Einstein Revisited - Gravity in Curved Spacetime Without Event Horizons

NASA Astrophysics Data System (ADS)

Leiter, Darryl

2000-04-01

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

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-02-25

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

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE

PubMed Central

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

2017-01-01

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

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

PubMed

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

2017-05-01

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

Tensor Galileons and gravity

NASA Astrophysics Data System (ADS)

Chatzistavrakidis, Athanasios; Khoo, Fech Scen; Roest, Diederik; Schupp, Peter

2017-03-01

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

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.

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

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

Langlois, David; Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr

2016-02-01

Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering ''degenerate'' Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degeneratemore » cases. We also identify new families of scalar-tensor theories with the property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.« 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

Higher-derivative operators and effective field theory for general scalar-tensor theories

NASA Astrophysics Data System (ADS)

Solomon, Adam R.; Trodden, Mark

2018-02-01

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order operators only, and demonstrate this using several different techniques, such as reduction of order and explicit field redefinitions. These methods are applied, in particular, to the much-studied Horndeski theories. The goal is to clarify the application of effective field theory techniques in the context of popular cosmological models, and to explicitly demonstrate how and when higher-derivative operators can be cast into lower-derivative forms suitable for numerical solution techniques.

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

NASA Technical Reports Server (NTRS)

Peterson, D.

1979-01-01

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

Killing vector fields in three dimensions: a method to solve massive gravity field equations

NASA Astrophysics Data System (ADS)

Gürses, Metin

2010-10-01

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

Entanglement branching operator

NASA Astrophysics Data System (ADS)

Harada, Kenji

2018-01-01

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

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

An optimization approach for fitting canonical tensor decompositions.

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

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

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

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Multilinear Computing and Multilinear Algebraic Geometry

DTIC Science & Technology

2016-08-10

landmark paper titled “Most tensor problems are NP-hard” (see [14] in Section 3) in the Journal of the ACM, the premier journal in Computer Science ...Higher-order cone programming,” Machine Learning Thematic Trimester, International Centre for Mathematics and Computer Science , Toulouse, France...geometry-and-data-analysis • 2014 SIMONS INSTITUTE WORKSHOP: Workshop on Tensors in Computer Science and Geometry, University of California, Berkeley, CA

Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817

NASA Astrophysics Data System (ADS)

Kobayashi, Tsutomu; Hiramatsu, Takashi

2018-05-01

We study relativistic stars in degenerate higher-order scalar-tensor theories that evade the constraint on the speed of gravitational waves imposed by GW170817. It is shown that the exterior metric is given by the usual Schwarzschild solution if the lower order Horndeski terms are ignored in the Lagrangian and a shift symmetry is assumed. However, this class of theories exhibits partial breaking of Vainshtein screening in the stellar interior and thus modifies the structure of a star. Employing a simple concrete model, we show that for high-density stars the mass-radius relation is altered significantly even if the parameters are chosen so that only a tiny correction is expected in the Newtonian regime. We also find that, depending on the parameters, there is a maximum central density above which solutions cease to exist.

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.

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

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2015-04-01

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

Higher Order First Integrals of Motion in a Gauge Covariant Hamiltonian Framework

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out.

Graviton multipoint amplitudes for higher-derivative gravity in anti-de Sitter space

NASA Astrophysics Data System (ADS)

Shawa, M. M. W.; Medved, A. J. M.

2018-04-01

We calculate graviton multipoint amplitudes in an anti-de Sitter black brane background for higher-derivative gravity of arbitrary order in numbers of derivatives. The calculations are performed using tensor graviton modes in a particular regime of comparatively high energies and large scattering angles. The regime simplifies the calculations but, at the same time, is well suited for translating these results into the language of the dually related gauge theory. After considering theories whose Lagrangians consist of contractions of up to four Riemann tensors, we generalize to even higher-derivative theories by constructing a "basis" for the relevant scattering amplitudes. This construction enables one to find the basic form of the n -point amplitude for arbitrary n and any number of derivatives. Additionally, using the four-point amplitudes for theories whose Lagrangians carry contractions of either three or four Riemann tensors, we reexpress the scattering properties in terms of the Mandelstam variables.

Beyond generalized Proca theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-09-01

We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new interactions follow the similar construction criteria to those arising in the extension of scalar-tensor Horndeski theories to Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological background, we show the existence of a constraint with a vanishing Hamiltonian that removes the would-be Ostrogradski ghost. We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories (two tensor polarizations, two transverse vector modes, and two scalar modes). Moreover, we obtain the conditions for the avoidance of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations. We observe key differences in the scalar sound speed, which is mixed with the matter sound speed outside the domain of generalized Proca theories.

Turbulent fluid motion 2: Scalars, vectors, and tensors

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

The author shows that the sum or difference of two vectors is a vector. Similarly the sum of any two tensors of the same order is a tensor of that order. No meaning is attached to the sum of tensors of different orders, say u(sub i) + u(sub ij); that is not a tensor. In general, an equation containing tensors has meaning only if all the terms in the equation are tensors of the same order, and if the same unrepeated subscripts appear in all the terms. These facts will be used in obtaining appropriate equations for fluid turbulence. With the foregoing background, the derivation of appropriate continuum equations for turbulence should be straightforward.

Effective description of higher-order scalar-tensor theories

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

Langlois, David; Mancarella, Michele; Vernizzi, Filippo

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initialmore » Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.« less

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

Lyakh, Dmitry I.

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

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

DOE PAGES

Lyakh, Dmitry I.

2015-01-05

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

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

Extended mimetic gravity: Hamiltonian analysis and gradient instabilities

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Kobayashi, Tsutomu

2017-11-01

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

Killing-Yano tensors of order n - 1

NASA Astrophysics Data System (ADS)

Batista, Carlos

2014-08-01

The properties of a Killing-Yano tensor of order n-1 in an n-dimensional manifold are investigated. The integrability conditions are worked out and all metrics admitting a Killing-Yano tensor of order n-1 are found. A connection between such tensors and a generalization of the concept of angular momentum is pointed out. A theorem on how to generate closed conformal Killing vectors using the symmetries of a manifold is proved and used to find all Killing-Yano tensors of order n-1 of a maximally symmetric space.

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.

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

NASA Astrophysics Data System (ADS)

Troisi, Antonio

2017-03-01

Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f( R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R)=f_0R^n the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions.

Visualizing second order tensor fields with hyperstreamlines

NASA Technical Reports Server (NTRS)

Delmarcelle, Thierry; Hesselink, Lambertus

1993-01-01

Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.

Tensorial Calibration. 2. Second Order Tensorial Calibration.

DTIC Science & Technology

1987-10-12

index is repeated more than once only in one side of an equation, it implies a summation over the index valid range. 12 To avoid confusion of terms...and higher order tensor, the rank can be higher than the maximum dimensionality. 13 ,ON 6 LINEAR SECOND ORDER TENSORIAL CALIBRATION MODEL From...these equations are valid only if all the elements of the diagonal matrix B3 are non-zero because its inverse (-1) must be computed. This implies that M

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*

PubMed Central

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

2012-01-01

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

Decomposition of a symmetric second-order tensor

NASA Astrophysics Data System (ADS)

Heras, José A.

2018-05-01

In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.

Conformal killing tensors and covariant Hamiltonian dynamics

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

Cariglia, M., E-mail: marco@iceb.ufop.br; Gibbons, G. W., E-mail: G.W.Gibbons@damtp.cam.ac.uk; LE STUDIUM, Loire Valley Institute for Advanced Studies, Tours and Orleans

2014-12-15

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector formore » planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.« less

Lovelock branes

NASA Astrophysics Data System (ADS)

Kastor, David; Ray, Sourya; Traschen, Jennie

2017-10-01

We study the problem of finding brane-like solutions to Lovelock gravity, adopting a general approach to establish conditions that a lower dimensional base metric must satisfy in order that a solution to a given Lovelock theory can be constructed in one higher dimension. We find that for Lovelock theories with generic values of the coupling constants, the Lovelock tensors (higher curvature generalizations of the Einstein tensor) of the base metric must all be proportional to the metric. Hence, allowed base metrics form a subclass of Einstein metrics. This subclass includes so-called ‘universal metrics’, which have been previously investigated as solutions to quantum-corrected field equations. For specially tuned values of the Lovelock couplings, we find that the Lovelock tensors of the base metric need to satisfy fewer constraints. For example, for Lovelock theories with a unique vacuum there is only a single such constraint, a case previously identified in the literature, and brane solutions can be straightforwardly constructed.

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

PubMed

Freistühler, Heinrich; Temple, Blake

2014-06-08

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

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

PubMed Central

Freistühler, Heinrich; Temple, Blake

2014-01-01

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

A C++11 implementation of arbitrary-rank tensors for high-performance computing

NASA Astrophysics Data System (ADS)

Aragón, Alejandro M.

2014-06-01

This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for high-performance computing, a single Array class template is carefully crafted, from which vectors, matrices, and even higher-order tensors can be created. An expression template facility is also built around the array class template to provide convenient mathematical syntax. As a result, by using templates, an extra high-level layer is added to the C++ language when dealing with algebraic objects and their operations, without compromising performance. The implementation is tested running on both CPU and GPU.

A C++11 implementation of arbitrary-rank tensors for high-performance computing

NASA Astrophysics Data System (ADS)

Aragón, Alejandro M.

2014-11-01

This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for high-performance computing, a single Array class template is carefully crafted, from which vectors, matrices, and even higher-order tensors can be created. An expression template facility is also built around the array class template to provide convenient mathematical syntax. As a result, by using templates, an extra high-level layer is added to the C++ language when dealing with algebraic objects and their operations, without compromising performance. The implementation is tested running on both CPU and GPU.

Boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Panaras, Argyris G.

1987-01-01

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

Vainshtein mechanism after GW170817

NASA Astrophysics Data System (ADS)

Crisostomi, Marco; Koyama, Kazuya

2018-01-01

The almost simultaneous detection of gravitational waves and a short gamma-ray burst from a neutron star merger has put a tight constraint on the difference between the speed of gravity and light. In the four-dimensional scalar-tensor theory with second-order equations of motion, the Horndeski theory, this translates into a significant reduction of the viable parameter space of the theory. Recently, extensions of Horndeski theory, which are free from Ostrogradsky ghosts despite the presence of higher-order derivatives in the equations of motion, have been identified and classified exploiting the degeneracy criterium. In these new theories, the fifth force mediated by the scalar field must be suppressed in order to evade the stringent Solar System constraints. We study the Vainshtein mechanism in the most general degenerate higher-order scalar-tensor theory in which light and gravity propagate at the same speed. We find that the Vainshtein mechanism generally works outside a matter source but it is broken inside matter, similarly to beyond Horndeski theories. This leaves interesting possibilities to test these theories that are compatible with gravitational wave observations using astrophysical objects.

Impact of Next-to-Leading Order Contributions to Cosmic Microwave Background Lensing.

PubMed

Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth

2017-05-26

In this Letter we study the impact on cosmological parameter estimation, from present and future surveys, due to lensing corrections on cosmic microwave background temperature and polarization anisotropies beyond leading order. In particular, we show how post-Born corrections, large-scale structure effects, and the correction due to the change in the polarization direction between the emission at the source and the detection at the observer are non-negligible in the determination of the polarization spectra. They have to be taken into account for an accurate estimation of cosmological parameters sensitive to or even based on these spectra. We study in detail the impact of higher order lensing on the determination of the tensor-to-scalar ratio r and on the estimation of the effective number of relativistic species N_{eff}. We find that neglecting higher order lensing terms can lead to misinterpreting these corrections as a primordial tensor-to-scalar ratio of about O(10^{-3}). Furthermore, it leads to a shift of the parameter N_{eff} by nearly 2σ considering the level of accuracy aimed by future S4 surveys.

Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise.

PubMed

Wang, Junxiang; Wang, Xianpeng; Xu, Dingjie; Bi, Guoan

2018-03-09

This paper deals with joint estimation of direction-of-departure (DOD) and direction-of- arrival (DOA) in bistatic multiple-input multiple-output (MIMO) radar with the coexistence of unknown mutual coupling and spatial colored noise by developing a novel robust covariance tensor-based angle estimation method. In the proposed method, a third-order tensor is firstly formulated for capturing the multidimensional nature of the received data. Then taking advantage of the temporal uncorrelated characteristic of colored noise and the banded complex symmetric Toeplitz structure of the mutual coupling matrices, a novel fourth-order covariance tensor is constructed for eliminating the influence of both spatial colored noise and mutual coupling. After a robust signal subspace estimation is obtained by using the higher-order singular value decomposition (HOSVD) technique, the rotational invariance technique is applied to achieve the DODs and DOAs. Compared with the existing HOSVD-based subspace methods, the proposed method can provide superior angle estimation performance and automatically jointly perform the DODs and DOAs. Results from numerical experiments are presented to verify the effectiveness of the proposed method.

Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise

PubMed Central

Wang, Junxiang; Wang, Xianpeng; Xu, Dingjie; Bi, Guoan

2018-01-01

This paper deals with joint estimation of direction-of-departure (DOD) and direction-of- arrival (DOA) in bistatic multiple-input multiple-output (MIMO) radar with the coexistence of unknown mutual coupling and spatial colored noise by developing a novel robust covariance tensor-based angle estimation method. In the proposed method, a third-order tensor is firstly formulated for capturing the multidimensional nature of the received data. Then taking advantage of the temporal uncorrelated characteristic of colored noise and the banded complex symmetric Toeplitz structure of the mutual coupling matrices, a novel fourth-order covariance tensor is constructed for eliminating the influence of both spatial colored noise and mutual coupling. After a robust signal subspace estimation is obtained by using the higher-order singular value decomposition (HOSVD) technique, the rotational invariance technique is applied to achieve the DODs and DOAs. Compared with the existing HOSVD-based subspace methods, the proposed method can provide superior angle estimation performance and automatically jointly perform the DODs and DOAs. Results from numerical experiments are presented to verify the effectiveness of the proposed method. PMID:29522499

Frame-dependence of higher-order inflationary observables in scalar-tensor theories

NASA Astrophysics Data System (ADS)

Karam, Alexandros; Pappas, Thomas; Tamvakis, Kyriakos

2017-09-01

In the context of scalar-tensor theories of gravity we compute the third-order corrected spectral indices in the slow-roll approximation. The calculation is carried out by employing the Green's function method for scalar and tensor perturbations in both the Einstein and Jordan frames. Then, using the interrelations between the Hubble slow-roll parameters in the two frames we find that the frames are equivalent up to third order. Since the Hubble slow-roll parameters are related to the potential slow-roll parameters, we express the observables in terms of the latter which are manifestly invariant. Nevertheless, the same inflaton excursion leads to different predictions in the two frames since the definition of the number of e -folds differs. To illustrate this effect we consider a nonminimal inflationary model and find that the difference in the predictions grows with the nonminimal coupling, and it can actually be larger than the difference between the first and third order results for the observables. Finally, we demonstrate the effect of various end-of-inflation conditions on the observables. These effects will become important for the analyses of inflationary models in view of the improved sensitivity of future experiments.

