensor form. The distinguishing features of the algorithm are: (i) efficient repackaging of the individual blocks into large matrices and back, which affords efficient graphics processing unit (GPU)-enabled calculations without modifications of higher-level codes; (ii) fully asynchronous data transfer between disk storage and fast memory. The algorithm enables canonical all-electron coupled-cluster and equation-of-motion coupled-cluster calculations with single and double substitutions (CCSD and EOM-CCSD) with over 1000 basis functions on a single quad-GPU machine. We show that the algorithm exhibits predicted theoretical scaling for canonical CCSD calculations, O(N 6 ), irrespective of the data size on disk. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Structural characterization, solvent effects on nuclear magnetic shielding tensors, experimental and theoretical DFT studies on the vibrational and NMR spectra of 3-(acrylamido)phenylboronic acid

NASA Astrophysics Data System (ADS)

Alver, Özgür; Kaya, Mehmet Fatih; Dikmen, Gökhan

2015-12-01

Structural elucidation of 3-(acrylamido)phenylboronic acid (C9H10BNO3) was carried out with 1H, 13C and HETCOR NMR techniques. Solvent effects on nuclear magnetic shielding tensors were examined with deuterated dimethyl sulfoxide, acetone, methanol and water solvents. The correct order of appearance of carbon and hydrogen atoms on NMR scale from highest magnetic field region to the lowest one were investigated using different types of theoretical levels and the details of the levels were presented in this study. Stable structural conformers and vibrational band analysis of the title molecule (C9H10BNO3) were studied both experimental and theoretical viewpoints using FT-IR, Raman spectroscopic methods and density functional theory (DFT). FT-IR and Raman spectra were obtained in the region of 4000-400 cm-1, and 3700-10 cm-1, respectively. Becke-3-Lee-Yang-Parr (B3LYP) hybrid density functional theory method with 6-31++G(d, p) basis set was included in the search for optimized structures and vibrational wavenumbers. Experimental and theoretical results show that after application of a suitable scaling factor density functional B3LYP method resulted in acceptable results for predicting vibrational wavenumbers except OH and NH stretching modes which is most likely arising from increasing unharmonicity in the high wave number region and possible intra and inter molecular interaction at OH edges those of which are not fully taken into consideration in theoretical processes. To make a more quantitative vibrational assignments, potential energy distribution (PED) values were calculated using VEDA 4 (Vibrational Energy Distribution Analysis) program.

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

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-09-01

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

Tensor products of U{sub q}{sup Prime }sl-caret(2)-modules and the big q{sup 2}-Jacobi function transform

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

Gade, R. M.

2013-01-15

Four tensor products of evaluation modules of the quantum affine algebra U{sub q}{sup Prime }sl-caret(2) obtained from the negative and positive series, the complementary and the strange series representations are investigated. Linear operators R(z) satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} and {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} involving big q{sup 2}-Jacobi functions or related nonterminating basic hypergeometric series. Inhomogeneous recurrence relations can be derived for both sets. Evaluations of the simplestmore » sums provide the corresponding initial conditions. For the first set of sums the relations entail a big q{sup 2}-Jacobi function transform pair. An integral decomposition is obtained for the sum {tau}{sup (r,t)}. A partial description of the relation between the decompositions of the tensor products with respect to U{sub q}sl(2) or with respect to its complement in U{sub q}{sup Prime }sl-caret(2) can be formulated in terms of Askey-Wilson function transforms. For a particular combination of two tensor products, the occurrence of proper U{sub q}{sup Prime }sl-caret(2)-submodules is discussed.« less

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.

Large number limit of multifield inflation

NASA Astrophysics Data System (ADS)

Guo, Zhong-Kai

2017-12-01

We compute the tensor and scalar spectral index nt, ns, the tensor-to-scalar ratio r , and the consistency relation nt/r in the general monomial multifield slow-roll inflation models with potentials V ˜∑iλi|ϕi| pi . The general models give a novel relation that nt, ns and nt/r are all proportional to the logarithm of the number of fields Nf when Nf is getting extremely large with the order of magnitude around O (1040). An upper bound Nf≲N*eZ N* is given by requiring the slow variation parameter small enough where N* is the e -folding number and Z is a function of distributions of λi and pi. Besides, nt/r differs from the single-field result -1 /8 with substantial probability except for a few very special cases. Finally, we derive theoretical bounds r >2 /N* (r ≳0.03 ) and for nt, which can be tested by observation in the near future.

Vibrational algorithms for quantitative crystallographic analyses of hydroxyapatite-based biomaterials: I, theoretical foundations.

PubMed

Pezzotti, Giuseppe; Zhu, Wenliang; Boffelli, Marco; Adachi, Tetsuya; Ichioka, Hiroaki; Yamamoto, Toshiro; Marunaka, Yoshinori; Kanamura, Narisato

2015-05-01

The Raman spectroscopic method has quantitatively been applied to the analysis of local crystallographic orientation in both single-crystal hydroxyapatite and human teeth. Raman selection rules for all the vibrational modes of the hexagonal structure were expanded into explicit functions of Euler angles in space and six Raman tensor elements (RTE). A theoretical treatment has also been put forward according to the orientation distribution function (ODF) formalism, which allows one to resolve the statistical orientation patterns of the nm-sized hydroxyapatite crystallite comprised in the Raman microprobe. Close-form solutions could be obtained for the Euler angles and their statistical distributions resolved with respect to the direction of the average texture axis. Polarized Raman spectra from single-crystalline hydroxyapatite and textured polycrystalline (teeth enamel) samples were compared, and a validation of the proposed Raman method could be obtained through confirming the agreement between RTE values obtained from different samples.

Action principle for Coulomb collisions in plasmas

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

Hirvijoki, Eero

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

Action principle for Coulomb collisions in plasmas

DOE PAGES

Hirvijoki, Eero

2016-09-14

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

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

PubMed Central

2015-01-01

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

Reactive scattering with row-orthonormal hyperspherical coordinates. 4. Four-dimensional-space Wigner rotation function for pentaatomic systems.

PubMed

Kuppermann, Aron

2011-05-14

The row-orthonormal hyperspherical coordinate (ROHC) approach to calculating state-to-state reaction cross sections and bound state levels of N-atom systems requires the use of angular momentum tensors and Wigner rotation functions in a space of dimension N - 1. The properties of those tensors and functions are discussed for arbitrary N and determined for N = 5 in terms of the 6 Euler angles involved in 4-dimensional space.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Detecting brain dynamics during resting state: a tensor based evolutionary clustering approach

NASA Astrophysics Data System (ADS)

Al-sharoa, Esraa; Al-khassaweneh, Mahmood; Aviyente, Selin

2017-08-01

Human brain is a complex network with connections across different regions. Understanding the functional connectivity (FC) of the brain is important both during resting state and task; as disruptions in connectivity patterns are indicators of different psychopathological and neurological diseases. In this work, we study the resting state functional connectivity networks (FCNs) of the brain from fMRI BOLD signals. Recent studies have shown that FCNs are dynamic even during resting state and understanding the temporal dynamics of FCNs is important for differentiating between different conditions. Therefore, it is important to develop algorithms to track the dynamic formation and dissociation of FCNs of the brain during resting state. In this paper, we propose a two step tensor based community detection algorithm to identify and track the brain network community structure across time. First, we introduce an information-theoretic function to reduce the dynamic FCN and identify the time points that are similar topologically to combine them into a tensor. These time points will be used to identify the different FC states. Second, a tensor based spectral clustering approach is developed to identify the community structure of the constructed tensors. The proposed algorithm applies Tucker decomposition to the constructed tensors and extract the orthogonal factor matrices along the connectivity mode to determine the common subspace within each FC state. The detected community structure is summarized and described as FC states. The results illustrate the dynamic structure of resting state networks (RSNs), including the default mode network, somatomotor network, subcortical network and visual network.

Tensor Minkowski Functionals: first application to the CMB

NASA Astrophysics Data System (ADS)

Ganesan, Vidhya; Chingangbam, Pravabati

2017-06-01

Tensor Minkowski Functionals (TMFs) are tensor generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze the Cosmic Microwave Background (CMB) radiation. They encapsulate information about the shapes of structures and the orientation of distributions of structures. We focus on one of the TMFs, namely W21,1, which is the (1,1) rank tensor generalization of the genus. The ratio of the eigenvalues of the average of W21,1 over all structures, α, encodes the net orientation of the structures; and the average of the ratios of the eigenvalues of W21,1 for each structure, β, encodes the net intrinsic anisotropy of the structures. We have developed a code that computes W21,1, and from it α and β, for a set of structures on the 2-dimensional Euclidean plane. We use it to compute α and β as functions of chosen threshold levels for simulated Gaussian and isotropic CMB temperature and E mode fields. We obtain the value of α to be one for both temperature and E mode, which means that we recover the statistical isotropy of density fluctuations that we input in the simulations. We find that the standard ΛCDM model predicts a charateristic shape of β for temperature and E mode as a function of the threshold, and the average over thresholds is β~ 0.62 for temperature and β~ 0.63 for E mode. Accurate measurements of α and β can be used to test the standard model of cosmology and to search for deviations from it. For this purpose we compute α and β for temperature and E mode data of various data sets from PLANCK mission. We compare the values measured from observed data with those obtained from simulations to which instrument beam and noise characteristics of the 44GHz frequency channel have been added (which are provided as part of the PLANCK data release). We find very good agreement of β and α between all PLANCK temperature data sets with ΛCDM expectations. E mode data show good agreement for β but α for all data sets deviate from ΛCDM predictions higher than 3-σ. It is most likely that the deviations are probing the anisotropy of the noise field and beam characteristics of the detector rather than the true E mode signal since for 44GHz the signal-to-noise ratio is well below one. This will be further investigated after the full PLANCK data becomes publicly available.

Analytical effective tensor for flow-through composites

DOEpatents

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.

A multiple scattering theory for EM wave propagation in a dense random medium

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.; Wong, K. W.

1985-01-01

For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.

Skeletal effects in Angle Class II/1 patients treated with the functional regulator type II : Cephalometric and tensor analysis.

PubMed

Schulz, Simone; Koos, Bernd; Duske, Kathrin; Stahl, Franka

2016-11-01

The purpose of this work was to employ both cephalometric and tensor analysis in characterizing the skeletal changes experienced by patients with Angle Class II/1 malocclusion during functional orthodontic treatment with the functional regulator type II. A total of 23 patients with Class II/1 malocclusion based on lateral cephalograms obtained before and after treatment with the functional regulator type II were analyzed. Another 23 patients with Angle Class II/1 malocclusion who had not undergone treatment were included as controls. Our cephalometric data attest to significant therapeutic effects of the functional regulator type II on the skeletal mandibular system, including significant advancement of the mandible, increases in effective mandibular length with enhancement of the chin profile, and reduction of growth-related bite deepening. No treatment-related effects were observed at the cranial-base and midface levels. In addition, tensor analysis revealed significant stimulation of mandibular growth in sagittal directions, without indications of growth effects on the maxilla. Its growth-pattern findings differed from those of cephalometric analysis by indicating that the appliance did promote horizontal development, which supports the functional orthodontic treatment effect in Angle Class II/1 cases. Tensor analysis yielded additional insights into sagittal and vertical growth changes not identifiable by strictly cephalometric means. The functional regulator type II was an effective treatment modality for Angle Class II/1 malocclusion and influenced the skeletal development of these patients in favorable ways.

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.

Multilinear Computing and Multilinear Algebraic Geometry

DTIC Science & Technology

2016-08-10

instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send...performance period of this project. 15. SUBJECT TERMS Tensors , multilinearity, algebraic geometry, numerical computations, computational tractability, high...Reset DISTRIBUTION A: Distribution approved for public release. DISTRIBUTION A: Distribution approved for public release. INSTRUCTIONS FOR COMPLETING

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

PubMed

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

2015-01-01

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

Multimodal MRI in cerebral small vessel disease: its relationship with cognition and sensitivity to change over time.

PubMed

Nitkunan, Arani; Barrick, Tom R; Charlton, Rebecca A; Clark, Chris A; Markus, Hugh S

2008-07-01

Cerebral small vessel disease is the most common cause of vascular dementia. Interest in using MRI parameters as surrogate markers of disease to assess therapies is increasing. In patients with symptomatic sporadic small vessel disease, we determined which MRI parameters best correlated with cognitive function on cross-sectional analysis and which changed over a period of 1 year. Thirty-five patients with lacunar stroke and leukoaraiosis were recruited. They underwent multimodal MRI (brain volume, fluid-attenuated inversion recovery lesion load, lacunar infarct number, fractional anisotropy, and mean diffusivity from diffusion tensor imaging) and neuropsychological testing. Twenty-seven agreed to reattend for repeat MRI and neuropsychology at 1 year. An executive function score correlated most strongly with diffusion tensor imaging (fractional anisotropy histogram, r=-0.640, P=0.004) and brain volume (r=0.501, P=0.034). Associations with diffusion tensor imaging were stronger than with all other MRI parameters. On multiple regression of all imaging parameters, a model that contained brain volume and fractional anisotropy, together with age, gender, and premorbid IQ, explained 74% of the variance of the executive function score (P=0.0001). Changes in mean diffusivity and fractional anisotropy were detectable over the 1-year follow-up; in contrast, no change in other MRI parameters was detectable over this time period. A multimodal MRI model explains a large proportion of the variation in executive function in cerebral small vessel disease. In particular, diffusion tensor imaging correlates best with executive function and is the most sensitive to change. This supports the use of MRI, in particular diffusion tensor imaging, as a surrogate marker in treatment trials.

Diffusion Weighted/Tensor Imaging, Functional MRI and Perfusion Weighted Imaging in Glioblastoma-Foundations and Future.

PubMed

Salama, Gayle R; Heier, Linda A; Patel, Praneil; Ramakrishna, Rohan; Magge, Rajiv; Tsiouris, Apostolos John

2017-01-01

In this article, we review the basics of diffusion tensor imaging and functional MRI, their current utility in preoperative neurosurgical mapping, and their limitations. We also discuss potential future applications, including implementation of resting state functional MRI. We then discuss perfusion and diffusion-weighted imaging and their application in advanced neuro-oncologic practice. We explain how these modalities can be helpful in guiding surgical biopsies and differentiating recurrent tumor from treatment related changes.

Diffusion Weighted/Tensor Imaging, Functional MRI and Perfusion Weighted Imaging in Glioblastoma—Foundations and Future

PubMed Central

Salama, Gayle R.; Heier, Linda A.; Patel, Praneil; Ramakrishna, Rohan; Magge, Rajiv; Tsiouris, Apostolos John

2018-01-01

In this article, we review the basics of diffusion tensor imaging and functional MRI, their current utility in preoperative neurosurgical mapping, and their limitations. We also discuss potential future applications, including implementation of resting state functional MRI. We then discuss perfusion and diffusion-weighted imaging and their application in advanced neuro-oncologic practice. We explain how these modalities can be helpful in guiding surgical biopsies and differentiating recurrent tumor from treatment related changes. PMID:29403420

Jensen-Bregman LogDet Divergence for Efficient Similarity Computations on Positive Definite Tensors

DTIC Science & Technology

2012-05-02

function of Legendre-type on int(domS) [29]. From (7) the following properties of dφ(x, y) are apparent: strict convexity in x; asym- metry; non ...tensor imaging. An important task in all of these applications is to compute the distance between covariance matrices using a (dis)similarity function ...important task in all of these applications is to compute the distance between covariance matrices using a (dis)similarity function , for which the natural

Features of plastic strain localization at the yield plateau in Hadfield steel single crystals

NASA Astrophysics Data System (ADS)

Barannikova, S. A.; Zuev, L. B.

2008-07-01

Spatiotemporal distributions of local components of the plastic distortion tensor in Hadfield steel single crystals oriented for single twinning have been studied under active tensile straining conditions using the double-exposure speckle photography technique. Features of the macroscopically inhomogeneous strain localization at the yield plateau are considered. Relations between local components of the plastic distortion tensor in the zone of strain localization are analyzed.

Positivity bound on the imaginary part of the right-chiral tensor coupling gR in polarized top quark decay

NASA Astrophysics Data System (ADS)

Groote, S.; Körner, J. G.

2017-12-01

We derive a positivity bound on the right-chiral tensor coupling Im gR in polarized top quark decay by analyzing the angular decay distribution of the three-body polarized top quark decay t (↑)→b +ℓ++νℓ in next-to-leading order QCD. We obtain the bound -0.0420 ≤Im gR≤0.0420 .

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

TWave: High-Order Analysis of Functional MRI

PubMed Central

Barnathan, Michael; Megalooikonomou, Vasileios; Faloutsos, Christos; Faro, Scott; Mohamed, Feroze B.

2011-01-01

The traditional approach to functional image analysis models images as matrices of raw voxel intensity values. Although such a representation is widely utilized and heavily entrenched both within neuroimaging and in the wider data mining community, the strong interactions among space, time, and categorical modes such as subject and experimental task inherent in functional imaging yield a dataset with “high-order” structure, which matrix models are incapable of exploiting. Reasoning across all of these modes of data concurrently requires a high-order model capable of representing relationships between all modes of the data in tandem. We thus propose to model functional MRI data using tensors, which are high-order generalizations of matrices equivalent to multidimensional arrays or data cubes. However, several unique challenges exist in the high-order analysis of functional medical data: naïve tensor models are incapable of exploiting spatiotemporal locality patterns, standard tensor analysis techniques exhibit poor efficiency, and mixtures of numeric and categorical modes of data are very often present in neuroimaging experiments. Formulating the problem of image clustering as a form of Latent Semantic Analysis and using the WaveCluster algorithm as a baseline, we propose a comprehensive hybrid tensor and wavelet framework for clustering, concept discovery, and compression of functional medical images which successfully addresses these challenges. Our approach reduced runtime and dataset size on a 9.3 GB finger opposition motor task fMRI dataset by up to 98% while exhibiting improved spatiotemporal coherence relative to standard tensor, wavelet, and voxel-based approaches. Our clustering technique was capable of automatically differentiating between the frontal areas of the brain responsible for task-related habituation and the motor regions responsible for executing the motor task, in contrast to a widely used fMRI analysis program, SPM, which only detected the latter region. Furthermore, our approach discovered latent concepts suggestive of subject handedness nearly 100x faster than standard approaches. These results suggest that a high-order model is an integral component to accurate scalable functional neuroimaging. PMID:21729758

Flexible Force Field Parameterization through Fitting on the Ab Initio-Derived Elastic Tensor

PubMed Central

2017-01-01

Constructing functional forms and their corresponding force field parameters for the metal–linker interface of metal–organic frameworks is challenging. We propose fitting these parameters on the elastic tensor, computed from ab initio density functional theory calculations. The advantage of this top-down approach is that it becomes evident if functional forms are missing when components of the elastic tensor are off. As a proof-of-concept, a new flexible force field for MIL-47(V) is derived. Negative thermal expansion is observed and framework flexibility has a negligible effect on adsorption and transport properties for small guest molecules. We believe that this force field parametrization approach can serve as a useful tool for developing accurate flexible force field models that capture the correct mechanical behavior of the full periodic structure. PMID:28661672

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

PubMed

Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

2015-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Technical Reports Server (NTRS)

Lee, Moon Joo

1990-01-01

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

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

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

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

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

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

DOE PAGES

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

2018-05-17

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

Theory of electron g-tensor in bulk and quantum-well semiconductors

NASA Astrophysics Data System (ADS)

Lau, Wayne H.; Flatte', Michael E.

2004-03-01

We present quantitative calculations for the electron g-tensors in bulk and quantum-well semiconductors based on a generalized P.p envelope function theory solved in a fourteen-band restricted basis set. The dependences of g-tensor on structure, magnetic field, carrier density, temperature, and spin polarization have been explored and will be described. It is found that at temperatures of a few Kelvin and fields of a few Tesla, the g-tensors for bulk semiconductors develop quasi-steplike dependences on carrier density or magnetic field due to magnetic quantization, and this effect is even more pronounced in quantum-well semiconductors due to the additional electric quantization along the growth direction. The influence of quantum confinement on the electron g-tensors in QWs is studied by examining the dependence of electron g-tensors on well width. Excellent agreement between these calculated electron g-tensors and measurements [1-2] is found for GaAs/AlGaAs QWs. This work was supported by DARPA/ARO. [1] A. Malinowski and R. T. Harley, Phys. Rev. B 62, 2051 (2000);[2] Le Jeune et al., Semicond. Sci. Technol. 12, 380 (1997).

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.

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

NASA Astrophysics Data System (ADS)

Martin, Alexandre; Torrent, Marc; Caracas, Razvan

2015-03-01

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

BRIEF COMMUNICATION: A note on the Coulomb collision operator in curvilinear coordinates

NASA Astrophysics Data System (ADS)

Goncharov, P. R.

2010-10-01

The dynamic friction force, diffusion tensor, flux density in velocity space and Coulomb collision term are expressed in curvilinear coordinates via Trubnikov potential functions corresponding to each species of a background plasma. For comparison, explicit formulae are given for the dynamic friction force, diffusion tensor and collisional flux density in velocity space in curvilinear coordinates via Rosenbluth potential functions summed over all species of the background plasma.

Autism Spectrum Disorder: Does Neuroimaging Support the DSM-5 Proposal for a Symptom Dyad? A Systematic Review of Functional Magnetic Resonance Imaging and Diffusion Tensor Imaging Studies

ERIC Educational Resources Information Center

Pina-Camacho, Laura; Villero, Sonia; Fraguas, David; Boada, Leticia; Janssen, Joost; Navas-Sanchez, Francisco J.; Mayoral, Maria; Llorente, Cloe; Arango, Celso; Parellada, Mara

2012-01-01

A systematic review of 208 studies comprising functional magnetic resonance imaging and diffusion tensor imaging data in patients with "autism spectrum disorder" (ASD) was conducted, in order to determine whether these data support the forthcoming DSM-5 proposal of a social communication and behavioral symptom dyad. Studies consistently reported…

Diffusion approximation with polarization and resonance effects for the modelling of seismic waves in strongly scattering small-scale media

NASA Astrophysics Data System (ADS)

Margerin, Ludovic

2013-01-01

This paper presents an analytical study of the multiple scattering of seismic waves by a collection of randomly distributed point scatterers. The theory assumes that the energy envelopes are smooth, but does not require perturbations to be small, thereby allowing the modelling of strong, resonant scattering. The correlation tensor of seismic coda waves recorded at a three-component sensor is decomposed into a sum of eigenmodes of the elastodynamic multiple scattering (Bethe-Salpeter) equation. For a general moment tensor excitation, a total number of four modes is necessary to describe the transport of seismic waves polarization. Their spatio-temporal dependence is given in closed analytical form. Two additional modes transporting exclusively shear polarizations may be excited by antisymmetric moment tensor sources only. The general solution converges towards an equipartition mixture of diffusing P and S waves which allows the retrieval of the local Green's function from coda waves. The equipartition time is obtained analytically and the impact of absorption on Green's function reconstruction is discussed. The process of depolarization of multiply scattered waves and the resulting loss of information is illustrated for various seismic sources. It is shown that coda waves may be used to characterize the source mechanism up to lapse times of the order of a few mean free times only. In the case of resonant scatterers, a formula for the diffusivity of seismic waves incorporating the effect of energy entrapment inside the scatterers is obtained. Application of the theory to high-contrast media demonstrates that coda waves are more sensitive to slow rather than fast velocity anomalies by several orders of magnitude. Resonant scattering appears as an attractive physical phenomenon to explain the small values of the diffusion constant of seismic waves reported in volcanic areas.

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

PubMed

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

2011-01-01

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

DTI segmentation by statistical surface evolution.

PubMed

Lenglet, Christophe; Rousson, Mikaël; Deriche, Rachid

2006-06-01

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

Parallel language constructs for tensor product computations on loosely coupled architectures

NASA Technical Reports Server (NTRS)

Mehrotra, Piyush; Vanrosendale, John

1989-01-01

Distributed memory architectures offer high levels of performance and flexibility, but have proven awkard to program. Current languages for nonshared memory architectures provide a relatively low level programming environment, and are poorly suited to modular programming, and to the construction of libraries. A set of language primitives designed to allow the specification of parallel numerical algorithms at a higher level is described. Tensor product array computations are focused on along with a simple but important class of numerical algorithms. The problem of programming 1-D kernal routines is focused on first, such as parallel tridiagonal solvers, and then how such parallel kernels can be combined to form parallel tensor product algorithms is examined.

Finsler geometry of nonlinear elastic solids with internal structure

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

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

A General Sparse Tensor Framework for Electronic Structure Theory

DOE PAGES

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

2017-01-24

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

Octupolar tensors for liquid crystals

NASA Astrophysics Data System (ADS)

Chen, Yannan; Qi, Liqun; Virga, Epifanio G.

2018-01-01

A third-rank three-dimensional symmetric traceless tensor, called the octupolar tensor, has been introduced to study tetrahedratic nematic phases in liquid crystals. The octupolar potential, a scalar-valued function generated on the unit sphere by that tensor, should ideally have four maxima (on the vertices of a tetrahedron), but it was recently found to possess an equally generic variant with three maxima instead of four. It was also shown that the irreducible admissible region for the octupolar tensor in a three-dimensional parameter space is bounded by a dome-shaped surface, beneath which is a separatrix surface connecting the two generic octupolar states. The latter surface, which was obtained through numerical continuation, may be physically interpreted as marking a possible intra-octupolar transition. In this paper, by using the resultant theory of algebraic geometry and the E-characteristic polynomial of spectral theory of tensors, we give a closed-form, algebraic expression for both the dome-shaped surface and the separatrix surface. This turns the envisaged intra-octupolar transition into a quantitative, possibly observable prediction.

Fluid Registration of Diffusion Tensor Images Using Information Theory

PubMed Central

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

2008-01-01

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

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

Bordin, Lorenzo; Creminelli, Paolo; Mirbabayi, Mehrdad

We point out that tensor consistency relations—i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum—are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: de Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor consistency relations in observations, asmore » a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) graviton exchange contribution to the scalar four-point function; (b) quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.« less

Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

NASA Astrophysics Data System (ADS)

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo; Vernizzi, Filippo

2017-09-01

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlator can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.

Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model

NASA Astrophysics Data System (ADS)

Chen, Junlong; Liu, Jueping

2017-01-01

The more carefully defined and more appropriate 2++ tensor glueball current is a S Uc(3 ) gauge-invariant, symmetric, traceless, and conserved Lorentz-irreducible tensor. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted and calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. In addition to taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the 2++ tensor glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width, and coupling constants for the 2++ resonance in which the glueball fraction is dominant are obtained.

Approximate bound-state solutions of the Dirac equation for the generalized yukawa potential plus the generalized tensor interaction

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Maghsoodi, Elham; Hassanabadi, Hassan; Obu, Joseph A.

2014-05-01

In this paper, we obtain the approximate analytical bound-state solutions of the Dirac particle with the generalized Yukawa potential within the framework of spin and pseudospin symmetries for the arbitrary к state with a generalized tensor interaction. The generalized parametric Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wave functions in closed form. We also report some numerical results and present figures to show the effect of the tensor interaction.

Stochastic Gravity: Theory and Applications.

PubMed

Hu, Bei Lok; Verdaguer, Enric

2004-01-01

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

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

Berezhiani, Lasha; Khoury, Justin; Wang, Junpu, E-mail: lashaber@gmail.com, E-mail: jkhoury@sas.upenn.edu, E-mail: jwang217@jhu.edu

Single-field perturbations satisfy an infinite number of consistency relations constraining the squeezed limit of correlation functions at each order in the soft momentum. These can be understood as Ward identities for an infinite set of residual global symmetries, or equivalently as Slavnov-Taylor identities for spatial diffeomorphisms. In this paper, we perform a number of novel, non-trivial checks of the identities in the context of single field inflationary models with arbitrary sound speed. We focus for concreteness on identities involving 3-point functions with a soft external mode, and consider all possible scalar and tensor combinations for the hard-momentum modes. In allmore » these cases, we check the consistency relations up to and including cubic order in the soft momentum. For this purpose, we compute for the first time the 3-point functions involving 2 scalars and 1 tensor, as well as 2 tensors and 1 scalar, for arbitrary sound speed.« less

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

NASA Astrophysics Data System (ADS)

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

2012-05-01

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

Analysis of the total kinetic energy of fission fragments with the Langevin equation

NASA Astrophysics Data System (ADS)

Usang, M. D.; Ivanyuk, F. A.; Ishizuka, C.; Chiba, S.

2017-12-01

We analyzed the total kinetic energy (TKE) of fission fragments with three-dimensional Langevin calculations for a series of actinides and Fm isotopes at various excitation energies. This allowed us to establish systematic trends of TKE with Z2/A1 /3 of the fissioning system and as a function of excitation energy. In the mass-energy distributions of fission fragments we see the contributions from the standard, super-long, and super-short (in the case of 258Fm) fission modes. For the fission fragments mass distribution of 258Fm we obtained a single peak mass distribution. The decomposition of TKE into the prescission kinetic energy and Coulomb repulsion showed that decrease of TKE with growing excitation energy is accompanied by a decrease of prescission kinetic energy. It was also found that transport coefficients (friction and inertia tensors) calculated by a microscopic model and by macroscopic models give drastically different behaviors of TKE as a function of excitation energy. The results obtained with microscopic transport coefficients are much closer to experimental data than those calculated with macroscopic ones.

Analysis of stress fields and elastic energies in the vicinity of nanograin boundaries using the disclination approach

NASA Astrophysics Data System (ADS)

Sukhanov, Ivan I.; Ditenberg, Ivan A.

2017-12-01

The paper provides a theoretical analysis of elastic stresses and elastic energy distribution in nanostructured metal materials in the vicinity of nanograin boundaries with a high partial disclination density. The analysis demonstrates the stress field distribution in disclination grain boundary configurations as a function of nanograin size, taking into account the superposition of these stresses in screening the disclination pile-ups. It is found that the principal stress tensor components reach maximum values only in disclination planes P ≈ E/25 and that the stress gradients peak at nodal points ∂P/∂x ≈ 0.08E nm-1. The shear stress components are localized within the physical grain size, and the specific elastic energy distribution for such configurations reveals characteristic local maxima which can be the cause for physical broadening of nanograin boundaries.

Multidimensional Skyrme-density-functional study of the spontaneous fission of 238U

DOE PAGES

Sadhukhan, J.; Mazurek, K.; Dobaczewski, J.; ...

2015-01-01

We determined the spontaneous fission lifetime of 238U by a minimization of the action integral in a three-dimensional space of collective variables. Apart from the mass-distribution multipole moments Q 20 (elongation) and Q 30 (left–right asymmetry), we also considered the pairing-fluctuation parameter λ 2 as a collective coordinate. The collective potential was obtained self-consistently using the Skyrme energy density functional SkM*. The inertia tensor was obtained within the nonperturbative cranking approximation to the adiabatic time-dependent Hartree–Fock–Bogoliubov approach. As a result, the pairing-fluctuation parameter λ 2 allowed us to control the pairing gap along the fission path, which significantly changed themore » spontaneous fission lifetime.« less

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory.

PubMed

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M; Dean, David S

2018-02-28

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M.; Dean, David S.

2018-02-01

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

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

Liakh, Dmitry I

While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locallymore » supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).« less

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.

Cross-scale efficient tensor contractions for coupled cluster computations through multiple programming model backends

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

Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel

Coupled-cluster methods provide highly accurate models of molecular structure through explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix–matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts tomore » extend the Libtensor framework to work in the distributed memory environment in a scalable and energy-efficient manner. We achieve up to 240× speedup compared with the optimized shared memory implementation of Libtensor. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures (Cray XC30 and XC40, and IBM Blue Gene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance, tasking and bulk synchronous models. Nevertheless, we preserve a unified interface to both programming models to maintain the productivity of computational quantum chemists.« less

Cross-scale efficient tensor contractions for coupled cluster computations through multiple programming model backends

DOE PAGES

Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel; ...

2017-03-08

Coupled-cluster methods provide highly accurate models of molecular structure through explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix–matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts tomore » extend the Libtensor framework to work in the distributed memory environment in a scalable and energy-efficient manner. We achieve up to 240× speedup compared with the optimized shared memory implementation of Libtensor. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures (Cray XC30 and XC40, and IBM Blue Gene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance, tasking and bulk synchronous models. Nevertheless, we preserve a unified interface to both programming models to maintain the productivity of computational quantum chemists.« less

Lattice QCD calculations of nucleon transverse momentum-dependent parton distributions using clover and domain wall fermions

DOE PAGES

Yoon, Boram; Bhattacharya, Tanmoy; Gupta, Rajan; ...

2015-01-01

Here, we present a lattice QCD calculation of transverse momentum dependent parton distribution functions (TMDs) of protons using staple-shaped Wilson lines. For time-reversal odd observables, we calculate the generalized Sivers and Boer-Mulders transverse momentum shifts in SIDIS and DY cases, and for T-even observables we calculate the transversity related to the tensor charge and the generalized worm-gear shift. The calculation is done on two different n f = 2+1 ensembles: domain-wall fermion (DWF) with lattice spacing 0:084fm and pion mass of 297 MeV, and clover fermion with lattice spacing 0:114 fm and pion mass of 317 MeV. The results frommore » those two different discretizations are consistent with each other.« less

Behavior of the Position-Spread Tensor in Diatomic Systems.

PubMed

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

2013-12-10

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

Complex conductivity of organic-rich shales

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Stochastic Theory for the Clustering of Rapidly Settling, Low-Inertia Particle Pairs in Isotropic Turbulence - II

NASA Astrophysics Data System (ADS)

Rani, Sarma; Gupta, Vijay; Koch, Donald

2017-11-01

A stochastic theory is developed to predict the Radial Distribution Function (RDF) of monodisperse, rapidly settling, low-inertia particle pairs in isotropic turbulence. In the second version of the theory (T2), the dimensionless strain-rate and rotation-rate tensors ``seen'' by the primary particle are assumed to be Gaussian distributed, where the strain-rate and rotation-rate tensors are non-dimensionlized using the instantaneous dissipation rate and enstrophy, respectively. Accordingly, closure is again derived for the drift flux driving particle clustering, in the asympotic limits of Stokes number St =τp /τη << 1 , and settling paramater Sv = gτp /uη >> 1 . Only the drift flux differs for T1 and T2, while the diffusive flux remains the same. The RDFs for rapidly settling pairs again show an inverse power dependency on pair separation r with an exponent, c1, that is proportional to St2 . However, in contrast to T1, the c1 values predicted by T2 show good qualitative and resonable quantitative agreement with the c1 values obtained from DNS of settling particles in isotropic turbulence. Further, the T2-predicted c1 values are smaller than those obtained from DNS of non-settling particles in isotropic turbulence. Funding from the CBET Division of the National Science Foundation is gratefully acknowledged.

The influence of coordinated defects on inhomogeneous broadening in cubic lattices

NASA Astrophysics Data System (ADS)

Matheson, P. L.; Sullivan, Francis P.; Evenson, William E.

2016-12-01

The joint probability distribution function (JPDF) of electric field gradient (EFG) tensor components in cubic materials is dominated by coordinated pairings of defects in shells near probe nuclei. The contributions from these inner shell combinations and their surrounding structures contain the essential physics that determine the PAC-relevant quantities derived from them. The JPDF can be used to predict the nature of inhomogeneous broadening (IHB) in perturbed angular correlation (PAC) experiments by modeling the G 2 spectrum and finding expectation values for V zz and η. The ease with which this can be done depends upon the representation of the JPDF. Expanding on an earlier work by Czjzek et al. (Hyperfine Interact. 14, 189-194, 1983), Evenson et al. (Hyperfine Interact. 237, 119, 2016) provide a set of coordinates constructed from the EFG tensor invariants they named W 1 and W 2. Using this parameterization, the JPDF in cubic structures was constructed using a point charge model in which a single trapped defect (TD) is the nearest neighbor to a probe nucleus. Individual defects on nearby lattice sites pair with the TD to provide a locus of points in the W 1- W 2 plane around which an amorphous-like distribution of probability density grows. Interestingly, however, marginal, separable PDFs appear adequate to model IHB relevant cases. We present cases from simulations in cubic materials illustrating the importance of these near-shell coordinations.

Precision Cosmology

NASA Astrophysics Data System (ADS)

Jones, Bernard J. T.

2017-04-01

Preface; Notation and conventions; Part I. 100 Years of Cosmology: 1. Emerging cosmology; 2. The cosmic expansion; 3. The cosmic microwave background; 4. Recent cosmology; Part II. Newtonian Cosmology: 5. Newtonian cosmology; 6. Dark energy cosmological models; 7. The early universe; 8. The inhomogeneous universe; 9. The inflationary universe; Part III. Relativistic Cosmology: 10. Minkowski space; 11. The energy momentum tensor; 12. General relativity; 13. Space-time geometry and calculus; 14. The Einstein field equations; 15. Solutions of the Einstein equations; 16. The Robertson-Walker solution; 17. Congruences, curvature and Raychaudhuri; 18. Observing and measuring the universe; Part IV. The Physics of Matter and Radiation: 19. Physics of the CMB radiation; 20. Recombination of the primeval plasma; 21. CMB polarisation; 22. CMB anisotropy; Part V. Precision Tools for Precision Cosmology: 23. Likelihood; 24. Frequentist hypothesis testing; 25. Statistical inference: Bayesian; 26. CMB data processing; 27. Parametrising the universe; 28. Precision cosmology; 29. Epilogue; Appendix A. SI, CGS and Planck units; Appendix B. Magnitudes and distances; Appendix C. Representing vectors and tensors; Appendix D. The electromagnetic field; Appendix E. Statistical distributions; Appendix F. Functions on a sphere; Appendix G. Acknowledgements; References; Index.

Nonlinear resistivity for magnetohydrodynamical models

DOE PAGES

Lingam, M.; Hirvijoki, E.; Pfefferlé, D.; ...

2017-04-20

A new formulation of the plasma resistivity that stems from the collisional momentum-transfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocity-space moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentum-transfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional tomore » a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the well-established electron inertia and Hall terms is also examined. Lastly, the subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.« less

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.

Mean-intercept anisotropy analysis of porous media. II. Conceptual shortcomings of the MIL tensor definition and Minkowski tensors as an alternative.

PubMed

Klatt, Michael A; Schröder-Turk, Gerd E; Mecke, Klaus

2017-07-01

Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors to quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, e.g., of trabecular bone in medical physics. Yet, in this series of two papers we demonstrate that it has conceptual shortcomings that limit the validity of its results. We test the validity of general assumptions regarding the properties of the mean-intercept length tensor using analytical formulas for the mean-intercept lengths in anisotropic Boolean models (derived in part I of this series), augmented by numerical simulations. We discuss in detail the functional form of the mean intercept length as a function of the test line orientations. As the most prominent result, we find that, at least for the example of overlapping grains modeling porous media, the polar plot of the mean intercept length is in general not an ellipse and hence not represented by a second-rank tensor. This is in stark contrast to the common understanding that for a large collection of grains the mean intercept length figure averages to an ellipse. The standard mean intercept length tensor defined by a least-square fit of an ellipse is based on a model mismatch, which causes an intrinsic lack of accuracy. Our analysis reveals several shortcomings of the mean intercept length tensor analysis that pose conceptual problems and limitations on the information content of this commonly used analysis method. We suggest the Minkowski tensors from integral geometry as alternative sensitive measures of anisotropy. The Minkowski tensors allow for a robust, comprehensive, and systematic approach to quantify various aspects of structural anisotropy. We show the Minkowski tensors to be more sensitive, in the sense, that they can quantify the remnant anisotropy of structures not captured by the mean intercept length analysis. If applied to porous tissue and microstructures, this improved structure characterization can yield new insights into the relationships between geometry and material properties. © 2017 American Association of Physicists in Medicine.

Symmetric factorization of the conformation tensor in viscoelastic fluid models

NASA Astrophysics Data System (ADS)

Thomases, Becca; Balci, Nusret; Renardy, Michael; Doering, Charles

2010-11-01

The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.

LiDAR point classification based on sparse representation

NASA Astrophysics Data System (ADS)

Li, Nan; Pfeifer, Norbert; Liu, Chun

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2007-03-01

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

The Electron Diffusion Region: Forces and Currents

NASA Technical Reports Server (NTRS)

Hesse, Michael

2008-01-01

The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertia1 effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.

The Electron Diffusion Region: Forces and Currents

NASA Technical Reports Server (NTRS)

Hesse, Michael

2009-01-01

The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertial effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.

Conformal Collineations of the Ricci and Energy-Momentum Tensors in Static Plane Symmetric Space-Times

NASA Astrophysics Data System (ADS)

Akhtar, S. S.; Hussain, T.; Bokhari, A. H.; Khan, F.

2018-04-01

We provide a complete classification of static plane symmetric space-times according to conformal Ricci collineations (CRCs) and conformal matter collineations (CMCs) in both the degenerate and nondegenerate cases. In the case of a nondegenerate Ricci tensor, we find a general form of the vector field generating CRCs in terms of unknown functions of t and x subject to some integrability conditions. We then solve the integrability conditions in different cases depending upon the nature of the Ricci tensor and conclude that the static plane symmetric space-times have a 7-, 10- or 15-dimensional Lie algebra of CRCs. Moreover, we find that these space-times admit an infinite number of CRCs if the Ricci tensor is degenerate. We use a similar procedure to study CMCs in the case of a degenerate or nondegenerate matter tensor. We obtain the exact form of some static plane symmetric space-time metrics that admit nontrivial CRCs and CMCs. Finally, we present some physical applications of our obtained results by considering a perfect fluid as a source of the energy-momentum tensor.

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

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

Ye, Zhihong; Sato, Nobuo; Allada, Kalyan

© 2017 The Authors Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate themore » uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.« less

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

NASA Astrophysics Data System (ADS)

Ye, Zhihong; Sato, Nobuo; Allada, Kalyan; Liu, Tianbo; Chen, Jian-Ping; Gao, Haiyan; Kang, Zhong-Bo; Prokudin, Alexei; Sun, Peng; Yuan, Feng

2017-04-01

Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate the uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

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

Ye, Zhihong; Sato, Nobuo; Allada, Kalyan

2017-01-27

Here, future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the transversity quark distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID. Especially, we develop a model-independent method based on the hessian matrix analysis that allows to estimate the uncertainties of the transversity quarkmore » distributions and their tensor charge contributions extracted from the pseudo-data for the SoLID. Both u and d-quark transversity distributions are shown to be very well constrained in the kinematical region of the future experiments with the proton and the effective neutron targets.« less

Mueller tensor approach for nonlinear optics in turbid media

NASA Astrophysics Data System (ADS)

Ulcickas, James R. W.; Deng, Fengyuan; Ding, Changqin; Simpson, Garth J.

2018-02-01

As plane-polarized light propagates through a turbid medium, scattering alters the phase and polarization differently in different locations. The corresponding depolarization of the beam complicates recovery of the rich information content contained within the polarization-dependence of second harmonic generation (SHG) microscopy. A theoretical framework connecting Jones and Stokes formalisms for describing optical polarization allows prediction of the polarization-dependent SHG produced from "ballistic", but depolarized incident light. Measurements with collagen-rich tissue sections support the predictions of the framework. Partially polarized SHG produced from a depolarized source enabled recovery of local orientation distribution for collagen and local tensor information. Bridging the gap between SHG instigated by fully depolarized light and partially polarized light more common to practical turbid systems, a method for predicting local nonlinear optical susceptibility tensor elements was developed and applied to collagen in thick sections. Recovered values for the tensor element ratio ρ are in good agreement with previous results for thin tissue and literature reports.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

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

PubMed

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

2017-05-24

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

Cohomologie des Groupes Localement Compacts et Produits Tensoriels Continus de Representations

ERIC Educational Resources Information Center

Guichardet, A.

1976-01-01

Contains few and sometimes incomplete proofs on continuous tensor products of Hilbert spaces and of group representations, and on the irreducibility of the latter. Theory of continuous tensor products of Hilbert Spaces is closely related to that of conditionally positive definite functions; it relies on the technique of symmetric Hilbert spaces,…

A Variational Framework for Exemplar-Based Image Inpainting

DTIC Science & Technology

2010-04-01

Physical Review 106(4), 620–30 (1957) 37. Jia, J., Tang, C.K.: Inference of segmented color and texture description by tensor voting . IEEE Trans. on PAMI 26...use of other patch error functions based on the comparison of structure tensors , which could provide a more robust estimation of the morpho- logical

Bivariate tensor product [Formula: see text]-analogue of Kantorovich-type Bernstein-Stancu-Schurer operators.

PubMed

Cai, Qing-Bo; Xu, Xiao-Wei; Zhou, Guorong

2017-01-01

In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of [Formula: see text]-integers. We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of continuity for the bivariate case and estimate a convergence theorem for the Lipschitz continuous functions. We also give some graphs and numerical examples to illustrate the convergence properties of these operators to certain functions.

Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

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

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlatormore » can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.« less

Contrasting SYK-like models

NASA Astrophysics Data System (ADS)

Krishnan, Chethan; Pavan Kumar, K. V.; Rosa, Dario

2018-01-01

We contrast some aspects of various SYK-like models with large- N melonic behavior. First, we note that ungauged tensor models can exhibit symmetry breaking, even though these are 0+1 dimensional theories. Related to this, we show that when gauged, some of them admit no singlets, and are anomalous. The uncolored Majorana tensor model with even N is a simple case where gauge singlets can exist in the spectrum. We outline a strategy for solving for the singlet spectrum, taking advantage of the results in arXiv:1706.05364, and reproduce the singlet states expected in N = 2. In the second part of the paper, we contrast the random matrix aspects of some ungauged tensor models, the original SYK model, and a model due to Gross and Rosenhaus. The latter, even though disorder averaged, shows parallels with the Gurau-Witten model. In particular, the two models fall into identical Andreev ensembles as a function of N . In an appendix, we contrast the (expected) spectra of AdS2 quantum gravity, SYK and SYK-like tensor models, and the zeros of the Riemann Zeta function.

Tensorial Minkowski functionals of triply periodic minimal surfaces

PubMed Central

Mickel, Walter; Schröder-Turk, Gerd E.; Mecke, Klaus

2012-01-01

A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors. PMID:24098847

Myofiber Architecture of the Human Atria as Revealed by Submillimeter Diffusion Tensor Imaging.

PubMed

Pashakhanloo, Farhad; Herzka, Daniel A; Ashikaga, Hiroshi; Mori, Susumu; Gai, Neville; Bluemke, David A; Trayanova, Natalia A; McVeigh, Elliot R

2016-04-01

Accurate knowledge of the human atrial fibrous structure is paramount in understanding the mechanisms of atrial electric function in health and disease. Thus far, such knowledge has been acquired from destructive sectioning, and there is a paucity of data about atrial fiber architecture variability in the human population. In this study, we have developed a customized 3-dimensional diffusion tensor magnetic resonance imaging sequence on a clinical scanner that makes it possible to image an entire intact human heart specimen ex vivo at submillimeter resolution. The data from 8 human atrial specimens obtained with this technique present complete maps of the fibrous organization of the human atria. The findings demonstrate that the main features of atrial anatomy are mostly preserved across subjects although the exact location and orientation of atrial bundles vary. Using the full tractography data, we were able to cluster, visualize, and characterize the distinct major bundles in the human atria. Furthermore, quantitative characterization of the fiber angles across the atrial wall revealed that the transmural fiber angle distribution is heterogeneous throughout different regions of the atria. The application of submillimeter diffusion tensor magnetic resonance imaging provides an unprecedented level of information on both human atrial structure, as well as its intersubject variability. The high resolution and fidelity of this data could enhance our understanding of structural contributions to atrial rhythm and pump disorders and lead to improvements in their targeted treatment. © 2016 American Heart Association, Inc.

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

Attractor cosmology from nonminimally coupled gravity

NASA Astrophysics Data System (ADS)

Odintsov, S. D.; Oikonomou, V. K.

2018-03-01

By using a bottom-up reconstruction technique for nonminimally coupled scalar-tensor theories, we realize the Einstein frame attractor cosmologies in the Ω (ϕ )-Jordan frame. For our approach, what is needed for the reconstruction method to work is the functional form of the nonminimal coupling Ω (ϕ ) and of the scalar-to-tensor ratio, and also the assumption of the slow-roll inflation in the Ω (ϕ )-Jordan frame. By appropriately choosing the scalar-to-tensor ratio, we demonstrate that the observational indices of the attractor cosmologies can be realized directly in the Ω (ϕ )-Jordan frame. We investigate the special conditions that are required to hold true in for this realization to occur, and we provide the analytic form of the potential in the Ω (ϕ )-Jordan frame. Also, by performing a conformal transformation, we find the corresponding Einstein frame canonical scalar-tensor theory, and we calculate in detail the corresponding observational indices. The result indicates that although the spectral index of the primordial curvature perturbations is the same in the Jordan and Einstein frames, at leading order in the e -foldings number, the scalar-to-tensor ratio differs. We discuss the possible reasons behind this discrepancy, and we argue that the difference is due to some approximation we performed to the functional form of the potential in the Einstein frame, in order to obtain analytical results, and also due to the difference in the definition of the e -foldings number in the two frames, which is also pointed out in the related literature. Finally, we find the F (R ) gravity corresponding to the Einstein frame canonical scalar-tensor theory.

An infinite set of Ward identities for adiabatic modes in cosmology

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

Hinterbichler, Kurt; Hui, Lam; Khoury, Justin, E-mail: khinterbichler@perimeterinstitute.ca, E-mail: lh399@columbia.edu, E-mail: jkhoury@sas.upenn.edu

2014-01-01

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate N+1-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes. We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations. These symmetries can be labeled by an integer n. At each order n, the consistency relations constrain — completely for n = 0,1, and partially for n ≥ 2 — themore » q{sup n} behavior of the soft limits. The identities at n = 0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n = 1 gives the recently-discovered conformal consistency relations, and the identities for n ≥ 2 are new. As a check, we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation.« less

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

USGS Publications Warehouse

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

2003-01-01

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

Somatosensory attunement to the rigid body laws.

PubMed

Shockley, K; Grocki, M; Carello, C; Turvey, M T

2001-01-01

In the most general case, haptic perception of an object's heaviness is most likely the perception of the object's resistance to movement, determined jointly by the object's mass and mass distribution. In two experiments with occluded objects wielded freely in three dimensions, we showed additive effects on perceived heaviness of mass and the inertia tensor. Our manipulations of the inertia tensor were directed specifically at the volume and symmetry of the inertia ellipsoid, quantities that can be understood as important to controlling the level and patterning of muscular forces, respectively. Ellipsoid volume and symmetry were found to have separate effects on perceptual reports of heaviness that were invariant over different tensors. Independent sensitivities to translational inertia and particular characterizations of rotational inertia suggest specialized somatosensory attunement to the rigid body laws.

TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS

PubMed Central

Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.

2017-01-01

Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions. PMID:29332971

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

DOE PAGES

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

2015-04-30

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

Diffractometric measurement of the temperature dependence of piezoelectric tensor in GMO monocrystal

NASA Astrophysics Data System (ADS)

Breczko, Teodor; Lempaszek, Andrzej

2007-04-01

Functional materials, of which an example is ferroelectric, ferroelastic monocrystal of molybdate (III) gadolinium (VI), are often used in the micro-motor operators (micro-servo motors) working in changeable environment conditions. Most frequently this change refers to temperature. That is why the important practical problem is the precise measurement of the value of piezoelectric tensor elements in dependence on the temperature of a particular monocrystal. In the presented article for this kind of measurements, the use of X-ray diffractometer has been shown. The advantage of the method presented is that, apart from precise dependence measurement between the temperature of a monocrystal and the value of piezoelectric tensor elements, it enables synchronous measurement of the value of thermal expansion tensor elements for a monocrystal.

Functional Generalized Additive Models.

PubMed

McLean, Mathew W; Hooker, Giles; Staicu, Ana-Maria; Scheipl, Fabian; Ruppert, David

2014-01-01

We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F { X ( t ), t } where F (·,·) is an unknown regression function and X ( t ) is a functional covariate. Rather than having an additive model in a finite number of principal components as in Müller and Yao (2008), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate F (·,·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where X ( t ) is a signal from diffusion tensor imaging at position, t , along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. R code for performing the simulations and fitting the FGAM can be found in supplemental materials available online.

White Matter Compromise of Callosal and Subcortical Fiber Tracts in Children with Autism Spectrum Disorder: A Diffusion Tensor Imaging Study

ERIC Educational Resources Information Center

Shukla, Dinesh K.; Keehn, Brandon; Lincoln, Alan J.; Muller, Ralph-Axel

2010-01-01

Objective: Autism spectrum disorder (ASD) is increasingly viewed as a disorder of functional networks, highlighting the importance of investigating white matter and interregional connectivity. We used diffusion tensor imaging (DTI) to examine white matter integrity for the whole brain and for corpus callosum, internal capsule, and middle…

Invariant operators, orthogonal bases and correlators in general tensor models

NASA Astrophysics Data System (ADS)

Diaz, Pablo; Rey, Soo-Jong

2018-07-01

We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry Gd = U (N1) ⊗ ⋯ ⊗ U (Nd). As a continuation and completion of our earlier work, we present two natural ways of counting invariants, one for arbitrary Gd and another valid for large rank of Gd. We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of Gd diagonalizes the two-point function of the free theory. It is analogous to the restricted Schur basis used in matrix models. We show that the constructions get almost identical as we swap the Littlewood-Richardson numbers in multi-matrix models with Kronecker coefficients in general tensor models. We explore the parallelism between matrix model and tensor model in depth from the perspective of representation theory and comment on several ideas for future investigation.

Variational optical flow estimation based on stick tensor voting.

PubMed

Rashwan, Hatem A; Garcia, Miguel A; Puig, Domenec

2013-07-01

Variational optical flow techniques allow the estimation of flow fields from spatio-temporal derivatives. They are based on minimizing a functional that contains a data term and a regularization term. Recently, numerous approaches have been presented for improving the accuracy of the estimated flow fields. Among them, tensor voting has been shown to be particularly effective in the preservation of flow discontinuities. This paper presents an adaptation of the data term by using anisotropic stick tensor voting in order to gain robustness against noise and outliers with significantly lower computational cost than (full) tensor voting. In addition, an anisotropic complementary smoothness term depending on directional information estimated through stick tensor voting is utilized in order to preserve discontinuity capabilities of the estimated flow fields. Finally, a weighted non-local term that depends on both the estimated directional information and the occlusion state of pixels is integrated during the optimization process in order to denoise the final flow field. The proposed approach yields state-of-the-art results on the Middlebury benchmark.

Constant-roll tachyon inflation and observational constraints

NASA Astrophysics Data System (ADS)

Gao, Qing; Gong, Yungui; Fei, Qin

2018-05-01

For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio to the first order of epsilon1 by using the method of Bessel function approximation. The derived ns-r results are compared with the observations, we find that only the constant-roll inflation with ηH being a constant is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflation which is consistent with the observations.

A Landau fluid model for dispersive magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Passot, T.; Sulem, P. L.

2004-11-01

A monofluid model with Landau damping is presented for strongly magnetized electron-proton collisionless plasmas whose distribution functions are close to bi-Maxwellians. This description that includes dynamical equations for the gyrotropic components of the pressure and heat flux tensors, extends the Landau-fluid model of Snyder, Hammett, and Dorland [Phys. Plasmas 4, 3974 (1997)] by retaining Hall effect and finite Larmor radius corrections. It accurately reproduces the weakly nonlinear dynamics of dispersive Alfvén waves whose wavelengths are large compared to the ion inertial length, whatever their direction of propagation, and also the rapid Landau dissipation of long magnetosonic waves in a warm plasma.

Relativistic fluid dynamics with spin

NASA Astrophysics Data System (ADS)

Florkowski, Wojciech; Friman, Bengt; Jaiswal, Amaresh; Speranza, Enrico

2018-04-01

Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the polarization tensor, starting from local equilibrium distribution functions for particles and antiparticles with spin 1/2. The resulting set of differential equations extends the standard picture of perfect-fluid hydrodynamics with a conserved entropy current in a minimal way. This framework can be used in space-time analyses of the evolution of spin and polarization in various physical systems including high-energy nuclear collisions. We demonstrate that a stationary vortex, which exhibits vorticity-spin alignment, corresponds to a special solution of the spin-hydrodynamical equations.

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

PubMed Central

SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY

2016-01-01

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031

Impaired functional but preserved structural connectivity in limbic white matter tracts in youth with conduct disorder or oppositional defiant disorder plus psychopathic traits.

PubMed

Finger, Elizabeth Carrie; Marsh, Abigail; Blair, Karina Simone; Majestic, Catherine; Evangelou, Iordanis; Gupta, Karan; Schneider, Marguerite Reid; Sims, Courtney; Pope, Kayla; Fowler, Katherine; Sinclair, Stephen; Tovar-Moll, Fernanda; Pine, Daniel; Blair, Robert James

2012-06-30

Youths with conduct disorder or oppositional defiant disorder and psychopathic traits (CD/ODD+PT) are at high risk of adult antisocial behavior and psychopathy. Neuroimaging studies demonstrate functional abnormalities in orbitofrontal cortex and the amygdala in both youths and adults with psychopathic traits. Diffusion tensor imaging in psychopathic adults demonstrates disrupted structural connectivity between these regions (uncinate fasiculus). The current study examined whether functional neural abnormalities present in youths with CD/ODD+PT are associated with similar white matter abnormalities. Youths with CD/ODD+PT and comparison participants completed 3.0 T diffusion tensor scans and functional magnetic resonance imaging scans. Diffusion tensor imaging did not reveal disruption in structural connections within the uncinate fasiculus or other white matter tracts in youths with CD/ODD+PT, despite the demonstration of disrupted amygdala-prefrontal functional connectivity in these youths. These results suggest that disrupted amygdala-frontal white matter connectivity as measured by fractional anisotropy is less sensitive than imaging measurements of functional perturbations in youths with psychopathic traits. If white matter tracts are intact in youths with this disorder, childhood may provide a critical window for intervention and treatment, before significant structural brain abnormalities solidify. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Motor programme activating therapy influences adaptive brain functions in multiple sclerosis: clinical and MRI study.

PubMed

Rasova, Kamila; Prochazkova, Marie; Tintera, Jaroslav; Ibrahim, Ibrahim; Zimova, Denisa; Stetkarova, Ivana

2015-03-01

There is still little scientific evidence for the efficacy of neurofacilitation approaches and their possible influence on brain plasticity and adaptability. In this study, the outcome of a new kind of neurofacilitation approach, motor programme activating therapy (MPAT), was evaluated on the basis of a set of clinical functions and with MRI. Eighteen patients were examined four times with standardized clinical tests and diffusion tensor imaging to monitor changes without therapy, immediately after therapy and 1 month after therapy. Moreover, the strength of effective connectivity was analysed before and after therapy. Patients underwent a 1-h session of MPAT twice a week for 2 months. The data were analysed by nonparametric tests of association and were subsequently statistically evaluated. The therapy led to significant improvement in clinical functions, significant increment of fractional anisotropy and significant decrement of mean diffusivity, and decrement of effective connectivity at supplementary motor areas was observed immediately after the therapy. Changes in clinical functions and diffusion tensor images persisted 1 month after completing the programme. No statistically significant changes in clinical functions and no differences in MRI-diffusion tensor images were observed without physiotherapy. Positive immediate and long-term effects of MPAT on clinical and brain functions, as well as brain microstructure, were confirmed.

A review of anisotropic conductivity models of brain white matter based on diffusion tensor imaging.

PubMed

Wu, Zhanxiong; Liu, Yang; Hong, Ming; Yu, Xiaohui

2018-06-01

The conductivity of brain tissues is not only essential for electromagnetic source estimation (ESI), but also a key reflector of the brain functional changes. Different from the other brain tissues, the conductivity of whiter matter (WM) is highly anisotropic and a tensor is needed to describe it. The traditional electrical property imaging methods, such as electrical impedance tomography (EIT) and magnetic resonance electrical impedance tomography (MREIT), usually fail to image the anisotropic conductivity tensor of WM with high spatial resolution. The diffusion tensor imaging (DTI) is a newly developed technique that can fulfill this purpose. This paper reviews the existing anisotropic conductivity models of WM based on the DTI and discusses their advantages and disadvantages, as well as identifies opportunities for future research on this subject. It is crucial to obtain the linear conversion coefficient between the eigenvalues of anisotropic conductivity tensor and diffusion tensor, since they share the same eigenvectors. We conclude that the electrochemical model is suitable for ESI analysis because the conversion coefficient can be directly obtained from the concentration of ions in extracellular liquid and that the volume fraction model is appropriate to study the influence of WM structural changes on electrical conductivity. Graphical abstract ᅟ.

Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding.

PubMed

Hanni, Matti; Lantto, Perttu; Runeberg, Nino; Jokisaari, Jukka; Vaara, Juha

2004-09-22

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order Møller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.

Particle acceleration very near an x-line in a collisionless plasma

NASA Technical Reports Server (NTRS)

Lyons, L. R.; Pridmore-Brown, D. C.

1995-01-01

In a previous paper, we applied a simplified model for particle motion in the vicinity of a magnetic X-line that had been introduced by Dungey. We used the model to quantitatively show that an electric force along an X-line can be balanced by the gyroviscous force associated with the off-diagonal elements of the pressure tensor. Distribution functions near the X-line were shown to be skewed in azimuth about the magnetic field and to include particles accelerated to very high energies. In the present paper, we apply the previous model and use the distribution functions to evaluate the energization that results from particle interactions with the X-line. We find that, in general, this interaction gives a spectrum of energized particles that can be represented by a Maxwellian distribution. A power-law, high-energy tail does not develop. The thermal energy, K, of the Maxwellian can be expressed simply in terms of the field parameters and particle mass and charge. It is independent of the thermal energy, K(sub i), of the particle distribution incident upon the region of the X-line, provided that K(sub i) is less than K. Significant energization is not found for K(sub i) is greater than K.