Extended scalar-tensor theories of gravity

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

Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo

2016-04-21

We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators inmore » the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.« less

Self-accelerating universe in scalar-tensor theories after GW170817

NASA Astrophysics Data System (ADS)

Crisostomi, Marco; Koyama, Kazuya

2018-04-01

The recent simultaneous detection of gravitational waves and a gamma-ray burst from a neutron star merger significantly shrank the space of viable scalar-tensor theories by demanding that the speed of gravity is equal to that of light. The survived theories belong to the class of degenerate higher order scalar-tensor theories. We study whether these theories are suitable as dark energy candidates. We find scaling solutions in the matter dominated universe that lead to de Sitter solutions at late times without the cosmological constant, realizing self-acceleration. We evaluate quasistatic perturbations around self-accelerating solutions and show that the stringent constraints coming from astrophysical objects and gravitational waves can be satisfied, leaving interesting possibilities to test these theories by cosmological observations.

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

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

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

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

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

PubMed Central

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

2015-01-01

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

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

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

Brink, Jeandrew

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

Primordial spectra of slow-roll inflation at second-order with the Gauss-Bonnet correction

NASA Astrophysics Data System (ADS)

Wu, Qiang; Zhu, Tao; Wang, Anzhong

2018-05-01

The slow-roll inflation for a single scalar field that couples to the Gauss-Bonnet (GB) term represents an important higher-order curvature correction inspired by string theory. With the arrival of the era of precision cosmology, it is expected that the high-order corrections become more and more important. In this paper we study the observational predictions of the slow-roll inflation with the GB term by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble and GB coupling flow parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. In addition, by studying the theoretical predictions of the scalar spectral index and the tensor-to-scalar ratio with the Planck 2015 constraints in a model with power-law potential and GB coupling, we show that the second-order corrections are important in the future measurements. We expect that the understanding of the GB corrections in the primordial spectra and their constraints by forthcoming observational data will provide clues for the UV complete theory of quantum gravity, such as the string/M-theory.

Diffusion tensor analysis with invariant gradients and rotation tangents.

PubMed

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

2007-11-01

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

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1983-01-01

Tensor model order reduction, recursive tensor model identification, input design for tensor model identification, software development for nonlinear feedback control laws based upon tensors, and development of the CATNAP software package for tensor modeling, identification and simulation were studied. The last of these are discussed.

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

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

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

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

Nambu-Poisson gauge theory

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-06-01

We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg-Witten map. We construct a covariant Nambu-Poisson gauge theory action, give its first order expansion in the Nambu-Poisson tensor and relate it to a Nambu-Poisson matrix model.

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

PubMed

Jia, Chengcheng; Fu, Yun

2016-07-09

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

Scalar-tensor theories and modified gravity in the wake of GW170817

NASA Astrophysics Data System (ADS)

Langlois, David; Saito, Ryo; Yamauchi, Daisuke; Noui, Karim

2018-03-01

Theories of dark energy and modified gravity can be strongly constrained by astrophysical or cosmological observations, as illustrated by the recent observation of the gravitational wave event GW170817 and of its electromagnetic counterpart GRB 170817A, which showed that the speed of gravitational waves, cg , is the same as the speed of light, within deviations of order 10-15 . This observation implies severe restrictions on scalar-tensor theories, in particular theories whose action depends on second derivatives of a scalar field. Working in the very general framework of degenerate higher-order scalar-tensor (DHOST) theories, which encompass Horndeski and beyond Horndeski theories, we present the DHOST theories that satisfy cg=c . We then examine, for these theories, the screening mechanism that suppresses scalar interactions on small scales, namely the Vainshtein mechanism, and compute the corresponding gravitational laws for a nonrelativistic spherical body. We show that it can lead to a deviation from standard gravity inside matter, parametrized by three coefficients which satisfy a consistency relation and can be constrained by present and future astrophysical observations.

Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Karmakar, Purnendu; Matarrese, Sabino; Scomparin, Mattia

2018-05-01

We study cosmic structures in the quadratic Degenerate Higher Order Scalar Tensor (qDHOST) model, which has been proposed as the most general scalar-tensor theory (up to quadratic dependence on the covariant derivatives of the scalar field), which is not plagued by the presence of ghost instabilities. We then study a static, spherically symmetric object embedded in de Sitter space-time for the qDHOST model. This model exhibits breaking of the Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter space-time outside, where General Relativity (GR) can be recovered within the Vainshtein radius. We constrained the parameters of the qDHOST model by requiring the validity of the Vainshtein screening mechanism inside the cosmic structures and the consistency with the recently established bounds on gravitational wave speed from GW170817/GRB170817A event. We find that these two constraints rule out the same set of parameters, corresponding to the Lagrangians that are quadratic in second-order derivatives of the scalar field, for the shift symmetric qDHOST.

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

NASA Astrophysics Data System (ADS)

Mukherjee, Suvodip; Das, Santanu; Joy, Minu; Souradeep, Tarun

2015-01-01

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass meff for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation νt and change in spectral index for scalar perturbation νst to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of ns=0.96 by having a non-zero value of effective mass of the inflaton field m2eff/H2. The analysis with WP + Planck likelihood shows a non-zero detection of m2eff/H2 with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m2eff/H2 = -0.0237 ± 0.0135 which is consistent with zero.

On the Tensorial Nature of Fluxes in Continuous Media.

ERIC Educational Resources Information Center

Stokes, Vijay Kumar; Ramkrishna, Doraiswami

1982-01-01

Argues that mass and energy fluxes in a fluid are vectors. Topics include the stress tensor, theorem for tensor fields, mass flux as a vector, stress as a second order tensor, and energy flux as a tensor. (SK)

A new Weyl-like tensor of geometric origin

NASA Astrophysics Data System (ADS)

Vishwakarma, Ram Gopal

2018-04-01

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

Site-resolved multiple-quantum filtered correlations and distance measurements by magic-angle spinning NMR: Theory and applications to spins with weak to vanishing quadrupolar couplings

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

Eliav, U., E-mail: amirgo@tau.ac.il, E-mail: eliav@tau.ac.il; Haimovich, A.; Goldbourt, A., E-mail: amirgo@tau.ac.il, E-mail: eliav@tau.ac.il

2016-01-14

We discuss and analyze four magic-angle spinning solid-state NMR methods that can be used to measure internuclear distances and to obtain correlation spectra between a spin I = 1/2 and a half-integer spin S > 1/2 having a small quadrupolar coupling constant. Three of the methods are based on the heteronuclear multiple-quantum and single-quantum correlation experiments, that is, high rank tensors that involve the half spin and the quadrupolar spin are generated. Here, both zero and single-quantum coherence of the half spins are allowed and various coherence orders of the quadrupolar spin are generated, and filtered, via active recoupling ofmore » the dipolar interaction. As a result of generating coherence orders larger than one, the spectral resolution for the quadrupolar nucleus increases linearly with the coherence order. Since the formation of high rank tensors is independent of the existence of a finite quadrupolar interaction, these experiments are also suitable to materials in which there is high symmetry around the quadrupolar spin. A fourth experiment is based on the initial quadrupolar-driven excitation of symmetric high order coherences (up to p = 2S, where S is the spin number) and subsequently generating by the heteronuclear dipolar interaction higher rank (l + 1 or higher) tensors that involve also the half spins. Due to the nature of this technique, it also provides information on the relative orientations of the quadrupolar and dipolar interaction tensors. For the ideal case in which the pulses are sufficiently strong with respect to other interactions, we derive analytical expressions for all experiments as well as for the transferred echo double resonance experiment involving a quadrupolar spin. We show by comparison of the fitting of simulations and the analytical expressions to experimental data that the analytical expressions are sufficiently accurate to provide experimental {sup 7}Li–{sup 13}C distances in a complex of lithium, glycine, and water. Discussion of the regime for which such an approach is valid is given.« less

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

Ip, Hiu Yan; Schmidt, Fabian, E-mail: iphys@mpa-garching.mpg.de, E-mail: fabians@mpa-garching.mpg.de

Density perturbations in cosmology, i.e. spherically symmetric adiabatic perturbations of a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime, are locally exactly equivalent to a different FLRW solution, as long as their wavelength is much larger than the sound horizon of all fluid components. This fact is known as the 'separate universe' paradigm. However, no such relation is known for anisotropic adiabatic perturbations, which correspond to an FLRW spacetime with large-scale tidal fields. Here, we provide a closed, fully relativistic set of evolutionary equations for the nonlinear evolution of such modes, based on the conformal Fermi (CFC) frame. We show explicitly that the tidal effectsmore » are encoded by the Weyl tensor, and are hence entirely different from an anisotropic Bianchi I spacetime, where the anisotropy is sourced by the Ricci tensor. In order to close the system, certain higher derivative terms have to be dropped. We show that this approximation is equivalent to the local tidal approximation of Hui and Bertschinger [1]. We also show that this very simple set of equations matches the exact evolution of the density field at second order, but fails at third and higher order. This provides a useful, easy-to-use framework for computing the fully relativistic growth of structure at second order.« less

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.

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Killing(-Yano) tensors in string theory

NASA Astrophysics Data System (ADS)

Chervonyi, Yuri; Lunin, Oleg

2015-09-01

We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.

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.

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.

Molecular Eigensolution Symmetry Analysis and Fine Structure

PubMed Central

Harter, William G.; Mitchell, Justin C.

2013-01-01

Spectra of high-symmetry molecules contain fine and superfine level cluster structure related to J-tunneling between hills and valleys on rovibronic energy surfaces (RES). Such graphic visualizations help disentangle multi-level dynamics, selection rules, and state mixing effects including widespread violation of nuclear spin symmetry species. A review of RES analysis compares it to that of potential energy surfaces (PES) used in Born–Oppenheimer approximations. Both take advantage of adiabatic coupling in order to visualize Hamiltonian eigensolutions. RES of symmetric and D2 asymmetric top rank-2-tensor Hamiltonians are compared with Oh spherical top rank-4-tensor fine-structure clusters of 6-fold and 8-fold tunneling multiplets. Then extreme 12-fold and 24-fold multiplets are analyzed by RES plots of higher rank tensor Hamiltonians. Such extreme clustering is rare in fundamental bands but prevalent in hot bands, and analysis of its superfine structure requires more efficient labeling and a more powerful group theory. This is introduced using elementary examples involving two groups of order-6 (C6 and D3~C3v), then applied to families of Oh clusters in SF6 spectra and to extreme clusters. PMID:23344041

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.…

Constraining modified theories of gravity with the galaxy bispectrum

NASA Astrophysics Data System (ADS)

Yamauchi, Daisuke; Yokoyama, Shuichiro; Tashiro, Hiroyuki

2017-12-01

We explore the use of the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to test general scalar-tensor theories with second-order equations of motion. We find that time dependence of the leading second-order kernel is approximately characterized by one parameter, the second-order index, which is expected to trace the higher-order growth history of the Universe. We show that our new parameter can significantly carry new information about the nonlinear growth of structure. We forecast future constraints on the second-order index as well as the equation-of-state parameter and the growth index.

Classification of materials for conducting spheroids based on the first order polarization tensor

NASA Astrophysics Data System (ADS)

Khairuddin, TK Ahmad; Mohamad Yunos, N.; Aziz, ZA; Ahmad, T.; Lionheart, WRB

2017-09-01

Polarization tensor is an old terminology in mathematics and physics with many recent industrial applications including medical imaging, nondestructive testing and metal detection. In these applications, it is theoretically formulated based on the mathematical modelling either in electrics, electromagnetics or both. Generally, polarization tensor represents the perturbation in the electric or electromagnetic fields due to the presence of conducting objects and hence, it also desribes the objects. Understanding the properties of the polarization tensor is necessary and important in order to apply it. Therefore, in this study, when the conducting object is a spheroid, we show that the polarization tensor is positive-definite if and only if the conductivity of the object is greater than one. In contrast, we also prove that the polarization tensor is negative-definite if and only if the conductivity of the object is between zero and one. These features categorize the conductivity of the spheroid based on in its polarization tensor and can then help to classify the material of the spheroid.

Linear and angular coherence momenta in the classical second-order coherence theory of vector electromagnetic fields.

PubMed

Wang, Wei; Takeda, Mitsuo

2006-09-01

A new concept of vector and tensor densities is introduced into the general coherence theory of vector electromagnetic fields that is based on energy and energy-flow coherence tensors. Related coherence conservation laws are presented in the form of continuity equations that provide new insights into the propagation of second-order correlation tensors associated with stationary random classical electromagnetic fields.

Perturbative reduction of derivative order in EFT

NASA Astrophysics Data System (ADS)

Glavan, Dražen

2018-02-01

Higher derivative corrections are ubiquitous in effective field theories, which seemingly introduces new degrees of freedom at successive orders. This is actually an artefact of the implicit local derivative expansion defining effective field theories. We argue that higher derivative corrections that introduce additional degrees of freedom should be removed and their effects captured either by lower derivative corrections, or special combinations of higher derivative corrections not propagating extra degrees of freedom. Three methods adapted for this task are examined and field redefinitions are found to be most appropriate. First order higher derivative corrections in a scalar tensor theory are removed by field redefinition and it is found that their effects are captured by a subset of Horndeski theories. A case is made for restricting the effective field theory expansions in principle to only terms not introducing additional degrees of freedom.

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.

First integrals of motion in a gauge covariant framework, Killing-Maxwell system and quantum anomalies

NASA Astrophysics Data System (ADS)

Visinescu, M.

2012-10-01

Hidden symmetries in a covariant Hamiltonian framework are investigated. The special role of the Stackel-Killing and Killing-Yano tensors is pointed out. The covariant phase-space is extended to include external gauge fields and scalar potentials. We investigate the possibility for a higher-order symmetry to survive when the electromagnetic interactions are taken into account. Aconcrete realization of this possibility is given by the Killing-Maxwell system. The classical conserved quantities do not generally transfer to the quantized systems producing quantum gravitational anomalies. As a rule the conformal extension of the Killing vectors and tensors does not produce symmetry operators for the Klein-Gordon operator.

Fermionic topological quantum states as tensor networks

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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.

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

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

Mukherjee, Suvodip; Das, Santanu; Souradeep, Tarun

2015-01-01

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass m{sub eff} for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independentmore » parameters, namely spectral index for tensor perturbation ν{sub t} and change in spectral index for scalar perturbation ν{sub st} to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of n{sub s}=0.96 by having a non-zero value of effective mass of the inflaton field m{sup 2}{sub eff}/H{sup 2}. The analysis with WP + Planck likelihood shows a non-zero detection of m{sup 2}{sub eff}/H{sup 2} with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m{sup 2}{sub eff}/H{sup 2} = −0.0237 ± 0.0135 which is consistent with zero.« less

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

PubMed

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

2017-08-02

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

On improving the efficiency of tensor voting.

PubMed

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

2011-11-01

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

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

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

1997-01-01

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

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

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

Applications of Cosmological Perturbation Theory

NASA Astrophysics Data System (ADS)

Christopherson, Adam J.

2011-06-01

Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expansion of the universe, the same is not true at higher orders. This will have important implications on future measurements of the polarisation of the Cosmic Microwave Background, and could give rise to the generation of a primordial seed magnetic field. Having derived this qualitative result, we then estimate the scale dependence and magnitude of the vorticity power spectrum, finding, for simple power law inputs a small, blue spectrum. The final part of this thesis concerns higher order perturbation theory, deriving, for the first time, the metric tensor, gauge transformation rules and governing equations for fully general third order perturbations. We close with a discussion of natural extensions to this work and other possible ideas for off-shooting projects in this continually growing field.