The study of autism as a distributed disorder

PubMed Central

Müller, Ralph-Axel

2010-01-01

Past autism research has often been dedicated to tracing the causes of the disorder to a localized neurological abnormality, a single functional network, or a single cognitive-behavioral domain. In this review, I argue that autism is a ‘distributed disorder’ on various levels of study (genetic, neuroanatomical, neurofunctional, behavioral). ‘Localizing’ models are therefore not promising. The large array of potential genetic risk factors suggests that multiple (or all) emerging functional brain networks are affected during early development. This is supported by widespread growth abnormalities throughout the brain. Interactions during development between affected functional networks and atypical experiential effects (associated with atypical behavior) in children with autism further complicate the neurological bases of the disorder, resulting in an ‘exponentially distributed’ profile. Promising approaches to a better characterization of neural endophenotypes in autism are provided by techniques investigating white matter and connectivity, such as MR spectroscopy, diffusion tensor imaging (DTI), and functional connectivity MRI. According to a recent hypothesis, the autistic brain is generally characterized by ‘underconnectivity’. However, not all findings are consistent with this view. The concepts and methodology of functional connectivity need to be refined and results need to be corroborated by anatomical studies (such as DTI tractography) before definitive conclusions can be drawn. PMID:17326118

Optimizing the Four-Index Integral Transform Using Data Movement Lower Bounds Analysis

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

Rajbhandari, Samyam; Rastello, Fabrice; Kowalski, Karol

The four-index integral transform is a fundamental and computationally demanding calculation used in many computational chemistry suites such as NWChem. It transforms a four-dimensional tensor from an atomic basis to a molecular basis. This transformation is most efficiently implemented as a sequence of four tensor contractions that each contract a four-dimensional tensor with a two-dimensional transformation matrix. Differing degrees of permutation symmetry in the intermediate and final tensors in the sequence of contractions cause intermediate tensors to be much larger than the final tensor and limit the number of electronic states in the modeled systems. Loop fusion, in conjunction withmore » tiling, can be very effective in reducing the total space requirement, as well as data movement. However, the large number of possible choices for loop fusion and tiling, and data/computation distribution across a parallel system, make it challenging to develop an optimized parallel implementation for the four-index integral transform. We develop a novel approach to address this problem, using lower bounds modeling of data movement complexity. We establish relationships between available aggregate physical memory in a parallel computer system and ineffective fusion configurations, enabling their pruning and consequent identification of effective choices and a characterization of optimality criteria. This work has resulted in the development of a significantly improved implementation of the four-index transform that enables higher performance and the ability to model larger electronic systems than the current implementation in the NWChem quantum chemistry software suite.« 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.

Reconstruction of apparent orthotropic conductivity tensor image using magnetic resonance electrical impedance tomography

NASA Astrophysics Data System (ADS)

Sajib, Saurav Z. K.; Kim, Ji Eun; Jeong, Woo Chul; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je

2015-03-01

Magnetic resonance electrical impedance tomography visualizes current density and/or conductivity distributions inside an electrically conductive object. Injecting currents into the imaging object along at least two different directions, induced magnetic flux density data can be measured using a magnetic resonance imaging scanner. Without rotating the object inside the scanner, we can measure only one component of the magnetic flux density denoted as Bz. Since the biological tissues such as skeletal muscle and brain white matter show strong anisotropic properties, the reconstruction of anisotropic conductivity tensor is indispensable for the accurate observations in the biological systems. In this paper, we propose a direct method to reconstruct an axial apparent orthotropic conductivity tensor by using multiple Bz data subject to multiple injection currents. To investigate the anisotropic conductivity properties, we first recover the internal current density from the measured Bz data. From the recovered internal current density and the curl-free condition of the electric field, we derive an over-determined matrix system for determining the internal absolute orthotropic conductivity tensor. The over-determined matrix system is designed to use a combination of two loops around each pixel. Numerical simulations and phantom experimental results demonstrate that the proposed algorithm stably determines the orthotropic conductivity tensor.

Investigating Musical Disorders with Diffusion Tensor Imaging: a Comparison of Imaging Parameters

PubMed Central

Loui, Psyche; Schlaug, Gottfried

2009-01-01

The Arcuate Fasciculus (AF) is a bundle of white matter traditionally thought to be responsible for language function. However, its role in music is not known. Here we investigate the connectivity of the AF using Diffusion Tensor Imaging (DTI) and show that musically tone-deaf individuals, who show impairments in pitch discrimination, have reduced connectivity in the AF relative to musically normal-functioning control subjects. Results were robust to variations in imaging parameters and emphasize the importance of brain connectivity in para-linguistic processes such as music. PMID:19673766

Charged Vaidya solution satisfies weak energy condition

NASA Astrophysics Data System (ADS)

Chatterjee, Soumyabrata; Ganguli, Suman; Virmani, Amitabh

2016-07-01

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

Dark matter relics and the expansion rate in scalar-tensor theories

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

Dutta, Bhaskar; Jimenez, Esteban; Zavala, Ivonne, E-mail: dutta@physics.tamu.edu, E-mail: este1985@physics.tamu.edu, E-mail: e.i.zavalacarrasco@swansea.ac.uk

We study the impact of a modified expansion rate on the dark matter relic abundance in a class of scalar-tensor theories. The scalar-tensor theories we consider are motivated from string theory constructions, which have conformal as well as disformally coupled matter to the scalar. We investigate the effects of such a conformal coupling to the dark matter relic abundance for a wide range of initial conditions, masses and cross-sections. We find that exploiting all possible initial conditions, the annihilation cross-section required to satisfy the dark matter content can differ from the thermal average cross-section in the standard case. We alsomore » study the expansion rate in the disformal case and find that physically relevant solutions require a nontrivial relation between the conformal and disformal functions. We study the effects of the disformal coupling in an explicit example where the disformal function is quadratic.« less

The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains

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

Fertitta, Edoardo; Paulus, Beate; El Khatib, Muammar

2015-12-28

The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum ismore » associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection S{sub z} has been derived.« less

Cosmological singularities in Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Woolgar, Eric

2014-12-01

We consider spacetimes consisting of a manifold with Lorentzian metric and a weight function or scalar field. These spacetimes admit a Bakry-Émery-Ricci tensor which is a natural generalization of the Ricci tensor. We impose an energy condition on the Bakry-Émery-Ricci tensor and obtain singularity theorems of a cosmological type, both for zero and for positive cosmological constant. That is, we find conditions under which every timelike geodesic is incomplete. These conditions are given by 'open' inequalities, so we examine the borderline (equality) cases and show that certain singularities are avoided in these cases only if the geometry is rigid; i.e., if it splits as a Lorentzian product or, for a positive cosmological constant, a warped product, and the weight function is constant along the time direction. Then the product case is future timelike geodesically complete while, in the warped product case, worldlines of certain conformally static observers are complete. Our results answer a question posed by J Case. We then apply our results to the cosmology of scalar-tensor gravitation theories. We focus on the Brans-Dicke family of theories in 4 spacetime dimensions, where we obtain 'Jordan frame' singularity theorems for big bang singularities.

New seismogenic stress fields for southern Italy from a Bayesian approach

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

A localized Richardson-Lucy algorithm for fiber orientation estimation in high angular resolution diffusion imaging.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Guo, Zhongwei; Xu, Dongrong

2015-05-01

Diffusion tensor imaging is widely used for studying neural fiber trajectories in white matter and for quantifying changes in tissue using diffusion properties at each voxel in the brain. To better model the nature of crossing fibers within complex architectures, rather than using a simplified tensor model that assumes only a single fiber direction at each image voxel, a model mixing multiple diffusion tensors is used to profile diffusion signals from high angular resolution diffusion imaging (HARDI) data. Based on the HARDI signal and a multiple tensors model, spherical deconvolution methods have been developed to overcome the limitations of the diffusion tensor model when resolving crossing fibers. The Richardson-Lucy algorithm is a popular spherical deconvolution method used in previous work. However, it is based on a Gaussian distribution, while HARDI data are always very noisy, and the distribution of HARDI data follows a Rician distribution. This current work aims to present a novel solution to address these issues. By simultaneously considering both the Rician bias and neighbor correlation in HARDI data, the authors propose a localized Richardson-Lucy (LRL) algorithm to estimate fiber orientations for HARDI data. The proposed method can simultaneously reduce noise and correct the Rician bias. Mean angular error (MAE) between the estimated Fiber orientation distribution (FOD) field and the reference FOD field was computed to examine whether the proposed LRL algorithm offered any advantage over the conventional RL algorithm at various levels of noise. Normalized mean squared error (NMSE) was also computed to measure the similarity between the true FOD field and the estimated FOD filed. For MAE comparisons, the proposed LRL approach obtained the best results in most of the cases at different levels of SNR and b-values. For NMSE comparisons, the proposed LRL approach obtained the best results in most of the cases at b-value = 3000 s/mm(2), which is the recommended schema for HARDI data acquisition. In addition, the FOD fields estimated by the proposed LRL approach in regions of fiber crossing regions using real data sets also showed similar fiber structures which agreed with common acknowledge in these regions. The novel spherical deconvolution method for improved accuracy in investigating crossing fibers can simultaneously reduce noise and correct Rician bias. With the noise smoothed and bias corrected, this algorithm is especially suitable for estimation of fiber orientations in HARDI data. Experimental results using both synthetic and real imaging data demonstrated the success and effectiveness of the proposed LRL algorithm.

A Mass Diffusion Model for Dry Snow Utilizing a Fabric Tensor to Characterize Anisotropy

NASA Astrophysics Data System (ADS)

Shertzer, Richard H.; Adams, Edward E.

2018-03-01

A homogenization algorithm for randomly distributed microstructures is applied to develop a mass diffusion model for dry snow. Homogenization is a multiscale approach linking constituent behavior at the microscopic level—among ice and air—to the macroscopic material—snow. Principles of continuum mechanics at the microscopic scale describe water vapor diffusion across an ice grain's surface to the air-filled pore space. Volume averaging and a localization assumption scale up and down, respectively, between microscopic and macroscopic scales. The model yields a mass diffusivity expression at the macroscopic scale that is, in general, a second-order tensor parameterized by both bulk and microstructural variables. The model predicts a mass diffusivity of water vapor through snow that is less than that through air. Mass diffusivity is expected to decrease linearly with ice volume fraction. Potential anisotropy in snow's mass diffusivity is captured due to the tensor representation. The tensor is built from directional data assigned to specific, idealized microstructural features. Such anisotropy has been observed in the field and laboratories in snow morphologies of interest such as weak layers of depth hoar and near-surface facets.

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

RPYFMM: Parallel adaptive fast multipole method for Rotne-Prager-Yamakawa tensor in biomolecular hydrodynamics simulations

NASA Astrophysics Data System (ADS)

Guan, W.; Cheng, X.; Huang, J.; Huber, G.; Li, W.; McCammon, J. A.; Zhang, B.

2018-06-01

RPYFMM is a software package for the efficient evaluation of the potential field governed by the Rotne-Prager-Yamakawa (RPY) tensor interactions in biomolecular hydrodynamics simulations. In our algorithm, the RPY tensor is decomposed as a linear combination of four Laplace interactions, each of which is evaluated using the adaptive fast multipole method (FMM) (Greengard and Rokhlin, 1997) where the exponential expansions are applied to diagonalize the multipole-to-local translation operators. RPYFMM offers a unified execution on both shared and distributed memory computers by leveraging the DASHMM library (DeBuhr et al., 2016, 2018). Preliminary numerical results show that the interactions for a molecular system of 15 million particles (beads) can be computed within one second on a Cray XC30 cluster using 12,288 cores, while achieving approximately 54% strong-scaling efficiency.

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

NASA Astrophysics Data System (ADS)

Cui, S. T.

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

Coupling coefficients for tensor product representations of quantum SU(2)

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

Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

2014-10-15

We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

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.

Asymptotic safety of quantum gravity beyond Ricci scalars

NASA Astrophysics Data System (ADS)

Falls, Kevin; King, Callum R.; Litim, Daniel F.; Nikolakopoulos, Kostas; Rahmede, Christoph

2018-04-01

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from f (R ) -type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

Application of Second-Moment Source Analysis to Three Problems in Earthquake Forecasting

NASA Astrophysics Data System (ADS)

Donovan, J.; Jordan, T. H.

2011-12-01

Though earthquake forecasting models have often represented seismic sources as space-time points (usually hypocenters), a more complete hazard analysis requires the consideration of finite-source effects, such as rupture extent, orientation, directivity, and stress drop. The most compact source representation that includes these effects is the finite moment tensor (FMT), which approximates the degree-two polynomial moments of the stress glut by its projection onto the seismic (degree-zero) moment tensor. This projection yields a scalar space-time source function whose degree-one moments define the centroid moment tensor (CMT) and whose degree-two moments define the FMT. We apply this finite-source parameterization to three forecasting problems. The first is the question of hypocenter bias: can we reject the null hypothesis that the conditional probability of hypocenter location is uniformly distributed over the rupture area? This hypothesis is currently used to specify rupture sets in the "extended" earthquake forecasts that drive simulation-based hazard models, such as CyberShake. Following McGuire et al. (2002), we test the hypothesis using the distribution of FMT directivity ratios calculated from a global data set of source slip inversions. The second is the question of source identification: given an observed FMT (and its errors), can we identify it with an FMT in the complete rupture set that represents an extended fault-based rupture forecast? Solving this problem will facilitate operational earthquake forecasting, which requires the rapid updating of earthquake triggering and clustering models. Our proposed method uses the second-order uncertainties as a norm on the FMT parameter space to identify the closest member of the hypothetical rupture set and to test whether this closest member is an adequate representation of the observed event. Finally, we address the aftershock excitation problem: given a mainshock, what is the spatial distribution of aftershock probabilities? The FMT representation allows us to generalize the models typically used for this purpose (e.g., marked point process models, such as ETAS), which will again be necessary in operational earthquake forecasting. To quantify aftershock probabilities, we compare mainshock FMTs with the first and second spatial moments of weighted aftershock hypocenters. We will describe applications of these results to the Uniform California Earthquake Rupture Forecast, version 3, which is now under development by the Working Group on California Earthquake Probabilities.

On the origin independence of the Verdet tensor†

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

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

PubMed

Carmichael, Owen; Sakhanenko, Lyudmila

2015-05-15

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

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

PubMed Central

Carmichael, Owen; Sakhanenko, Lyudmila

2015-01-01

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

Reactivated faulting near Cushing, Oklahoma: Increased potential for a triggered earthquake in an area of United States strategic infrastructure

USGS Publications Warehouse

McNamara, Daniel E.; Hayes, Gavin; Benz, Harley M.; Williams, Robert; McMahon, Nicole D; Aster, R.C.; Holland, Austin F.; Sickbert, T; Herrmann, Robert B.; Briggs, Richard; Smoczyk, Gregory M.; Bergman, Eric; Earle, Paul S.

2015-01-01

In October 2014 two moderate-sized earthquakes (Mw 4.0 and 4.3) struck south of Cushing, Oklahoma, below the largest crude oil storage facility in the world. Combined analysis of the spatial distribution of earthquakes and regional moment tensor focal mechanisms indicate reactivation of a subsurface unnamed and unmapped left-lateral strike-slip fault. Coulomb failure stress change calculations using the relocated seismicity and slip distribution determined from regional moment tensors, allow for the possibility that the Wilzetta-Whitetail fault zone south of Cushing, Oklahoma, could produce a large, damaging earthquake comparable to the 2011 Prague event. Resultant very strong shaking levels (MMI VII) in the epicentral region present the possibility of this potential earthquake causing moderate to heavy damage to national strategic infrastructure and local communities.

Is the permeability of naturally fractured rocks scale dependent?

NASA Astrophysics Data System (ADS)

Azizmohammadi, Siroos; Matthäi, Stephan K.

2017-09-01

The equivalent permeability, keq of stratified fractured porous rocks and its anisotropy is important for hydrocarbon reservoir engineering, groundwater hydrology, and subsurface contaminant transport. However, it is difficult to constrain this tensor property as it is strongly influenced by infrequent large fractures. Boreholes miss them and their directional sampling bias affects the collected geostatistical data. Samples taken at any scale smaller than that of interest truncate distributions and this bias leads to an incorrect characterization and property upscaling. To better understand this sampling problem, we have investigated a collection of outcrop-data-based Discrete Fracture and Matrix (DFM) models with mechanically constrained fracture aperture distributions, trying to establish a useful Representative Elementary Volume (REV). Finite-element analysis and flow-based upscaling have been used to determine keq eigenvalues and anisotropy. While our results indicate a convergence toward a scale-invariant keq REV with increasing sample size, keq magnitude can have multi-modal distributions. REV size relates to the length of dilated fracture segments as opposed to overall fracture length. Tensor orientation and degree of anisotropy also converge with sample size. However, the REV for keq anisotropy is larger than that for keq magnitude. Across scales, tensor orientation varies spatially, reflecting inhomogeneity of the fracture patterns. Inhomogeneity is particularly pronounced where the ambient stress selectively activates late- as opposed to early (through-going) fractures. While we cannot detect any increase of keq with sample size as postulated in some earlier studies, our results highlight a strong keq anisotropy that influences scale dependence.

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

PubMed Central

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

2017-01-01

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

Discrete gravity on random tensor network and holographic Rényi entropy

NASA Astrophysics Data System (ADS)

Han, Muxin; Huang, Shilin

2017-11-01

In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ〉 using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement Rényi entropy of |Ψ〉 is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting Rényi entropy S n of |Ψ〉 approximates with high precision the Rényi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS3/CFT2 correspondence on random tensor networks, and provide a new proposal to approximate the CFT ground state.

General Second-Order Scalar-Tensor Theory and Self-Tuning

NASA Astrophysics Data System (ADS)

Charmousis, Christos; Copeland, Edmund J.; Padilla, Antonio; Saffin, Paul M.

2012-02-01

Starting from the most general scalar-tensor theory with second-order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on Friedmann-Lemaître-Robertson-Walker backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor, and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining nontrivial cosmological solutions.

Beam-plasma dielectric tensor with Mathematica

NASA Astrophysics Data System (ADS)

Bret, A.

2007-03-01

We present a Mathematica notebook allowing for the symbolic calculation of the 3×3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summaryTitle of program: Tensor Catalog identifier: ADYT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère-Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the dimensionless variables. Restrictions on the complexity of the problem: Temperature effects are limited to small, i.e. non-relativistic, temperatures. The kinetic counterpart of the present Mathematica will usually not compute the required integrals. Typical running time: About 1 minute on a Intel Centrino 1.5 GHz Laptop with 512 MB of RAM. Unusual features of the program: None.

Universal hydrodynamic flow in holographic planar shock collisions

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

Chesler, Paul M.; Kilbertus, Niki; van der Schee, Wilke

2015-11-20

We study the collision of planar shock waves in AdS 5 as a function of shock profile. In the dual field theory the shock waves describe planar sheets of energy whose collision results in the formation of a plasma which behaves hydrodynamically at late times. We find that the post-collision stress tensor near the light cone exhibits transient non-universal behavior which depends on both the shock width and the precise functional form of the shock profile. However, over a large range of shock widths, including those which yield qualitative different behavior near the future light cone, and for different shockmore » profiles, we find universal behavior in the subsequent hydrodynamic evolution. In addition, we compute the rapidity distribution of produced particles and find it to be well described by a Gaussian.« less

The theory of spherically symmetric thin shells in conformal gravity

NASA Astrophysics Data System (ADS)

Berezin, Victor; Dokuchaev, Vyacheslav; Eroshenko, Yury

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl-Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ( = massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl-Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

Tensor and Spin Representations of SO(4) and Discrete Quantum Gravity

NASA Astrophysics Data System (ADS)

Lorente, M.; Kramer, P.

Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. These mathematical results help us to a more complete description of the Barret-Crane model in Quantum Gravity. In particular a complete realization of the weight function for the partition function is given and a new geometrical interpretation of the asymptotic limit for the Regge action is presented.

Scale-invariant curvature fluctuations from an extended semiclassical gravity

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

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

2015-02-15

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

Fabrication and properties of multilayer structures

NASA Astrophysics Data System (ADS)

Tiller, W. A.

1983-09-01

The synthesis of SiC films and Pd2Si films via single source and dual source sputtering, respectively, has been experimentally investigated while the reactive sputter deposition of SiO sub x films has been theoretically analyzed. The SiO sub x film data requires a mobile precursor adsorption process to be operative for the oxygen and an oxygen sticking coefficient of between 1.56 x 10 to the minus 3rd power and 4.17 x 10 to the minus 3rd power. An analysis of in-situ electrical diagnostics of the films via a non-contact technique shows the method to be of marginal accuracy for the example selected. An important new formulation of the stress and elastic constant tensors in the vicinity of interfaces has been developed and applied to the simple example of adsorbed layer/substrate interactions via a parametric analysis. Atomic modeling of the SiO system yields peroxide bond formation for oxygen-rich (100) alpha-cristobalite surfaces. Radial distribution function and angular distribution function data have been calculated for bulk alpha-quartz and bulk alpha-cristobalite in good agreement with experiment.

Viable inflationary evolution from Einstein frame loop quantum cosmology

NASA Astrophysics Data System (ADS)

de Haro, Jaume; Odintsov, S. D.; Oikonomou, V. K.

2018-04-01

In this work we construct a bottom-up reconstruction technique for loop quantum cosmology scalar-tensor theories, from the observational indices. Particularly, the reconstruction technique is based on fixing the functional form of the scalar-to-tensor ratio as a function of the e -foldings number. The aim of the technique is to realize viable inflationary scenarios, and the only assumption that must hold true in order for the reconstruction technique to work is that the dynamical evolution of the scalar field obeys the slow-roll conditions. We use two functional forms for the scalar-to-tensor ratio, one of which corresponds to a popular inflationary class of models, the α attractors. For the latter, we calculate the leading order behavior of the spectral index and we demonstrate that the resulting inflationary theory is viable and compatible with the latest Planck and BICEP2/Keck-Array data. In addition, we find the classical limit of the theory, and as we demonstrate, the loop quantum cosmology corrected theory and the classical theory are identical at leading order in the perturbative expansion quantified by the parameter ρc, which is the critical density of the quantum theory. Finally, by using the formalism of slow-roll scalar-tensor loop quantum cosmology, we investigate how several inflationary potentials can be realized by the quantum theory, and we calculate directly the slow-roll indices and the corresponding observational indices. In addition, the f (R ) gravity frame picture is presented.

The Constantine (Algeria) seismic sequence of 27 October 1985: a new rupture model from aftershock relocation, focal mechanisms, and stress tensors

NASA Astrophysics Data System (ADS)

Ousadou, F.; Dorbath, L.; Dorbath, C.; Bounif, M. A.; Benhallou, H.

2013-04-01

The October 27, 1985 Constantine earthquake of magnitude MS 5.9 (NEIC) although moderate is the strongest earthquake recorded in the eastern Tellian Atlas (northeast Algeria) since the beginning of instrumental seismology. The main shock locations given by different institutions are scattered and up to 10 km away northwest from the NE-SW 30 km long elongated aftershocks cloud localized by a dedicated temporary portable network. The focal mechanism indicates left-lateral strike-slip on an almost vertical fault with a small reverse component on the northwest dipping plane. This paper presents relocations of the main shock and aftershocks using TomoDD. One hundred thirty-eight individual focal mechanisms have been built allowing the determination of the stress tensor at different scales. A rupture model has been suggested, which explains the different observations of aftershock distribution and stress tensor rotation.

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

PubMed Central

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

2016-01-01

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

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

PubMed

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Time-Optimized High-Resolution Readout-Segmented Diffusion Tensor Imaging

PubMed Central

Reishofer, Gernot; Koschutnig, Karl; Langkammer, Christian; Porter, David; Jehna, Margit; Enzinger, Christian; Keeling, Stephen; Ebner, Franz

2013-01-01

Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min) generates results comparable to the un-regularized data with three averages (48 min). This significant reduction in scan time renders high resolution (1×1×2.5 mm3) diffusion tensor imaging of the entire brain applicable in a clinical context. PMID:24019951

The advantages of complementing MT profiles in 3-D environments with geomagnetic transfer function and interstation horizontal magnetic transfer function data: results from a synthetic case study

NASA Astrophysics Data System (ADS)

Campanyà, Joan; Ogaya, Xènia; Jones, Alan G.; Rath, Volker; Vozar, Jan; Meqbel, Naser

2016-12-01

As a consequence of measuring time variations of the electric and the magnetic field, which are related to current flow and charge distribution, magnetotelluric (MT) data in 2-D and 3-D environments are not only sensitive to the geoelectrical structures below the measuring points but also to any lateral anomalies surrounding the acquisition site. This behaviour complicates the characterization of the electrical resistivity distribution of the subsurface, particularly in complex areas. In this manuscript we assess the main advantages of complementing the standard MT impedance tensor (Z) data with interstation horizontal magnetic tensor (H) and geomagnetic transfer function (T) data in constraining the subsurface in a 3-D environment beneath a MT profile. Our analysis was performed using synthetic responses with added normally distributed and scattered random noise. The sensitivity of each type of data to different resistivity anomalies was evaluated, showing that the degree to which each site and each period is affected by the same anomaly depends on the type of data. A dimensionality analysis, using Z, H and T data, identified the presence of the 3-D anomalies close to the profile, suggesting a 3-D approach for recovering the electrical resistivity values of the subsurface. Finally, the capacity for recovering the geoelectrical structures of the subsurface was evaluated by performing joint inversion using different data combinations, quantifying the differences between the true synthetic model and the models from inversion process. Four main improvements were observed when performing joint inversion of Z, H and T data: (1) superior precision and accuracy at characterizing the electrical resistivity values of the anomalies below and outside the profile; (2) the potential to recover high electrical resistivity anomalies that are poorly recovered using Z data alone; (3) improvement in the characterization of the bottom and lateral boundaries of the anomalies with low electrical resistivity; and (4) superior imaging of the horizontal continuity of structures with low electrical resistivity. These advantages offer new opportunities for the MT method by making the results from a MT profile in a 3-D environment more convincing, supporting the possibility of high-resolution studies in 3-D areas without expending a large amount of economical and computational resources, and also offering better resolution of targets with high electrical resistivity.

Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Rioseco, Paola; Sarbach, Olivier

2017-05-01

We provide a systematic study for the accretion of a collisionless, relativistic kinetic gas into a nonrotating black hole. To this end, we first solve the relativistic Liouville equation on a Schwarzschild background spacetime. The most general solution for the distribution function is given in terms of appropriate symplectic coordinates on the cotangent bundle, and the associated observables, including the particle current density and stress energy-momentum tensor, are determined. Next, we explore the case where the flow is steady-state and spherically symmetric. Assuming that in the asymptotic region the gas is described by an equilibrium distribution function, we determine the relevant parameters of the accretion flow as a function of the particle density and the temperature of the gas at infinity. In particular, we find that in the low temperature limit the tangential pressure at the horizon is about an order of magnitude larger than the radial one, showing explicitly that a collisionless gas, despite exerting kinetic pressure, behaves very differently than an isotropic perfect fluid, and providing a partial explanation for the known fact that the accretion rate is much lower than in the hydrodynamic case of Bondi-Michel accretion. Finally, we establish the asymptotic stability of the steady-state spherical flows by proving pointwise convergence results which show that a large class of (possibly nonstationary and nonspherical) initial conditions for the distribution function lead to solutions of the Liouville equation which relax in time to a steady-state, spherically symmetric configuration.

Angular analysis of the decay B$^+$$\\to$$ K$$^+\\mu^+\\mu^-$$ in proton-proton collisions at $$\\sqrt{s} =$$ 8 TeV

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

Sirunyan, Albert M; et al.

The angular distribution of the flavor-changing neutral current decay Bmore » $^+$$\\to$$ K$$^+\\mu^+\\mu^-$$ is studied in proton-proton collisions at a center-of-mass energy of 8 TeV. The analysis is based on data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 20.5 fb$$^{-1}$$. The forward-backward asymmetry $$A_{\\mathrm{FB}}$$ of the dimuon system and the contribution $$F_{\\mathrm{H}}$$ from the pseudoscalar, scalar, and tensor amplitudes to the decay width are measured as a function of the dimuon mass squared. The measurements are consistent with the standard model expectations.« less

Irradiation direction from texture

NASA Astrophysics Data System (ADS)

Koenderink, Jan J.; Pont, Sylvia C.

2003-10-01

We present a theory of image texture resulting from the shading of corrugated (three-dimensional textured) surfaces, Lambertian on the micro scale, in the domain of geometrical optics. The derivation applies to isotropic Gaussian random surfaces, under collimated illumination, in normal view. The theory predicts the structure tensors from either the gradient or the Hessian of the image intensity and allows inferences of the direction of irradiation of the surface. Although the assumptions appear prima facie rather restrictive, even for surfaces that are not at all Gaussian, with the bidirectional reflectance distribution function far from Lambertian and vignetting and multiple scattering present, we empirically recover the direction of irradiation with an accuracy of a few degrees.

Neuropsychological Correlates of Diffusion Tensor Imaging in Schizophrenia

PubMed Central

Nestor, Paul G.; Kubicki, Marek; Gurrera, Ronald J.; Niznikiewicz, Margaret; Frumin, Melissa; McCarley, Robert W.; Shenton, Martha E.

2009-01-01

Patients with schizophrenia (n = 41) and healthy comparison participants (n = 46) completed neuropsychological measures of intelligence, memory, and executive function. A subset of each group also completed magnetic resonance diffusion tensor imaging (DTI) studies (fractional anisotropy and cross-sectional area) of the uncinate fasciculus (UF) and cingulate bundle (CB). Patients with schizophrenia showed reduced levels of functioning across all neuropsychological measures. In addition, selective neuropsychological–DTI relationships emerged. Among patients but not controls, lower levels of declarative–episodic verbal memory correlated with reduced left UF, whereas executive function errors related to performance monitoring correlated with reduced left CB. The data suggested abnormal DTI patterns linking declarative–episodic verbal memory deficits to the left UF and executive function deficits to the left CB among patients with schizophrenia. PMID:15506830

A high performance data parallel tensor contraction framework: Application to coupled electro-mechanics

NASA Astrophysics Data System (ADS)

Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio

2017-07-01

The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.

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

PubMed

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

2014-02-01

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

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.

Observing the inflation potential. [in models of cosmological inflation

NASA Technical Reports Server (NTRS)

Copeland, Edmund J.; Kolb, Edward W.; Liddle, Andrew R.; Lidsey, James E.

1993-01-01

We show how observations of the density perturbation (scalar) spectrum and the gravitational wave (tensor) spectrum allow a reconstruction of the potential responsible for cosmological inflation. A complete functional reconstruction or a perturbative approximation about a single scale are possible; the suitability of each approach depends on the data available. Consistency equations between the scalar and tensor spectra are derived, which provide a powerful signal of inflation.

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Gravitational wave memory in an expanding universe

NASA Astrophysics Data System (ADS)

Tolish, Alexander; Wald, Robert

2016-03-01

We investigate the gravitational wave memory effect in an expanding FLRW spacetime. We find that if the gravitational field is decomposed into gauge-invariant scalar, vector, and tensor modes after the fashion of Bardeen, only the tensor mode gives rise to memory, and this memory can be calculated using the retarded Green's function associated with the tensor wave equation. If locally similar radiation source events occur on flat and FLRW backgrounds, we find that the resulting memories will differ only by a redshift factor, and we explore whether or not this factor depends on the expansion history of the FLRW universe. We compare our results to related work by Bieri, Garfinkle, and Yau.

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

Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel W.

Coupled-cluster methods provide highly accurate models of molecular structure by explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix-matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts tomore » extend the Libtensor framework to work in the distributed memory environment in a scalable and energy efficient manner. We achieve up to 240 speedup compared with the best optimized shared memory implementation. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures, (Cray XC30&XC40, BlueGene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance. Nevertheless, we preserve a uni ed interface to both programming models to maintain the productivity of computational quantum chemists.« less

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

PubMed

Li, Zhendong; Liu, Wenjian

2010-08-14

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

Towards the Irving-Kirkwood limit of the mechanical stress tensor

NASA Astrophysics Data System (ADS)

Smith, E. R.; Heyes, D. M.; Dini, D.

2017-06-01

The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V =ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ =1.0 , a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.

Towards the Irving-Kirkwood limit of the mechanical stress tensor.

PubMed

Smith, E R; Heyes, D M; Dini, D

2017-06-14

The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V=ℓ 3 . Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ=1.0, a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.

Towards the Irving-Kirkwood limit of the mechanical stress tensor

PubMed Central

Heyes, D. M.; Dini, D.

2017-01-01

The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V=ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ=1.0, a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems. PMID:29166053

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.

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

PubMed

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

2017-12-07

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

Analysis of the bond-valence method for calculating (29) Si and (31) P magnetic shielding in covalent network solids.

PubMed

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

2016-07-05

(29) Si and (31) P magnetic-shielding tensors in covalent network solids have been evaluated using periodic and cluster-based calculations. The cluster-based computational methodology employs pseudoatoms to reduce the net charge (resulting from missing co-ordination on the terminal atoms) through valence modification of terminal atoms using bond-valence theory (VMTA/BV). The magnetic-shielding tensors computed with the VMTA/BV method are compared to magnetic-shielding tensors determined with the periodic GIPAW approach. The cluster-based all-electron calculations agree with experiment better than the GIPAW calculations, particularly for predicting absolute magnetic shielding and for predicting chemical shifts. The performance of the DFT functionals CA-PZ, PW91, PBE, rPBE, PBEsol, WC, and PBE0 are assessed for the prediction of (29) Si and (31) P magnetic-shielding constants. Calculations using the hybrid functional PBE0, in combination with the VMTA/BV approach, result in excellent agreement with experiment. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Mitchell, Travis; Leonardi, Christopher; Bolster, Diogo

2017-11-01

Based on phase-field theory, we introduce a robust lattice-Boltzmann equation for modeling immiscible multiphase flows at large density and viscosity contrasts. Our approach is built by modifying the method proposed by Zu and He [Phys. Rev. E 87, 043301 (2013), 10.1103/PhysRevE.87.043301] in such a way as to improve efficiency and numerical stability. In particular, we employ a different interface-tracking equation based on the so-called conservative phase-field model, a simplified equilibrium distribution that decouples pressure and velocity calculations, and a local scheme based on the hydrodynamic distribution functions for calculation of the stress tensor. In addition to two distribution functions for interface tracking and recovery of hydrodynamic properties, the only nonlocal variable in the proposed model is the phase field. Moreover, within our framework there is no need to use biased or mixed difference stencils for numerical stability and accuracy at high density ratios. This not only simplifies the implementation and efficiency of the model, but also leads to a model that is better suited to parallel implementation on distributed-memory machines. Several benchmark cases are considered to assess the efficacy of the proposed model, including the layered Poiseuille flow in a rectangular channel, Rayleigh-Taylor instability, and the rise of a Taylor bubble in a duct. The numerical results are in good agreement with available numerical and experimental data.

Diffusion of phonons through (along and across) the ultrathin crystalline films

NASA Astrophysics Data System (ADS)

Šetrajčić, J. P.; Jaćimovski, S. K.; Vučenović, S. M.

2017-11-01

Instead of usual approach, applying displacement-displacement Green's functions, the momentum-momentum Green's functions will be used to calculate the diffusion tensor. With this type of Green's function we have calculated and analyzed dispersion law in film-structures. A small number of phonon energy levels along the direction of boundary surfaces joint of the film are discrete-ones and in this case standing waves could occur. This is consequence of quantum size effects. These Green's functions enter into Kubo's formula defining diffusion properties of the system and possible heat transfer direction through observed structures. Calculation of the diffusion tensor for phonons in film-structure requires solving of the system of difference equations. Boundary conditions are included into mentioned system through the Hamiltonian of the film-structure. It has been shown that the diagonal elements of the diffusion tensor express discrete behavior of the dispersion law of elementary excitations. More important result is-that they are temperature independent and that their values are much higher comparing with bulk structures. This result favors better heat conduction of the film, but in direction which is perpendicular to boundary film surface. In the same time this significantly favors appearance 2D superconducting surfaces inside the ultra-thin crystal structure, which are parallel to the boundary surface.

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

NASA Astrophysics Data System (ADS)

Rai, Prashant; Sargsyan, Khachik; Najm, Habib; Hermes, Matthew R.; Hirata, So

2017-09-01

A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss-Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm-1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

Autism spectrum disorder: does neuroimaging support the DSM-5 proposal for a symptom dyad? A systematic review of functional magnetic resonance imaging and diffusion tensor imaging studies.

PubMed

Pina-Camacho, Laura; Villero, Sonia; Fraguas, David; Boada, Leticia; Janssen, Joost; Navas-Sánchez, Francisco J; Mayoral, Maria; Llorente, Cloe; Arango, Celso; Parellada, Mara

2012-07-01

A systematic review of 208 studies comprising functional magnetic resonance imaging and diffusion tensor imaging data in patients with 'autism spectrum disorder' (ASD) was conducted, in order to determine whether these data support the forthcoming DSM-5 proposal of a social communication and behavioral symptom dyad. Studies consistently reported abnormal function and structure of fronto-temporal and limbic networks with social and pragmatic language deficits, of temporo-parieto-occipital networks with syntactic-semantic language deficits, and of fronto-striato-cerebellar networks with repetitive behaviors and restricted interests in ASD patients. Therefore, this review partially supports the DSM-5 proposal for the ASD dyad.

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

NASA Astrophysics Data System (ADS)

Ohtsu, Masayasu

1991-04-01

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

White Matter Connectivity of the Thalamus Delineates the Functional Architecture of Competing Thalamocortical Systems

PubMed Central

O'Muircheartaigh, Jonathan; Keller, Simon S.; Barker, Gareth J.; Richardson, Mark P.

2015-01-01

There is an increasing awareness of the involvement of thalamic connectivity on higher level cortical functioning in the human brain. This is reflected by the influence of thalamic stimulation on cortical activity and behavior as well as apparently cortical lesion syndromes occurring as a function of small thalamic insults. Here, we attempt to noninvasively test the correspondence of structural and functional connectivity of the human thalamus using diffusion-weighted and resting-state functional MRI. Using a large sample of 102 adults, we apply tensor independent component analysis to diffusion MRI tractography data to blindly parcellate bilateral thalamus according to diffusion tractography-defined structural connectivity. Using resting-state functional MRI collected in the same subjects, we show that the resulting structurally defined thalamic regions map to spatially distinct, and anatomically predictable, whole-brain functional networks in the same subjects. Although there was significant variability in the functional connectivity patterns, the resulting 51 structural and functional patterns could broadly be reduced to a subset of 7 similar core network types. These networks were distinct from typical cortical resting-state networks. Importantly, these networks were distributed across the brain and, in a subset, map extremely well to known thalamocortico-basal-ganglial loops. PMID:25899706

Obliquely Propagating Waves in Bi-Kappa Plasmas

NASA Astrophysics Data System (ADS)

Gaelzer, R.; Ziebell, L. F.; Meneses, A. R.

2016-12-01

The effects of kappa velocity distribution functions (VDFs) have been the subjectof intense research. Such functions have beenfound to provide a better fitting to the VDFs measured by spacecraftin the solar wind. An anisotropic VDF contains free energy that can excite wavesin the plasma. The induced turbulence also determines the observed shape of the VDF.The general treatment for waves excited by (bi-)Maxwellian plasmas is well-established.However, for kappa distributions (isotropic or anisotropic), the majority of the studieswere restricted to the limiting cases of purely parallel or perpendicular propagation.Contributions to the general case of obliquely-propagating waves have been scarcely reported.The absence of a general treatment prevents a complete analysis of the wave-particle interactionin kappa plasmas, since some instabilities can operate both in the parallel and oblique directions.A series of papers published by the authors begin to remedy this situation. In a first work [1],we have obtained the dielectric tensor and dispersion relations for quasi-perpendicular dispersive Alfvén waves resulting from a kappa VDF. This approach was later generalized by [2],where the formalism was extended to the general case of electrostatic/electromagnetic waves propagatingin an isotropic kappa plasma in any frequency range and for arbitrary angles.In the present work [3], we generalize even further the formalism by the derivation of thegeneral dielectric tensor of an anisotropic bi-kappa plasma. We present the state-of-the-art of theformalism and show how it enables a systematic study of waves and instabilities propagating inarbitrary directions and frequencies in a bi-kappa plasma.[1] R. Gaelzer, L. F. Ziebell, J. Geophys. Res. 119, 9334 (2014), doi: 10.1002/2014JA020667.[2] R. Gaelzer, L. F. Ziebell, Phys. Plasmas 23, 022110 (2016), doi: 10.1063/1.4941260.[3] R. Gaelzer et al., Phys. Plasmas 23, 062108 (2016), doi: 10.1063/1.4953430.

Fisher statistics for analysis of diffusion tensor directional information.

PubMed

Hutchinson, Elizabeth B; Rutecki, Paul A; Alexander, Andrew L; Sutula, Thomas P

2012-04-30

A statistical approach is presented for the quantitative analysis of diffusion tensor imaging (DTI) directional information using Fisher statistics, which were originally developed for the analysis of vectors in the field of paleomagnetism. In this framework, descriptive and inferential statistics have been formulated based on the Fisher probability density function, a spherical analogue of the normal distribution. The Fisher approach was evaluated for investigation of rat brain DTI maps to characterize tissue orientation in the corpus callosum, fornix, and hilus of the dorsal hippocampal dentate gyrus, and to compare directional properties in these regions following status epilepticus (SE) or traumatic brain injury (TBI) with values in healthy brains. Direction vectors were determined for each region of interest (ROI) for each brain sample and Fisher statistics were applied to calculate the mean direction vector and variance parameters in the corpus callosum, fornix, and dentate gyrus of normal rats and rats that experienced TBI or SE. Hypothesis testing was performed by calculation of Watson's F-statistic and associated p-value giving the likelihood that grouped observations were from the same directional distribution. In the fornix and midline corpus callosum, no directional differences were detected between groups, however in the hilus, significant (p<0.0005) differences were found that robustly confirmed observations that were suggested by visual inspection of directionally encoded color DTI maps. The Fisher approach is a potentially useful analysis tool that may extend the current capabilities of DTI investigation by providing a means of statistical comparison of tissue structural orientation. Copyright © 2012 Elsevier B.V. All rights reserved.

Distribution and Network of Basal Temporal Language Areas: A Study of the Combination of Electric Cortical Stimulation and Diffusion Tensor Imaging.

PubMed

Enatsu, Rei; Kanno, Aya; Ookawa, Satoshi; Ochi, Satoko; Ishiai, Sumio; Nagamine, Takashi; Mikuni, Nobuhiro

2017-10-01

The basal temporal language area (BTLA) is considered to have several functions in language processing; however, its brain network is still unknown. This study investigated the distribution and networks of the BTLA using a combination of electric cortical stimulation and diffusion tensor imaging (DTI). 10 patients with intractable focal epilepsy who underwent presurgical evaluation with subdural electrodes were enrolled in this study (language dominant side: 6 patients, language nondominant side: 4 patients). Electric stimulation at 50 Hz was applied to the electrodes during Japanese sentence reading, morphograms (kanji) reading, and syllabograms (kana) reading tasks to identify the BTLA. DTI was used to identify the subcortical fibers originating from the BTLA found by electric stimulation. The BTLA was found in 6 patients who underwent implantation of the subdural electrodes in the dominant hemisphere. The BTLA was located anywhere between 20 mm and 56 mm posterior to the temporal tips. In 3 patients, electric stimulation of some or all areas within the BTLA induced disturbance in reading of kanji words only. DTI detected the inferior longitudinal fasciculus (ILF) in all patients and the uncinate fasciculus (UF) in 1 patient, originating from the BTLA. ILF was detected from both kanji-specific areas and kanji-nonspecific areas. This study indicates that the network of the BTLA is a part of a ventral stream and is mainly composed of the ILF, which acts as a critical structure for lexical retrieval. ILF is also associated with the specific processing of kanji words. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

The scalar-scalar-tensor inflationary three-point function in the axion monodromy model

NASA Astrophysics Data System (ADS)

Chowdhury, Debika; Sreenath, V.; Sriramkumar, L.

2016-11-01

The axion monodromy model involves a canonical scalar field that is governed by a linear potential with superimposed modulations. The modulations in the potential are responsible for a resonant behavior which gives rise to persisting oscillations in the scalar and, to a smaller extent, in the tensor power spectra. Interestingly, such spectra have been shown to lead to an improved fit to the cosmological data than the more conventional, nearly scale invariant, primordial power spectra. The scalar bi-spectrum in the model too exhibits continued modulations and the resonance is known to boost the amplitude of the scalar non-Gaussianity parameter to rather large values. An analytical expression for the scalar bi-spectrum had been arrived at earlier which, in fact, has been used to compare the model with the cosmic microwave background anisotropies at the level of three-point functions involving scalars. In this work, with future applications in mind, we arrive at a similar analytical template for the scalar-scalar-tensor cross-correlation. We also analytically establish the consistency relation (in the squeezed limit) for this three-point function. We conclude with a summary of the main results obtained.

Global regionalized seismicity in view of Non-Extensive Statistical Physics

NASA Astrophysics Data System (ADS)

Chochlaki, Kalliopi; Vallianatos, Filippos; Michas, Georgios

2018-03-01

In the present work we study the distribution of Earth's shallow seismicity on different seismic zones, as occurred from 1981 to 2011 and extracted from the Centroid Moment Tensor (CMT) catalog. Our analysis is based on the subdivision of the Earth's surface into seismic zones that are homogeneous with regards to seismic activity and orientation of the predominant stress field. For this, we use the Flinn-Engdahl regionalization (FE) (Flinn and Engdahl, 1965), which consists of fifty seismic zones as modified by Lombardi and Marzocchi (2007). The latter authors grouped the 50 FE zones into larger tectonically homogeneous ones, utilizing the cumulative moment tensor method, resulting into thirty-nine seismic zones. In each one of these seismic zones we study the distribution of seismicity in terms of the frequency-magnitude distribution and the inter-event time distribution between successive earthquakes, a task that is essential for hazard assessments and to better understand the global and regional geodynamics. In our analysis we use non-extensive statistical physics (NESP), which seems to be one of the most adequate and promising methodological tools for analyzing complex systems, such as the Earth's seismicity, introducing the q-exponential formulation as the expression of probability distribution function that maximizes the Sq entropy as defined by Tsallis, (1988). The qE parameter is significantly greater than one for all the seismic regions analyzed with value range from 1.294 to 1.504, indicating that magnitude correlations are particularly strong. Furthermore, the qT parameter shows some temporal correlations but variations with cut-off magnitude show greater temporal correlations when the smaller magnitude earthquakes are included. The qT for earthquakes with magnitude greater than 5 takes values from 1.043 to 1.353 and as we increase the cut-off magnitude to 5.5 and 6 the qT value ranges from 1.001 to 1.242 and from 1.001 to 1.181 respectively, presenting a significant decrease. Our findings support the ideas of universality within the Tsallis approach to describe Earth's seismicity and present strong evidence ontemporal clustering and long-range correlations of seismicity in each of the tectonic zonesanalyzed.

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

PubMed

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

2011-05-01

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

Diffusion Tensor Analysis by Two-Dimensional Pair Correlation of Fluorescence Fluctuations in Cells.

PubMed

Di Rienzo, Carmine; Cardarelli, Francesco; Di Luca, Mariagrazia; Beltram, Fabio; Gratton, Enrico

2016-08-23

In a living cell, the movement of biomolecules is highly regulated by the cellular organization into subcompartments that impose barriers to diffusion, can locally break the spatial isotropy, and ultimately guide these molecules to their targets. Despite the pivotal role of these processes, experimental tools to fully probe the complex connectivity (and accessibility) of the cell interior with adequate spatiotemporal resolution are still lacking. Here, we show how the heterogeneity of molecular dynamics and the location of barriers to molecular motion can be mapped in live cells by exploiting a two-dimensional (2D) extension of the pair correlation function (pCF) analysis. Starting from a time series of images collected for the same field of view, the resulting 2D pCF is calculated in the proximity of each point for each time delay and allows us to probe the spatial distribution of the molecules that started from a given pixel. This 2D pCF yields an accurate description of the preferential diffusive routes. Furthermore, we combine this analysis with the image-derived mean-square displacement approach and gain information on the average nanoscopic molecular displacements in different directions. Through these quantities, we build a fluorescence-fluctuation-based diffusion tensor that contains information on speed and directionality of the local dynamical processes. Contrary to classical fluorescence correlation spectroscopy and related methods, this combined approach can distinguish between isotropic and anisotropic local diffusion. We argue that the measurement of this iMSD tensor will contribute to advance our understanding of the role played by the intracellular environment in the regulation of molecular diffusion at the nanoscale. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Electron configuration and hydrogen-bonding pattern in several thymine and uracil analogues studied by 1H-14N NQDR and DFT/QTAIM.

PubMed

Seliger, Janez; Žagar, Veselko; Latosińska, Magdalena; Latosińska, Jolanta Natalia

2012-08-02

Some thio- and aza-derivatives of natural nucleobases uracil and thymine: 2-thiouracil, 4-thiouracil, 6-methyl-2-thiouracil, 6-azauracil, and 6-aza-2-thiothymine have been studied experimentally in solid state by (1)H-(14)N NMR-NQR double resonance (NQDR) and theoretically by the Density Functional Theory (DFT)/Quantum Theory of Atoms in Molecules (QTAIM). The (14)N resonance frequencies have been measured at 173 and 295 K and assigned to particular nitrogen sites (-N═ and -NH-). The temperature factor has been found negligible. The changes in the molecular skeletons, electric charge distribution, intermolecular interactions pattern, and molecular aggregations caused by oxygen replacement with sulfur and carbon replacement with nitrogen are discussed in detail. Correlations between all the principal components of the (14)N quadrupole coupling tensor have been found helpful in the search for the experimental (14)N NQR frequencies, their assignment to a particular nitrogen positions and estimation of the strength of the inter- and intramolecular interactions. The variation in the NQR parameters have been mainly related to the variation in the population of π-electron orbital. For thiouracil derivatives a general trend is that the stronger the hydrogen bond is, the lower is the asymmetry parameter, while for thymine and 6-aza-2-thiotymine, the opposite relation holds. Differences in correlations of the principal components of the (14)N quadrupole coupling tensor at the amino and iminonitrogen positions in heterocyclic rings are discussed. The effect of C→H and C→N substitution at the amino nitrogen position and C→N substitution at the iminonitrogen position on the quadrupole coupling tensor is analyzed. This study also demonstrates the advantages of combining NQR and DFT/QTAIM to predict an unsolved crystalline structure of 4-thiouracil.

Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

NASA Astrophysics Data System (ADS)

Kamala Latha, B.; Murthy, K. P. N.; Sastry, V. S. S.

2017-09-01

General quadratic Hamiltonian models, describing the interaction between liquid-crystal molecules (typically with D2 h symmetry), take into account couplings between their uniaxial and biaxial tensors. While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram (contravening in some regions of model parameter space), the predictions of mean-field theory, and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase. The free-energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes. On the one hand, these profiles account for the unusual thermal behavior of the biaxial order parameter under significant destabilizing influence from the cross terms. On the other, they also allude to the possibility that in real systems, these complexities might indeed be inhibiting the formation of a low-temperature biaxial order itself—perhaps reflecting the difficulties in their ready realization in the laboratory.

Region-specific connectivity in patients with periventricular nodular heterotopia and epilepsy: A study combining diffusion tensor imaging and functional MRI.

PubMed

Liu, Wenyu; An, Dongmei; Tong, Xin; Niu, Running; Gong, Qiyong; Zhou, Dong

2017-10-01

Periventricular nodular heterotopia (PNH) is an important cause of chronic epilepsy. The purpose of this study was to evaluate region-specific connectivity in PNH patients with epilepsy and assess correlation between connectivity strength and clinical factors including duration and prognosis. Diffusion tensor imaging (DTI) and resting state functional MRI (fMRI) were performed in 28 subjects (mean age 27.4years; range 9-56years). The structural connectivity of fiber bundles passing through the manually-selected segmented nodules and other brain regions were analyzed by tractography. Cortical lobes showing functional correlations to nodules were also determined. For all heterotopic gray matter nodules, including at least one in each subject, the most frequent segments to which nodular heterotopia showed structural (132/151) and functional (146/151) connectivity were discrete regions of the ipsilateral overlying cortex. Agreement between diffusion tensor tractography and functional connectivity analyses was conserved in 81% of all nodules (122/151). In patients with longer duration or refractory epilepsy, the connectivity was significantly stronger, particularly to the frontal and temporal lobes (P<0.05). Nodules in PNH were structurally and functionally connected to the cortex. The extent is stronger in patients with longstanding or intractable epilepsy. These findings suggest the region-specific interactions may help better evaluate prognosis and seek medical or surgical interventions of PNH-related epilepsy. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Arc-driven rail gun research

NASA Technical Reports Server (NTRS)

Ray, P. K.

1984-01-01

The equations describing the performance of an inductively-driven rail gun are analyzed numerically. Friction between the projectile and rails is included through an empirical formulation. The equations are applied to the experiment of Rashleigh and Marshall to obtain an estimate of energy distribution in rail guns as a function of time. The effect of frictional heat dissipation on the bore of the gun is calculated. The mechanism of plasma and projectile acceleration in a dc rail gun is described from a microscopic point of view through the establishment of the Hall field. The plasma conductivity is shown to be a tensor indicating that there is a small component of current parallel to the direction of acceleration. The plasma characteristics are evaluated as a function of plasma mass through a simple fluid mechanical analysis of the plasma. By equating the energy dissipated in the plasma with the radiation heat loss, the properties of the plasma are determined.

Monte Carlo simulation of errors in the anisotropy of magnetic susceptibility - A second-rank symmetric tensor. [for grains in sedimentary and volcanic rocks

NASA Technical Reports Server (NTRS)

Lienert, Barry R.

1991-01-01

Monte Carlo perturbations of synthetic tensors to evaluate the Hext/Jelinek elliptical confidence regions for anisotropy of magnetic susceptibility (AMS) eigenvectors are used. When the perturbations are 33 percent of the minimum anisotropy, both the shapes and probability densities of the resulting eigenvector distributions agree with the elliptical distributions predicted by the Hext/Jelinek equations. When the perturbation size is increased to 100 percent of the minimum eigenvalue difference, the major axis of the 95 percent confidence ellipse underestimates the observed eigenvector dispersion by about 10 deg. The observed distributions of the principal susceptibilities (eigenvalues) are close to being normal, with standard errors that agree well with the calculated Hext/Jelinek errors. The Hext/Jelinek ellipses are also able to describe the AMS dispersions due to instrumental noise and provide reasonable limits for the AMS dispersions observed in two Hawaiian basaltic dikes. It is concluded that the Hext/Jelinek method provides a satisfactory description of the errors in AMS data and should be a standard part of any AMS data analysis.

Accessing the nucleon transverse structure in inclusive deep inelastic scattering

DOE PAGES

Accardi, Alberto; Bacchetta, Alessandro

2017-09-06

Here, we revisit the standard analysis of inclusive Deep Inelastic Scattering off nucleons taking into account the fact that on-shell quarks cannot be present in the final state, but they rather decay into hadrons - a process that can be described in terms of suitable "jet" correlators. As a consequence, a spin-flip term associated with the invariant mass of the produced hadrons is generated non perturbatively and couples to the target's transversity distribution function. In inclusive cross sections, this provides an hitherto neglected and large contribution to the twist-3 part of the g 2 structure function, that can explain themore » discrepancy between recent calculations and fits of this quantity. It also provides an extension of the Burkhardt-Cottingham sum rule, putting constraints on the small-x behavior of the transversity function, as well as an extension of the Efremov-Teryaev-Leader sum rule, suggesting a novel way to measure the tensor charge of the proton.« less

Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r {sup 6}) to O(r {sup 4})

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

Shenvi, Neil; Yang, Yang; Yang, Weitao

In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase approximation with tensor hypercontraction to produce the tensor-hypercontracted particle-particle RPA (THC-ppRPA) algorithm. Unlike previous implementations of ppRPA which scale as O(r{sup 6}), the THC-ppRPA algorithm scales asymptotically as only O(r{sup 4}), albeit with a much larger prefactor than the traditional algorithm. We apply THC-ppRPA to several model systems and show that it yields the same results as traditionalmore » ppRPA to within mH accuracy. Our method opens the door to the development of post-Kohn Sham functionals based on ppRPA without the excessive asymptotic cost of traditional ppRPA implementations.« less

Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r 6) to O(r 4)

NASA Astrophysics Data System (ADS)

Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao

2014-07-01

In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase approximation with tensor hypercontraction to produce the tensor-hypercontracted particle-particle RPA (THC-ppRPA) algorithm. Unlike previous implementations of ppRPA which scale as O(r6), the THC-ppRPA algorithm scales asymptotically as only O(r4), albeit with a much larger prefactor than the traditional algorithm. We apply THC-ppRPA to several model systems and show that it yields the same results as traditional ppRPA to within mH accuracy. Our method opens the door to the development of post-Kohn Sham functionals based on ppRPA without the excessive asymptotic cost of traditional ppRPA implementations.

Energy Flux Positivity and Unitarity in Conformal Field Theories

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

Kulaxizi, Manuela; Parnachev, Andrei

2011-01-07

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

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.

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

NASA Astrophysics Data System (ADS)

Monthus, Cécile

2018-03-01

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

An improved Bayesian tensor regularization and sampling algorithm to track neuronal fiber pathways in the language circuit.

PubMed

Mishra, Arabinda; Anderson, Adam W; Wu, Xi; Gore, John C; Ding, Zhaohua

2010-08-01

The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework. To estimate the true fiber direction (propagation vector), the a priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work. The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for in vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., "In vivo fiber tractography using DT-MRI data," Magn. Reson. Med. 44(4), 625-632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., "Improved fiber tractography with Bayesian tensor regularization," Neuroimage 31(3), 1061-1074 (2006)] and Friman's stochastic approach [O. Friman et al., "A Bayesian approach for stochastic white matter tractography," IEEE Trans. Med. Imaging 25(8), 965-978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low. The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated and in vivo results are in good agreement with the theoretical aspects of the algorithm.

Geometrical approach to neural net control of movements and posture

NASA Technical Reports Server (NTRS)

Pellionisz, A. J.; Ramos, C. F.

1993-01-01

In one approach to modeling brain function, sensorimotor integration is described as geometrical mapping among coordinates of non-orthogonal frames that are intrinsic to the system; in such a case sensors represent (covariant) afferents and motor effectors represent (contravariant) motor efferents. The neuronal networks that perform such a function are viewed as general tensor transformations among different expressions and metric tensors determining the geometry of neural functional spaces. Although the non-orthogonality of a coordinate system does not impose a specific geometry on the space, this "Tensor Network Theory of brain function" allows for the possibility that the geometry is non-Euclidean. It is suggested that investigation of the non-Euclidean nature of the geometry is the key to understanding brain function and to interpreting neuronal network function. This paper outlines three contemporary applications of such a theoretical modeling approach. The first is the analysis and interpretation of multi-electrode recordings. The internal geometries of neural networks controlling external behavior of the skeletomuscle system is experimentally determinable using such multi-unit recordings. The second application of this geometrical approach to brain theory is modeling the control of posture and movement. A preliminary simulation study has been conducted with the aim of understanding the control of balance in a standing human. The model appears to unify postural control strategies that have previously been considered to be independent of each other. Third, this paper emphasizes the importance of the geometrical approach for the design and fabrication of neurocomputers that could be used in functional neuromuscular stimulation (FNS) for replacing lost motor control.

A supersymmetric SYK-like tensor model

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

Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia

2017-05-11

We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic Ν = 1 tensor-valued superfields, ''quarks'' and ''mesons''. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic ''melon'' diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.

Multiscale finite element modeling of sheet molding compound (SMC) composite structure based on stochastic mesostructure reconstruction

DOE PAGES

Chen, Zhangxing; Huang, Tianyu; Shao, Yimin; ...

2018-03-15

Predicting the mechanical behavior of the chopped carbon fiber Sheet Molding Compound (SMC) due to spatial variations in local material properties is critical for the structural performance analysis but is computationally challenging. Such spatial variations are induced by the material flow in the compression molding process. In this work, a new multiscale SMC modeling framework and the associated computational techniques are developed to provide accurate and efficient predictions of SMC mechanical performance. The proposed multiscale modeling framework contains three modules. First, a stochastic algorithm for 3D chip-packing reconstruction is developed to efficiently generate the SMC mesoscale Representative Volume Element (RVE)more » model for Finite Element Analysis (FEA). A new fiber orientation tensor recovery function is embedded in the reconstruction algorithm to match reconstructions with the target characteristics of fiber orientation distribution. Second, a metamodeling module is established to improve the computational efficiency by creating the surrogates of mesoscale analyses. Third, the macroscale behaviors are predicted by an efficient multiscale model, in which the spatially varying material properties are obtained based on the local fiber orientation tensors. Our approach is further validated through experiments at both meso- and macro-scales, such as tensile tests assisted by Digital Image Correlation (DIC) and mesostructure imaging.« less

Structure analysis and spectroscopic characterization of 2-Fluoro-3-Methylpyridine-5-Boronic Acid with experimental (FT-IR, Raman, NMR and XRD) techniques and quantum chemical calculations

NASA Astrophysics Data System (ADS)

Alver, Özgür; Dikmen, Gökhan

2016-03-01

Possible stable conformers, geometrical molecular structures, vibrational properties as well as band assignments, nuclear magnetic shielding tensors of 2-Fluoro-3-Methylpyridine-5-Boronic Acid (2F3MP5BA) were studied experimentally and theoretically using FT-IR, Raman, (CP/MAS) NMR and XRD spectroscopic methods. FT-IR and Raman spectra were evaluated in the region of 3500-400 cm-1, and 3200-400 cm-1, respectively. The optimized geometric structures, vibrational wavenumbers and nuclear magnetic shielding tensors were examined using Becke-3-Lee-Yang-Parr (B3LYP) hybrid density functional theory method with 6-311++G(d, p) basis set. 1H, 13C NMR chemical shifts were calculated using the gauge invariant atomic orbital (GIAO) method. 1H, 13C, APT and HETCOR NMR experiments of title molecule were carried out in DMSO solution. 13C CP/MAS NMR measurement was done with 4 mm zirconium rotor and glycine was used as an external standard. Single crystal of 2F3MP5BA was also prepared for XRD measurements. Assignments of vibrational wavenumbers were also strengthened by calculating the total energy distribution (TED) values using scaled quantum mechanical (SQM) method.