Chapter 5. Hidden Symmetry and Exact Solutions in Einstein Gravity

NASA Astrophysics Data System (ADS)

Yasui, Y.; Houri, T.

Conformal Killing-Yano tensors are introduced as ageneralization of Killing vectors. They describe symmetries of higher-dimensional rotating black holes. In particular, a rank-2 closed conformal Killing-Yano tensor generates the tower of both hidden symmetries and isometries. We review a classification of higher-dimensional spacetimes admitting such a tensor, and present exact solutions to the Einstein equations for these spacetimes.

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.

Cosmological models in energy-momentum-squared gravity

NASA Astrophysics Data System (ADS)

Board, Charles V. R.; Barrow, John D.

2017-12-01

We study the cosmological effects of adding terms of higher order in the usual energy-momentum tensor to the matter Lagrangian of general relativity. This is in contrast to most studies of higher-order gravity which focus on generalizing the Einstein-Hilbert curvature contribution to the Lagrangian. The resulting cosmological theories give rise to field equations of similar form to several particular theories with different fundamental bases, including bulk viscous cosmology, loop quantum gravity, k -essence, and brane-world cosmologies. We find a range of exact solutions for isotropic universes, discuss their behaviors with reference to the early- and late-time evolution, accelerated expansion, and the occurrence or avoidance of singularities. We briefly discuss extensions to anisotropic cosmologies and delineate the situations where the higher-order matter terms will dominate over anisotropies on approach to cosmological singularities.

Covariance and the hierarchy of frame bundles

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.

1987-01-01

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

On butterfly effect in higher derivative gravities

NASA Astrophysics Data System (ADS)

Alishahiha, Mohsen; Davody, Ali; Naseh, Ali; Taghavi, Seyed Farid

2016-11-01

We study butterfly effect in D-dimensional gravitational theories containing terms quadratic in Ricci scalar and Ricci tensor. One observes that due to higher order derivatives in the corresponding equations of motion there are two butterfly velocities. The velocities are determined by the dimension of operators whose sources are provided by the metric. The three dimensional TMG model is also studied where we get two butterfly velocities at generic point of the moduli space of parameters. At critical point two velocities coincide.

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

PubMed

Brand, H R; Pleiner, H; Svenšek, D

2014-09-01

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

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

PubMed

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

2013-09-07

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

Semi-Supervised Tensor-Based Graph Embedding Learning and Its Application to Visual Discriminant Tracking.

PubMed

Hu, Weiming; Gao, Jin; Xing, Junliang; Zhang, Chao; Maybank, Stephen

2017-01-01

An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a two-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learning- based semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object's appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm.

Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms

NASA Astrophysics Data System (ADS)

Mondal, Ritwik; Berritta, Marco; Oppeneer, Peter M.

2018-07-01

The phenomenological Landau–Lifshitz–Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy–Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms.

PubMed

Mondal, Ritwik; Berritta, Marco; Oppeneer, Peter M

2018-05-17

The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy-Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

Integrability conditions for Killing-Yano tensors and maximally symmetric spaces in the presence of torsion

NASA Astrophysics Data System (ADS)

Batista, Carlos

2015-04-01

The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order n -1 are obtained. Finally, the issue of defining a maximally symmetric space with respect to connections with torsion is addressed.

On Adapting the Tensor Voting Framework to Robust Color Image Denoising

NASA Astrophysics Data System (ADS)

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Julià, Carme

This paper presents an adaptation of the tensor voting framework for color image denoising, while preserving edges. Tensors are used in order to encode the CIELAB color channels, the uniformity and the edginess of image pixels. A specific voting process is proposed in order to propagate color from a pixel to its neighbors by considering the distance between pixels, the perceptual color difference (by using an optimized version of CIEDE2000), a uniformity measurement and the likelihood of the pixels being impulse noise. The original colors are corrected with those encoded by the tensors obtained after the voting process. Peak to noise ratios and visual inspection show that the proposed methodology has a better performance than state-of-the-art techniques.

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.

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

Sergyeyev, Artur; Krtous, Pavel; Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, Prague

We consider the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetime without imposing any restrictions on the functional parameters characterizing the metric. We establish commutativity of the second-order operators constructed from the Killing tensors found in [J. High Energy Phys. 02 (2007) 004] and show that these operators, along with the first-order operators originating from the Killing vectors, form a complete set of commuting symmetry operators (i.e., integrals of motion) for the Klein-Gordon equation. Moreover, we demonstrate that the separated solutions of the Klein-Gordon equation obtained in [J. High Energy Phys. 02 (2007) 005] are joint eigenfunctions for all of thesemore » operators. We also present an explicit form of the zero mode for the Klein-Gordon equation with zero mass. In the semiclassical approximation we find that the separated solutions of the Hamilton-Jacobi equation for geodesic motion are also solutions for a set of Hamilton-Jacobi-type equations which correspond to the quadratic conserved quantities arising from the above Killing tensors.« less

Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations.

PubMed

Wilm, Bertram J; Barmet, Christoph; Pavan, Matteo; Pruessmann, Klaas P

2011-06-01

Despite continuous hardware advances, MRI is frequently subject to field perturbations that are of higher than first order in space and thus violate the traditional k-space picture of spatial encoding. Sources of higher order perturbations include eddy currents, concomitant fields, thermal drifts, and imperfections of higher order shim systems. In conventional MRI with Fourier reconstruction, they give rise to geometric distortions, blurring, artifacts, and error in quantitative data. This work describes an alternative approach in which the entire field evolution, including higher order effects, is accounted for by viewing image reconstruction as a generic inverse problem. The relevant field evolutions are measured with a third-order NMR field camera. Algebraic reconstruction is then formulated such as to jointly minimize artifacts and noise in the resulting image. It is solved by an iterative conjugate-gradient algorithm that uses explicit matrix-vector multiplication to accommodate arbitrary net encoding. The feasibility and benefits of this approach are demonstrated by examples of diffusion imaging. In a phantom study, it is shown that higher order reconstruction largely overcomes variable image distortions that diffusion gradients induce in EPI data. In vivo experiments then demonstrate that the resulting geometric consistency permits straightforward tensor analysis without coregistration. Copyright © 2011 Wiley-Liss, Inc.

Phasic action of the tensor muscle modulates the calling song in cicadas

PubMed

Fonseca; Hennig

1996-01-01

The effect of tensor muscle contraction on sound production by the tymbal was investigated in three species of cicadas (Tettigetta josei, Tettigetta argentata and Tympanistalna gastrica). All species showed a strict time correlation between the activity of the tymbal motoneurone and the discharge of motor units in the tensor nerve during the calling song. Lesion of the tensor nerve abolished the amplitude modulation of the calling song, but this modulation was restored by electrical stimulation of the tensor nerve or by mechanically pushing the tensor sclerite. Electrical stimulation of the tensor nerve at frequencies higher than 30­40 Hz changed the sound amplitude. In Tett. josei and Tett. argentata there was a gradual increase in sound amplitude with increasing frequency of tensor nerve stimulation, while in Tymp. gastrica there was a sudden reduction in sound amplitude at stimulation frequencies higher than 30 Hz. This contrasting effect in Tymp. gastrica was due to a bistable tymbal frame. Changes in sound pulse amplitude were positively correlated with changes in the time lag measured from tymbal motoneurone stimulation to the sound pulse. The tensor muscle acted phasically because electrical stimulation of the tensor nerve during a time window (0­10 ms) before electrical stimulation of the tymbal motoneurone was most effective in eliciting amplitude modulations. In all species, the tensor muscle action visibly changed the shape of the tymbal. Despite the opposite effects of the tensor muscle on sound pulse amplitude observed between Tettigetta and Tympanistalna species, the tensor muscle of both acts by modulating the shape of the tymbal, which changes the force required for the tymbal muscle to buckle the tymbal.

On Lovelock analogs of the Riemann tensor

NASA Astrophysics Data System (ADS)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

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

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.

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

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.

Dynamical structure of pure Lovelock gravity

NASA Astrophysics Data System (ADS)

Dadhich, Naresh; Durka, Remigiusz; Merino, Nelson; Miskovic, Olivera

2016-03-01

We study the dynamical structure of pure Lovelock gravity in spacetime dimensions higher than four using the Hamiltonian formalism. The action consists of a cosmological constant and a single higher-order polynomial in the Riemann tensor. Similarly to the Einstein-Hilbert action, it possesses a unique constant curvature vacuum and charged black hole solutions. We analyze physical degrees of freedom and local symmetries in this theory. In contrast to the Einstein-Hilbert case, the number of degrees of freedom depends on the background and can vary from zero to the maximal value carried by the Lovelock theory.

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

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

Gu Zhengcheng; Wen Xiaogang

2009-10-15

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

Holographic heat current as Noether current

NASA Astrophysics Data System (ADS)

Liu, Hai-Shan; Lü, H.; Pope, C. N.

2017-09-01

We employ the Noether procedure to derive a general formula for the radially conserved heat current in AdS planar black holes with certain transverse and traceless perturbations, for a general class of gravity theories. For Einstein gravity, the general higher-order Lovelock gravities and also a class of Horndeski gravities, we derive the boundary stress tensor and show that the resulting boundary heat current matches precisely the bulk Noether current.

Triangular Alignment (TAME). A Tensor-based Approach for Higher-order Network Alignment

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

Mohammadi, Shahin; Gleich, David F.; Kolda, Tamara G.

2015-11-01

Network alignment is an important tool with extensive applications in comparative interactomics. Traditional approaches aim to simultaneously maximize the number of conserved edges and the underlying similarity of aligned entities. We propose a novel formulation of the network alignment problem that extends topological similarity to higher-order structures and provide a new objective function that maximizes the number of aligned substructures. This objective function corresponds to an integer programming problem, which is NP-hard. Consequently, we approximate this objective function as a surrogate function whose maximization results in a tensor eigenvalue problem. Based on this formulation, we present an algorithm called Triangularmore » AlignMEnt (TAME), which attempts to maximize the number of aligned triangles across networks. We focus on alignment of triangles because of their enrichment in complex networks; however, our formulation and resulting algorithms can be applied to general motifs. Using a case study on the NAPABench dataset, we show that TAME is capable of producing alignments with up to 99% accuracy in terms of aligned nodes. We further evaluate our method by aligning yeast and human interactomes. Our results indicate that TAME outperforms the state-of-art alignment methods both in terms of biological and topological quality of the alignments.« less

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

PubMed Central

Seppecher, P.

2015-01-01

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

A unified tensor level set for image segmentation.

PubMed

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

2010-06-01

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

A Review of Tensors and Tensor Signal Processing

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Lorentzian Goldstone modes shared among photons and gravitons

NASA Astrophysics Data System (ADS)

Chkareuli, J. L.; Jejelava, J.; Kepuladze, Z.

2018-02-01

It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor-field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, A_{μ }2=± MA2 and H_{μ ν }2=± MH2 (MA and MH are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared by photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry SO(1, 3) of the electrogravity Lagrangian, the tensor-field constraint itself possesses much higher global symmetry SO(7, 3), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while the photon may only contain true Goldstone modes, the graviton appears at least partially to be composed of pseudo-Goldstone modes rather than of pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes considered in some detail. How this emergent electrogravity theory could be observationally different from conventional QED and GR theories is also briefly discussed.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

NASA Astrophysics Data System (ADS)

Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required.

Hamiltonian approach to second order gauge invariant cosmological perturbations

NASA Astrophysics Data System (ADS)

Domènech, Guillem; Sasaki, Misao

2018-01-01

In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.

Computerized implementation of higher-order electron-correlation methods and their linear-scaling divide-and-conquer extensions.

PubMed

Nakano, Masahiko; Yoshikawa, Takeshi; Hirata, So; Seino, Junji; Nakai, Hiromi

2017-11-05

We have implemented a linear-scaling divide-and-conquer (DC)-based higher-order coupled-cluster (CC) and Møller-Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC-based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2) TQ ]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC-based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Research on third-order susceptibility tensor of silicon at telecom wavelength

NASA Astrophysics Data System (ADS)

Zhang, Yu-Hong; Liu, Hang; Chen, Zhan-Guo; Jia, Gang; Ren, Ce

2010-10-01

In this paper, the electro-induced birefringence based on Kerr effect and Franz-Keldysh effect in bulk silicon crystal at 1.3μm wavelengths has been measured. By using Kerr effect, the third-order susceptibility tensor of bulk crystalline silicon has been calculated.The two independent tensor of silicon X (3) susceptibility can be obtained by calculation (3) 6.22 (1 2.2%) 10 -20 m2 V2 and Xxyxy(3) = and xxxx(3) 9.13 (1 +/-2.2%) 10-20 m2 V 2 = m2/V2. The research can drive the silicon utility in the photo-electricity field.

An efficient matrix-matrix multiplication based antisymmetric tensor contraction engine for general order coupled cluster.

PubMed

Hanrath, Michael; Engels-Putzka, Anna

2010-08-14

In this paper, we present an efficient implementation of general tensor contractions, which is part of a new coupled-cluster program. The tensor contractions, used to evaluate the residuals in each coupled-cluster iteration are particularly important for the performance of the program. We developed a generic procedure, which carries out contractions of two tensors irrespective of their explicit structure. It can handle coupled-cluster-type expressions of arbitrary excitation level. To make the contraction efficient without loosing flexibility, we use a three-step procedure. First, the data contained in the tensors are rearranged into matrices, then a matrix-matrix multiplication is performed, and finally the result is backtransformed to a tensor. The current implementation is significantly more efficient than previous ones capable of treating arbitrary high excitations.

Critical phenomena at the complex tensor ordering phase transition

NASA Astrophysics Data System (ADS)

Boettcher, Igor; Herbut, Igor F.

2018-02-01

We investigate the critical properties of the phase transition towards complex tensor order that has been proposed to occur in spin-orbit-coupled superconductors. For this purpose, we formulate the bosonic field theory for fluctuations of the complex irreducible second-rank tensor order parameter close to the transition. We then determine the scale dependence of the couplings of the theory by means of the perturbative renormalization group (RG). For the isotropic system, we generically detect a fluctuation-induced first-order phase transition. The initial values for the running couplings are determined by the underlying microscopic model for the tensorial order. As an example, we study three-dimensional Luttinger semimetals with electrons at a quadratic band-touching point. Whereas the strong-coupling transition of the model receives substantial fluctuation corrections, the weak-coupling transition at low temperatures is rendered only weakly first order due to the presence of a fixed point in the vicinity of the RG trajectory. If the number of fluctuating complex components of the order parameter is reduced by cubic anisotropy, the theory maps onto the field theory for frustrated magnetism.

HOKF: High Order Kalman Filter for Epilepsy Forecasting Modeling.