Multiscale finite element modeling of sheet molding compound (SMC) composite structure based on stochastic mesostructure reconstruction

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

Chen, Zhangxing; Huang, Tianyu; Shao, Yimin

Predicting the mechanical behavior of the chopped carbon fiber Sheet Molding Compound (SMC) due to spatial variations in local material properties is critical for the structural performance analysis but is computationally challenging. Such spatial variations are induced by the material flow in the compression molding process. In this work, a new multiscale SMC modeling framework and the associated computational techniques are developed to provide accurate and efficient predictions of SMC mechanical performance. The proposed multiscale modeling framework contains three modules. First, a stochastic algorithm for 3D chip-packing reconstruction is developed to efficiently generate the SMC mesoscale Representative Volume Element (RVE)more » model for Finite Element Analysis (FEA). A new fiber orientation tensor recovery function is embedded in the reconstruction algorithm to match reconstructions with the target characteristics of fiber orientation distribution. Second, a metamodeling module is established to improve the computational efficiency by creating the surrogates of mesoscale analyses. Third, the macroscale behaviors are predicted by an efficient multiscale model, in which the spatially varying material properties are obtained based on the local fiber orientation tensors. Our approach is further validated through experiments at both meso- and macro-scales, such as tensile tests assisted by Digital Image Correlation (DIC) and mesostructure imaging.« less

The role of meson exchanges in light-by-light scattering

NASA Astrophysics Data System (ADS)

Lebiedowicz, Piotr; Szczurek, Antoni

2017-09-01

We discuss the role of meson exchange mechanisms in γγ → γγ scattering. Several pseudoscalar (π0, η, η‧ (958), ηc (1 S), ηc (2 S)), scalar (f0 (500), f0 (980), a0 (980), f0 (1370), χc0 (1 P)) and tensor (f2 (1270), a2 (1320), f2‧ (1525), f2 (1565), a2 (1700)) mesons are taken into account. We consider not only s-channel but also for the first time t- and u-channel meson exchange amplitudes corrected for off-shell effects including vertex form factors. We find that, depending on not well known vertex form factors, the meson exchange amplitudes interfere among themselves and could interfere with fermion-box amplitudes and modify the resulting cross sections. The meson contributions are shown as a function of collision energy as well as angular distributions are presented. Interesting interference effects separately for light pseudoscalar, scalar and tensor meson groups are discussed. The meson exchange contributions may be potentially important in the context of a measurement performed recently in ultraperipheral collisions of heavy ions by the ATLAS collaboration. The light-by-light interactions could be studied in future in electron-positron collisions by the Belle II at SuperKEKB accelerator.

Timescales of isotropic and anisotropic cluster collapse

NASA Astrophysics Data System (ADS)

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

1993-12-01

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

Resting state networks in empirical and simulated dynamic functional connectivity.

PubMed

Glomb, Katharina; Ponce-Alvarez, Adrián; Gilson, Matthieu; Ritter, Petra; Deco, Gustavo

2017-10-01

It is well-established that patterns of functional connectivity (FC) - measures of correlated activity between pairs of voxels or regions observed in the human brain using neuroimaging - are robustly expressed in spontaneous activity during rest. These patterns are not static, but exhibit complex spatio-temporal dynamics. Over the last years, a multitude of methods have been proposed to reveal these dynamics on the level of the whole brain. One finding is that the brain transitions through different FC configurations over time, and substantial effort has been put into characterizing these configurations. However, the dynamics governing these transitions are more elusive, specifically, the contribution of stationary vs. non-stationary dynamics is an active field of inquiry. In this study, we use a whole-brain approach, considering FC dynamics between 66 ROIs covering the entire cortex. We combine an innovative dimensionality reduction technique, tensor decomposition, with a mean field model which possesses stationary dynamics. It has been shown to explain resting state FC averaged over time and multiple subjects, however, this average FC summarizes the spatial distribution of correlations while hiding their temporal dynamics. First, we apply tensor decomposition to resting state scans from 24 healthy controls in order to characterize spatio-temporal dynamics present in the data. We simultaneously utilize temporal and spatial information by creating tensors that are subsequently decomposed into sets of brain regions ("communities") that share similar temporal dynamics, and their associated time courses. The tensors contain pairwise FC computed inside of overlapping sliding windows. Communities are discovered by clustering features pooled from all subjects, thereby ensuring that they generalize. We find that, on the group level, the data give rise to four distinct communities that resemble known resting state networks (RSNs): default mode network, visual network, control networks, and somatomotor network. Second, we simulate data with our stationary mean field model whose nodes are connected according to results from DTI and fiber tracking. In this model, all spatio-temporal structure is due to noisy fluctuations around the average FC. We analyze the simulated data in the same way as the empirical data in order to determine whether stationary dynamics can explain the emergence of distinct FC patterns (RSNs) which have their own time courses. We find that this is the case for all four networks using the spatio-temporal information revealed by tensor decomposition if nodes in the simulation are connected according to model-based effective connectivity. Furthermore, we find that these results require only a small part of the FC values, namely the highest values that occur across time and ROI pair. Our findings show that stationary dynamics can account for the emergence of RSNs. We provide an innovative method that does not make strong assumptions about the underlying data and is generally applicable to resting state or task data from different subject populations. Copyright © 2017 Elsevier Inc. All rights reserved.

8 January 2013 Mw=5.7 North Aegean Sea Earthquake Sequence

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Metric anisotropies and emergent anisotropic hydrodynamics

NASA Astrophysics Data System (ADS)

Dash, Ashutosh; Jaiswal, Amaresh

2018-05-01

Expansion of a locally equilibrated fluid is considered in an anisotropic space-time given by the Bianchi type-I metric. Starting from the isotropic equilibrium phase-space distribution function in the local rest frame, we obtain expressions for components of the energy-momentum tensor and conserved current, such as number density, energy density, and pressure components. In the case of an axissymmetric Bianchi type-I metric, we show that they are identical to those obtained within the setup of anisotropic hydrodynamics. We further consider the case in which the Bianchi type-I metric is a vacuum solution of the Einstein equation: the Kasner metric. For the axissymmetric Kasner metric, we discuss the implications of our results in the context of anisotropic hydrodynamics.

Study of the O-mode in a relativistic degenerate electron plasma

NASA Astrophysics Data System (ADS)

Azra, Kalsoom; Ali, Muddasir; Hussain, Azhar

2017-03-01

Using the linearized relativistic Vlasov-Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. The dispersion relation for the O-mode in a relativistic degenerate electron plasma is investigated by employing the Fermi-Dirac distribution function. The propagation characteristics of the O-mode (cut offs, resonances, propagation regimes, harmonic structure) are examined by using specific values of the density and the magnetic field that correspond to different relativistic dense environments. Further, it is observed that due to the relativistic effects the cut off and the resonance points are shifted to low frequency values, as a result the propagation regime is reduced. The dispersion relations for the non-relativistic and the ultra-relativistic limits are also presented.

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

PubMed

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

2012-01-01

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

Nonlinear optical anisotropy and molecular orientational distribution in poly(p-phenylene benzobisthiazole) Langmuir-Blodgett films

NASA Astrophysics Data System (ADS)

Wang, Liming; Wada, Tatsuo; Yuba, Tomoyuki; Kakimoto, Masaaki; Imai, Yoshio; Sasabe, Hiroyuki

1996-06-01

The orientational distribution and packing of polymer chains were investigated in poly(p-phenylene benzobisthiazole) (PBT) Langmuir-Blodgett (LB) films by nonresonant third-harmonic generation measurement at a wavelength of 1907 nm. The tensor components of the third-harmonic susceptibility on the PBT LB film with a surface pressure of 50 mN/m were determined to be χ(3)XXXX=(16.6±2.5)×10-12 and χ(3)YYYY=(2.0±0.3)×10-12. The large nonlinear optical anisotropy can be explained as a result of highly oriented packing of the polymer chains induced by a flow orientation. A Gaussian distribution function with a standard deviation of σ=0.40 gives a practical description of the orientational distribution of PBT polymer chains. A maximum χ(3) value of (26.8±4.4)×10-12 esu is predicted assuming a perfect alignment of polymer chains. The χ(3)XXXX value increased by factor of 2 with the surface pressure from 30 to 50 mN/m mainly due to the packing density of the polymer chains, while the orientational degree did not change.

Nontrivial thermodynamics in 't Hooft's large-N limit

NASA Astrophysics Data System (ADS)

Cubero, Axel Cortés

2015-05-01

We study the finite volume/temperature correlation functions of the (1 +1 )-dimensional SU (N ) principal chiral sigma model in the planar limit. The exact S-matrix of the sigma model is known to simplify drastically at large N , and this leads to trivial thermodynamic Bethe ansatz (TBA) equations. The partition function, if derived using the TBA, can be shown to be that of free particles. We show that the correlation functions and expectation values of operators at finite volume/temperature are not those of the free theory, and that the TBA does not give enough information to calculate them. Our analysis is done using the Leclair-Mussardo formula for finite-volume correlators, and knowledge of the exact infinite-volume form factors. We present analytical results for the one-point function of the energy-momentum tensor, and the two-point function of the renormalized field operator. The results for the energy-momentum tensor can be used to define a nontrivial partition function.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Robust dynamic myocardial perfusion CT deconvolution for accurate residue function estimation via adaptive-weighted tensor total variation regularization: a preclinical study.

PubMed

Zeng, Dong; Gong, Changfei; Bian, Zhaoying; Huang, Jing; Zhang, Xinyu; Zhang, Hua; Lu, Lijun; Niu, Shanzhou; Zhang, Zhang; Liang, Zhengrong; Feng, Qianjin; Chen, Wufan; Ma, Jianhua

2016-11-21

Dynamic myocardial perfusion computed tomography (MPCT) is a promising technique for quick diagnosis and risk stratification of coronary artery disease. However, one major drawback of dynamic MPCT imaging is the heavy radiation dose to patients due to its dynamic image acquisition protocol. In this work, to address this issue, we present a robust dynamic MPCT deconvolution algorithm via adaptive-weighted tensor total variation (AwTTV) regularization for accurate residue function estimation with low-mA s data acquisitions. For simplicity, the presented method is termed 'MPD-AwTTV'. More specifically, the gains of the AwTTV regularization over the original tensor total variation regularization are from the anisotropic edge property of the sequential MPCT images. To minimize the associative objective function we propose an efficient iterative optimization strategy with fast convergence rate in the framework of an iterative shrinkage/thresholding algorithm. We validate and evaluate the presented algorithm using both digital XCAT phantom and preclinical porcine data. The preliminary experimental results have demonstrated that the presented MPD-AwTTV deconvolution algorithm can achieve remarkable gains in noise-induced artifact suppression, edge detail preservation, and accurate flow-scaled residue function and MPHM estimation as compared with the other existing deconvolution algorithms in digital phantom studies, and similar gains can be obtained in the porcine data experiment.

Robust dynamic myocardial perfusion CT deconvolution for accurate residue function estimation via adaptive-weighted tensor total variation regularization: a preclinical study

NASA Astrophysics Data System (ADS)

Zeng, Dong; Gong, Changfei; Bian, Zhaoying; Huang, Jing; Zhang, Xinyu; Zhang, Hua; Lu, Lijun; Niu, Shanzhou; Zhang, Zhang; Liang, Zhengrong; Feng, Qianjin; Chen, Wufan; Ma, Jianhua

2016-11-01

Dynamic myocardial perfusion computed tomography (MPCT) is a promising technique for quick diagnosis and risk stratification of coronary artery disease. However, one major drawback of dynamic MPCT imaging is the heavy radiation dose to patients due to its dynamic image acquisition protocol. In this work, to address this issue, we present a robust dynamic MPCT deconvolution algorithm via adaptive-weighted tensor total variation (AwTTV) regularization for accurate residue function estimation with low-mA s data acquisitions. For simplicity, the presented method is termed ‘MPD-AwTTV’. More specifically, the gains of the AwTTV regularization over the original tensor total variation regularization are from the anisotropic edge property of the sequential MPCT images. To minimize the associative objective function we propose an efficient iterative optimization strategy with fast convergence rate in the framework of an iterative shrinkage/thresholding algorithm. We validate and evaluate the presented algorithm using both digital XCAT phantom and preclinical porcine data. The preliminary experimental results have demonstrated that the presented MPD-AwTTV deconvolution algorithm can achieve remarkable gains in noise-induced artifact suppression, edge detail preservation, and accurate flow-scaled residue function and MPHM estimation as compared with the other existing deconvolution algorithms in digital phantom studies, and similar gains can be obtained in the porcine data experiment.

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

DOE PAGES

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

2017-03-07

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrationalmore » zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.« less

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

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

Rai, Prashant; Sargsyan, Khachik; Najm, Habib

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrationalmore » zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.« less

The relationship between functional magnetic resonance imaging activation, diffusion tensor imaging, and training effects.

PubMed

Farrar, Danielle; Budson, Andrew E

2017-04-01

While the relationship between diffusion tensor imaging (DTI) measurements and training effects is explored by Voelker et al. (this issue), a cursory discussion of functional magnetic resonance imaging (fMRI) measurements categorizes increased activation with findings of greater white matter integrity. Evidence of the relationship between fMRI activation and white matter integrity is conflicting, as is the relationship between fMRI activation and training effects. An examination of the changes in fMRI activation in response to training is helpful, but the relationship between DTI and fMRI activation, particularly in the context of white matter changes, must be examined further before general conclusions can be drawn.

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.

How to use retarded Green's functions in de Sitter spacetime

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

Higuchi, Atsushi; Cheong, Lee Yen

2008-10-15

We demonstrate in examples that the covariant retarded Green's functions in electromagnetism and linearized gravity work as expected in de Sitter spacetime. We first clarify how retarded Green's functions should be used in spacetimes with spacelike past infinity such as de Sitter spacetime. In particular, we remind the reader of a general formula which gives the field for given initial data on a Cauchy surface and a given source (a charge or stress-energy tensor distribution) in its future. We then apply this formula to three examples: (i) electromagnetism in the future of a Cauchy surface in Minkowski spacetime, (ii) electromagnetismmore » in de Sitter spacetime, and (iii) linearized gravity in de Sitter spacetime. In each example the field is reproduced correctly as predicted by the general argument. In the third example we construct a linearized gravitational field from two equal point masses located at the 'North and South Poles' which is nonsingular on the cosmological horizon and satisfies a covariant gauge condition and show that this field is reproduced by the retarded Green's function with corresponding gauge parameters.« less

Symmetries of the Space of Linear Symplectic Connections

NASA Astrophysics Data System (ADS)

Fox, Daniel J. F.

2017-01-01

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt moment map, the Ricci tensor, and a translational term. The critical points of a functional constructed from it interpolate between the equations for preferred symplectic connections and the equations for critical symplectic connections. The commutative algebra of formal sums of symmetric tensors on a symplectic manifold carries a pair of compatible Poisson structures, one induced from the canonical Poisson bracket on the space of functions on the cotangent bundle polynomial in the fibers, and the other induced from the algebraic fiberwise Schouten bracket on the symmetric algebra of each fiber of the cotangent bundle. These structures are shown to be compatible, and the required Lie algebras are constructed as central extensions of their! linear combinations restricted to formal sums of symmetric tensors whose first order term is a multiple of the differential of its zeroth order term.

Emergent symmetries in the canonical tensor model

NASA Astrophysics Data System (ADS)

Obster, Dennis; Sasakura, Naoki

2018-04-01

The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent description of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. The classical CTM produces a general relativistic system in a formal continuum limit, the emergence of which should be explained by the quantum CTM. In this paper we study the symmetry properties of a wave function that exactly solves the quantum constraints of the CTM. We have found that it has strong peaks at configurations invariant under some Lie groups, as predicted by a mechanism described in our previous paper. A surprising result is the preference for configurations invariant not only under Lie groups with positive definite signature, but also with Lorentzian signature. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behavior, which for the most part seems to be well under control.

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.

Waveform inversion of oscillatory signatures in long-period events beneath volcanoes

USGS Publications Warehouse

Kumagai, H.; Chouet, B.A.; Nakano, M.

2002-01-01

The source mechanism of long-period (LP) events is examined using synthetic waveforms generated by the acoustic resonance of a fluid-filled crack. We perform a series of numerical tests in which the oscillatory signatures of synthetic LP waveforms are used to determine the source time functions of the six moment tensor components from waveform inversions assuming a point source. The results indicate that the moment tensor representation is valid for the odd modes of crack resonance with wavelengths 2L/n, 2W/n, n = 3, 5, 7, ..., where L and W are the crack length and width, respectively. For the even modes with wavelengths 2L/n, 2W/n, n = 2, 4, 6,..., a generalized source representation using higher-order tensors is required, although the efficiency of seismic waves radiated by the even modes is expected to be small. We apply the moment tensor inversion to the oscillatory signatures of an LP event observed at Kusatsu-Shirane Volcano, central Japan. Our results point to the resonance of a subhorizontal crack located a few hundred meters beneath the summit crater lakes. The present approach may be useful to quantify the source location, geometry, and force system of LP events, and opens the way for moment tensor inversions of tremor.

Full moment tensors for small events (Mw < 3) at Uturuncu volcano, Bolivia

NASA Astrophysics Data System (ADS)

Alvizuri, Celso; Tape, Carl

2016-09-01

We present a catalogue of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broad-band stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the 6-D space of moment tensors. For each event, we show the misfit function in eigenvalue space, represented by a lune. We identify three subsets of the catalogue: (1) six isotropic events, (2) five tensional crack events, and (3) a swarm of 14 events southeast of the volcanic centre that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model. Proper characterization of uncertainties for full moment tensors is critical for distinguishing among physical models of source processes.

Tensor models, Kronecker coefficients and permutation centralizer algebras

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.

Spacetime encodings. III. Second order Killing tensors

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

Brink, Jeandrew

2010-01-15

This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture ofmore » what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.« less

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

DOE PAGES

Yang, Xiaoning

2016-08-01

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

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

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

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

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

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

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

Self-adaptive tensor network states with multi-site correlators

NASA Astrophysics Data System (ADS)

Kovyrshin, Arseny; Reiher, Markus

2017-12-01

We introduce the concept of self-adaptive tensor network states (SATNSs) based on multi-site correlators. The SATNS ansatz gradually extends its variational space incorporating the most important next-order correlators into the ansatz for the wave function. The selection of these correlators is guided by entanglement-entropy measures from quantum information theory. By sequentially introducing variational parameters and adjusting them to the system under study, the SATNS ansatz achieves keeping their number significantly smaller than the total number of full-configuration interaction parameters. The SATNS ansatz is studied for manganocene in its lowest-energy sextet and doublet states; the latter of which is known to be difficult to describe. It is shown that the SATNS parametrization solves the convergence issues found for previous correlator-based tensor network states.

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

NASA Astrophysics Data System (ADS)

Bukchin, B. G.

1995-08-01

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

Intellectual abilities and white matter microstructure in development: a diffusion tensor imaging study.

PubMed

Tamnes, Christian K; Østby, Ylva; Walhovd, Kristine B; Westlye, Lars T; Due-Tønnessen, Paulina; Fjell, Anders M

2010-10-01

Higher-order cognitive functions are supported by distributed networks of multiple interconnected cortical and subcortical regions. Efficient cognitive processing depends on fast communication between these regions, so the integrity of the connections between them is of great importance. It is known that white matter (WM) development is a slow process, continuing into adulthood. While the significance of cortical maturation for intellectual development is described, less is known about the relationships between cognitive functions and maturation of WM connectivity. In this cross-sectional study, we investigated the associations between intellectual abilities and development of diffusion tensor imaging (DTI) derived measures of WM microstructure in 168 right-handed participants aged 8-30 years. Independently of age and sex, both verbal and performance abilities were positively related to fractional anisotropy (FA) and negatively related to mean diffusivity (MD) and radial diffusivity (RD), predominantly in the left hemisphere. Further, verbal, but not performance abilities, were associated with developmental differences in DTI indices in widespread regions in both hemispheres. Regional analyses showed relations with both FA and RD bilaterally in the anterior thalamic radiation and the cortico-spinal tract and in the right superior longitudinal fasciculus. In these regions, our results suggest that participants with high verbal abilities may show accelerated WM development in late childhood and a subsequent earlier developmental plateau, in contrast to a steadier and prolonged development in participants with average verbal abilities. Longitudinal data are needed to validate these interpretations. The results provide insight into the neurobiological underpinnings of intellectual development. © 2010 Wiley-Liss, Inc.

High-resolution dynamic 31 P-MRSI using a low-rank tensor model.

PubMed

Ma, Chao; Clifford, Bryan; Liu, Yuchi; Gu, Yuning; Lam, Fan; Yu, Xin; Liang, Zhi-Pei

2017-08-01

To develop a rapid 31 P-MRSI method with high spatiospectral resolution using low-rank tensor-based data acquisition and image reconstruction. The multidimensional image function of 31 P-MRSI is represented by a low-rank tensor to capture the spatial-spectral-temporal correlations of data. A hybrid data acquisition scheme is used for sparse sampling, which consists of a set of "training" data with limited k-space coverage to capture the subspace structure of the image function, and a set of sparsely sampled "imaging" data for high-resolution image reconstruction. An explicit subspace pursuit approach is used for image reconstruction, which estimates the bases of the subspace from the "training" data and then reconstructs a high-resolution image function from the "imaging" data. We have validated the feasibility of the proposed method using phantom and in vivo studies on a 3T whole-body scanner and a 9.4T preclinical scanner. The proposed method produced high-resolution static 31 P-MRSI images (i.e., 6.9 × 6.9 × 10 mm 3 nominal resolution in a 15-min acquisition at 3T) and high-resolution, high-frame-rate dynamic 31 P-MRSI images (i.e., 1.5 × 1.5 × 1.6 mm 3 nominal resolution, 30 s/frame at 9.4T). Dynamic spatiospectral variations of 31 P-MRSI signals can be efficiently represented by a low-rank tensor. Exploiting this mathematical structure for data acquisition and image reconstruction can lead to fast 31 P-MRSI with high resolution, frame-rate, and SNR. Magn Reson Med 78:419-428, 2017. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Emerging Structure–Function Relations in the Developing Face Processing System

PubMed Central

Suzanne Scherf, K.; Thomas, Cibu; Doyle, Jaime; Behrmann, Marlene

2014-01-01

To evaluate emerging structure–function relations in a neural circuit that mediates complex behavior, we investigated age-related differences among cortical regions that support face recognition behavior and the fiber tracts through which they transmit and receive signals using functional neuroimaging and diffusion tensor imaging. In a large sample of human participants (aged 6–23 years), we derived the microstructural and volumetric properties of the inferior longitudinal fasciculus (ILF), the inferior fronto-occipital fasciculus, and control tracts, using independently defined anatomical markers. We also determined the functional characteristics of core face- and place-selective regions that are distributed along the trajectory of the pathways of interest. We observed disproportionately large age-related differences in the volume, fractional anisotropy, and mean and radial, but not axial, diffusivities of the ILF. Critically, these differences in the structural properties of the ILF were tightly and specifically linked with an age-related increase in the size of a key face-selective functional region, the fusiform face area. This dynamic association between emerging structural and functional architecture in the developing brain may provide important clues about the mechanisms by which neural circuits become organized and optimized in the human cortex. PMID:23765156

Quantification of Uncertainty in Full-Waveform Moment Tensor Inversion for Regional Seismicity

NASA Astrophysics Data System (ADS)

Jian, P.; Hung, S.; Tseng, T.

2013-12-01

Routinely and instantaneously determined moment tensor solutions deliver basic information for investigating faulting nature of earthquakes and regional tectonic structure. The accuracy of full-waveform moment tensor inversion mostly relies on azimuthal coverage of stations, data quality and previously known earth's structure (i.e., impulse responses or Green's functions). However, intrinsically imperfect station distribution, noise-contaminated waveform records and uncertain earth structure can often result in large deviations of the retrieved source parameters from the true ones, which prohibits the use of routinely reported earthquake catalogs for further structural and tectonic interferences. Duputel et al. (2012) first systematically addressed the significance of statistical uncertainty estimation in earthquake source inversion and exemplified that the data covariance matrix, if prescribed properly to account for data dependence and uncertainty due to incomplete and erroneous data and hypocenter mislocation, cannot only be mapped onto the uncertainty estimate of resulting source parameters, but it also aids obtaining more stable and reliable results. Over the past decade, BATS (Broadband Array in Taiwan for Seismology) has steadily devoted to building up a database of good-quality centroid moment tensor (CMT) solutions for moderate to large magnitude earthquakes that occurred in Taiwan area. Because of the lack of the uncertainty quantification and reliability analysis, it remains controversial to use the reported CMT catalog directly for further investigation of regional tectonics, near-source strong ground motions, and seismic hazard assessment. In this study, we develop a statistical procedure to make quantitative and reliable estimates of uncertainty in regional full-waveform CMT inversion. The linearized inversion scheme adapting efficient estimation of the covariance matrices associated with oversampled noisy waveform data and errors of biased centroid positions is implemented and inspected for improving source parameter determination of regional seismicity in Taiwan. Synthetic inversion tests demonstrate the resolved moment tensors would better match the hypothetical CMT solutions, and tend to suppress unreal non-double-couple components and reduce the trade-off between focal mechanism and centroid depth if individual signal-to-noise ratios and correlation lengths for 3-component seismograms at each station and mislocation uncertainties are properly taken into account. We further testify the capability of our scheme in retrieving the robust CMT information for mid-sized (Mw~3.5) and offshore earthquakes in Taiwan, which offers immediate and broad applications in detailed modelling of regional stress field and deformation pattern and mapping of subsurface velocity structures.

Moment tensor solutions estimated using optimal filter theory for 51 selected earthquakes, 1980-1984

USGS Publications Warehouse

Sipkin, S.A.

1987-01-01

The 51 global events that occurred from January 1980 to March 1984, which were chosen by the convenors of the Symposium on Seismological Theory and Practice, have been analyzed using a moment tensor inversion algorithm (Sipkin). Many of the events were routinely analyzed as part of the National Earthquake Information Center's (NEIC) efforts to publish moment tensor and first-motion fault-plane solutions for all moderate- to large-sized (mb>5.7) earthquakes. In routine use only long-period P-waves are used and the source-time function is constrained to be a step-function at the source (??-function in the far-field). Four of the events were of special interest, and long-period P, SH-wave solutions were obtained. For three of these events, an unconstrained inversion was performed. The resulting time-dependent solutions indicated that, for many cases, departures of the solutions from pure double-couples are caused by source complexity that has not been adequately modeled. These solutions also indicate that source complexity of moderate-sized events can be determined from long-period data. Finally, for one of the events of special interest, an inversion of the broadband P-waveforms was also performed, demonstrating the potential for using broadband waveform data in inversion procedures. ?? 1987.

Corticospinal tract asymmetry and handedness in right- and left-handers by diffusion tensor tractography.

PubMed

Seizeur, Romuald; Magro, Elsa; Prima, Sylvain; Wiest-Daesslé, Nicolas; Maumet, Camille; Morandi, Xavier

2014-03-01

Cerebral hemispheres represent both structural and functional asymmetry, which differs among right- and left-handers. The left hemisphere is specialised for language and task execution of the right hand in right-handers. We studied the corticospinal tract in right- and left-handers by diffusion tensor imaging and tractography. The present study aimed at revealing a morphological difference resulting from a region of interest (ROI) obtained by functional MRI (fMRI). Twenty-five healthy participants (right-handed: 15, left-handed: 10) were enrolled in our assessment of morphological, functional and diffusion tensor MRI. Assessment of brain fibre reconstruction (tractography) was done using a deterministic algorithm. Fractional anisotropy (FA) and mean diffusivity (MD) were studied on the tractography traces of the reference slices. We observed a significant difference in number of leftward fibres based on laterality. The significant difference in regard to FA and MD was based on the slices obtained at different levels and the laterality index. We found left-hand asymmetry and right-hand asymmetry, respectively, for the MD and FA. Our study showed the presence of hemispheric asymmetry based on laterality index in right- and left-handers. These results are inconsistent with some studies and consistent with others. The reported difference in hemispheric asymmetry could be related to dexterity (manual skill).

FADTTSter: accelerating hypothesis testing with functional analysis of diffusion tensor tract statistics

NASA Astrophysics Data System (ADS)

Noel, Jean; Prieto, Juan C.; Styner, Martin

2017-03-01

Functional Analysis of Diffusion Tensor Tract Statistics (FADTTS) is a toolbox for analysis of white matter (WM) fiber tracts. It allows associating diffusion properties along major WM bundles with a set of covariates of interest, such as age, diagnostic status and gender, and the structure of the variability of these WM tract properties. However, to use this toolbox, a user must have an intermediate knowledge in scripting languages (MATLAB). FADTTSter was created to overcome this issue and make the statistical analysis accessible to any non-technical researcher. FADTTSter is actively being used by researchers at the University of North Carolina. FADTTSter guides non-technical users through a series of steps including quality control of subjects and fibers in order to setup the necessary parameters to run FADTTS. Additionally, FADTTSter implements interactive charts for FADTTS' outputs. This interactive chart enhances the researcher experience and facilitates the analysis of the results. FADTTSter's motivation is to improve usability and provide a new analysis tool to the community that complements FADTTS. Ultimately, by enabling FADTTS to a broader audience, FADTTSter seeks to accelerate hypothesis testing in neuroimaging studies involving heterogeneous clinical data and diffusion tensor imaging. This work is submitted to the Biomedical Applications in Molecular, Structural, and Functional Imaging conference. The source code of this application is available in NITRC.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Combined analysis of magnetic and gravity anomalies using normalized source strength (NSS)

NASA Astrophysics Data System (ADS)

Li, L.; Wu, Y.

2017-12-01

Gravity field and magnetic field belong to potential fields which lead inherent multi-solution. Combined analysis of magnetic and gravity anomalies based on Poisson's relation is used to determinate homology gravity and magnetic anomalies and decrease the ambiguity. The traditional combined analysis uses the linear regression of the reduction to pole (RTP) magnetic anomaly to the first order vertical derivative of the gravity anomaly, and provides the quantitative or semi-quantitative interpretation by calculating the correlation coefficient, slope and intercept. In the calculation process, due to the effect of remanent magnetization, the RTP anomaly still contains the effect of oblique magnetization. In this case the homology gravity and magnetic anomalies display irrelevant results in the linear regression calculation. The normalized source strength (NSS) can be transformed from the magnetic tensor matrix, which is insensitive to the remanence. Here we present a new combined analysis using NSS. Based on the Poisson's relation, the gravity tensor matrix can be transformed into the pseudomagnetic tensor matrix of the direction of geomagnetic field magnetization under the homologous condition. The NSS of pseudomagnetic tensor matrix and original magnetic tensor matrix are calculated and linear regression analysis is carried out. The calculated correlation coefficient, slope and intercept indicate the homology level, Poisson's ratio and the distribution of remanent respectively. We test the approach using synthetic model under complex magnetization, the results show that it can still distinguish the same source under the condition of strong remanence, and establish the Poisson's ratio. Finally, this approach is applied in China. The results demonstrated that our approach is feasible.

Modeling fluid diffusion in cerebral white matter with random walks in complex environments

NASA Astrophysics Data System (ADS)

Levy, Amichai; Cwilich, Gabriel; Buldyrev, Sergey V.; Weeden, Van J.

2012-02-01

Recent studies with diffusion MRI have shown new aspects of geometric order in the brain, including complex path coherence within the cerebral cortex, and organization of cerebral white matter and connectivity across multiple scales. The main assumption of these studies is that water molecules diffuse along myelin sheaths of neuron axons in the white matter and thus the anisotropy of their diffusion tensor observed by MRI can provide information about the direction of the axons connecting different parts of the brain. We model the diffusion of particles confined in the space of between the bundles of cylindrical obstacles representing fibrous structures of various orientations. We have investigated the directional properties of the diffusion, by studying the angular distribution of the end point of the random walks as a function of their length, to understand the scale over which the distribution randomizes. We will show evidence of qualitative change in the behavior of the diffusion for different volume fractions of obstacles. Comparisons with three-dimensional MRI images will be illustrated.

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

NASA Astrophysics Data System (ADS)

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

2012-07-01

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

An improved nearly-orthogonal structured mesh generation system with smoothness control functions

USDA-ARS?s Scientific Manuscript database

This paper presents an improved nearly-orthogonal structured mesh generation system with a set of smoothness control functions, which were derived based on the ratio between the Jacobian of the transformation matrix and the Jacobian of the metric tensor. The proposed smoothness control functions are...

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Structural abnormalities and altered regional brain activity in multiple sclerosis with simple spinal cord involvement.

PubMed

Yin, Ping; Liu, Yi; Xiong, Hua; Han, Yongliang; Sah, Shambhu Kumar; Zeng, Chun; Wang, Jingjie; Li, Yongmei

2018-02-01

To assess the changes of the structural and functional abnormalities in multiple sclerosis with simple spinal cord involvement (MS-SSCI) by using resting-state functional MRI (RS-fMRI), voxel based morphology (VBM) and diffusion tensor tractography. The amplitude of low-frequency fluctuation (ALFF) of 22 patients with MS-SSCI and 22 healthy controls (HCs) matched for age, gender and education were compared by using RS-fMRI. We also compared the volume, fractional anisotropy (FA) and apparent diffusion coefficient of the brain regions in baseline brain activity by using VBM and diffusion tensor imaging. The relationships between the expanded disability states scale (EDSS) scores, changed parameters of structure and function were further explored. (1) Compared with HCs, the ALFF of the bilateral hippocampus and right middle temporal gyrus in MS-SSCI decreased significantly. However, patients exhibited increased ALFF in the left middle frontal gyrus, left posterior cingulate gyrus and right middle occipital gyrus ( two-sample t-test, after AlphaSim correction, p < 0.01, voxel size > 40). The volume of right middle frontal gyrus reduced significantly (p < 0.01). The FA and ADC of right hippocampus, the FA of left hippocampus and right middle temporal gyrus were significantly different. (2) A significant correlation between EDSS scores and ALFF was noted only in the left posterior cingulate gyrus. Our results detected structural and functional abnormalities in MS-SSCI and functional parameters were associated with clinical abnormalities. Multimodal imaging plays an important role in detecting structural and functional abnormalities in MS-SSCI. Advances in knowledge: This is the first time to apply RS-fMRI, VBM and diffusion tensor tractography to study the structural and functional abnormalities in MS-SSCI, and to explore its correlation with EDSS score.

FADTTS: functional analysis of diffusion tensor tract statistics.

PubMed

Zhu, Hongtu; Kong, Linglong; Li, Runze; Styner, Martin; Gerig, Guido; Lin, Weili; Gilmore, John H

2011-06-01

The aim of this paper is to present a functional analysis of a diffusion tensor tract statistics (FADTTS) pipeline for delineating the association between multiple diffusion properties along major white matter fiber bundles with a set of covariates of interest, such as age, diagnostic status and gender, and the structure of the variability of these white matter tract properties in various diffusion tensor imaging studies. The FADTTS integrates five statistical tools: (i) a multivariate varying coefficient model for allowing the varying coefficient functions in terms of arc length to characterize the varying associations between fiber bundle diffusion properties and a set of covariates, (ii) a weighted least squares estimation of the varying coefficient functions, (iii) a functional principal component analysis to delineate the structure of the variability in fiber bundle diffusion properties, (iv) a global test statistic to test hypotheses of interest, and (v) a simultaneous confidence band to quantify the uncertainty in the estimated coefficient functions. Simulated data are used to evaluate the finite sample performance of FADTTS. We apply FADTTS to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. FADTTS can be used to facilitate the understanding of normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles. The advantages of FADTTS compared with the other existing approaches are that they are capable of modeling the structured inter-subject variability, testing the joint effects, and constructing their simultaneous confidence bands. However, FADTTS is not crucial for estimation and reduces to the functional analysis method for the single measure. Copyright © 2011 Elsevier Inc. All rights reserved.

Taking Measure of the Milky Way

NASA Technical Reports Server (NTRS)

Majewski, Steven R.; Bahcall, John N.; Geisler, Douglas; Gieren, Wolfgang; Grebel, Eva; Grillmair, Carl; Irwin, Michael; Johnston, Kathryn V.; Patterson, Richard J.; Reid, Neill I.

2004-01-01

We intend to use SIM to make definitive measurements of fundamental structural and dynamical parameters of the Milky Way. The important niche in dynamical parameter space afforded by SIM can be exploited to resolve, with unprecedented precision, a number of classical problems of Galactic astronomy. In addition, we have developed new tests of the Galactic mass distribution specifically designed for data with the special properties of SIM products. Our proposed suite of experiments will utilize the SIM Astrometric Grid as well as complementary observations of star clusters and other strategically-selected, distant "test particles" for a definitive characterization of the major components (bulge, disk, halo, satellite system) of the Milky Way. Specifically, our goals will be: 1) The determination of two fundamental parameters that play a central role in virtually every problem in Galactic astronomy, namely (a) the solar distance to the center of the Milky Way, R(sub 0); (b) the solar angular velocity around the Galactic: center, omega(sub 0). 2) The measurement of fundamental dynamical properties of the Milky Way, among them (a) the pattern speed of the central bar (b) the rotation field and velocity-dispersion tensor in the disk (c) the kinematics (mean rotational velocity and velocity dispersion tensor) of the halo as a function of position 3. The definition of the mass distribution of the Galaxy, which is dominated by the presence of dark matter. We intend to measure (a) the relative contribution of the disk and halo to the gravitational potential (b) the local volume and surface mass density of the disk (c) the shape, mass and extent of the dark halo of the Milky Way out to 250 kpc.

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.

Probabilistic-driven oriented Speckle reducing anisotropic diffusion with application to cardiac ultrasonic images.

PubMed

Vegas-Sanchez-Ferrero, G; Aja-Fernandez, S; Martin-Fernandez, M; Frangi, A F; Palencia, C

2010-01-01

A novel anisotropic diffusion filter is proposed in this work with application to cardiac ultrasonic images. It includes probabilistic models which describe the probability density function (PDF) of tissues and adapts the diffusion tensor to the image iteratively. For this purpose, a preliminary study is performed in order to select the probability models that best fit the stastitical behavior of each tissue class in cardiac ultrasonic images. Then, the parameters of the diffusion tensor are defined taking into account the statistical properties of the image at each voxel. When the structure tensor of the probability of belonging to each tissue is included in the diffusion tensor definition, a better boundaries estimates can be obtained instead of calculating directly the boundaries from the image. This is the main contribution of this work. Additionally, the proposed method follows the statistical properties of the image in each iteration. This is considered as a second contribution since state-of-the-art methods suppose that noise or statistical properties of the image do not change during the filter process.

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.

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.

DR-TAMAS: Diffeomorphic Registration for Tensor Accurate alignMent of Anatomical Structures

PubMed Central

Irfanoglu, M. Okan; Nayak, Amritha; Jenkins, Jeffrey; Hutchinson, Elizabeth B.; Sadeghi, Neda; Thomas, Cibu P.; Pierpaoli, Carlo

2016-01-01

In this work, we propose DR-TAMAS (Diffeomorphic Registration for Tensor Accurate alignMent of Anatomical Structures), a novel framework for intersubject registration of Diffusion Tensor Imaging (DTI) data sets. This framework is optimized for brain data and its main goal is to achieve an accurate alignment of all brain structures, including white matter (WM), gray matter (GM), and spaces containing cerebrospinal fluid (CSF). Currently most DTI-based spatial normalization algorithms emphasize alignment of anisotropic structures. While some diffusion-derived metrics, such as diffusion anisotropy and tensor eigenvector orientation, are highly informative for proper alignment of WM, other tensor metrics such as the trace or mean diffusivity (MD) are fundamental for a proper alignment of GM and CSF boundaries. Moreover, it is desirable to include information from structural MRI data, e.g., T1-weighted or T2-weighted images, which are usually available together with the diffusion data. The fundamental property of DR-TAMAS is to achieve global anatomical accuracy by incorporating in its cost function the most informative metrics locally. Another important feature of DR-TAMAS is a symmetric time-varying velocity-based transformation model, which enables it to account for potentially large anatomical variability in healthy subjects and patients. The performance of DR-TAMAS is evaluated with several data sets and compared with other widely-used diffeomorphic image registration techniques employing both full tensor information and/or DTI-derived scalar maps. Our results show that the proposed method has excellent overall performance in the entire brain, while being equivalent to the best existing methods in WM. PMID:26931817

The total position-spread tensor: Spin partition

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

El Khatib, Muammar, E-mail: elkhatib@irsamc.ups-tlse.fr; Evangelisti, Stefano, E-mail: stefano@irsamc.ups-tlse.fr; Leininger, Thierry, E-mail: Thierry.Leininger@irsamc.ups-tlse.fr

2015-03-07

The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interactionmore » (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H{sub n} (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system.« less

A Catalog of Moment Tensors and Source-type Characterization for Small Events at Uturuncu Volcano, Bolivia

NASA Astrophysics Data System (ADS)

Alvizuri, C. R.; Tape, C.

2015-12-01

We present a catalog of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broadband stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we also used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the six-dimensional space of moment tensors. For each event we characterize the variation of moment tensor source type by plotting the misfit function in eigenvalue space, represented by a lune. We plot the optimal solutions for the 63 events on the lune in order to identify three subsets of the catalog: (1) a set of isotropic events, (2) a set of tensional crack events, and (3) a swarm of events southeast of the volcanic center that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model; instead they require a multiple-process source model. Our study emphasizes the importance of characterizing uncertainties for full moment tensors, and it provides strong support for isotropic events at Uturuncu volcano.

DR-TAMAS: Diffeomorphic Registration for Tensor Accurate Alignment of Anatomical Structures.

PubMed

Irfanoglu, M Okan; Nayak, Amritha; Jenkins, Jeffrey; Hutchinson, Elizabeth B; Sadeghi, Neda; Thomas, Cibu P; Pierpaoli, Carlo

2016-05-15

In this work, we propose DR-TAMAS (Diffeomorphic Registration for Tensor Accurate alignMent of Anatomical Structures), a novel framework for intersubject registration of Diffusion Tensor Imaging (DTI) data sets. This framework is optimized for brain data and its main goal is to achieve an accurate alignment of all brain structures, including white matter (WM), gray matter (GM), and spaces containing cerebrospinal fluid (CSF). Currently most DTI-based spatial normalization algorithms emphasize alignment of anisotropic structures. While some diffusion-derived metrics, such as diffusion anisotropy and tensor eigenvector orientation, are highly informative for proper alignment of WM, other tensor metrics such as the trace or mean diffusivity (MD) are fundamental for a proper alignment of GM and CSF boundaries. Moreover, it is desirable to include information from structural MRI data, e.g., T1-weighted or T2-weighted images, which are usually available together with the diffusion data. The fundamental property of DR-TAMAS is to achieve global anatomical accuracy by incorporating in its cost function the most informative metrics locally. Another important feature of DR-TAMAS is a symmetric time-varying velocity-based transformation model, which enables it to account for potentially large anatomical variability in healthy subjects and patients. The performance of DR-TAMAS is evaluated with several data sets and compared with other widely-used diffeomorphic image registration techniques employing both full tensor information and/or DTI-derived scalar maps. Our results show that the proposed method has excellent overall performance in the entire brain, while being equivalent to the best existing methods in WM. Copyright © 2016 Elsevier Inc. All rights reserved.

Spin echo versus stimulated echo diffusion tensor imaging of the in vivo human heart

PubMed Central

von Deuster, Constantin; Stoeck, Christian T.; Genet, Martin; Atkinson, David

2015-01-01

Purpose To compare signal‐to‐noise ratio (SNR) efficiency and diffusion tensor metrics of cardiac diffusion tensor mapping using acceleration‐compensated spin‐echo (SE) and stimulated echo acquisition mode (STEAM) imaging. Methods Diffusion weighted SE and STEAM sequences were implemented on a clinical 1.5 Tesla MR system. The SNR efficiency of SE and STEAM was measured (b = 50–450 s/mm2) in isotropic agar, anisotropic diffusion phantoms and the in vivo human heart. Diffusion tensor analysis was performed on mean diffusivity, fractional anisotropy, helix and transverse angles. Results In the isotropic phantom, the ratio of SNR efficiency for SE versus STEAM, SNRt(SE/STEAM), was 2.84 ± 0.08 for all tested b‐values. In the anisotropic diffusion phantom the ratio decreased from 2.75 ± 0.05 to 2.20 ± 0.13 with increasing b‐value, similar to the in vivo decrease from 2.91 ± 0.43 to 2.30 ± 0.30. Diffusion tensor analysis revealed reduced deviation of helix angles from a linear transmural model and reduced transverse angle standard deviation for SE compared with STEAM. Mean diffusivity and fractional anisotropy were measured to be statistically different (P < 0.001) between SE and STEAM. Conclusion Cardiac DTI using motion‐compensated SE yields a 2.3–2.9× increase in SNR efficiency relative to STEAM and improved accuracy of tensor metrics. The SE method hence presents an attractive alternative to STEAM based approaches. Magn Reson Med 76:862–872, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. PMID:26445426

Mass Function of Galaxy Clusters in Relativistic Inhomogeneous Cosmology

NASA Astrophysics Data System (ADS)

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

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

Neuroimaging of the Functional and Structural Networks Underlying Visuospatial vs. Linguistic Reasoning in High-Functioning Autism

ERIC Educational Resources Information Center

Sahyoun, Cherif P.; Belliveau, John W.; Soulieres, Isabelle; Schwartz, Shira; Mody, Maria

2010-01-01

High-functioning individuals with autism have been found to favor visuospatial processing in the face of typically poor language abilities. We aimed to examine the neurobiological basis of this difference using functional magnetic resonance imaging and diffusion tensor imaging. We compared 12 children with high functioning autism (HFA) to 12 age-…

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2016-05-01

We present a tensor hypercontracted (THC) scaled opposite spin second order Møller-Plesset perturbation theory (SOS-MP2) method. By using THC, we reduce the formal scaling of SOS-MP2 with respect to molecular size from quartic to cubic. We achieve further efficiency by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs) to accelerate integral construction and matrix multiplication. The practical scaling of GPU-accelerated atomic orbital-based THC-SOS-MP2 calculations is found to be N2.6 for reference data sets of water clusters and alanine polypeptides containing up to 1600 basis functions. The errors in correlation energy with respect to density-fitting-SOS-MP2 are less than 0.5 kcal/mol for all systems tested (up to 162 atoms).

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity.

PubMed

Song, Chenchen; Martínez, Todd J

2016-05-07

We present a tensor hypercontracted (THC) scaled opposite spin second order Møller-Plesset perturbation theory (SOS-MP2) method. By using THC, we reduce the formal scaling of SOS-MP2 with respect to molecular size from quartic to cubic. We achieve further efficiency by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs) to accelerate integral construction and matrix multiplication. The practical scaling of GPU-accelerated atomic orbital-based THC-SOS-MP2 calculations is found to be N(2.6) for reference data sets of water clusters and alanine polypeptides containing up to 1600 basis functions. The errors in correlation energy with respect to density-fitting-SOS-MP2 are less than 0.5 kcal/mol for all systems tested (up to 162 atoms).

δ M formalism and anisotropic chaotic inflation power spectrum

NASA Astrophysics Data System (ADS)

Talebian-Ashkezari, A.; Ahmadi, N.

2018-05-01

A new analytical approach to linear perturbations in anisotropic inflation has been introduced in [A. Talebian-Ashkezari, N. Ahmadi and A.A. Abolhasani, JCAP 03 (2018) 001] under the name of δ M formalism. In this paper we apply the mentioned approach to a model of anisotropic inflation driven by a scalar field, coupled to the kinetic term of a vector field with a U(1) symmetry. The δ M formalism provides an efficient way of computing tensor-tensor, tensor-scalar as well as scalar-scalar 2-point correlations that are needed for the analysis of the observational features of an anisotropic model on the CMB. A comparison between δ M results and the tedious calculations using in-in formalism shows the aptitude of the δ M formalism in calculating accurate two point correlation functions between physical modes of the system.

Seismotectonics and crustal stress across the northern Arabian plate

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Identifying isotropic events using a regional moment tensor inversion

DOE PAGES

Ford, Sean R.; Dreger, Douglas S.; Walter, William R.

2009-01-17

We calculate the deviatoric and isotropic source components for 17 explosions at the Nevada Test Site, as well as 12 earthquakes and 3 collapses in the surrounding region of the western United States, using a regional time domain full waveform inversion for the complete moment tensor. The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination between explosions, earthquakes, and collapses. Confidence regions of the model parameters are estimated from the data misfit by assuming normally distributed parameter values. Wemore » investigate the sensitivity of the resolved parameters of an explosion to imperfect Earth models, inaccurate event depths, and data with low signal-to-noise ratio (SNR) assuming a reasonable azimuthal distribution of stations. In the band of interest (0.02–0.10 Hz) the source-type calculated from complete moment tensor inversion is insensitive to velocity model perturbations that cause less than a half-cycle shift (<5 s) in arrival time error if shifting of the waveforms is allowed. The explosion source-type is insensitive to an incorrect depth assumption (for a true depth of 1 km), and the goodness of fit of the inversion result cannot be used to resolve the true depth of the explosion. Noise degrades the explosive character of the result, and a good fit and accurate result are obtained when the signal-to-noise ratio is greater than 5. We assess the depth and frequency dependence upon the resolved explosive moment. As the depth decreases from 1 km to 200 m, the isotropic moment is no longer accurately resolved and is in error between 50 and 200%. Furthermore, even at the most shallow depth the resultant moment tensor is dominated by the explosive component when the data have a good SNR.« less

Intermediate Templates Guided Groupwise Registration of Diffusion Tensor Images

PubMed Central

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

2010-01-01

Registration of a population of diffusion tensor images (DTIs) is one of the key steps in medical image analysis, and it plays an important role in the statistical analysis of white matter related neurological diseases. However, pairwise registration with respect to a pre-selected template may not give precise results if the selected template deviates significantly from the distribution of images. To cater for more accurate and consistent registration, a novel framework is proposed for groupwise registration with the guidance from one or more intermediate templates determined from the population of images. Specifically, we first use a Euclidean distance, defined as a combinative measure based on the FA map and ADC map, for gauging the similarity of each pair of DTIs. A fully connected graph is then built with each node denoting an image and each edge denoting the distance between a pair of images. The root template image is determined automatically as the image with the overall shortest path length to all other images on the minimum spanning tree (MST) of the graph. Finally, a sequence of registration steps is applied to progressively warping each image towards the root template image with the help of intermediate templates distributed along its path to the root node on the MST. Extensive experimental results using diffusion tensor images of real subjects indicate that registration accuracy and fiber tract alignment are significantly improved, compared with the direct registration from each image to the root template image. PMID:20851197

Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory

NASA Astrophysics Data System (ADS)

Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J.

2012-07-01

Many approximations have been developed to help deal with the O(N4) growth of the electron repulsion integral (ERI) tensor, where N is the number of one-electron basis functions used to represent the electronic wavefunction. Of these, the density fitting (DF) approximation is currently the most widely used despite the fact that it is often incapable of altering the underlying scaling of computational effort with respect to molecular size. We present a method for exploiting sparsity in three-center overlap integrals through tensor decomposition to obtain a low-rank approximation to density fitting (tensor hypercontraction density fitting or THC-DF). This new approximation reduces the 4th-order ERI tensor to a product of five matrices, simultaneously reducing the storage requirement as well as increasing the flexibility to regroup terms and reduce scaling behavior. As an example, we demonstrate such a scaling reduction for second- and third-order perturbation theory (MP2 and MP3), showing that both can be carried out in O(N4) operations. This should be compared to the usual scaling behavior of O(N5) and O(N6) for MP2 and MP3, respectively. The THC-DF technique can also be applied to other methods in electronic structure theory, such as coupled-cluster and configuration interaction, promising significant gains in computational efficiency and storage reduction.

Characterizing Atomistic Geometries and Potential Functions Using Strain Functionals

NASA Astrophysics Data System (ADS)

Kober, Edward; Mathew, Nithin; Rudin, Sven

2017-06-01

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

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

DOE PAGES

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

2015-11-12

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

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

USGS Publications Warehouse

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

2003-01-01

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

Quantitative analysis of diffusion tensor orientation: theoretical framework.

PubMed

Wu, Yu-Chien; Field, Aaron S; Chung, Moo K; Badie, Benham; Alexander, Andrew L

2004-11-01

Diffusion-tensor MRI (DT-MRI) yields information about the magnitude, anisotropy, and orientation of water diffusion of brain tissues. Although white matter tractography and eigenvector color maps provide visually appealing displays of white matter tract organization, they do not easily lend themselves to quantitative and statistical analysis. In this study, a set of visual and quantitative tools for the investigation of tensor orientations in the human brain was developed. Visual tools included rose diagrams, which are spherical coordinate histograms of the major eigenvector directions, and 3D scatterplots of the major eigenvector angles. A scatter matrix of major eigenvector directions was used to describe the distribution of major eigenvectors in a defined anatomic region. A measure of eigenvector dispersion was developed to describe the degree of eigenvector coherence in the selected region. These tools were used to evaluate directional organization and the interhemispheric symmetry of DT-MRI data in five healthy human brains and two patients with infiltrative diseases of the white matter tracts. In normal anatomical white matter tracts, a high degree of directional coherence and interhemispheric symmetry was observed. The infiltrative diseases appeared to alter the eigenvector properties of affected white matter tracts, showing decreased eigenvector coherence and interhemispheric symmetry. This novel approach distills the rich, 3D information available from the diffusion tensor into a form that lends itself to quantitative analysis and statistical hypothesis testing. (c) 2004 Wiley-Liss, Inc.

The Tensor and the Scalar Charges of the Nucleon from Hadron Phenomenology

NASA Astrophysics Data System (ADS)

Courtoy, A.

2018-01-01

We discuss the impact of the determination of the nucleon tensor charge on searches for physics Beyond the Standard Model. We also comment on the future extraction of the subleading-twist PDF e(x) from Jefferson Lab soon-to-be-released Beam Spin Asymmetry data as well as from the expected data of CLAS12 and SoLID, as the latter is related to the scalar charge. These analyses are possible through the phenomenology of Dihadron Fragmentation Functions related processes, which we report on here as well.

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

DTIC Science & Technology

1997-01-01

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

Temperature dependence of the dielectric tensor of monoclinic Ga2O3 single crystals in the spectral range 1.0-8.5 eV

NASA Astrophysics Data System (ADS)

Sturm, C.; Schmidt-Grund, R.; Zviagin, V.; Grundmann, M.

2017-08-01

The full dielectric tensor of monoclinic Ga2O3 (β-phase) was determined by generalized spectroscopic ellipsometry in the spectral range from 1.0 eV up to 8.5 eV and temperatures in the range from 10 K up to 300 K. By using the oriented dipole approach, the energies and broadenings of the excitonic transitions are determined as a function of the temperature, and the exciton-phonon coupling properties are deduced.

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.

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

DTIC Science & Technology

2012-06-20

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

Brownian thermal noise in functional optical surfaces

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2003-05-01

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

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

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.

Adaptive local thresholding for robust nucleus segmentation utilizing shape priors

NASA Astrophysics Data System (ADS)

Wang, Xiuzhong; Srinivas, Chukka

2016-03-01

This paper describes a novel local thresholding method for foreground detection. First, a Canny edge detection method is used for initial edge detection. Then, tensor voting is applied on the initial edge pixels, using a nonsymmetric tensor field tailored to encode prior information about nucleus size, shape, and intensity spatial distribution. Tensor analysis is then performed to generate the saliency image and, based on that, the refined edge. Next, the image domain is divided into blocks. In each block, at least one foreground and one background pixel are sampled for each refined edge pixel. The saliency weighted foreground histogram and background histogram are then created. These two histograms are used to calculate a threshold by minimizing the background and foreground pixel classification error. The block-wise thresholds are then used to generate the threshold for each pixel via interpolation. Finally, the foreground is obtained by comparing the original image with the threshold image. The effective use of prior information, combined with robust techniques, results in far more reliable foreground detection, which leads to robust nucleus segmentation.

Study of the spin and parity of the Higgs boson in diboson decays with the ATLAS detector.