PubMed

Nguyen, Ngoc Anh Thi; Yang, Hyung-Jeong; Kim, Sunhee

2017-08-01

Epilepsy forecasting has been extensively studied using high-order time series obtained from scalp-recorded electroencephalography (EEG). An accurate seizure prediction system would not only help significantly improve patients' quality of life, but would also facilitate new therapeutic strategies to manage epilepsy. This paper thus proposes an improved Kalman Filter (KF) algorithm to mine seizure forecasts from neural activity by modeling three properties in the high-order EEG time series: noise, temporal smoothness, and tensor structure. The proposed High-Order Kalman Filter (HOKF) is an extension of the standard Kalman filter, for which higher-order modeling is limited. The efficient dynamic of HOKF system preserves the tensor structure of the observations and latent states. As such, the proposed method offers two main advantages: (i) effectiveness with HOKF results in hidden variables that capture major evolving trends suitable to predict neural activity, even in the presence of missing values; and (ii) scalability in that the wall clock time of the HOKF is linear with respect to the number of time-slices of the sequence. The HOKF algorithm is examined in terms of its effectiveness and scalability by conducting forecasting and scalability experiments with a real epilepsy EEG dataset. The results of the simulation demonstrate the superiority of the proposed method over the original Kalman Filter and other existing methods. Copyright © 2017 Elsevier B.V. All rights reserved.

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

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.

Comparison of scalar measures used in magnetic resonance diffusion tensor imaging.

PubMed

Bahn, M M

1999-07-01

The tensors derived from diffusion tensor imaging describe complex diffusion in tissues. However, it is difficult to compare tensors directly or to produce images that contain all of the information of the tensor. Therefore, it is convenient to produce scalar measures that extract desired aspects of the tensor. These measures map the three-dimensional eigenvalues of the diffusion tensor into scalar values. The measures impose an order on eigenvalue space. Many invariant scalar measures have been introduced in the literature. In the present manuscript, a general approach for producing invariant scalar measures is introduced. Because it is often difficult to determine in clinical practice which of the many measures is best to apply to a given situation, two formalisms are introduced for the presentation, definition, and comparison of measures applied to eigenvalues: (1) normalized eigenvalue space, and (2) parametric eigenvalue transformation plots. All of the anisotropy information contained in the three eigenvalues can be retained and displayed in a two-dimensional plot, the normalized eigenvalue plot. An example is given of how to determine the best measure to use for a given situation by superimposing isometric contour lines from various anisotropy measures on plots of actual measured eigenvalue data points. Parametric eigenvalue transformation plots allow comparison of how different measures impose order on normalized eigenvalue space to determine whether the measures are equivalent and how the measures differ. These formalisms facilitate the comparison of scalar invariant measures for diffusion tensor imaging. Normalized eigenvalue space allows presentation of eigenvalue anisotropy information. Copyright 1999 Academic Press.

Modulated Hawking radiation and a nonviolent channel for information release

NASA Astrophysics Data System (ADS)

Giddings, Steven B.

2014-11-01

Unitarization of black hole evaporation requires that quantum information escapes a black hole; an important question is to identify the mechanism or channel by which it does so. Accurate counting of black hole states via the Bekenstein-Hawking entropy would indicate this information should be encoded in radiation with average energy flux matching Hawking's. Information can be encoded with no change in net flux via fine-grained modulation of the Hawking radiation. In an approximate effective field theory description, couplings to the stress tensor of the black hole atmosphere that depend on the internal state of the black hole are a promising alternative for inducing such modulation. These can be picturesquely thought of as due to state-dependent metric fluctuations in the vicinity of the horizon. Such couplings offer the prospect of emitting information without extra energy flux, and can be shown to do so at linear order in the couplings, with motivation given for possible extension of this result to higher orders. The potential advantages of such couplings to the stress tensor thus extend beyond their universality, which is helpful in addressing constraints from black hole mining.

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.

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

Reisert, Marco; Burkhardt, Hans

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

Scalar field coupling to Einstein tensor in regular black hole spacetime

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wu, Chen

2018-02-01

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

Hidden discriminative features extraction for supervised high-order time series modeling.

PubMed

Nguyen, Ngoc Anh Thi; Yang, Hyung-Jeong; Kim, Sunhee

2016-11-01

In this paper, an orthogonal Tucker-decomposition-based extraction of high-order discriminative subspaces from a tensor-based time series data structure is presented, named as Tensor Discriminative Feature Extraction (TDFE). TDFE relies on the employment of category information for the maximization of the between-class scatter and the minimization of the within-class scatter to extract optimal hidden discriminative feature subspaces that are simultaneously spanned by every modality for supervised tensor modeling. In this context, the proposed tensor-decomposition method provides the following benefits: i) reduces dimensionality while robustly mining the underlying discriminative features, ii) results in effective interpretable features that lead to an improved classification and visualization, and iii) reduces the processing time during the training stage and the filtering of the projection by solving the generalized eigenvalue issue at each alternation step. Two real third-order tensor-structures of time series datasets (an epilepsy electroencephalogram (EEG) that is modeled as channel×frequency bin×time frame and a microarray data that is modeled as gene×sample×time) were used for the evaluation of the TDFE. The experiment results corroborate the advantages of the proposed method with averages of 98.26% and 89.63% for the classification accuracies of the epilepsy dataset and the microarray dataset, respectively. These performance averages represent an improvement on those of the matrix-based algorithms and recent tensor-based, discriminant-decomposition approaches; this is especially the case considering the small number of samples that are used in practice. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

Third-order optical conductivity of an electron fluid

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Basov, D. N.; Fogler, M. M.

2018-02-01

We derive the nonlinear optical conductivity of an isotropic electron fluid at frequencies below the interparticle collision rate. In this regime, governed by hydrodynamics, the conductivity acquires a universal form at any temperature, chemical potential, and spatial dimension. We show that the nonlinear response of the fluid to a uniform field is dominated by the third-order conductivity tensor σ(3 ) whose magnitude and temperature dependence differ qualitatively from those in the conventional kinetic regime of higher frequencies. We obtain explicit formulas for σ(3 ) for Dirac materials such as graphene and Weyl semimetals. We make predictions for the third-harmonic generation, renormalization of the collective-mode spectrum, and the third-order circular magnetic birefringence experiments.

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.

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.

Growth, Characterization and Applications of Beta-Barium Borate and Related Crystals

DTIC Science & Technology

1993-10-31

Crystal symmetry determines the form of the second order polarization tensor. The second order polarizability tensor is defined by the piezoelectric...cold finger. A temperature oscillation technique1 I was used to limit the number of nuclei formed . These experiments typically yielded thin crystal...statistically sampled to determine the optimal seeding orientation. % was reasoned that the large crystal plates were formed from nucleii which had a favorable

An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs

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

Kolda, Tamara G.; Mayo, Jackson R.

2014-12-11

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

The Twist Tensor Nuclear Norm for Video Completion.

PubMed

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

2017-12-01

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

Observational constraints on loop quantum cosmology.

PubMed

Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji

2011-11-18

In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.

Assessment of diffusion tensor image quality across sites and vendors using the American College of Radiology head phantom.

PubMed

Wang, Zhiyue J; Seo, Youngseob; Babcock, Evelyn; Huang, Hao; Bluml, Stefan; Wisnowski, Jessica; Holshouser, Barbara; Panigrahy, Ashok; Shaw, Dennis W W; Altman, Nolan; McColl, Roderick W; Rollins, Nancy K

2016-05-08

The purpose of this study was to explore the feasibility of assessing quality of diffusion tensor imaging (DTI) from multiple sites and vendors using American College of Radiology (ACR) phantom. Participating sites (Siemens (n = 2), GE (n= 2), and Philips (n = 4)) reached consensus on parameters for DTI and used the widely available ACR phantom. Tensor data were processed at one site. B0 and eddy current distortions were assessed using grid line displacement on phantom Slice 5; signal-to-noise ratio (SNR) was measured at the center and periphery of the b = 0 image; fractional anisotropy (FA) and mean diffusivity (MD) were assessed using phantom Slice 7. Variations of acquisition parameters and deviations from specified sequence parameters were recorded. Nonlinear grid line distortion was higher with linear shimming and could be corrected using the 2nd order shimming. Following image registration, eddy current distortion was consistently smaller than acquisi-tion voxel size. SNR was consistently higher in the image periphery than center by a factor of 1.3-2.0. ROI-based FA ranged from 0.007 to 0.024. ROI-based MD ranged from 1.90 × 10-3 to 2.33 × 10-3 mm2/s (median = 2.04 × 10-3 mm2/s). Two sites had image void artifacts. The ACR phantom can be used to compare key qual-ity measures of diffusion images acquired from multiple vendors at multiple sites.

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

Decay constants of the charmed tensor mesons at finite temperature

NASA Astrophysics Data System (ADS)

Azizi, K.; Sundu, H.; Türkan, A.; Veliev, E. Veli

2016-01-01

Investigation of the thermal properties of the mesons with higher spin is one of the important problems in the hadron physics. At finite temperature, the Lorentz invariance is broken by the choice of a preferred frame of reference and some new operators appear in the Wilson expansion. Taking into account these additional operators, we calculate the thermal two-point correlation function for D2*(2460 ) and Ds2 *(2573 ) tensor mesons. In order to perform the numerical analysis, we use the fermionic part of the energy density obtained both from lattice QCD and Chiral perturbation theory. We also use the temperature dependent continuum threshold and show that the values of the decay constants decrease considerably near to the critical temperature compared to their values in the vacuum. Our results at zero temperature are in good consistency with predictions of other nonperturbative models.

Embeddings of the "New Massive Gravity"

NASA Astrophysics Data System (ADS)

Dalmazi, D.; Mendonça, E. L.

2016-07-01

Here we apply different types of embeddings of the equations of motion of the linearized "New Massive Gravity" in order to generate alternative and even higher-order (in derivatives) massive gravity theories in D=2+1. In the first part of the work we use the Weyl symmetry as a guiding principle for the embeddings. First we show that a Noether gauge embedding of the Weyl symmetry leads to a sixth-order model in derivatives with either a massive or a massless ghost, according to the chosen overall sign of the theory. On the other hand, if the Weyl symmetry is implemented by means of a Stueckelberg field we obtain a new scalar-tensor model for massive gravitons. It is ghost-free and Weyl invariant at the linearized level around Minkowski space. The model can be nonlinearly completed into a scalar field coupled to the NMG theory. The elimination of the scalar field leads to a nonlocal modification of the NMG. In the second part of the work we prove to all orders in derivatives that there is no local, ghost-free embedding of the linearized NMG equations of motion around Minkowski space when written in terms of one symmetric tensor. Regarding that point, NMG differs from the Fierz-Pauli theory, since in the latter case we can replace the Einstein-Hilbert action by specific f(R,Box R) generalizations and still keep the theory ghost-free at the linearized level.

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%.

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.

Ordered rate constitutive theories for thermoviscoelastic solids with memory in Lagrangian description using Gibbs potential

NASA Astrophysics Data System (ADS)

Surana, K. S.; Reddy, J. N.; Nunez, Daniel

2015-11-01

This paper presents ordered rate constitutive theories of orders m and n, i.e., ( m, n) for finite deformation of homogeneous, isotropic, compressible and incompressible thermoviscoelastic solids with memory in Lagrangian description using entropy inequality in Gibbs potential Ψ as an alternate approach of deriving constitutive theories using entropy inequality in terms of Helmholtz free energy density Φ. Second Piola-Kirchhoff stress σ [0] and Green's strain tensor ɛ [0] are used as conjugate pair. We consider Ψ, heat vector q, entropy density η and rates of upto orders m and n of σ [0] and ɛ [0], i.e., σ [ i]; i = 0, 1, . . . , m and ɛ [ j]; j = 0, 1, . . . , n. We choose Ψ, ɛ [ n], q and η as dependent variables in the constitutive theories with ɛ [ j]; j = 0, 1, . . . , n - 1, σ [ i]; i = 0, 1, . . . , m, temperature gradient g and temperature θ as their argument tensors. Rationale for this choice is explained in the paper. Entropy inequality, decomposition of σ [0] into equilibrium and deviatoric stresses, the conditions resulting from entropy inequality and the theory of generators and invariants are used in the derivations of ordered rate constitutive theories of orders m and n in stress and strain tensors. Constitutive theories for the heat vector q (of up to orders m and n - 1) that are consistent (in terms of the argument tensors) with the constitutive theories for ɛ [ n] (of up to orders m and n) are also derived. Many simplified forms of the rate theories of orders ( m, n) are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing ɛ [ n] and q using the combined generators of the argument tensors about a known configuration {{\\underline{\\varOmega}}} in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one ( m = 1, n = 1) when further simplified result in constitutive theories that resemble currently used theories but are in fact different. The solid continua characterized by these theories have mechanisms of elasticity, dissipation and memory, i.e., relaxation behavior or rheology. Fourier heat conduction law is shown to be an over simplified case of the rate theory of order one ( m = 1, n = 1) for q. The paper establishes when there is equivalence between the constitutive theories derived here using Ψ and those presented in reference Surana et al. (Acta Mech. doi:10.1007/s00707-014-1173-6, 2014) that are derived using Helmholtz free energy density Φ. The fundamental differences between the two constitutive theories in terms of physics and their explicit forms using Φ and Ψ are difficult to distinguish from the ordered theories of orders ( m, n) due to complexity of expressions. However, by choosing lower ordered theories, the difference between the two approaches can be clearly seen.

Affinity learning with diffusion on tensor product graph.

PubMed

Yang, Xingwei; Prasad, Lakshman; Latecki, Longin Jan

2013-01-01

In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples. As observed in several recent approaches, more reliable similarities can be obtained if the original similarities are diffused in the context of other data points, where the context of each point is a set of points most similar to it. Compared to the existing methods, our approach differs in two main aspects. First, instead of diffusing the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. Since TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities. However, it comes at the price of higher order computational complexity and storage requirement. The key contribution of the proposed approach is that the information propagation on TPG can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph. We prove that a graph diffusion process on TPG is equivalent to a novel iterative algorithm on the original graph, which is guaranteed to converge. After its convergence we obtain new edge weights that can be interpreted as new, learned affinities. We stress that the affinities are learned in an unsupervised setting. We illustrate the benefits of the proposed approach for data manifolds composed of shapes, images, and image patches on two very different tasks of image retrieval and image segmentation. With learned affinities, we achieve the bull's eye retrieval score of 99.99 percent on the MPEG-7 shape dataset, which is much higher than the state-of-the-art algorithms. When the data- points are image patches, the NCut with the learned affinities not only significantly outperforms the NCut with the original affinities, but it also outperforms state-of-the-art image segmentation methods.

Advanced Computational Techniques in Regional Wave Studies

DTIC Science & Technology

1990-01-03

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

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.