PubMed

Aad, G; Abbott, B; Abdallah, J; Abdinov, O; Aben, R; Abolins, M; AbouZeid, O S; Abramowicz, H; Abreu, H; Abreu, R; Abulaiti, Y; Acharya, B S; Adamczyk, L; Adams, D L; Adelman, J; Adomeit, S; Adye, T; Affolder, A A; Agatonovic-Jovin, T; Agricola, J; Aguilar-Saavedra, J A; Ahlen, S P; Ahmadov, F; Aielli, G; Akerstedt, H; Åkesson, T P A; Akimov, A V; Alberghi, G L; Albert, J; Albrand, S; Alconada Verzini, M J; Aleksa, M; Aleksandrov, I N; Alexa, C; Alexander, G; Alexopoulos, T; Alhroob, M; Alimonti, G; Alio, L; Alison, J; Alkire, S P; Allbrooke, B M M; Allport, P P; Aloisio, A; Alonso, A; Alonso, F; Alpigiani, C; Altheimer, A; Alvarez Gonzalez, B; Álvarez Piqueras, D; Alviggi, M G; Amadio, B T; Amako, K; Amaral Coutinho, Y; Amelung, C; Amidei, D; Amor Dos Santos, S P; Amorim, A; Amoroso, S; Amram, N; Amundsen, G; Anastopoulos, C; Ancu, L S; Andari, N; Andeen, T; Anders, C F; Anders, G; Anders, J K; Anderson, K J; Andreazza, A; Andrei, V; Angelidakis, S; Angelozzi, I; Anger, P; Angerami, A; Anghinolfi, F; Anisenkov, A V; Anjos, N; Annovi, A; Antonelli, M; Antonov, A; Antos, J; Anulli, F; Aoki, M; Aperio Bella, L; Arabidze, G; Arai, Y; Araque, J P; Arce, A T H; Arduh, F A; Arguin, J-F; Argyropoulos, S; Arik, M; Armbruster, A J; Arnaez, O; Arnal, V; Arnold, H; Arratia, M; Arslan, O; Artamonov, A; Artoni, G; Asai, S; Asbah, N; Ashkenazi, A; Åsman, B; Asquith, L; Assamagan, K; Astalos, R; Atkinson, M; Atlay, N B; Auerbach, B; Augsten, K; Aurousseau, M; Avolio, G; Axen, B; Ayoub, M K; Azuelos, G; Baak, M A; Baas, A E; Bacci, C; Bachacou, H; Bachas, K; Backes, M; Backhaus, M; Bagiacchi, P; Bagnaia, P; Bai, Y; Bain, T; Baines, J T; Baker, O K; Baldin, E M; Balek, P; Balestri, T; Balli, F; Banas, E; Banerjee, Sw; Bannoura, A A E; Bansil, H S; Barak, L; Barberio, E L; Barberis, D; Barbero, M; Barillari, T; Barisonzi, M; Barklow, T; Barlow, N; Barnes, S L; Barnett, B M; Barnett, R M; Barnovska, Z; Baroncelli, A; Barone, G; Barr, A J; Barreiro, F; Barreiro Guimarães da Costa, J; Bartoldus, R; Barton, A E; Bartos, P; Basalaev, A; Bassalat, A; Basye, A; Bates, R L; Batista, S J; Batley, J R; Battaglia, M; Bauce, M; Bauer, F; Bawa, H S; Beacham, J B; Beattie, M D; Beau, T; Beauchemin, P H; Beccherle, R; Bechtle, P; Beck, H P; Becker, K; Becker, M; Becker, S; Beckingham, M; Becot, C; Beddall, A J; Beddall, A; Bednyakov, V A; Bee, C P; Beemster, L J; Beermann, T A; Begel, M; Behr, J K; Belanger-Champagne, C; Bell, W H; Bella, G; Bellagamba, L; Bellerive, A; Bellomo, M; Belotskiy, K; Beltramello, O; Benary, O; Benchekroun, D; Bender, M; Bendtz, K; Benekos, N; Benhammou, Y; Benhar Noccioli, E; Benitez Garcia, J A; Benjamin, D P; Bensinger, J R; Bentvelsen, S; Beresford, L; Beretta, M; Berge, D; Bergeaas Kuutmann, E; Berger, N; Berghaus, F; Beringer, J; Bernard, C; Bernard, N R; Bernius, C; Bernlochner, F U; Berry, T; Berta, P; Bertella, C; Bertoli, G; Bertolucci, F; Bertsche, C; Bertsche, D; Besana, M I; Besjes, G J; Bessidskaia Bylund, O; Bessner, M; Besson, N; Betancourt, C; Bethke, S; Bevan, A J; Bhimji, W; Bianchi, R M; Bianchini, L; Bianco, M; Biebel, O; Biedermann, D; Bieniek, S P; Biglietti, M; Bilbao De Mendizabal, J; Bilokon, H; Bindi, M; Binet, S; Bingul, A; Bini, C; Biondi, S; Black, C W; Black, J E; Black, K M; Blackburn, D; Blair, R E; Blanchard, J-B; Blanco, J E; Blazek, T; Bloch, I; Blocker, C; Blum, W; Blumenschein, U; Bobbink, G J; Bobrovnikov, V S; Bocchetta, S S; Bocci, A; Bock, C; Boehler, M; Bogaerts, J A; Bogavac, D; Bogdanchikov, A G; Bohm, C; Boisvert, V; Bold, T; Boldea, V; Boldyrev, A S; Bomben, M; Bona, M; Boonekamp, M; Borisov, A; Borissov, G; Borroni, S; Bortfeldt, J; Bortolotto, V; Bos, K; Boscherini, D; Bosman, M; Boudreau, J; Bouffard, J; Bouhova-Thacker, E V; Boumediene, D; Bourdarios, C; Bousson, N; Boveia, A; Boyd, J; Boyko, I R; Bozic, I; Bracinik, J; Brandt, A; Brandt, G; Brandt, O; Bratzler, U; Brau, B; Brau, J E; Braun, H M; Brazzale, S F; Breaden Madden, W D; Brendlinger, K; Brennan, A J; Brenner, L; Brenner, R; Bressler, S; Bristow, K; Bristow, T M; Britton, D; Britzger, D; Brochu, F M; Brock, I; Brock, R; Bronner, J; Brooijmans, G; Brooks, T; Brooks, W K; Brosamer, J; Brost, E; Brown, J; Bruckman de Renstrom, P A; Bruncko, D; Bruneliere, R; Bruni, A; Bruni, G; Bruschi, M; Bruscino, N; Bryngemark, L; Buanes, T; Buat, Q; Buchholz, P; Buckley, A G; Buda, S I; Budagov, I A; Buehrer, F; Bugge, L; Bugge, M K; Bulekov, O; Bullock, D; Burckhart, H; Burdin, S; Burghgrave, B; Burke, S; Burmeister, I; Busato, E; Büscher, D; Büscher, V; Bussey, P; Butler, J M; Butt, A I; Buttar, C M; Butterworth, J M; Butti, P; Buttinger, W; Buzatu, A; Buzykaev, A R; Cabrera Urbán, S; Caforio, D; Cairo, V M; Cakir, O; Calafiura, P; Calandri, A; Calderini, G; Calfayan, P; Caloba, L P; Calvet, D; Calvet, S; Camacho Toro, R; Camarda, S; Camarri, P; Cameron, D; Caminal Armadans, R; Campana, S; Campanelli, M; Campoverde, A; Canale, V; Canepa, A; Cano Bret, M; Cantero, J; Cantrill, R; Cao, T; Capeans Garrido, M D M; Caprini, I; Caprini, M; Capua, M; Caputo, R; Cardarelli, R; Cardillo, F; Carli, T; Carlino, G; Carminati, L; Caron, S; Carquin, E; Carrillo-Montoya, G D; Carter, J R; Carvalho, J; Casadei, D; Casado, M P; Casolino, M; Castaneda-Miranda, E; Castelli, A; Castillo Gimenez, V; Castro, N F; Catastini, P; Catinaccio, A; Catmore, J R; Cattai, A; Caudron, J; Cavaliere, V; Cavalli, D; Cavalli-Sforza, M; Cavasinni, V; Ceradini, F; Cerio, B C; Cerny, K; Cerqueira, A S; Cerri, A; Cerrito, L; Cerutti, F; Cerv, M; Cervelli, A; Cetin, S A; Chafaq, A; Chakraborty, D; Chalupkova, I; Chang, P; Chapman, J D; Charlton, D G; Chau, C C; Chavez Barajas, C A; Cheatham, S; Chegwidden, A; Chekanov, S; Chekulaev, S V; Chelkov, G A; Chelstowska, M A; Chen, C; Chen, H; Chen, K; Chen, L; Chen, S; Chen, X; Chen, Y; Cheng, H C; Cheng, Y; Cheplakov, A; Cheremushkina, E; Cherkaoui El Moursli, R; Chernyatin, V; Cheu, E; Chevalier, L; Chiarella, V; Childers, J T; Chiodini, G; Chisholm, A S; Chislett, R T; Chitan, A; Chizhov, M V; Choi, K; Chouridou, S; Chow, B K B; Christodoulou, V; Chromek-Burckhart, D; Chudoba, J; Chuinard, A J; Chwastowski, J J; Chytka, L; Ciapetti, G; Ciftci, A K; Cinca, D; Cindro, V; Cioara, I A; Ciocio, A; Cirotto, F; Citron, Z H; Ciubancan, M; Clark, A; Clark, B L; Clark, P J; Clarke, R N; Cleland, W; Clement, C; Coadou, Y; Cobal, M; Coccaro, A; Cochran, J; Coffey, L; Cogan, J G; Cole, B; Cole, S; Colijn, A P; Collot, J; Colombo, T; Compostella, G; Conde Muiño, P; Coniavitis, E; Connell, S H; Connelly, I A; Consonni, S M; Consorti, V; Constantinescu, S; Conta, C; Conti, G; Conventi, F; Cooke, M; Cooper, B D; Cooper-Sarkar, A M; Cornelissen, T; Corradi, M; Corriveau, F; Corso-Radu, A; Cortes-Gonzalez, A; Cortiana, G; Costa, G; Costa, M J; Costanzo, D; Côté, D; Cottin, G; Cowan, G; Cox, B E; Cranmer, K; Cree, G; Crépé-Renaudin, S; Crescioli, F; Cribbs, W A; Crispin Ortuzar, M; Cristinziani, M; Croft, V; Crosetti, G; Cuhadar Donszelmann, T; Cummings, J; Curatolo, M; Cuthbert, C; Czirr, H; Czodrowski, P; D'Auria, S; D'Onofrio, M; Da Cunha Sargedas De Sousa, M J; Da Via, C; Dabrowski, W; Dafinca, A; Dai, T; Dale, O; Dallaire, F; Dallapiccola, C; Dam, M; Dandoy, J R; Dang, N P; Daniells, A C; Danninger, M; Dano Hoffmann, M; Dao, V; Darbo, G; Darmora, S; Dassoulas, J; Dattagupta, A; Davey, W; David, C; Davidek, T; Davies, E; Davies, M; Davison, P; Davygora, Y; Dawe, E; Dawson, I; Daya-Ishmukhametova, R K; De, K; de Asmundis, R; De Castro, S; De Cecco, S; De Groot, N; de Jong, P; De la Torre, H; De Lorenzi, F; De Nooij, L; De Pedis, D; De Salvo, A; De Sanctis, U; De Santo, A; De Vivie De Regie, J B; Dearnaley, W J; Debbe, R; Debenedetti, C; Dedovich, D V; Deigaard, I; Del Peso, J; Del Prete, T; Delgove, D; Deliot, F; Delitzsch, C M; Deliyergiyev, M; Dell'Acqua, A; Dell'Asta, L; Dell'Orso, M; Della Pietra, M; Della Volpe, D; Delmastro, M; Delsart, P A; Deluca, C; DeMarco, D A; Demers, S; Demichev, M; Demilly, A; Denisov, S P; Derendarz, D; Derkaoui, J E; Derue, F; Dervan, P; Desch, K; Deterre, C; Deviveiros, P O; Dewhurst, A; Dhaliwal, S; Di Ciaccio, A; Di Ciaccio, L; Di Domenico, A; Di Donato, C; Di Girolamo, A; Di Girolamo, B; Di Mattia, A; Di Micco, B; Di Nardo, R; Di Simone, A; Di Sipio, R; Di Valentino, D; Diaconu, C; Diamond, M; Dias, F A; Diaz, M A; Diehl, E B; Dietrich, J; Diglio, S; Dimitrievska, A; Dingfelder, J; Dita, P; Dita, S; Dittus, F; Djama, F; Djobava, T; Djuvsland, J I; do Vale, M A B; Dobos, D; Dobre, M; Doglioni, C; Dohmae, T; Dolejsi, J; Dolezal, Z; Dolgoshein, B A; Donadelli, M; Donati, S; Dondero, P; Donini, J; Dopke, J; Doria, A; Dova, M T; Doyle, A T; Drechsler, E; Dris, M; Dubreuil, E; Duchovni, E; Duckeck, G; Ducu, O A; Duda, D; Dudarev, A; Duflot, L; Duguid, L; Dührssen, M; Dunford, M; Duran Yildiz, H; Düren, M; Durglishvili, A; Duschinger, D; Dyndal, M; Eckardt, C; Ecker, K M; Edgar, R C; Edson, W; Edwards, N C; Ehrenfeld, W; Eifert, T; Eigen, G; Einsweiler, K; Ekelof, T; El Kacimi, M; Ellert, M; Elles, S; Ellinghaus, F; Elliot, A A; Ellis, N; Elmsheuser, J; Elsing, M; Emeliyanov, D; Enari, Y; Endner, O C; Endo, M; Erdmann, J; Ereditato, A; Ernis, G; Ernst, J; Ernst, M; Errede, S; Ertel, E; Escalier, M; Esch, H; Escobar, C; Esposito, B; Etienvre, A I; Etzion, E; Evans, H; Ezhilov, A; Fabbri, L; Facini, G; Fakhrutdinov, R M; Falciano, S; Falla, R J; Faltova, J; Fang, Y; Fanti, M; Farbin, A; Farilla, A; Farooque, T; Farrell, S; Farrington, S M; Farthouat, P; Fassi, F; Fassnacht, P; Fassouliotis, D; Faucci Giannelli, M; Favareto, A; Fayard, L; Federic, P; Fedin, O L; Fedorko, W; Feigl, S; Feligioni, L; Feng, C; Feng, E J; Feng, H; Fenyuk, A B; Feremenga, L; Fernandez Martinez, P; Fernandez Perez, S; Ferrando, J; Ferrari, A; Ferrari, P; Ferrari, R; Ferreira de Lima, D E; Ferrer, A; Ferrere, D; Ferretti, C; Ferretto Parodi, A; Fiascaris, M; Fiedler, F; Filipčič, A; Filipuzzi, M; Filthaut, F; Fincke-Keeler, M; Finelli, K D; Fiolhais, M C N; Fiorini, L; Firan, A; Fischer, A; Fischer, C; Fischer, J; Fisher, W C; Fitzgerald, E A; Flaschel, N; Fleck, I; Fleischmann, P; Fleischmann, S; Fletcher, G T; Fletcher, G; Fletcher, R R M; Flick, T; Floderus, A; Flores Castillo, L R; Flowerdew, M J; Formica, A; Forti, A; Fournier, D; Fox, H; Fracchia, S; Francavilla, P; Franchini, M; Francis, D; Franconi, L; Franklin, M; Frate, M; Fraternali, M; Freeborn, D; French, S T; Friedrich, F; Froidevaux, D; Frost, J A; Fukunaga, C; Fullana Torregrosa, E; Fulsom, B G; Fuster, J; Gabaldon, C; Gabizon, O; Gabrielli, A; Gabrielli, A; Gadatsch, S; Gadomski, S; Gagliardi, G; Gagnon, P; Galea, C; Galhardo, B; Gallas, E J; Gallop, B J; Gallus, P; Galster, G; Gan, K K; Gao, J; Gao, Y; Gao, Y S; Garay Walls, F M; Garberson, F; García, C; García Navarro, J E; Garcia-Sciveres, M; Gardner, R W; Garelli, N; Garonne, V; Gatti, C; Gaudiello, A; Gaudio, G; Gaur, B; Gauthier, L; Gauzzi, P; Gavrilenko, I L; Gay, C; Gaycken, G; Gazis, E N; Ge, P; Gecse, Z; Gee, C N P; Geerts, D A A; Geich-Gimbel, Ch; Geisler, M P; Gemme, C; Genest, M H; Gentile, S; George, M; George, S; Gerbaudo, D; Gershon, A; Ghasemi, S; Ghazlane, H; Giacobbe, B; Giagu, S; Giangiobbe, V; Giannetti, P; Gibbard, B; Gibson, S M; Gilchriese, M; Gillam, T P S; Gillberg, D; Gilles, G; Gingrich, D M; Giokaris, N; Giordani, M P; Giorgi, F M; Giorgi, F M; Giraud, P F; Giromini, P; Giugni, D; Giuliani, C; Giulini, M; Gjelsten, B K; Gkaitatzis, S; Gkialas, I; Gkougkousis, E L; Gladilin, L K; Glasman, C; Glatzer, J; Glaysher, P C F; Glazov, A; Goblirsch-Kolb, M; Goddard, J R; Godlewski, J; Goldfarb, S; Golling, T; Golubkov, D; Gomes, A; Gonçalo, R; Goncalves Pinto Firmino Da Costa, J; Gonella, L; González de la Hoz, S; Gonzalez Parra, G; Gonzalez-Sevilla, S; Goossens, L; Gorbounov, P A; Gordon, H A; Gorelov, I; Gorini, B; Gorini, E; Gorišek, A; Gornicki, E; Goshaw, A T; Gössling, C; Gostkin, M I; Goujdami, D; Goussiou, A G; Govender, N; Gozani, E; Grabas, H M X; Graber, L; Grabowska-Bold, I; Grafström, P; Grahn, K-J; Gramling, J; Gramstad, E; Grancagnolo, S; Grassi, V; Gratchev, V; Gray, H M; Graziani, E; Greenwood, Z D; Gregersen, K; Gregor, I M; Grenier, P; Griffiths, J; Grillo, A A; Grimm, K; Grinstein, S; Gris, Ph; Grivaz, J-F; Grohs, J P; Grohsjean, A; Gross, E; Grosse-Knetter, J; Grossi, G C; Grout, Z J; Guan, L; Guenther, J; Guescini, F; Guest, D; Gueta, O; Guido, E; Guillemin, T; Guindon, S; Gul, U; Gumpert, C; Guo, J; Guo, Y; Gupta, S; Gustavino, G; Gutierrez, P; Gutierrez Ortiz, N G; Gutschow, C; Guyot, C; Gwenlan, C; Gwilliam, C B; Haas, A; Haber, C; Hadavand, H K; Haddad, N; Haefner, P; Hageböck, S; Hajduk, Z; Hakobyan, H; Haleem, M; Haley, J; Hall, D; Halladjian, G; Hallewell, G D; Hamacher, K; Hamal, P; Hamano, K; Hamer, M; Hamilton, A; Hamity, G N; Hamnett, P G; Han, L; Hanagaki, K; Hanawa, K; Hance, M; Hanke, P; Hanna, R; Hansen, J B; Hansen, J D; Hansen, M C; Hansen, P H; Hara, K; Hard, A S; Harenberg, T; Hariri, F; Harkusha, S; Harrington, R D; Harrison, P F; Hartjes, F; Hasegawa, M; Hasegawa, S; Hasegawa, Y; Hasib, A; Hassani, S; Haug, S; Hauser, R; Hauswald, L; Havranek, M; Hawkes, C M; Hawkings, R J; Hawkins, A D; Hayashi, T; Hayden, D; Hays, C P; Hays, J M; Hayward, H S; Haywood, S J; Head, S J; Heck, T; Hedberg, V; Heelan, L; Heim, S; Heim, T; Heinemann, B; Heinrich, L; Hejbal, J; Helary, L; Hellman, S; Hellmich, D; Helsens, C; Henderson, J; Henderson, R C W; Heng, Y; Hengler, C; Henrichs, A; Henriques Correia, A M; Henrot-Versille, S; Herbert, G H; Hernández Jiménez, Y; Herrberg-Schubert, R; Herten, G; Hertenberger, R; Hervas, L; Hesketh, G G; Hessey, N P; Hetherly, J W; Hickling, R; Higón-Rodriguez, E; Hill, E; Hill, J C; Hiller, K H; Hillier, S J; Hinchliffe, I; Hines, E; Hinman, R R; Hirose, M; Hirschbuehl, D; Hobbs, J; Hod, N; Hodgkinson, M C; Hodgson, P; Hoecker, A; Hoeferkamp, M R; Hoenig, F; Hohlfeld, M; Hohn, D; Holmes, T R; Homann, M; Hong, T M; Hooft van Huysduynen, L; Hopkins, W H; Horii, Y; Horton, A J; Hostachy, J-Y; Hou, S; Hoummada, A; Howard, J; Howarth, J; Hrabovsky, M; Hristova, I; Hrivnac, J; Hryn'ova, T; Hrynevich, A; Hsu, C; Hsu, P J; Hsu, S-C; Hu, D; Hu, Q; Hu, X; Huang, Y; Hubacek, Z; Hubaut, F; Huegging, F; Huffman, T B; Hughes, E W; Hughes, G; Huhtinen, M; Hülsing, T A; Huseynov, N; Huston, J; Huth, J; Iacobucci, G; Iakovidis, G; Ibragimov, I; Iconomidou-Fayard, L; Ideal, E; Idrissi, Z; Iengo, P; Igonkina, O; Iizawa, T; Ikegami, Y; Ikematsu, K; Ikeno, M; Ilchenko, Y; Iliadis, D; Ilic, N; Ince, T; Introzzi, G; Ioannou, P; Iodice, M; Iordanidou, K; Ippolito, V; Irles Quiles, A; Isaksson, C; Ishino, M; Ishitsuka, M; Ishmukhametov, R; Issever, C; Istin, S; Iturbe Ponce, J M; Iuppa, R; Ivarsson, J; Iwanski, W; Iwasaki, H; Izen, J M; Izzo, V; Jabbar, S; Jackson, B; Jackson, M; Jackson, P; Jaekel, M R; Jain, V; Jakobs, K; Jakobsen, S; Jakoubek, T; Jakubek, J; Jamin, D O; Jana, D K; Jansen, E; Jansky, R; Janssen, J; Janus, M; Jarlskog, G; Javadov, N; Javůrek, T; Jeanty, L; Jejelava, J; Jeng, G-Y; Jennens, D; Jenni, P; Jentzsch, J; Jeske, C; Jézéquel, S; Ji, H; Jia, J; Jiang, Y; Jiggins, S; Jimenez Pena, J; Jin, S; Jinaru, A; Jinnouchi, O; Joergensen, M D; Johansson, P; Johns, K A; Jon-And, K; Jones, G; Jones, R W L; Jones, T J; Jongmanns, J; Jorge, P M; Joshi, K D; Jovicevic, J; Ju, X; Jung, C A; Jussel, P; Juste Rozas, A; Kaci, M; Kaczmarska, A; Kado, M; Kagan, H; Kagan, M; Kahn, S J; Kajomovitz, E; Kalderon, C W; Kama, S; Kamenshchikov, A; Kanaya, N; Kaneti, S; Kantserov, V A; Kanzaki, J; Kaplan, B; Kaplan, L S; Kapliy, A; Kar, D; Karakostas, K; Karamaoun, A; Karastathis, N; Kareem, M J; Karnevskiy, M; Karpov, S N; Karpova, Z M; Karthik, K; Kartvelishvili, V; Karyukhin, A N; Kashif, L; Kass, R D; Kastanas, A; Kataoka, Y; Katre, A; Katzy, J; Kawagoe, K; Kawamoto, T; Kawamura, G; Kazama, S; Kazanin, V F; Kazarinov, M Y; Keeler, R; Kehoe, R; Keller, J S; Kempster, J J; Keoshkerian, H; Kepka, O; Kerševan, B P; Kersten, S; Keyes, R A; Khalil-Zada, F; Khandanyan, H; Khanov, A; Kharlamov, A G; Khoo, T J; Khovanskiy, V; Khramov, E; Khubua, J; Kim, H Y; Kim, H; Kim, S H; Kim, Y; Kimura, N; Kind, O M; King, B T; King, M; King, S B; Kirk, J; Kiryunin, A E; Kishimoto, T; Kisielewska, D; Kiss, F; Kiuchi, K; Kivernyk, O; Kladiva, E; Klein, M H; Klein, M; Klein, U; Kleinknecht, K; Klimek, P; Klimentov, A; Klingenberg, R; Klinger, J A; Klioutchnikova, T; Kluge, E-E; Kluit, P; Kluth, S; Knapik, J; Kneringer, E; Knoops, E B F G; Knue, A; Kobayashi, A; Kobayashi, D; Kobayashi, T; Kobel, M; Kocian, M; Kodys, P; Koffas, T; Koffeman, E; Kogan, L A; Kohlmann, S; Kohout, Z; Kohriki, T; Koi, T; Kolanoski, H; Koletsou, I; Komar, A A; Komori, Y; Kondo, T; Kondrashova, N; Köneke, K; König, A C; Kono, T; Konoplich, R; Konstantinidis, N; Kopeliansky, R; Koperny, S; Köpke, L; Kopp, A K; Korcyl, K; Kordas, K; Korn, A; Korol, A A; Korolkov, I; Korolkova, E V; Kortner, O; Kortner, S; Kosek, T; Kostyukhin, V V; Kotov, V M; Kotwal, A; Kourkoumeli-Charalampidi, A; Kourkoumelis, C; Kouskoura, V; Koutsman, A; Kowalewski, R; Kowalski, T Z; Kozanecki, W; Kozhin, A S; Kramarenko, V A; Kramberger, G; Krasnopevtsev, D; Krasny, M W; Krasznahorkay, A; Kraus, J K; Kravchenko, A; Kreiss, S; Kretz, M; Kretzschmar, J; Kreutzfeldt, K; Krieger, P; Krizka, K; Kroeninger, K; Kroha, H; Kroll, J; Kroseberg, J; Krstic, J; Kruchonak, U; Krüger, H; Krumnack, N; Krumshteyn, Z V; Kruse, A; Kruse, M C; Kruskal, M; Kubota, T; Kucuk, H; Kuday, S; Kuehn, S; Kugel, A; Kuger, F; Kuhl, A; Kuhl, T; Kukhtin, V; Kulchitsky, Y; Kuleshov, S; Kuna, M; Kunigo, T; Kupco, A; Kurashige, H; Kurochkin, Y A; Kus, V; Kuwertz, E S; Kuze, M; Kvita, J; Kwan, T; Kyriazopoulos, D; La Rosa, A; La Rosa Navarro, J L; La Rotonda, L; Lacasta, C; Lacava, F; Lacey, J; Lacker, H; Lacour, D; Lacuesta, V R; Ladygin, E; Lafaye, R; Laforge, B; Lagouri, T; Lai, S; Lambourne, L; Lammers, S; Lampen, C L; Lampl, W; Lançon, E; Landgraf, U; Landon, M P J; Lang, V S; Lange, J C; Lankford, A J; Lanni, F; Lantzsch, K; Lanza, A; Laplace, S; Lapoire, C; Laporte, J F; Lari, T; Lasagni Manghi, F; Lassnig, M; Laurelli, P; Lavrijsen, W; Law, A T; Laycock, P; Lazovich, T; Le Dortz, O; Le Guirriec, E; Le Menedeu, E; LeBlanc, M; LeCompte, T; Ledroit-Guillon, F; Lee, C A; Lee, S C; Lee, L; Lefebvre, G; Lefebvre, M; Legger, F; Leggett, C; Lehan, A; Lehmann Miotto, G; Lei, X; Leight, W A; Leisos, A; Leister, A G; Leite, M A L; Leitner, R; Lellouch, D; Lemmer, B; Leney, K J C; Lenz, T; Lenzi, B; Leone, R; Leone, S; Leonidopoulos, C; Leontsinis, S; Leroy, C; Lester, C G; Levchenko, M; Levêque, J; Levin, D; Levinson, L J; Levy, M; Lewis, A; Leyko, A M; Leyton, M; Li, B; Li, H; Li, H L; Li, L; Li, L; Li, S; Li, Y; Liang, Z; Liao, H; Liberti, B; Liblong, A; Lichard, P; Lie, K; Liebal, J; Liebig, W; Limbach, C; Limosani, A; Lin, S C; Lin, T H; Linde, F; Lindquist, B E; Linnemann, J T; Lipeles, E; Lipniacka, A; Lisovyi, M; Liss, T M; Lissauer, D; Lister, A; Litke, A M; Liu, B; Liu, D; Liu, H; Liu, J; Liu, J B; Liu, K; Liu, L; Liu, M; Liu, M; Liu, Y; Livan, M; Lleres, A; Llorente Merino, J; Lloyd, S L; Lo Sterzo, F; Lobodzinska, E; Loch, P; Lockman, W S; Loebinger, F K; Loevschall-Jensen, A E; Loginov, A; Lohse, T; Lohwasser, K; Lokajicek, M; Long, B A; Long, J D; Long, R E; Looper, K A; Lopes, L; Lopez Mateos, D; Lopez Paredes, B; Lopez Paz, I; Lorenz, J; Lorenzo Martinez, N; Losada, M; Loscutoff, P; Lösel, P J; Lou, X; Lounis, A; Love, J; Love, P A; Lu, N; Lubatti, H J; Luci, C; Lucotte, A; Luehring, F; Lukas, W; Luminari, L; Lundberg, O; Lund-Jensen, B; Lynn, D; Lysak, R; Lytken, E; Ma, H; Ma, L L; Maccarrone, G; Macchiolo, A; Macdonald, C M; Machado Miguens, J; Macina, D; Madaffari, D; Madar, R; Maddocks, H J; Mader, W F; Madsen, A; Maeland, S; Maeno, T; Maevskiy, A; Magradze, E; Mahboubi, K; Mahlstedt, J; Maiani, C; Maidantchik, C; Maier, A A; Maier, T; Maio, A; Majewski, S; Makida, Y; Makovec, N; Malaescu, B; Malecki, Pa; Maleev, V P; Malek, F; Mallik, U; Malon, D; Malone, C; Maltezos, S; Malyshev, V M; Malyukov, S; Mamuzic, J; Mancini, G; Mandelli, B; Mandelli, L; Mandić, I; Mandrysch, R; Maneira, J; Manfredini, A; Manhaes de Andrade Filho, L; Manjarres Ramos, J; Mann, A; Manning, P M; Manousakis-Katsikakis, A; Mansoulie, B; Mantifel, R; Mantoani, M; Mapelli, L; March, L; Marchiori, G; Marcisovsky, M; Marino, C P; Marjanovic, M; Marley, D E; Marroquim, F; Marsden, S P; Marshall, Z; Marti, L F; Marti-Garcia, S; Martin, B; Martin, T A; Martin, V J; Martin Dit Latour, B; Martinez, M; Martin-Haugh, S; Martoiu, V S; Martyniuk, A C; Marx, M; Marzano, F; Marzin, A; Masetti, L; Mashimo, T; Mashinistov, R; Masik, J; Maslennikov, A L; Massa, I; Massa, L; Massol, N; Mastrandrea, P; Mastroberardino, A; Masubuchi, T; Mättig, P; Mattmann, J; Maurer, J; Maxfield, S J; Maximov, D A; Mazini, R; Mazza, S M; Mazzaferro, L; Mc Goldrick, G; Mc Kee, S P; McCarn, A; McCarthy, R L; McCarthy, T G; McCubbin, N A; McFarlane, K W; Mcfayden, J A; Mchedlidze, G; McMahon, S J; McPherson, R A; Medinnis, M; Meehan, S; Mehlhase, S; Mehta, A; Meier, K; Meineck, C; Meirose, B; Mellado Garcia, B R; Meloni, F; Mengarelli, A; Menke, S; Meoni, E; Mercurio, K M; Mergelmeyer, S; Mermod, P; Merola, L; Meroni, C; Merritt, F S; Messina, A; Metcalfe, J; Mete, A S; Meyer, C; Meyer, C; Meyer, J-P; Meyer, J; Middleton, R P; Miglioranzi, S; Mijović, L; Mikenberg, G; Mikestikova, M; Mikuž, M; Milesi, M; Milic, A; Miller, D W; Mills, C; Milov, A; Milstead, D A; Minaenko, A A; Minami, Y; Minashvili, I A; Mincer, A I; Mindur, B; Mineev, M; Ming, Y; Mir, L M; Mitani, T; Mitrevski, J; Mitsou, V A; Miucci, A; Miyagawa, P S; Mjörnmark, J U; Moa, T; Mochizuki, K; Mohapatra, S; Mohr, W; Molander, S; Moles-Valls, R; Mönig, K; Monini, C; Monk, J; Monnier, E; Montejo Berlingen, J; Monticelli, F; Monzani, S; Moore, R W; Morange, N; Moreno, D; Moreno Llácer, M; Morettini, P; Morgenstern, M; Morii, M; Morinaga, M; Morisbak, V; Moritz, S; Morley, A K; Mornacchi, G; Morris, J D; Mortensen, S S; Morton, A; Morvaj, L; Mosidze, M; Moss, J; Motohashi, K; Mount, R; Mountricha, E; Mouraviev, S V; Moyse, E J W; Muanza, S; Mudd, R D; Mueller, F; Mueller, J; Mueller, R S P; Mueller, T; Muenstermann, D; Mullen, P; Mullier, G A; Murillo Quijada, J A; Murray, W J; Musheghyan, H; Musto, E; Myagkov, A G; Myska, M; Nackenhorst, O; Nadal, J; Nagai, K; Nagai, R; Nagai, Y; Nagano, K; Nagarkar, A; Nagasaka, Y; Nagata, K; Nagel, M; Nagy, E; Nairz, A M; Nakahama, Y; Nakamura, K; Nakamura, T; Nakano, I; Namasivayam, H; Naranjo Garcia, R F; Narayan, R; Naumann, T; Navarro, G; Nayyar, R; Neal, H A; Nechaeva, P Yu; Neep, T J; Nef, P D; Negri, A; Negrini, M; Nektarijevic, S; Nellist, C; Nelson, A; Nemecek, S; Nemethy, P; Nepomuceno, A A; Nessi, M; Neubauer, M S; Neumann, M; Neves, R M; Nevski, P; Newman, P R; Nguyen, D H; Nickerson, R B; Nicolaidou, R; Nicquevert, B; Nielsen, J; Nikiforou, N; Nikiforov, A; Nikolaenko, V; Nikolic-Audit, I; Nikolopoulos, K; Nilsen, J K; Nilsson, P; Ninomiya, Y; Nisati, A; Nisius, R; Nobe, T; Nomachi, M; Nomidis, I; Nooney, T; Norberg, S; Nordberg, M; Novgorodova, O; Nowak, S; Nozaki, M; Nozka, L; Ntekas, K; Nunes Hanninger, G; Nunnemann, T; Nurse, E; Nuti, F; O'Brien, B J; O'grady, F; O'Neil, D C; O'Shea, V; Oakham, F G; Oberlack, H; Obermann, T; Ocariz, J; Ochi, A; Ochoa, I; Ochoa-Ricoux, J P; Oda, S; Odaka, S; Ogren, H; Oh, A; Oh, S H; Ohm, C C; Ohman, H; Oide, H; Okamura, W; Okawa, H; Okumura, Y; Okuyama, T; Olariu, A; Olivares Pino, S A; Oliveira Damazio, D; Oliver Garcia, E; Olszewski, A; Olszowska, J; Onofre, A; Onyisi, P U E; Oram, C J; Oreglia, M J; Oren, Y; Orestano, D; Orlando, N; Oropeza Barrera, C; Orr, R S; Osculati, B; Ospanov, R; Otero Y Garzon, G; Otono, H; Ouchrif, M; Ouellette, E A; Ould-Saada, F; Ouraou, A; Oussoren, K P; Ouyang, Q; Ovcharova, A; Owen, M; Owen, R E; Ozcan, V E; Ozturk, N; Pachal, K; Pacheco Pages, A; Padilla Aranda, C; Pagáčová, M; Pagan Griso, S; Paganis, E; Paige, F; Pais, P; Pajchel, K; Palacino, G; Palestini, S; Palka, M; Pallin, D; Palma, A; Pan, Y B; Panagiotopoulou, E; Pandini, C E; Panduro Vazquez, J G; Pani, P; Panitkin, S; Pantea, D; Paolozzi, L; Papadopoulou, Th D; Papageorgiou, K; Paramonov, A; Paredes Hernandez, D; Parker, M A; Parker, K A; Parodi, F; Parsons, J A; Parzefall, U; Pasqualucci, E; Passaggio, S; Pastore, F; Pastore, Fr; Pásztor, G; Pataraia, S; Patel, N D; Pater, J R; Pauly, T; Pearce, J; Pearson, B; Pedersen, L E; Pedersen, M; Pedraza Lopez, S; Pedro, R; Peleganchuk, S V; Pelikan, D; Penc, O; Peng, C; Peng, H; Penning, B; Penwell, J; Perepelitsa, D V; Perez Codina, E; Pérez García-Estañ, M T; Perini, L; Pernegger, H; Perrella, S; Peschke, R; Peshekhonov, V D; Peters, K; Peters, R F Y; Petersen, B A; Petersen, T C; Petit, E; Petridis, A; Petridou, C; Petrolo, E; Petrucci, F; Pettersson, N E; Pezoa, R; Phillips, P W; Piacquadio, G; Pianori, E; Picazio, A; Piccaro, E; Piccinini, M; Pickering, M A; Piegaia, R; Pignotti, D T; Pilcher, J E; Pilkington, A D; Pina, J; Pinamonti, M; Pinfold, J L; Pingel, A; Pinto, B; Pires, S; Pirumov, H; Pitt, M; Pizio, C; Plazak, L; Pleier, M-A; Pleskot, V; Plotnikova, E; Plucinski, P; Pluth, D; Poettgen, R; Poggioli, L; Pohl, D; Polesello, G; Poley, A; Policicchio, A; Polifka, R; Polini, A; Pollard, C S; Polychronakos, V; Pommès, K; Pontecorvo, L; Pope, B G; Popeneciu, G A; Popovic, D S; Poppleton, A; Pospisil, S; Potamianos, K; Potrap, I N; Potter, C J; Potter, C T; Poulard, G; Poveda, J; Pozdnyakov, V; Pralavorio, P; Pranko, A; Prasad, S; Prell, S; Price, D; Price, L E; Primavera, M; Prince, S; Proissl, M; Prokofiev, K; Prokoshin, F; Protopapadaki, E; Protopopescu, S; Proudfoot, J; Przybycien, M; Ptacek, E; Puddu, D; Pueschel, E; Puldon, D; Purohit, M; Puzo, P; Qian, J; Qin, G; Qin, Y; Quadt, A; Quarrie, D R; Quayle, W B; Queitsch-Maitland, M; Quilty, D; Raddum, S; Radeka, V; Radescu, V; Radhakrishnan, S K; Radloff, P; Rados, P; Ragusa, F; Rahal, G; Rajagopalan, S; Rammensee, M; Rangel-Smith, C; Rauscher, F; Rave, S; Ravenscroft, T; Raymond, M; Read, A L; Readioff, N P; Rebuzzi, D M; Redelbach, A; Redlinger, G; Reece, R; Reeves, K; Rehnisch, L; Reisin, H; Relich, M; Rembser, C; Ren, H; Renaud, A; Rescigno, M; Resconi, S; Rezanova, O L; Reznicek, P; Rezvani, R; Richter, R; Richter, S; Richter-Was, E; Ricken, O; Ridel, M; Rieck, P; Riegel, C J; Rieger, J; Rijssenbeek, M; Rimoldi, A; Rinaldi, L; Ristić, B; Ritsch, E; Riu, I; Rizatdinova, F; Rizvi, E; Robertson, S H; Robichaud-Veronneau, A; Robinson, D; Robinson, J E M; Robson, A; Roda, C; Roe, S; Røhne, O; Rolli, S; Romaniouk, A; Romano, M; Romano Saez, S M; Romero Adam, E; Rompotis, N; Ronzani, M; Roos, L; Ros, E; Rosati, S; Rosbach, K; Rose, P; Rosendahl, P L; Rosenthal, O; Rossetti, V; Rossi, E; Rossi, L P; Rosten, R; Rotaru, M; Roth, I; Rothberg, J; Rousseau, D; Royon, C R; Rozanov, A; Rozen, Y; Ruan, X; Rubbo, F; Rubinskiy, I; Rud, V I; Rudolph, C; Rudolph, M S; Rühr, F; Ruiz-Martinez, A; Rurikova, Z; Rusakovich, N A; Ruschke, A; Russell, H L; Rutherfoord, J P; Ruthmann, N; Ryabov, Y F; Rybar, M; Rybkin, G; Ryder, N C; Saavedra, A F; Sabato, G; Sacerdoti, S; Saddique, A; Sadrozinski, H F-W; Sadykov, R; Safai Tehrani, F; Saimpert, M; Sakamoto, H; Sakurai, Y; Salamanna, G; Salamon, A; Saleem, M; Salek, D; Sales De Bruin, P H; Salihagic, D; Salnikov, A; Salt, J; Salvatore, D; Salvatore, F; Salvucci, A; Salzburger, A; Sampsonidis, D; Sanchez, A; Sánchez, J; Sanchez Martinez, V; Sandaker, H; Sandbach, R L; Sander, H G; Sanders, M P; Sandhoff, M; Sandoval, C; Sandstroem, R; Sankey, D P C; Sannino, M; Sansoni, A; Santoni, C; Santonico, R; Santos, H; Santoyo Castillo, I; Sapp, K; Sapronov, A; Saraiva, J G; Sarrazin, B; Sasaki, O; Sasaki, Y; Sato, K; Sauvage, G; Sauvan, E; Savage, G; Savard, P; Sawyer, C; Sawyer, L; Saxon, J; Sbarra, C; Sbrizzi, A; Scanlon, T; Scannicchio, D A; Scarcella, M; Scarfone, V; Schaarschmidt, J; Schacht, P; Schaefer, D; Schaefer, R; Schaeffer, J; Schaepe, S; Schaetzel, S; Schäfer, U; Schaffer, A C; Schaile, D; Schamberger, R D; Scharf, V; Schegelsky, V A; Scheirich, D; Schernau, M; Schiavi, C; Schillo, C; Schioppa, M; Schlenker, S; Schmidt, E; Schmieden, K; Schmitt, C; Schmitt, S; Schmitt, S; Schneider, B; Schnellbach, Y J; Schnoor, U; Schoeffel, L; Schoening, A; Schoenrock, B D; Schopf, E; Schorlemmer, A L S; Schott, M; Schouten, D; Schovancova, J; Schramm, S; Schreyer, M; Schroeder, C; Schuh, N; Schultens, M J; Schultz-Coulon, H-C; Schulz, H; Schumacher, M; Schumm, B A; Schune, Ph; Schwanenberger, C; Schwartzman, A; Schwarz, T A; Schwegler, Ph; Schweiger, H; Schwemling, Ph; Schwienhorst, R; Schwindling, J; Schwindt, T; Sciacca, F G; Scifo, E; Sciolla, G; Scuri, F; Scutti, F; Searcy, J; Sedov, G; Sedykh, E; Seema, P; Seidel, S C; Seiden, A; Seifert, F; Seixas, J M; Sekhniaidze, G; Sekhon, K; Sekula, S J; Seliverstov, D M; Semprini-Cesari, N; Serfon, C; Serin, L; Serkin, L; Serre, T; Sessa, M; Seuster, R; Severini, H; Sfiligoj, T; Sforza, F; Sfyrla, A; Shabalina, E; Shamim, M; Shan, L Y; Shang, R; Shank, J T; Shapiro, M; Shatalov, P B; Shaw, K; Shaw, S M; Shcherbakova, A; Shehu, C Y; Sherwood, P; Shi, L; Shimizu, S; Shimmin, C O; Shimojima, M; Shiyakova, M; Shmeleva, A; Shoaleh Saadi, D; Shochet, M J; Shojaii, S; Shrestha, S; Shulga, E; Shupe, M A; Shushkevich, S; Sicho, P; Sidebo, P E; Sidiropoulou, O; Sidorov, D; Sidoti, A; Siegert, F; Sijacki, Dj; Silva, J; Silver, Y; Silverstein, S B; Simak, V; Simard, O; Simic, Lj; Simion, S; Simioni, E; Simmons, B; Simon, D; Simoniello, R; Sinervo, P; Sinev, N B; Sioli, M; Siragusa, G; Sisakyan, A N; Sivoklokov, S Yu; Sjölin, J; Sjursen, T B; Skinner, M B; Skottowe, H P; Skubic, P; Slater, M; Slavicek, T; Slawinska, M; Sliwa, K; Smakhtin, V; Smart, B H; Smestad, L; Smirnov, S Yu; Smirnov, Y; Smirnova, L N; Smirnova, O; Smith, M N K; Smith, R W; Smizanska, M; Smolek, K; Snesarev, A A; Snidero, G; Snyder, S; Sobie, R; Socher, F; Soffer, A; Soh, D A; Solans, C A; Solar, M; Solc, J; Soldatov, E Yu; Soldevila, U; Solodkov, A A; Soloshenko, A; Solovyanov, O V; Solovyev, V; Sommer, P; Song, H Y; Soni, N; Sood, A; Sopczak, A; Sopko, B; Sopko, V; Sorin, V; Sosa, D; Sosebee, M; Sotiropoulou, C L; Soualah, R; Soukharev, A M; South, D; Sowden, B C; Spagnolo, S; Spalla, M; Spanò, F; Spearman, W R; Sperlich, D; Spettel, F; Spighi, R; Spigo, G; Spiller, L A; Spousta, M; Spreitzer, T; St Denis, R D; Staerz, S; Stahlman, J; Stamen, R; Stamm, S; Stanecka, E; Stanescu, C; Stanescu-Bellu, M; Stanitzki, M M; Stapnes, S; Starchenko, E A; Stark, J; Staroba, P; Starovoitov, P; Staszewski, R; Stavina, P; Steinberg, P; Stelzer, B; Stelzer, H J; Stelzer-Chilton, O; Stenzel, H; Stewart, G A; Stillings, J A; Stockton, M C; Stoebe, M; Stoicea, G; Stolte, P; Stonjek, S; Stradling, A R; Straessner, A; Stramaglia, M E; Strandberg, J; Strandberg, S; Strandlie, A; Strauss, E; Strauss, M; Strizenec, P; Ströhmer, R; Strom, D M; Stroynowski, R; Strubig, A; Stucci, S A; Stugu, B; Styles, N A; Su, D; Su, J; Subramaniam, R; Succurro, A; Sugaya, Y; Suhr, C; Suk, M; Sulin, V V; Sultansoy, S; Sumida, T; Sun, S; Sun, X; Sundermann, J E; Suruliz, K; Susinno, G; Sutton, M R; Suzuki, S; Svatos, M; Swedish, S; Swiatlowski, M; Sykora, I; Sykora, T; Ta, D; Taccini, C; Tackmann, K; Taenzer, J; Taffard, A; Tafirout, R; Taiblum, N; Takai, H; Takashima, R; Takeda, H; Takeshita, T; Takubo, Y; Talby, M; Talyshev, A A; Tam, J Y C; Tan, K G; Tanaka, J; Tanaka, R; Tanaka, S; Tannenwald, B B; Tannoury, N; Tapprogge, S; Tarem, S; Tarrade, F; Tartarelli, G F; Tas, P; Tasevsky, M; Tashiro, T; Tassi, E; Tavares Delgado, A; Tayalati, Y; Taylor, F E; Taylor, G N; Taylor, W; Teischinger, F A; Teixeira Dias Castanheira, M; Teixeira-Dias, P; Temming, K K; Ten Kate, H; Teng, P K; Teoh, J J; Tepel, F; Terada, S; Terashi, K; Terron, J; Terzo, S; Testa, M; Teuscher, R J; Theveneaux-Pelzer, T; Thomas, J P; Thomas-Wilsker, J; Thompson, E N; Thompson, P D; Thompson, R J; Thompson, A S; Thomsen, L A; Thomson, E; Thomson, M; Thun, R P; Tibbetts, M J; Ticse Torres, R E; Tikhomirov, V O; Tikhonov, Yu A; Timoshenko, S; Tiouchichine, E; Tipton, P; Tisserant, S; Todome, K; Todorov, T; Todorova-Nova, S; Tojo, J; Tokár, S; Tokushuku, K; Tollefson, K; Tolley, E; Tomlinson, L; Tomoto, M; Tompkins, L; Toms, K; Torrence, E; Torres, H; Torró Pastor, E; Toth, J; Touchard, F; Tovey, D R; Trefzger, T; Tremblet, L; Tricoli, A; Trigger, I M; Trincaz-Duvoid, S; Tripiana, M F; Trischuk, W; Trocmé, B; Troncon, C; Trottier-McDonald, M; Trovatelli, M; True, P; Truong, L; Trzebinski, M; Trzupek, A; Tsarouchas, C; Tseng, J C-L; Tsiareshka, P V; Tsionou, D; Tsipolitis, G; Tsirintanis, N; Tsiskaridze, S; Tsiskaridze, V; Tskhadadze, E G; Tsukerman, I I; Tsulaia, V; Tsuno, S; Tsybychev, D; Tudorache, A; Tudorache, V; Tuna, A N; Tupputi, S A; Turchikhin, S; Turecek, D; Turra, R; Turvey, A J; Tuts, P M; Tykhonov, A; Tylmad, M; Tyndel, M; Ueda, I; Ueno, R; Ughetto, M; Ugland, M; Uhlenbrock, M; Ukegawa, F; Unal, G; Undrus, A; Unel, G; Ungaro, F C; Unno, Y; Unverdorben, C; Urban, J; Urquijo, P; Urrejola, P; Usai, G; Usanova, A; Vacavant, L; Vacek, V; Vachon, B; Valderanis, C; Valencic, N; Valentinetti, S; Valero, A; Valery, L; Valkar, S; Valladolid Gallego, E; Vallecorsa, S; Valls Ferrer, J A; Van Den Wollenberg, W; Van Der Deijl, P C; van der Geer, R; van der Graaf, H; Van Der Leeuw, R; van Eldik, N; van Gemmeren, P; Van Nieuwkoop, J; van Vulpen, I; van Woerden, M C; Vanadia, M; Vandelli, W; Vanguri, R; Vaniachine, A; Vannucci, F; Vardanyan, G; Vari, R; Varnes, E W; Varol, T; Varouchas, D; Vartapetian, A; Varvell, K E; Vazeille, F; Vazquez Schroeder, T; Veatch, J; Veloce, L M; Veloso, F; Velz, T; Veneziano, S; Ventura, A; Ventura, D; Venturi, M; Venturi, N; Venturini, A; Vercesi, V; Verducci, M; Verkerke, W; Vermeulen, J C; Vest, A; Vetterli, M C; Viazlo, O; Vichou, I; Vickey, T; Vickey Boeriu, O E; Viehhauser, G H A; Viel, S; Vigne, R; Villa, M; Villaplana Perez, M; Vilucchi, E; Vincter, M G; Vinogradov, V B; Vivarelli, I; Vives Vaque, F; Vlachos, S; Vladoiu, D; Vlasak, M; Vogel, M; Vokac, P; Volpi, G; Volpi, M; von der Schmitt, H; von Radziewski, H; von Toerne, E; Vorobel, V; Vorobev, K; Vos, M; Voss, R; Vossebeld, J H; Vranjes, N; Vranjes Milosavljevic, M; Vrba, V; Vreeswijk, M; Vuillermet, R; Vukotic, I; Vykydal, Z; Wagner, P; Wagner, W; Wahlberg, H; Wahrmund, S; Wakabayashi, J; Walder, J; Walker, R; Walkowiak, W; Wang, C; Wang, F; Wang, H; Wang, H; Wang, J; Wang, J; Wang, K; Wang, R; Wang, S M; Wang, T; Wang, T; Wang, X; Wanotayaroj, C; Warburton, A; Ward, C P; Wardrope, D R; Warsinsky, M; Washbrook, A; Wasicki, C; Watkins, P M; Watson, A T; Watson, I J; Watson, M F; Watts, G; Watts, S; Waugh, B M; Webb, S; Weber, M S; Weber, S W; Webster, J S; Weidberg, A R; Weinert, B; Weingarten, J; Weiser, C; Weits, H; Wells, P S; Wenaus, T; Wengler, T; Wenig, S; Wermes, N; Werner, M; Werner, P; Wessels, M; Wetter, J; Whalen, K; Wharton, A M; White, A; White, M J; White, R; White, S; Whiteson, D; Wickens, F J; Wiedenmann, W; Wielers, M; Wienemann, P; Wiglesworth, C; Wiik-Fuchs, L A M; Wildauer, A; Wilkens, H G; Williams, H H; Williams, S; Willis, C; Willocq, S; Wilson, A; Wilson, J A; Wingerter-Seez, I; Winklmeier, F; Winter, B T; Wittgen, M; Wittkowski, J; Wollstadt, S J; Wolter, M W; Wolters, H; Wosiek, B K; Wotschack, J; Woudstra, M J; Wozniak, K W; Wu, M; Wu, M; Wu, S L; Wu, X; Wu, Y; Wyatt, T R; Wynne, B M; Xella, S; Xu, D; Xu, L; Yabsley, B; Yacoob, S; Yakabe, R; Yamada, M; Yamaguchi, Y; Yamamoto, A; Yamamoto, S; Yamanaka, T; Yamauchi, K; Yamazaki, Y; Yan, Z; Yang, H; Yang, H; Yang, Y; Yao, W-M; Yasu, Y; Yatsenko, E; Yau Wong, K H; Ye, J; Ye, S; Yeletskikh, I; Yen, A L; Yildirim, E; Yorita, K; Yoshida, R; Yoshihara, K; Young, C; Young, C J S; Youssef, S; Yu, D R; Yu, J; Yu, J M; Yu, J; Yuan, L; Yurkewicz, A; Yusuff, I; Zabinski, B; Zaidan, R; Zaitsev, A M; Zalieckas, J; Zaman, A; Zambito, S; Zanello, L; Zanzi, D; Zeitnitz, C; Zeman, M; Zemla, A; Zengel, K; Zenin, O; Ženiš, T; Zerwas, D; Zhang, D; Zhang, F; Zhang, H; Zhang, J; Zhang, L; Zhang, R; Zhang, X; Zhang, Z; Zhao, X; Zhao, Y; Zhao, Z; Zhemchugov, A; Zhong, J; Zhou, B; Zhou, C; Zhou, L; Zhou, L; Zhou, N; Zhu, C G; Zhu, H; Zhu, J; Zhu, Y; Zhuang, X; Zhukov, K; Zibell, A; Zieminska, D; Zimine, N I; Zimmermann, C; Zimmermann, S; Zinonos, Z; Zinser, M; Ziolkowski, M; Živković, L; Zobernig, G; Zoccoli, A; Zur Nedden, M; Zurzolo, G; Zwalinski, L