Advanced Signal Processing & Classification: UXO Standardized Test Site Data

DTIC Science & Technology

2012-04-01

magnetic polarizability tensor , and represent the response of the target along each of three principal axes. In order to reduce the number of fit...Oldenburg-Billings (POB) model – GPA version The full POB analysis assumes an axially symmetric (axial and transverse) tensor dipolar target response, and... tensor , and represent the response of the target along each of three principal axes. The β’s are in turn expressed in terms of an empirical five

Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge

NASA Astrophysics Data System (ADS)

Wang, Bo; Zhang, Yang

2017-11-01

We present a systematic study of the 2nd-order scalar, vector, and tensor metric perturbations in the Einstein-de Sitter Universe in synchronous coordinates. For the scalar-scalar coupling between 1st-order perturbations, we decompose the 2nd-order perturbed Einstein equation into the respective field equations of 2nd-order scalar, vector, and tensor perturbations, and obtain their solutions with general initial conditions. In particular, the decaying modes of solution are included, the 2nd-order vector is generated even if the 1st-order vector is absent, and the solution of the 2nd-order tensor corrects that in literature. We perform general synchronous-to-synchronous gauge transformations up to 2nd order generated by a 1st-order vector field ξ(1 )μ and a 2nd-order ξ(2 )μ . All the residual gauge modes of 2nd-order metric perturbations and density contrast are found, and their number is substantially reduced when the transformed 3-velocity of dust is set to zero. Moreover, we show that only ξ(2 )μ is effective in carrying out 2nd-order transformations that we consider, because ξ(1 )μ has been used in obtaining the 1st-order perturbations. Holding the 1st-order perturbations fixed, the transformations by ξ(2 )μ on the 2nd-order perturbations have the same structure as those by ξ(1 )μ on the 1st-order perturbations.

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

Sasakura, Naoki

The tensor model is discussed as theory of dynamical fuzzy spaces in order to formulate gravity on fuzzy spaces. The numerical analyses of the tensor models possessing Gaussian background solutions have shown that the low-lying long-wavelength fluctuations around the backgrounds are in remarkable agreement with the geometric fluctuations on flat spaces in the general relativity. It has also been shown that part of the orthogonal symmetry of the tensor model spontaneously broken by the backgrounds agrees with the local translation symmetry of the general relativity. Thus the tensor model provides an interesting model of simultaneous emergence of space, the generalmore » relativity, and its local translation symmetry.« less

Superconducting tensor gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

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

Brane f(R) gravity cosmologies

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

Balcerzak, Adam; DaPbrowski, Mariusz P.

2010-06-15

By the application of the generalized Israel junction conditions we derive cosmological equations for the fourth-order f(R) brane gravity and study their cosmological solutions. We show that there exists a nonstatic solution which describes a four-dimensional de Sitter (dS{sub 4}) brane embedded in a five-dimensional anti-de Sitter (AdS{sub 5}) bulk for a vanishing Weyl tensor contribution. On the other hand, for the case of a nonvanishing Weyl tensor contribution, there exists a static brane solution only. We claim that in order to get some more general nonstatic f(R) brane configurations, one needs to admit a dynamical matter energy-momentum tensor inmore » the bulk rather than just a bulk cosmological constant.« less

Diffusion tensor imaging in evaluation of human skeletal muscle injury.

PubMed

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

2006-08-01

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

Tensor Fermi liquid parameters in nuclear matter from chiral effective field theory

NASA Astrophysics Data System (ADS)

Holt, J. W.; Kaiser, N.; Whitehead, T. R.

2018-05-01

We compute from chiral two- and three-body forces the complete quasiparticle interaction in symmetric nuclear matter up to twice nuclear matter saturation density. Second-order perturbative contributions that account for Pauli blocking and medium polarization are included, allowing for an exploration of the full set of central and noncentral operator structures permitted by symmetries and the long-wavelength limit. At the Hartree-Fock level, the next-to-next-to-leading order three-nucleon force contributes to all noncentral interactions, and their strengths grow approximately linearly with the nucleon density up to that of saturated nuclear matter. Three-body forces are shown to enhance the already strong proton-neutron effective tensor interaction, while the corresponding like-particle tensor force remains small. We also find a large isovector cross-vector interaction but small center-of-mass tensor interactions in the isoscalar and isovector channels. The convergence of the expansion of the noncentral quasiparticle interaction in Landau parameters and Legendre polynomials is studied in detail.

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

Symmetric Topological Phases and Tensor Network States

NASA Astrophysics Data System (ADS)

Jiang, Shenghan

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

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

PubMed

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

2017-10-12

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

Extension of relativistic dissipative hydrodynamics to third order

NASA Astrophysics Data System (ADS)

El, Andrej; Xu, Zhe; Greiner, Carsten

2010-04-01

Following the procedure introduced by Israel and Stewart, we expand the entropy current up to the third order in the shear stress tensor παβ and derive a novel third-order evolution equation for παβ. This equation is solved for the one-dimensional Bjorken boost-invariant expansion. The scaling solutions for various values of the shear viscosity to the entropy density ratio η/s are shown to be in very good agreement with those obtained from kinetic transport calculations. For the pressure isotropy starting with 1 at τ0=0.4 fm/c, the third-order corrections to Israel-Stewart theory are approximately 10% for η/s=0.2 and more than a factor of 2 for η/s=3. We also estimate all higher-order corrections to Israel-Stewart theory and demonstrate their importance in describing highly viscous matters.

Mild hypothermia for treatment of diffuse axonal injury: a quantitative analysis of diffusion tensor imaging

PubMed Central

Jing, Guojie; Yao, Xiaoteng; Li, Yiyi; Xie, Yituan; Li, Wang#x2019;an; Liu, Kejun; Jing, Yingchao; Li, Baisheng; Lv, Yifan; Ma, Baoxin

2014-01-01

Fractional anisotropy values in diffusion tensor imaging can quantitatively reflect the consistency of nerve fibers after brain damage, where higher values generally indicate less damage to nerve fibers. Therefore, we hypothesized that diffusion tensor imaging could be used to evaluate the effect of mild hypothermia on diffuse axonal injury. A total of 102 patients with diffuse axonal injury were randomly divided into two groups: normothermic and mild hypothermic treatment groups. Patient's modified Rankin scale scores 2 months after mild hypothermia were significantly lower than those for the normothermia group. The difference in average fractional anisotropy value for each region of interest before and after mild hypothermia was 1.32-1.36 times higher than the value in the normothermia group. Quantitative assessment of diffusion tensor imaging indicates that mild hypothermia therapy may be beneficial for patients with diffuse axonal injury. PMID:25206800

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

Visualization of 3-D tensor fields

NASA Technical Reports Server (NTRS)

Hesselink, L.

1996-01-01

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

Simplified derivation of the gravitational wave stress tensor from the linearized Einstein field equations.

PubMed

Balbus, Steven A

2016-10-18

A conserved stress energy tensor for weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the tensor leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave stress tensor has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the stress tensor found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.

Hairy black hole solutions in U(1) gauge-invariant scalar-vector-tensor theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Tsujikawa, Shinji

2018-05-01

In U (1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar ϕ → ϕ + c, we show the existence of new hairy BH solutions where a cubic-order scalar-vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.

Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors

NASA Astrophysics Data System (ADS)

Böbel, A.; Knapek, C. A.; Räth, C.

2018-05-01

Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski tensor analysis turns out to be a powerful tool for investigations of crystallization processes. It is capable of revealing nonlinear local topological properties, however, still provides easily interpretable results founded on a solid mathematical framework.

Algebra of constraints for a string in curved background

NASA Astrophysics Data System (ADS)

Wess, Julius

1990-06-01

A string field theory with curved background develops anomalies and Schwinger terms in the conformal algebra. It is generally believed that these Schwinger terms and anomalies are expressible in terms of the curvature tensor of the background metric 1 and that, therefore, they are covariant under a change of coordinates in the target space. As far as I know, all the relevant computations have been done in special gauges, i.e. in Riemann normal coordinates. The question remains whether this is true in any gauge. We have tried to investigate this problem in a Hamiltonian formulation of the model. A classical Lagrangian serves to define the canonical variables and the classical constraints. They are expressed in terms of the canonical variables and, classically, they are first class. When quantized, an ordering prescription has to be imposed which leads to anomalies and Schwinger terms. We then try to redefine the constraints in such a way that the Schwinger terms depend on the curvature tensor only. The redefinition of the constraints is limited by the requirement that it should be local and that the energy momentum tensor should be conserved. In our approach, it is natural that the constraints are improved, order by order, in the number of derivatives: we find that, up to third order in the derivatives, Schwinger terms and anomalies are expressible in terms of the curvature tensor. In the fourth order of the derivaties however, we find a contribution to the Schwinger terms that cannot be removed by a redefinition and that cannot be cast in a covariant form. The anomaly on the other hand is fully expressible in terms of the curvature scalar. The energy momentum tensor ceases to be symmetric which indicates a Lorentz anomaly as well. The question remains if the Schwinger terms take a covariant form if we allow Einstein anomalies as well 2.

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

Rethinking moment tensor inversion methods to retrieve the source mechanisms of low-frequency seismic events

NASA Astrophysics Data System (ADS)

Karl, S.; Neuberg, J.

2011-12-01

Volcanoes exhibit a variety of seismic signals. One specific type, the so-called long-period (LP) or low-frequency event, has proven to be crucial for understanding the internal dynamics of the volcanic system. These long period (LP) seismic events have been observed at many volcanoes around the world, and are thought to be associated with resonating fluid-filled conduits or fluid movements (Chouet, 1996; Neuberg et al., 2006). While the seismic wavefield is well established, the actual trigger mechanism of these events is still poorly understood. Neuberg et al. (2006) proposed a conceptual model for the trigger of LP events at Montserrat involving the brittle failure of magma in the glass transition in response to the upwards movement of magma. In an attempt to gain a better quantitative understanding of the driving forces of LPs, inversions for the physical source mechanisms have become increasingly common. Previous studies have assumed a point source for waveform inversion. Knowing that applying a point source model to synthetic seismograms representing an extended source process does not yield the real source mechanism, it can, however, still lead to apparent moment tensor elements which then can be compared to previous results in the literature. Therefore, this study follows the proposed concepts of Neuberg et al. (2006), modelling the extended LP source as an octagonal arrangement of double couples approximating a circular ringfault bounding the circumference of the volcanic conduit. Synthetic seismograms were inverted for the physical source mechanisms of LPs using the moment tensor inversion code TDMTISO_INVC by Dreger (2003). Here, we will present the effects of changing the source parameters on the apparent moment tensor elements. First results show that, due to negative interference, the amplitude of the seismic signals of a ringfault structure is greatly reduced when compared to a single double couple source. Furthermore, best inversion results yield a solution comprised of positive isotropic and compensated linear vector dipole components. Thus, the physical source mechanisms of volcano seismic signals may be misinterpreted as opening shear or tensile cracks when wrongly assuming a point source. In order to approach the real physical sources with our models, inversions based on higher-order tensors might have to be considered in the future. An inversion technique where the point source is replaced by a so-called moment tensor density would allow inversions of volcano seismic signals for sources that can then be temporally and spatially extended.

Reducing tensor magnetic gradiometer data for unexploded ordnance detection

USGS Publications Warehouse

Bracken, Robert E.; Brown, Philip J.

2005-01-01

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

Modulated Hawking radiation and a nonviolent channel for information release

DOE PAGES

Giddings, Steven B.

2014-09-16

The unitarization of black hole evaporation requires that quantum information escapes a black hole; an important question is to identify the mechanism or channel by which it does so. Accurate counting of black hole states via the Bekenstein–Hawking entropy would indicate this information should be encoded in radiation with average energy flux matching Hawking’s. Information can be encoded with no change in net flux via fine-grained modulation of the Hawking radiation. In an approximate effective field theory description, couplings to the stress tensor of the black hole atmosphere that depend on the internal state of the black hole are amore » promising alternative for inducing such modulation. These can be picturesquely thought of as due to state-dependent metric fluctuations in the vicinity of the horizon. Such couplings offer the prospect of emitting information without extra energy flux, and can be shown to do so at linear order in the couplings, with motivation given for possible extension of this result to higher orders. The potential advantages of such couplings to the stress tensor thus extend beyond their universality, which is helpful in addressing constraints from black hole mining.« less

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE PAGES

Peng, Bo; Kowalski, Karol

2017-01-25

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

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.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

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

Peng, Bo; Kowalski, Karol

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Parallel language constructs for tensor product computations on loosely coupled architectures

NASA Technical Reports Server (NTRS)

Mehrotra, Piyush; Van Rosendale, John

1989-01-01

A set of language primitives designed to allow the specification of parallel numerical algorithms at a higher level is described. The authors focus on tensor product array computations, a simple but important class of numerical algorithms. They consider first the problem of programming one-dimensional kernel routines, such as parallel tridiagonal solvers, and then look at how such parallel kernels can be combined to form parallel tensor product algorithms.

Scalar and tensor perturbations in loop quantum cosmology: high-order corrections

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

Zhu, Tao; Wang, Anzhong; Wu, Qiang

2015-10-01

Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using the third-order uniform asymptotic approximations, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratiomore » is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are ∼< 0.15%, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.« 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

Tensor hypercontraction. II. Least-squares renormalization

NASA Astrophysics Data System (ADS)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Tensor hypercontraction. II. Least-squares renormalization.

PubMed

Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

2012-12-14

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1∕r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N(5)) effort if exact integrals are decomposed, or O(N(4)) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N(4)) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

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

NASA Astrophysics Data System (ADS)

Pazner, Will; Persson, Per-Olof

2018-02-01

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

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

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

Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn; Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn; Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate newmore » cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required. - Highlights: • Higher-order cubature points for degrees 7 to 9 are developed. • The effects of quadrature rule on the mass and stiffness matrices has been conducted. • The cubature points have always positive integration weights. • Freeing from the inversion of a wide bandwidth mass matrix. • The accuracy of the TSEM has been improved in about one order of magnitude.« less

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1983-01-01

The technical progress of researches on alternatives for jet engine control, is reported. The principal new activities involved the initial testing of an input design method for choosing the inputs to a non-linear system to aid the approximation of its tensor parameters, and the beginning of order reduction studies designed to remove unnecessary monomials from tensor models.

Tensorial analysis of Eshelby stresses in 3D supercooled liquids

NASA Astrophysics Data System (ADS)

Lemaître, Anaël

2015-10-01

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

Generalization of Einstein's gravitational field equations

NASA Astrophysics Data System (ADS)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization.

PubMed

Sun, Yanfeng; Gao, Junbin; Hong, Xia; Mishra, Bamdev; Yin, Baocai

2016-03-01

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

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

Low-rank factorization of electron integral tensors and its application in electronic structure theory

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

Peng, Bo; Kowalski, Karol

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doublesmore » (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.« less

Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from Deuterium

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

Z.-L. Zhou; M. Bouwhuis; M. Ferro-Luzzi

1999-01-01

We report on a first measurement of tensor analyzing powers in quasi-elastic electron-deuteron scattering at an average three-momentum transfer of 1.7 fm{sup -1}. Data sensitive to the spin-dependent nucleon density in the deuteron were obtained for missing momenta up to 150 MeV/c with a tensor polarized {sup 2}H target internal to an electron storage ring. The data are well described by a calculation that includes the effects of final-state interaction, meson-exchange and isobar currents, and leading-order relativistic contributions.

Production of a tensor glueball in the reaction γγ → G2π0 at large momentum transfer

NASA Astrophysics Data System (ADS)

Kivel, N.; Vanderhaeghen, M.

2018-06-01

We study the production of a tensor glueball in the reaction γγ →G2π0. We compute the cross section at higher momentum transfer using the collinear factorisation approach. We find that for a value of the tensor gluon coupling of fgT ∼ 100 MeV, the cross section can be measured in the near future by the Belle II experiment.