Studies of the spin, parity and tensor couplings of the Higgs boson in the [Formula: see text], [Formula: see text] and [Formula: see text] decay processes at the LHC are presented. The investigations are based on [Formula: see text] of pp collision data collected by the ATLAS experiment at [Formula: see text] TeV and [Formula: see text] TeV. The Standard Model (SM) Higgs boson hypothesis, corresponding to the quantum numbers [Formula: see text], is tested against several alternative spin scenarios, including non-SM spin-0 and spin-2 models with universal and non-universal couplings to fermions and vector bosons. All tested alternative models are excluded in favour of the SM Higgs boson hypothesis at more than 99.9 % confidence level. Using the [Formula: see text] and [Formula: see text] decays, the tensor structure of the interaction between the spin-0 boson and the SM vector bosons is also investigated. The observed distributions of variables sensitive to the non-SM tensor couplings are compatible with the SM predictions and constraints on the non-SM couplings are derived.

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

Park, Jong-Kyu; Logan, Nikolas C.

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly formore » each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.« less

Impact of time-of-day on diffusivity measures of brain tissue derived from diffusion tensor imaging.

PubMed

Thomas, Cibu; Sadeghi, Neda; Nayak, Amrita; Trefler, Aaron; Sarlls, Joelle; Baker, Chris I; Pierpaoli, Carlo

2018-06-01

Diurnal fluctuations in MRI measures of structural and functional properties of the brain have been reported recently. These fluctuations may have a physiological origin, since they have been detected using different MRI modalities, and cannot be explained by factors that are typically known to confound MRI measures. While preliminary evidence suggests that measures of structural properties of the brain based on diffusion tensor imaging (DTI) fluctuate as a function of time-of-day (TOD), the underlying mechanism has not been investigated. Here, we used a longitudinal within-subjects design to investigate the impact of time-of-day on DTI measures. In addition to using the conventional monoexponential tensor model to assess TOD-related fluctuations, we used a dual compartment tensor model that allowed us to directly assess if any change in DTI measures is due to an increase in CSF/free-water volume fraction or due to an increase in water diffusivity within the parenchyma. Our results show that Trace or mean diffusivity, as measured using the conventional monoexponential tensor model tends to increase systematically from morning to afternoon scans at the interface of grey matter/CSF, most prominently in the major fissures and the sulci of the brain. Interestingly, in a recent study of the glymphatic system, these same regions were found to show late enhancement after intrathecal injection of a CSF contrast agent. The increase in Trace also impacts DTI measures of diffusivity such as radial and axial diffusivity, but does not affect fractional anisotropy. The dual compartment analysis revealed that the increase in diffusivity measures from PM to AM was driven by an increase in the volume fraction of CSF-like free-water. Taken together, our findings provide important insight into the likely physiological origins of diurnal fluctuations in MRI measurements of structural properties of the brain. Published by Elsevier Inc.

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

NASA Astrophysics Data System (ADS)

Ye, Qian; Lin, Haoze

2017-07-01

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

Two-site jumps in dimethyl sulfone studied by one- and two-dimensional 17O NMR spectroscopy

NASA Astrophysics Data System (ADS)

Beerwerth, J.; Storek, M.; Greim, D.; Lueg, J.; Siegel, R.; Cetinkaya, B.; Hiller, W.; Zimmermann, H.; Senker, J.; Böhmer, R.

2018-03-01

Polycrystalline dimethyl sulfone is studied using central-transition oxygen-17 exchange NMR. The quadrupolar and chemical shift tensors are determined by combining quantum chemical calculations with line shape analyses of rigid-lattice spectra measured for stationary and rotating samples at several external magnetic fields. Quantum chemical computations predict that the largest principal axes of the chemical shift anisotropy and electrical field gradient tensors enclose an angle of about 73°. This prediction is successfully tested by comparison with absorption spectra recorded at three different external magnetic fields. The experimental one-dimensional motionally narrowed spectra and the two-dimensional exchange spectrum are compatible with model calculations involving jumps of the molecules about their two-fold symmetry axis. This motion is additionally investigated by means of two-time stimulated-echo spectroscopy which allows for a determination of motional correlation functions over a wider temperature range than previously reported using carbon and deuteron NMR. On the basis of suitable second-order quadrupolar frequency distributions, sin-sin stimulated-echo amplitudes are calculated for a two-site model in the limit of vanishing evolution time and compared with experimental findings. The present study thus establishes oxygen-17 NMR as a powerful method that will be particularly useful for the study of solids and liquids devoid of nuclei governed by first-order anisotropies.

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

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

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

NASA Astrophysics Data System (ADS)

Czajka, Alina; Jeon, Sangyong

2017-06-01

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

Gluon and Wilson loop TMDs for hadrons of spin ≤ 1

NASA Astrophysics Data System (ADS)

Boer, Daniël; Cotogno, Sabrina; van Daal, Tom; Mulders, Piet J.; Signori, Andrea; Zhou, Ya-Jin

2016-10-01

In this paper we consider the parametrizations of gluon transverse momentum dependent (TMD) correlators in terms of TMD parton distribution functions (PDFs). These functions, referred to as TMDs, are defined as the Fourier transforms of hadronic matrix elements of nonlocal combinations of gluon fields. The nonlocality is bridged by gauge links, which have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. For gluons, the specific correlator with one future and one past pointing gauge link is, in the limit of small x, related to a correlator of a single Wilson loop. We present the parametrization of Wilson loop correlators in terms of Wilson loop TMDs and discuss the relation between these functions and the small- x `dipole' gluon TMDs. This analysis shows which gluon TMDs are leading or suppressed in the small- x limit. We discuss hadronic targets that are unpolarized, vector polarized (relevant for spin-1 /2 and spin-1 hadrons), and tensor polarized (relevant for spin-1 hadrons). The latter are of interest for studies with a future Electron-Ion Collider with polarized deuterons.

Large-Scale Computation of Nuclear Magnetic Resonance Shifts for Paramagnetic Solids Using CP2K.

PubMed

Mondal, Arobendo; Gaultois, Michael W; Pell, Andrew J; Iannuzzi, Marcella; Grey, Clare P; Hutter, Jürg; Kaupp, Martin

2018-01-09

Large-scale computations of nuclear magnetic resonance (NMR) shifts for extended paramagnetic solids (pNMR) are reported using the highly efficient Gaussian-augmented plane-wave implementation of the CP2K code. Combining hyperfine couplings obtained with hybrid functionals with g-tensors and orbital shieldings computed using gradient-corrected functionals, contact, pseudocontact, and orbital-shift contributions to pNMR shifts are accessible. Due to the efficient and highly parallel performance of CP2K, a wide variety of materials with large unit cells can be studied with extended Gaussian basis sets. Validation of various approaches for the different contributions to pNMR shifts is done first for molecules in a large supercell in comparison with typical quantum-chemical codes. This is then extended to a detailed study of g-tensors for extended solid transition-metal fluorides and for a series of complex lithium vanadium phosphates. Finally, lithium pNMR shifts are computed for Li 3 V 2 (PO 4 ) 3 , for which detailed experimental data are available. This has allowed an in-depth study of different approaches (e.g., full periodic versus incremental cluster computations of g-tensors and different functionals and basis sets for hyperfine computations) as well as a thorough analysis of the different contributions to the pNMR shifts. This study paves the way for a more-widespread computational treatment of NMR shifts for paramagnetic materials.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-01-01

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N2.5) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction.

PubMed

Song, Chenchen; Martínez, Todd J

2017-01-21

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N 2.5 ) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

Integrability conditions for Killing-Yano tensors and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Batista, Carlos

2015-01-01

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano tensor of order p to generate a Killing-Yano tensor of order (p -1 ) . Finally, it is proved that in maximally symmetric spaces the covariant derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor and that every conformal Killing-Yano tensor is uniquely decomposed as the sum of a Killing-Yano tensor and a closed conformal Killing-Yano tensor.

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.

Electronic Structure of Fullerene Acceptors in Organic Bulk-Heterojunctions. A Combined EPR and DFT Study

DOE PAGES

Mardis, Kristy L.; Webb, J.; Holloway, Tarita; ...

2015-12-03

Organic photovoltaic (OPV) devices are a promising alternative energy source. Attempts to improve their performance have focused on the optimization of electron-donating polymers, while electron-accepting fullerenes have received less attention. Here, we report an electronic structure study of the widely used soluble fullerene derivatives PC61BM and PC71BM in their singly reduced state, that are generated in the polymer:fullerene blends upon light-induced charge separation. Density functional theory (DFT) calculations characterize the electronic structures of the fullerene radical anions through spin density distributions and magnetic resonance parameters. The good agreement of the calculated magnetic resonance parameters with those determined experimentally by advancedmore » electron paramagnetic resonance (EPR) allows the validation of the DFT calculations. Thus, for the first time, the complete set of magnetic resonance parameters including directions of the principal g-tensor axes were determined. For both molecules, no spin density is present on the PCBM side chain, and the axis of the largest g-value lies along the PCBM molecular axis. While the spin density distribution is largely uniform for PC61BM, it is not evenly distributed for PC71BM.« less

High-order regularization in lattice-Boltzmann equations

NASA Astrophysics Data System (ADS)

Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

2017-04-01

A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

Advances in magnetic resonance neuroimaging techniques in the evaluation of neonatal encephalopathy.

PubMed

Panigrahy, Ashok; Blüml, Stefan

2007-02-01

Magnetic resonance (MR) imaging has become an essential tool in the evaluation of neonatal encephalopathy. Magnetic resonance-compatible neonatal incubators allow sick neonates to be transported to the MR scanner, and neonatal head coils can improve signal-to-noise ratio, critical for advanced MR imaging techniques. Refinement of conventional imaging techniques include the use of PROPELLER techniques for motion correction. Magnetic resonance spectroscopic imaging and diffusion tensor imaging provide quantitative assessment of both brain development and brain injury in the newborn with respect to metabolite abnormalities and hypoxic-ischemic injury. Knowledge of normal developmental changes in MR spectroscopy metabolite concentration and diffusion tensor metrics is essential to interpret pathological cases. Perfusion MR and functional MR can provide additional physiological information. Both MR spectroscopy and diffusion tensor imaging can provide additional information in the differential of neonatal encephalopathy, including perinatal white matter injury, hypoxic-ischemic brain injury, metabolic disease, infection, and birth injury.

Electrostatic forces in the Poisson-Boltzmann systems

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

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.

The observational constraint on constant-roll inflation

NASA Astrophysics Data System (ADS)

Gao, Qing

2018-07-01

We discuss the constant-roll inflation with constant ɛ2 and constant \\bar η . By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of ɛ1. The model with constant ɛ2 is ruled out by the observations at the 3σ confidence level, and the model with constant \\bar η is consistent with the observations at the 1σ confidence level. The potential for the model with constant \\bar η is also obtained from the Hamilton-Jacobi equation. Although the observations constrain the constant-roll inflation to be the slow-roll inflation, the n s- r results from the constant-roll inflation are not the same as those from the slow-roll inflation even when \\bar η 0.01.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity

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

Song, Chenchen; Martínez, Todd J.; SLAC National Accelerator Laboratory, Menlo Park, California 94025

We present a tensor hypercontracted (THC) scaled opposite spin second order Møller-Plesset perturbation theory (SOS-MP2) method. By using THC, we reduce the formal scaling of SOS-MP2 with respect to molecular size from quartic to cubic. We achieve further efficiency by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs) to accelerate integral construction and matrix multiplication. The practical scaling of GPU-accelerated atomic orbital-based THC-SOS-MP2 calculations is found to be N{sup 2.6} for reference data sets of water clusters and alanine polypeptides containing up to 1600 basis functions. The errors in correlation energy with respect to density-fitting-SOS-MP2 aremore » less than 0.5 kcal/mol for all systems tested (up to 162 atoms).« less

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

Longitudinal brain white matter alterations in minimal hepatic encephalopathy before and after liver transplantation.

PubMed

Lin, Wei-Che; Chou, Kun-Hsien; Chen, Chao-Long; Chen, Hsiu-Ling; Lu, Cheng-Hsien; Li, Shau-Hsuan; Huang, Chu-Chung; Lin, Ching-Po; Cheng, Yu-Fan

2014-01-01

Cerebral edema is the common pathogenic mechanism for cognitive impairment in minimal hepatic encephalopathy. Whether complete reversibility of brain edema, cognitive deficits, and their associated imaging can be achieved after liver transplantation remains an open question. To characterize white matter integrity before and after liver transplantation in patients with minimal hepatic encephalopathy, multiple diffusivity indices acquired via diffusion tensor imaging was applied. Twenty-eight patients and thirty age- and sex-matched healthy volunteers were included. Multiple diffusivity indices were obtained from diffusion tensor images, including mean diffusivity, fractional anisotropy, axial diffusivity and radial diffusivity. The assessment was repeated 6-12 month after transplantation. Differences in white matter integrity between groups, as well as longitudinal changes, were evaluated using tract-based spatial statistical analysis. Correlation analyses were performed to identify first scan before transplantation and interval changes among the neuropsychiatric tests, clinical laboratory tests, and diffusion tensor imaging indices. After transplantation, decreased water diffusivity without fractional anisotropy change indicating reversible cerebral edema was found in the left anterior cingulate, claustrum, postcentral gyrus, and right corpus callosum. However, a progressive decrease in fractional anisotropy and an increase in radial diffusivity suggesting demyelination were noted in temporal lobe. Improved pre-transplantation albumin levels and interval changes were associated with better recoveries of diffusion tensor imaging indices. Improvements in interval diffusion tensor imaging indices in the right postcentral gyrus were correlated with visuospatial function score correction. In conclusion, longitudinal voxel-wise analysis of multiple diffusion tensor imaging indices demonstrated different white matter changes in minimal hepatic encephalopathy patients. Transplantation improved extracellular cerebral edema and the results of associated cognition tests. However, white matter demyelination may advance in temporal lobe.

Minkowski Tensors in Two Dimensions: Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields

NASA Astrophysics Data System (ADS)

Appleby, Stephen; Chingangbam, Pravabati; Park, Changbom; Hong, Sungwook E.; Kim, Juhan; Ganesan, Vidhya

2018-05-01

We apply the Minkowski tensor statistics to two-dimensional slices of the three-dimensional matter density field. The Minkowski tensors are a set of functions that are sensitive to directionally dependent signals in the data and, furthermore, can be used to quantify the mean shape of density fields. We begin by reviewing the definition of Minkowski tensors and introducing a method of calculating them from a discretely sampled field. Focusing on the statistic {W}21,1—a 2 × 2 matrix—we calculate its value for both the entire excursion set and individual connected regions and holes within the set. To study the morphology of structures within the excursion set, we calculate the eigenvalues λ 1, λ 2 for the matrix {W}21,1 of each distinct connected region and hole and measure their mean shape using the ratio β \\equiv < {λ }2/{λ }1> . We compare both {W}21,1 and β for a Gaussian field and a smoothed density field generated from the latest Horizon Run 4 cosmological simulation to study the effect of gravitational collapse on these functions. The global statistic {W}21,1 is essentially independent of gravitational collapse, as the process maintains statistical isotropy. However, β is modified significantly, with overdensities becoming relatively more circular compared to underdensities at low redshifts. When applying the statistics to a redshift-space distorted density field, the matrix {W}21,1 is no longer proportional to the identity matrix, and measurements of its diagonal elements can be used to probe the large-scale velocity field.

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.