Ostrogradsky in theories with multiple fields

NASA Astrophysics Data System (ADS)

de Rham, Claudia; Matas, Andrew

2016-06-01

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

Extension of relativistic dissipative hydrodynamics to third order

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

El, Andrej; Xu Zhe; Greiner, Carsten

2010-04-15

Following the procedure introduced by Israel and Stewart, we expand the entropy current up to the third order in the shear stress tensor pi{sup a}lpha{sup b}eta and derive a novel third-order evolution equation for pi{sup a}lpha{sup b}eta. This equation is solved for the one-dimensional Bjorken boost-invariant expansion. The scaling solutions for various values of the shear viscosity to the entropy density ratio eta/s are shown to be in very good agreement with those obtained from kinetic transport calculations. For the pressure isotropy starting with 1 at tau{sub 0}=0.4 fm/c, the third-order corrections to Israel-Stewart theory are approximately 10% for eta/s=0.2more » and more than a factor of 2 for eta/s=3. We also estimate all higher-order corrections to Israel-Stewart theory and demonstrate their importance in describing highly viscous matters.« less

Symmetry breaking in tensor models

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2015-11-01

In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical point corresponds to a phase transition in the tensor model associated to a breaking of the unitary symmetry. We analyze the model in the two phases and prove that, in a double scaling limit, the symmetric phase corresponds to a theory of infinitely refined random surfaces, while the broken phase corresponds to a theory of infinitely refined random nodal surfaces. At leading order in the double scaling limit planar surfaces dominate in the symmetric phase, and planar nodal surfaces dominate in the broken phase.

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.

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.

Tensor contraction engine: Abstraction and automated parallel implementation of configuration-interaction, coupled-cluster, and many-body perturbation theories

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

Hirata, So

2003-11-20

We develop a symbolic manipulation program and program generator (Tensor Contraction Engine or TCE) that automatically derives the working equations of a well-defined model of second-quantized many-electron theories and synthesizes efficient parallel computer programs on the basis of these equations. Provided an ansatz of a many-electron theory model, TCE performs valid contractions of creation and annihilation operators according to Wick's theorem, consolidates identical terms, and reduces the expressions into the form of multiple tensor contractions acted by permutation operators. Subsequently, it determines the binary contraction order for each multiple tensor contraction with the minimal operation and memory cost, factorizes commonmore » binary contractions (defines intermediate tensors), and identifies reusable intermediates. The resulting ordered list of binary tensor contractions, additions, and index permutations is translated into an optimized program that is combined with the NWChem and UTChem computational chemistry software packages. The programs synthesized by TCE take advantage of spin symmetry, Abelian point-group symmetry, and index permutation symmetry at every stage of calculations to minimize the number of arithmetic operations and storage requirement, adjust the peak local memory usage by index range tiling, and support parallel I/O interfaces and dynamic load balancing for parallel executions. We demonstrate the utility of TCE through automatic derivation and implementation of parallel programs for various models of configuration-interaction theory (CISD, CISDT, CISDTQ), many-body perturbation theory [MBPT(2), MBPT(3), MBPT(4)], and coupled-cluster theory (LCCD, CCD, LCCSD, CCSD, QCISD, CCSDT, and CCSDTQ).« less

Multidimensional Compressed Sensing MRI Using Tensor Decomposition-Based Sparsifying Transform

PubMed Central

Yu, Yeyang; Jin, Jin; Liu, Feng; Crozier, Stuart

2014-01-01

Compressed Sensing (CS) has been applied in dynamic Magnetic Resonance Imaging (MRI) to accelerate the data acquisition without noticeably degrading the spatial-temporal resolution. A suitable sparsity basis is one of the key components to successful CS applications. Conventionally, a multidimensional dataset in dynamic MRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the image sparsity. Traditional methods typically sparsify the spatial and temporal information independently. In this work, we propose a novel concept of tensor sparsity for the application of CS in dynamic MRI, and present the Higher-order Singular Value Decomposition (HOSVD) as a practical example. Applications presented in the three- and four-dimensional MRI data demonstrate that HOSVD simultaneously exploited the correlations within spatial and temporal dimensions. Validations based on cardiac datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods and, outperformed the conventional sparse recovery methods. PMID:24901331

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

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

Davesne, D.; Becker, P., E-mail: pbecker@ipnl.in2p3.fr; Pastore, A.

2016-12-15

We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin–orbit terms from the spin–isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin–orbit ofmore » the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.« less

Simulations of anti-parallel reconnection using a nonlocal heat flux closure

DOE PAGES

Ng, Jonathan; Hakim, Ammar; Bhattacharjee, A.; ...

2017-08-08

The integration of kinetic effects in fluid models is important for global simulations of the Earth's magnetosphere. In particular, it has been shown that ion kinetics play a crucial role in the dynamics of large reconnecting systems, and that higher-order fluid moment models can account for some of these effects. Here, we use a ten-moment model for electrons and ions, which includes the off diagonal elements of the pressure tensor that are important for magnetic reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework. Moreover, the closure ismore » tested using the island coalescence problem, which is sensitive to ion dynamics. We also demonstrate that the nonlocal closure is able to self-consistently reproduce the structure of the ion diffusion region, pressure tensor, and ion velocity without the need for fine-tuning of relaxation coefficients present in earlier models.« less

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

Embedded Systems and TensorFlow Frameworks as Assistive Technology Solutions.

PubMed

Mulfari, Davide; Palla, Alessandro; Fanucci, Luca

2017-01-01

In the field of deep learning, this paper presents the design of a wearable computer vision system for visually impaired users. The Assistive Technology solution exploits a powerful single board computer and smart glasses with a camera in order to allow its user to explore the objects within his surrounding environment, while it employs Google TensorFlow machine learning framework in order to real time classify the acquired stills. Therefore the proposed aid can increase the awareness of the explored environment and it interacts with its user by means of audio messages.

Unbound motion on a Schwarzschild background: Practical approaches to frequency domain computations

NASA Astrophysics Data System (ADS)

Hopper, Seth

2018-03-01

Gravitational perturbations due to a point particle moving on a static black hole background are naturally described in Regge-Wheeler gauge. The first-order field equations reduce to a single master wave equation for each radiative mode. The master function satisfying this wave equation is a linear combination of the metric perturbation amplitudes with a source term arising from the stress-energy tensor of the point particle. The original master functions were found by Regge and Wheeler (odd parity) and Zerilli (even parity). Subsequent work by Moncrief and then Cunningham, Price and Moncrief introduced new master variables which allow time domain reconstruction of the metric perturbation amplitudes. Here, I explore the relationship between these different functions and develop a general procedure for deriving new higher-order master functions from ones already known. The benefit of higher-order functions is that their source terms always converge faster at large distance than their lower-order counterparts. This makes for a dramatic improvement in both the speed and accuracy of frequency domain codes when analyzing unbound motion.

Palatini versus metric formulation in higher-curvature gravity

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

Borunda, Monica; Janssen, Bert; Bastero-Gil, Mar, E-mail: mborunda@ugr.es, E-mail: bjanssen@ugr.es, E-mail: mbg@ugr.es

2008-11-15

We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an ansatz, the Palatini formalism is contained within the metric formalism, in the sense that any solution ofmore » the former also appears as a solution of the latter, but not necessarily the other way around. Finally we give the conditions the solutions of the metric equations should satisfy in order to solve the Palatini equations.« less

Interacting spin-2 fields in the Stückelberg picture

NASA Astrophysics Data System (ADS)

Noller, Johannes; Scargill, James H. C.; Ferreira, Pedro G.

2014-02-01

We revisit and extend the `Effective field theory for massive gravitons' constructed by Arkani-Hamed, Georgi and Schwartz in the light of recent progress in constructing ghost-free theories with multiple interacting spin-2 fields. We show that there exist several dual ways of restoring gauge invariance in such multi-gravity theories, find a generalised Fierz-Pauli tuning condition relevant in this context and highlight subtleties in demixing tensor and scalar modes. The generic multi-gravity feature of scalar mixing and its consequences for higher order interactions are discussed. In particular we show how the decoupling limit is qualitatively changed in theories of interacting spin-2 fields. We relate this to dRGT (de Rham, Gabadadze, Tolley) massive gravity, Hassan-Rosen bigravity and the multi-gravity constructions by Hinterbichler and Rosen. As an additional application we show that EBI (Eddington-Born-Infeld) bigravity and higher order generalisations thereof possess ghost-like instabilities.

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

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Suyama, Teruaki; Kobayashi, Tsutomu

2016-03-01

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

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State

NASA Astrophysics Data System (ADS)

Boettcher, Igor; Herbut, Igor F.

2018-02-01

We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d -wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg-Landau free energy and apply these concepts to the case of an isotropic band touching point. For a vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features line nodes in the excitation spectrum of quasiparticles. In contrast to the theory of real tensor order in liquid crystals, however, the ground state is selected here by the sextic terms in the free energy. At a finite chemical potential, the nematic state has an additional instability at weak coupling and low temperatures. In particular, the one-loop coefficients in the free energy indicate that at weak coupling genuinely complex orders, which break time-reversal symmetry, are energetically favored. We relate our analysis to recent measurements in the half-Heusler compound YPtBi and discuss the role of cubic crystal symmetry.

Mechanisms of the Third-Order Nonlinear Optical Response in Dye-Doped Polymers.

NASA Astrophysics Data System (ADS)

Poga, Constantina

Quadratic Electroabsorption is applied to thin -film solid solutions of squarylium dye molecules in poly(methyl methacrylate) polymer to study the mechanisms in the third order nonlinear optical susceptibility. The data are interpreted with the help of a generalized quadratic electrooptic response theory that includes both electronic and hindered molecular motion mechanisms. This theory predicts the tensor ratio of two independent third order susceptibility tensor components, chi_sp{3333}{(3)}/ chi_sp{1133}{(3)}, whose value distinctly characterizes the relative contribution of each mechanism. Although thickness change mechanisms have not been included in this theory, their effect on the tensor ratio chi_sp{3333 }{(3)}/chi_sp{1133} {(3)} has been taken into account for both electrostriction and electrode attraction mechanisms. We measure the tensor ratio with quadratic electroabsorption spectroscopy as a function of temperature and wavelength and find that the response is predominantly electronic at temperatures below the glass transition temperature, but at temperatures higher than the glass transition temperature both reorientational and thickness changes effects play a dominant role. In particular, the contribution of each mechanism has been found for all wavelengths in the visible and the dominant thickness change mechanism has been identified to be electrode attraction. Additionally, the real part of the third-order nonlinear susceptibility can be found through a Kramers-Kronig transformation of the experimentally measured imaginary part. The knowledge of both the real and imaginary part in the visible allows the calculation of the two-photon figure of merit (defined as the real over the imaginary part of chi^{(3) }) which is necessary for determining a material's suitability for all-optical devices. Furthermore, quadratic electroabsorption can be used to characterize the nature of the excited states which in turn can be used to understand the source of the electronic response. For the ISQ chromophore, a one-photon state (at 657nm) and a two-photon state (at 596nm) have been found, and a three-level fit based on these states has been successful in predicting the low temperature chi^{(3)}^ectrum. Quadratic electroabsorption has been proven to be a versatile tool to study the mechanisms of the third -order nonlinear optical response, to measure the electronic gamma, to study the symmetry of the excited states of a molecule and to characterize the suitability of a material for all-optical devices. In this chapter, we start by calculating the change in the imaginary part of the refractive index under the application of an electric field and proceed with connecting this change with the quantities that are experimentally measured by the quadratic electroabsorption experiment. The sample preparation and the data collection are also described.

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

Durrer, Ruth; Tansella, Vittorio, E-mail: ruth.durrer@unige.ch, E-mail: vittorio.tansella@unige.ch

We derive the contribution to relativistic galaxy number count fluctuations from vector and tensor perturbations within linear perturbation theory. Our result is consistent with the the relativistic corrections to number counts due to scalar perturbation, where the Bardeen potentials are replaced with line-of-sight projection of vector and tensor quantities. Since vector and tensor perturbations do not lead to density fluctuations the standard density term in the number counts is absent. We apply our results to vector perturbations which are induced from scalar perturbations at second order and give numerical estimates of their contributions to the power spectrum of relativistic galaxymore » number counts.« less

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.

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

Vector and tensor contributions to the curvature perturbation at second order

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

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

2016-02-01

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

Anisotropic rheology of a polycrystalline aggregate and convection in planetary mantles

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm

NASA Astrophysics Data System (ADS)

Nakatani, Naoki; Chan, Garnet Kin-Lic

2013-04-01

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

Ostrogradsky in theories with multiple fields

DOE PAGES

de Rham, Claudia; Matas, Andrew

2016-06-23

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

Ostrogradsky in theories with multiple fields

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

de Rham, Claudia; Matas, Andrew

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

Second-order closure models for supersonic turbulent flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu

1991-01-01

Recent work by the authors on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulence closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equation are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging.

Second-order closure models for supersonic turbulent flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu

1991-01-01

Recent work on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulent closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equations are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging.

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

NASA Astrophysics Data System (ADS)

Brandenburg, John

2012-10-01

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

Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory

NASA Astrophysics Data System (ADS)

Hohm, Olaf; Wang, Yi-Nan

2015-04-01

We construct exceptional field theory for the duality group SL(3) × SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the (3, 2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full D = 11 or type IIB supergravity, respectively.

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

NASA Astrophysics Data System (ADS)

Becattini, F.; Grossi, E.

2015-08-01

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

General Wahlquist metrics in all dimensions

NASA Astrophysics Data System (ADS)

Hinoue, Kazuki; Houri, Tsuyoshi; Rugina, Christina; Yasui, Yukinori

2014-07-01

It is shown that the Wahlquist metric, which is a stationary, axially symmetric perfect fluid solution with ρ +3p=const, admits a rank-2 generalized closed conformal Killing-Yano tensor with a skew-symmetric torsion. Taking advantage of the presence of such a tensor, we obtain a higher-dimensional generalization of the Wahlquist metric in arbitrary dimensions, including a family of vacuum black hole solutions with spherical horizon topology such as Schwarzschild-Tangherlini, Myers-Perry and higher-dimensional Kerr-NUT-(A)dS metrics and a family of static, spherically symmetric perfect fluid solutions in higher dimensions.

Promote quantitative ischemia imaging via myocardial perfusion CT iterative reconstruction with tensor total generalized variation regularization

NASA Astrophysics Data System (ADS)

Gu, Chengwei; Zeng, Dong; Lin, Jiahui; Li, Sui; He, Ji; Zhang, Hao; Bian, Zhaoying; Niu, Shanzhou; Zhang, Zhang; Huang, Jing; Chen, Bo; Zhao, Dazhe; Chen, Wufan; Ma, Jianhua

2018-06-01

Myocardial perfusion computed tomography (MPCT) imaging is commonly used to detect myocardial ischemia quantitatively. A limitation in MPCT is that an additional radiation dose is required compared to unenhanced CT due to its repeated dynamic data acquisition. Meanwhile, noise and streak artifacts in low-dose cases are the main factors that degrade the accuracy of quantifying myocardial ischemia and hamper the diagnostic utility of the filtered backprojection reconstructed MPCT images. Moreover, it is noted that the MPCT images are composed of a series of 2/3D images, which can be naturally regarded as a 3/4-order tensor, and the MPCT images are globally correlated along time and are sparse across space. To obtain higher fidelity ischemia from low-dose MPCT acquisitions quantitatively, we propose a robust statistical iterative MPCT image reconstruction algorithm by incorporating tensor total generalized variation (TTGV) regularization into a penalized weighted least-squares framework. Specifically, the TTGV regularization fuses the spatial correlation of the myocardial structure and the temporal continuation of the contrast agent intake during the perfusion. Then, an efficient iterative strategy is developed for the objective function optimization. Comprehensive evaluations have been conducted on a digital XCAT phantom and a preclinical porcine dataset regarding the accuracy of the reconstructed MPCT images, the quantitative differentiation of ischemia and the algorithm’s robustness and efficiency.

Separability of massive field equations for spin-0 and spin-1/2 charged particles in the general nonextremal rotating charged black hole spacetimes in minimal five-dimensional gauged supergravity

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

Wu Shuangqing

We continue to investigate the separability of massive field equations for spin-0 and spin-1/2 charged particles in the general, nonextremal, rotating, charged, Chong-Cvetic-Lue-Pope black holes with two independent angular momenta and a nonzero cosmological constant in minimal D=5 gauged supergravity theory. We show that the complex Klein-Gordon equation and the modified Dirac equation with the inclusion of an extra counterterm can be separated by variables into purely radial and purely angular parts in this general Einstein-Maxwell-Chern-Simons background spacetime. A second-order symmetry operator that commutes with the complex Laplacian operator is constructed from the separated solutions and expressed compactly in termsmore » of a rank-2 Staeckel-Killing tensor which admits a simple diagonal form in the chosen pentad one-forms so that it can be understood as the square of a rank-3 totally antisymmetric tensor. A first-order symmetry operator that commutes with the modified Dirac operator is expressed in terms of a rank-3 generalized Killing-Yano tensor and its covariant derivative. The Hodge dual of this generalized Killing-Yano tensor is a generalized principal conformal Killing-Yano tensor of rank-2, which can generate a 'tower' of generalized (conformal) Killing-Yano and Staeckel-Killing tensors that are responsible for the whole hidden symmetries of this general, rotating, charged, Kerr-anti-de Sitter black hole geometry. In addition, the first laws of black hole thermodynamics have been generalized to the case that the cosmological constant can be viewed as a thermodynamical variable.« less

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

Frusciante, Noemi; Papadomanolakis, Georgios; Silvestri, Alessandra, E-mail: fruscian@iap.fr, E-mail: papadomanolakis@lorentz.leidenuniv.nl, E-mail: silvestri@lorentz.leidenuniv.nl

We present a generalization of the effective field theory (EFT) formalism for dark energy and modified gravity models to include operators with higher order spatial derivatives. This allows the extension of the EFT framework to a wider class of gravity theories such as Hořava gravity. We present the corresponding extended action, both in the EFT and the Arnowitt-Deser-Misner (ADM) formalism, and proceed to work out a convenient mapping between the two, providing a self contained and general procedure to translate a given model of gravity into the EFT language at the basis of the Einstein-Boltzmann solver EFTCAMB. Putting this mappingmore » at work, we illustrate, for several interesting models of dark energy and modified gravity, how to express them in the ADM notation and then map them into the EFT formalism. We also provide for the first time, the full mapping of GLPV models into the EFT framework. We next perform a thorough analysis of the physical stability of the generalized EFT action, in absence of matter components. We work out viability conditions that correspond to the absence of ghosts and modes that propagate with a negative speed of sound in the scalar and tensor sector, as well as the absence of tachyonic modes in the scalar sector. Finally, we extend and generalize the phenomenological basis in terms of α-functions introduced to parametrize Horndeski models, to cover all theories with higher order spatial derivatives included in our extended action. We elaborate on the impact of the additional functions on physical quantities, such as the kinetic term and the speeds of propagation for scalar and tensor modes.« less

The Role of Standardized and Study-specific Human Brain Diffusion Tensor Templates in Inter-subject Spatial Normalization

PubMed Central

Zhang, Shengwei; Arfanakis, Konstantinos

2012-01-01

Purpose To investigate the effect of standardized and study-specific human brain diffusion tensor templates on the accuracy of spatial normalization, without ignoring the important roles of data quality and registration algorithm effectiveness. Materials and Methods Two groups of diffusion tensor imaging (DTI) datasets, with and without visible artifacts, were normalized to two standardized diffusion tensor templates (IIT2, ICBM81) as well as study-specific templates, using three registration approaches. The accuracy of inter-subject spatial normalization was compared across templates, using the most effective registration technique for each template and group of data. Results It was demonstrated that, for DTI data with visible artifacts, the study-specific template resulted in significantly higher spatial normalization accuracy than standardized templates. However, for data without visible artifacts, the study-specific template and the standardized template of higher quality (IIT2) resulted in similar normalization accuracy. Conclusion For DTI data with visible artifacts, a carefully constructed study-specific template may achieve higher normalization accuracy than that of standardized templates. However, as DTI data quality improves, a high-quality standardized template may be more advantageous than a study-specific template, since in addition to high normalization accuracy, it provides a standard reference across studies, as well as automated localization/segmentation when accompanied by anatomical labels. PMID:23034880

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Renormalization group analysis of the Reynolds stress transport equation

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Barton, J. M.

1992-01-01

The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

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.

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

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.

Gravitational waves and large field inflation

NASA Astrophysics Data System (ADS)

Linde, Andrei

2017-02-01

According to the famous Lyth bound, one can confirm large field inflation by finding tensor modes with sufficiently large tensor-to-scalar ratio r. Here we will try to answer two related questions: is it possible to rule out all large field inflationary models by not finding tensor modes with r above some critical value, and what can we say about the scale of inflation by measuring r? However, in order to answer these questions one should distinguish between two different definitions of the large field inflation and three different definitions of the scale of inflation. We will examine these issues using the theory of cosmological α-attractors as a convenient testing ground.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Diffusion weighted imaging for the differentiation of breast tumors: From apparent diffusion coefficient to high order diffusion tensor imaging.

PubMed

Teruel, Jose R; Goa, Pål E; Sjøbakk, Torill E; Østlie, Agnes; Fjøsne, Hans E; Bathen, Tone F

2016-05-01

To compare "standard" diffusion weighted imaging, and diffusion tensor imaging (DTI) of 2(nd) and 4(th) -order for the differentiation of malignant and benign breast lesions. Seventy-one patients were imaged at 3 Tesla with a 16-channel breast coil. A diffusion weighted MRI sequence including b = 0 and b = 700 in 30 directions was obtained for all patients. The image data were fitted to three different diffusion models: isotropic model - apparent diffusion coefficient (ADC), 2(nd) -order tensor model (the standard model used for DTI) and a 4(th) -order tensor model, with increased degrees of freedom to describe anisotropy. The ability of the fitted parameters in the different models to differentiate between malignant and benign tumors was analyzed. Seventy-two breast lesions were analyzed, out of which 38 corresponded to malignant and 34 to benign tumors. ADC (using any model) presented the highest discriminative ability of malignant from benign tumors with a receiver operating characteristic area under the curve (AUC) of 0.968, and sensitivity and specificity of 94.1% and 94.7% respectively for a 1.33 × 10(-3) mm(2) /s cutoff. Anisotropy measurements presented high statistical significance between malignant and benign tumors (P < 0.001), but with lower discriminative ability of malignant from benign tumors than ADC (AUC of 0.896 and 0.897 for fractional anisotropy and generalized anisotropy respectively). Statistical significant difference was found between generalized anisotropy and fractional anisotropy for cancers (P < 0.001) but not for benign lesions (P = 0.87). While anisotropy parameters have the potential to provide additional value for breast applications as demonstrated in this study, ADC exhibited the highest differentiation power between malignant and benign breast tumors. © 2015 Wiley Periodicals, Inc.

Observable cosmological vector mode in the dark ages

NASA Astrophysics Data System (ADS)

Saga, Shohei

2016-09-01

The second-order vector mode is inevitably induced from the coupling of first-order scalar modes in cosmological perturbation theory and might hinder a possible detection of primordial gravitational waves from inflation through 21 cm lensing observations. Here, we investigate the weak lensing signal in 21 cm photons emitted by neutral hydrogen atoms in the dark ages induced by the second-order vector mode by decomposing the deflection angle of the 21 cm lensing signal into the gradient and curl modes. The curl mode is a good tracer of the cosmological vector and tensor modes since the scalar mode does not induce the curl one. By comparing angular power spectra of the 21 cm lensing curl mode induced by the second-order vector mode and primordial gravitational waves whose amplitude is parametrized by the tensor-to-scalar ratio r , we find that the 21 cm curl mode from the second-order vector mode dominates over that from primordial gravitational waves on almost all scales if r ≲10-5. If we use the multipoles of the power spectrum up to ℓmax=1 05 and 1 06 in reconstructing the curl mode from 21 cm temperature maps, the signal-to-noise ratios of the 21 cm curl mode from the second-order vector mode achieve S /N ≈0.46 and 73, respectively. Observation of 21 cm radiation is, in principle, a powerful tool to explore not only the tensor mode but also the cosmological vector mode.

Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains

NASA Astrophysics Data System (ADS)

Zhao, Yan; Stratt, Richard M.

2018-05-01

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.

Gravitational Lagrangians, Mach's Principle, and the Equivalence Principle in an Expanding Universe

NASA Astrophysics Data System (ADS)

Essén, Hanno

2014-08-01

Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach's principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.

The Zeldovich & Adhesion approximations and applications to the local universe

NASA Astrophysics Data System (ADS)

Hidding, Johan; van de Weygaert, Rien; Shandarin, Sergei

2016-10-01

The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A 3 lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe.

Gaugeon formalism for the second-rank antisymmetric tensor gauge fields

NASA Astrophysics Data System (ADS)

Aochi, Masataka; Endo, Ryusuke; Miura, Hikaru

2018-02-01

We present a BRST symmetric gaugeon formalism for the second-rank antisymmetric tensor gauge fields. A set of vector gaugeon fields is introduced as a quantum gauge freedom. One of the gaugeon fields satisfies a higher-derivative field equation; this property is necessary to change the gauge-fixing parameter of the antisymmetric tensor gauge field. A naive Lagrangian for the vector gaugeon fields is itself invariant under a gauge transformation for the vector gaugeon field. The Lagrangian of our theory includes the gauge-fixing terms for the gaugeon fields and corresponding Faddeev-Popov ghost terms.

Extended effective field theory of inflation

NASA Astrophysics Data System (ADS)

Ashoorioon, Amjad; Casadio, Roberto; Cicoli, Michele; Geshnizjani, Ghazal; Kim, Hyung J.

2018-02-01

We present a general framework where the effective field theory of single field inflation is extended by the inclusion of operators with mass dimension 3 and 4 in the unitary gauge. These higher dimensional operators introduce quartic and sextic corrections to the dispersion relation. We study the regime of validity of this extended effective field theory of inflation and the effect of these higher dimensional operators on CMB observables associated with scalar perturbations, such as the speed of sound, the amplitude of the power spectrum and the tensor-to-scalar ratio. Tensor perturbations remain instead, unaltered.

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 .

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…

Interaction of non-Abelian tensor gauge fields

NASA Astrophysics Data System (ADS)

Savvidy, George

2018-01-01

The non-Abelian tensor gauge fields take value in extended Poincaré algebra. In order to define the invariant Lagrangian we introduce a vector variable in two alternative ways: through the transversal representation of the extended Poincaré algebra and through the path integral over the auxiliary vector field with the U(1) Abelian action. We demonstrate that this allows to fix the unitary gauge and derive scattering amplitudes in spinor representation.

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.

Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models.

PubMed

Azeyanagi, Tatsuo; Ferrari, Frank; Massolo, Fidel I Schaposnik

2018-02-09

We study the Schwinger-Dyson equations of a fermionic planar matrix quantum mechanics [or tensor and Sachdev-Ye-Kitaev (SYK) models] at leading melonic order. We find two solutions describing a high entropy, SYK black-hole-like phase and a low entropy one with trivial IR behavior. There is a line of first order phase transitions that terminates at a new critical point. Critical exponents are nonmean field and differ on the two sides of the transition. Interesting phenomena are also found in unstable and stable bosonic models, including Kazakov critical points and inconsistency of SYK-like solutions of the IR limit.

Measurement of third-order nonlinear susceptibility tensor in InP using extended Z-scan technique with elliptical polarization

NASA Astrophysics Data System (ADS)

Oishi, Masaki; Shinozaki, Tomohisa; Hara, Hikaru; Yamamoto, Kazunuki; Matsusue, Toshio; Bando, Hiroyuki

2018-05-01

The elliptical polarization dependence of the two-photon absorption coefficient β in InP has been measured by the extended Z-scan technique for thick materials in the wavelength range from 1640 to 1800 nm. The analytical formula of the Z-scan technique has been extended with consideration of multiple reflections. The Z-scan results have been fitted very well by the formula and β has been evaluated accurately. The three independent elements of the third-order nonlinear susceptibility tensor in InP have also been determined accurately from the elliptical polarization dependence of β.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

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

Tensor non-Gaussianity from axion-gauge-fields dynamics: parameter search

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Fujita, Tomohiro; Komatsu, Eiichiro

2018-06-01

We calculate the bispectrum of scale-invariant tensor modes sourced by spectator SU(2) gauge fields during inflation in a model containing a scalar inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is generated in this model at tree-level as the gauge fields contain a tensor degree of freedom, and its production is dominated by self-coupling of the gauge fields. This is a unique feature of non-Abelian gauge theory. The shape of the tensor bispectrum is approximately an equilateral shape for 3lesssim mQlesssim 4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/P2h, is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions.

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

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

Structural differences in interictal migraine attack after epilepsy: A diffusion tensor imaging analysis.

PubMed

Huang, Qi; Lv, Xin; He, Yushuang; Wei, Xing; Ma, Meigang; Liao, Yuhan; Qin, Chao; Wu, Yuan

2017-12-01

Patients with epilepsy (PWE) are more likely to suffer from migraine attack, and aberrant white matter (WM) organization may be the mechanism underlying this phenomenon. This study aimed to use diffusion tensor imaging (DTI) technique to quantify WM structural differences in PWE with interictal migraine. Diffusion tensor imaging data were acquired in 13 PWE with migraine and 12 PWE without migraine. Diffusion metrics were analyzed using tract-atlas-based spatial statistics analysis. Atlas-based and tract-based spatial statistical analyses were conducted for robustness analysis. Correlation was explored between altered DTI metrics and clinical parameters. The main results are as follows: (i) Axonal damage plays a key role in PWE with interictal migraine. (ii) Significant diffusing alterations included higher fractional anisotropy (FA) in the fornix, higher mean diffusivity (MD) in the middle cerebellar peduncle (CP), left superior CP, and right uncinate fasciculus, and higher axial diffusivity (AD) in the middle CP and right medial lemniscus. (iii) Diffusion tensor imaging metrics has the tendency of correlation with seizure/migraine type and duration. Results indicate that characteristic structural impairments exist in PWE with interictal migraine. Epilepsy may contribute to migraine by altering WMs in the brain stem. White matter tracts in the fornix and right uncinate fasciculus also mediate migraine after epilepsy. This finding may improve our understanding of the pathological mechanisms underlying migraine attack after epilepsy. Copyright © 2017 Elsevier Inc. All rights reserved.

The hidden flat like universe. Starobinsky-like inflation induced by f (T) gravity

NASA Astrophysics Data System (ADS)

El Hanafy, W.; Nashed, G. G. L.

2015-06-01

We study a single-fluid component in a flat like universe (FLU) governed by f( T) gravity theories, where T is the teleparallel torsion scalar. The FLU model, regardless of the value of the spatial curvature k, identifies a special class of f( T) gravity theories. Remarkably, FLU f( T) gravity does not reduce to teleparallel gravity theory. In large Hubble spacetime the theory is consistent with the inflationary universe scenario and respects the conservation principle. The equation of state evolves similarly in all models . We study the case when the torsion tensor consists of a scalar field, which enables to derive a quintessence potential from the obtained f( T) gravity theory. The potential produces Starobinsky-like model naturally without using a conformal transformation, with higher orders continuously interpolate between Starobinsky and quadratic inflation models. The slow-roll analysis shows double solutions, so that for a single value of the scalar tilt (spectral index) the theory can predict double tensor-to-scalar ratios r of E-mode and B-mode polarizations.

Learning to represent spatial transformations with factored higher-order Boltzmann machines.

PubMed

Memisevic, Roland; Hinton, Geoffrey E

2010-06-01

To allow the hidden units of a restricted Boltzmann machine to model the transformation between two successive images, Memisevic and Hinton (2007) introduced three-way multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned, symmetric weight between a pixel in the second image and a hidden unit. This creates cubically many parameters, which form a three-dimensional interaction tensor. We describe a low-rank approximation to this interaction tensor that uses a sum of factors, each of which is a three-way outer product. This approximation allows efficient learning of transformations between larger image patches. Since each factor can be viewed as an image filter, the model as a whole learns optimal filter pairs for efficiently representing transformations. We demonstrate the learning of optimal filter pairs from various synthetic and real image sequences. We also show how learning about image transformations allows the model to perform a simple visual analogy task, and we show how a completely unsupervised network trained on transformations perceives multiple motions of transparent dot patterns in the same way as humans.

Differentiation of fibroblastic meningiomas from other benign subtypes using diffusion tensor imaging.

PubMed

Tropine, Andrei; Dellani, Paulo D; Glaser, Martin; Bohl, Juergen; Plöner, Till; Vucurevic, Goran; Perneczky, Axel; Stoeter, Peter

2007-04-01

To differentiate fibroblastic meningiomas, usually considered to be of a hard consistency, from other benign subtypes using diffusion tensor imaging (DTI). From DTI data sets of 30 patients with benign meningiomas, we calculated diffusion tensors and mean diffusivity (MD) and fractional anisotropy (FA) maps as well as barycentric maps representing the geometrical shape of the tensors. The findings were compared to postoperative histology. The study was approved by the local ethics committee, and informed consent was given by the patients. According to one-way analysis of variance (ANOVA), FA was the best parameter to differentiate between the subtypes (F=32.2; p<0.0001). Regarding tensor shape, endothelial meningiomas were represented by spherical tensors (80%) corresponding to isotropic diffusion, whereas the fibroblastic meningiomas showed a high percentage (43%) of nonspherical tensors, indicating planar or longitudinal diffusion. The difference was highly significant (F=28.4; p<0.0001) and may be due to the fascicular arrangement of long spindle-shaped tumor cells and the high content of intra- and interfascicular fibers as shown in the histology. In addition, a capsule-like rim of the in-plane diffusion surrounded most meningiomas irrespective of their histological type. If these results correlate to the intraoperative findings of meningioma consistency, DTI-based measurement of FA and analysis of the shape of the diffusion tensor is a promising method to differentiate between fibroblastic and other subtypes of benign meningiomas in order to get information about their "hard" or "soft" consistency prior to removal. Copyright (c) 2007 Wiley-Liss, Inc.

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.

Einsteinian cubic gravity

NASA Astrophysics Data System (ADS)

Bueno, Pablo; Cano, Pablo A.

2016-11-01

We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives with respect to one of those parameters. We use our method to construct a D -dimensional cubic theory of gravity which satisfies the following properties: (1) it shares the spectrum of Einstein gravity, i.e., it only propagates a transverse and massless graviton on a maximally symmetric background; (2) it is defined in the same way in general dimensions; (3) it is neither trivial nor topological in four dimensions. Up to cubic order in curvature, the only previously known theories satisfying the first two requirements are the Lovelock ones. We show that, up to cubic order, there exists only one additional theory satisfying requirements (1) and (2). Interestingly, this theory is, along with Einstein gravity, the only one which also satisfies (3).

Spherical tensor analysis of polar liquid crystals with biaxial and chiral molecules

NASA Astrophysics Data System (ADS)

Iwamoto, Mitsumasa; Zhong-can, Ou-Yang

2012-11-01

With the help of spherical tensor expression, an irreducible calculus of a Lth-rank macroscopic susceptibility χ for a polar liquid crystal (PLC) of biaxial and chiral molecules written as the average of molecular hyperpolarizability tensor β associated with their spherical orientational order parameters (0⩽l⩽L) is presented. Comprehensive formulas of L=1,2 have been obtained and the latter explains the optical activity and spontaneous splay texture observed in bent-core PLC. The expression of L=3 specifies for the molecules with D2 symmetry which can be applied to analyze the nonlinear optical second harmonic generation (SHG) observed in proteins, peptides, and double-stranded DNA at interfaces.

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

NASA Astrophysics Data System (ADS)

Matyjasek, Jerzy; Sadurski, Paweł; Telecka, Małgorzata

2014-04-01

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

Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

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

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

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

Simultaneous Tensor Decomposition and Completion Using Factor Priors.

PubMed

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

2013-08-27

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

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree-Fock approximation

NASA Astrophysics Data System (ADS)

López-Quelle, M.; Marcos, S.; Niembro, R.; Savushkin, L. N.

2018-03-01

Within a nonlinear relativistic Hartree-Fock approximation combined with the BCS method, we study the effect of the nucleon-nucleon tensor force of the π-exchange potential on the spin- and pseudospin-orbit doublets along the Ca and Sn isotopic chains. We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect. Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon-nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2018-04-01

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.

Interacting spin-2 fields in the Stückelberg picture

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

Noller, Johannes; Ferreira, Pedro G.; Scargill, James H.C., E-mail: noller@physics.ox.ac.uk, E-mail: james.scargill@physics.ox.ac.uk, E-mail: p.ferreira1@physics.ox.ac.uk

2014-02-01

We revisit and extend the 'Effective field theory for massive gravitons' constructed by Arkani-Hamed, Georgi and Schwartz in the light of recent progress in constructing ghost-free theories with multiple interacting spin-2 fields. We show that there exist several dual ways of restoring gauge invariance in such multi-gravity theories, find a generalised Fierz-Pauli tuning condition relevant in this context and highlight subtleties in demixing tensor and scalar modes. The generic multi-gravity feature of scalar mixing and its consequences for higher order interactions are discussed. In particular we show how the decoupling limit is qualitatively changed in theories of interacting spin-2 fields.more » We relate this to dRGT (de Rham, Gabadadze, Tolley) massive gravity, Hassan-Rosen bigravity and the multi-gravity constructions by Hinterbichler and Rosen. As an additional application we show that EBI (Eddington-Born-Infeld) bigravity and higher order generalisations thereof possess ghost-like instabilities.« less

Global diffusion of cosmic rays in random magnetic fields

NASA Astrophysics Data System (ADS)

Snodin, A. P.; Shukurov, A.; Sarson, G. R.; Bushby, P. J.; Rodrigues, L. F. S.

2016-04-01

The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius RL and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g. there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of the order of 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 106 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10-2 ≲ RL/lc ≲ 103, where lc is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for RL/lc ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

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

DTIC Science & Technology

2007-11-08

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

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

Obtaining orthotropic elasticity tensor using entries zeroing method.

NASA Astrophysics Data System (ADS)

Gierlach, Bartosz; Danek, Tomasz

2017-04-01

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

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.

The generalized fracture criteria based on the multi-parameter representation of the crack tip stress field

NASA Astrophysics Data System (ADS)

Stepanova, L. V.

2017-12-01

The paper is devoted to the multi-parameter asymptotic description of the stress field near the crack tip of a finite crack in an infinite isotropic elastic plane medium subject to 1) tensile stress; 2) in-plane shear; 3) mixed mode loading for a wide range of mode-mixity situations (Mode I and Mode II). The multi-parameter series expansion of stress tensor components containing higher-order terms is obtained. All the coefficients of the multiparameter series expansion of the stress field are given. The main focus is on the discussion of the influence of considering the higher-order terms of the Williams expansion. The analysis of the higher-order terms in the stress field is performed. It is shown that the larger the distance from the crack tip, the more terms it is necessary to keep in the asymptotic series expansion. Therefore, it can be concluded that several more higher-order terms of the Williams expansion should be used for the stress field description when the distance from the crack tip is not small enough. The crack propagation direction angle is calculated. Two fracture criteria, the maximum tangential stress criterion and the strain energy density criterion, are used. The multi-parameter form of the two commonly used fracture criteria is introduced and tested. Thirty and more terms of the Williams series expansion for the near-crack-tip stress field enable the angle to be calculated more precisely.

Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality

NASA Astrophysics Data System (ADS)

Ciattoni, Alessandro; Rizza, Carlo

2015-05-01

We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with nonmagnetic inclusions in the long-wavelength limit, including spatial dispersion up to the second order. Specifically, by resorting to a suitable multiscale technique, we show that the effective medium permittivity tensor and the first- and second-order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly varying fields, each satisfying electrostatic-like equations within the metamaterial unit cell. For metamaterials with negligible second-order spatial dispersion, we exploit the equivalence of first-order spatial dispersion and reciprocal bianisotropic electromagnetic response to deduce a simple expression for the metamaterial chirality tensor. Such an expression allows us to systematically analyze the effect of the composite spatial symmetry properties on electromagnetic chirality. We find that even if a metamaterial is geometrically achiral, i.e., it is indistinguishable from its mirror image, it shows pseudo-chiral-omega electromagnetic chirality if the rotation needed to restore the dielectric profile after the reflection is either a 0∘ or 90∘ rotation around an axis orthogonal to the reflection plane. These two symmetric situations encompass two-dimensional and one-dimensional metamaterials with chiral response. As an example admitting full analytical description, we discuss one-dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures.

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

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.

Generalized Israel junction conditions for a fourth-order brane world

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

Balcerzak, Adam; Dabrowski, Mariusz P.

2008-01-15

We discuss a general fourth-order theory of gravity on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the higher powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, while the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to themore » field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second-order theory by introducing an extra tensor field. We formulate the appropriate junction conditions on the brane. We prove the equivalence of both theories. In particular, we prove the equivalence of the junction conditions with different assumptions related to the continuity of the metric along the brane.« less

New Views on Dark Matter from Emergent Gravity

NASA Astrophysics Data System (ADS)

Sun, Sichun; Zhang, Yun-Long

2018-01-01

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

ALLTEM Multi-Axis Electromagnetic Induction System Demonstration and Validation

DTIC Science & Technology

2012-08-01

threshold T-high higher threshold TMGS Tensor Magnetic Gradiometer System TOI target of interest Tx ALLTEM transmitter USGS U.S. Geological...the Tensor Magnetic Gradiometer System ( TMGS ) and two prototype EMI instruments, the Very Early Time-domain ElectroMagnetic (VETEM) system and the...project one prototype magnetic system, the TMGS , and two prototype EMI instruments, VETEM and the High Frequency Sounder, were evaluated. Subsequent

The Bargmann-Wigner equations in spherical space

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.; Sherry, T. N.

2006-01-01

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.

Coupling mesodomain positional ordering to intra-domain orientational ordering in block copolymer assembly

NASA Astrophysics Data System (ADS)

Burke, Christopher; Reddy, Abhiram; Prasad, Ishan; Grason, Gregory

Block copolymer (BCP) melts form a number of symmetric microphases, e.g. columnar or double gyroid phases. BCPs with a block composed of chiral monomers are observed to form bulk phases with broken chiral symmetry e.g. a phase of hexagonally ordered helical mesodomains. Other new structures may be possible, e.g. double gyroid with preferred chirality which has potential photonic applications. One approach to understanding chirality transfer from monomer to the bulk is to use self consistent field theory (SCFT) and incorporate an orientational order parameter with a preference for handed twist in chiral block segments, much like the texture of cholesteric liquid crystal. Polymer chains in achiral BCPs exhibit orientational ordering which couples to the microphase geometry; a spontaneous preference for ordering may have an effect on the geometry. The influence of a preference for chiral polar (vectorial) segment order has been studied to some extent, though the influence of coupling to chiral tensorial (nematic) order has not yet been developed. We present a computational approach using SCFT with vector and tensor order which employs well developed pseudo-spectral methods. Using this we explore how tensor order influences which structures form, and if it can promote chiral phases.

Higher groupoid bundles, higher spaces, and self-dual tensor field equations

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Sämann, Christian; Wolf, Martin

2016-08-01

We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general class of (higher) spaces comprising presentable differentiable stacks, as e.g. orbifolds. We start off with a self-contained review on simplicial sets as models of $(\\infty,1)$-categories. We then discuss principal bundles in terms of simplicial maps and their homotopies. We explain in detail a differentiation procedure, suggested by Severa, that maps higher groupoids to $L_\\infty$-algebroids. Generalising this procedure, we define connections for higher groupoid bundles. As an application, we obtain six-dimensional superconformal field theories via a Penrose-Ward transform of higher groupoid bundles over a twistor space. This construction reduces the search for non-Abelian self-dual tensor field equations in six dimensions to a search for the appropriate (higher) gauge structure. The treatment aims to be accessible to theoretical physicists.

Classical theory of radiating strings

NASA Technical Reports Server (NTRS)

Copeland, Edmund J.; Haws, D.; Hindmarsh, M.

1990-01-01

The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.

Minutia Tensor Matrix: A New Strategy for Fingerprint Matching

PubMed Central

Fu, Xiang; Feng, Jufu

2015-01-01

Establishing correspondences between two minutia sets is a fundamental issue in fingerprint recognition. This paper proposes a new tensor matching strategy. First, the concept of minutia tensor matrix (simplified as MTM) is proposed. It describes the first-order features and second-order features of a matching pair. In the MTM, the diagonal elements indicate similarities of minutia pairs and non-diagonal elements indicate pairwise compatibilities between minutia pairs. Correct minutia pairs are likely to establish both large similarities and large compatibilities, so they form a dense sub-block. Minutia matching is then formulated as recovering the dense sub-block in the MTM. This is a new tensor matching strategy for fingerprint recognition. Second, as fingerprint images show both local rigidity and global nonlinearity, we design two different kinds of MTMs: local MTM and global MTM. Meanwhile, a two-level matching algorithm is proposed. For local matching level, the local MTM is constructed and a novel local similarity calculation strategy is proposed. It makes full use of local rigidity in fingerprints. For global matching level, the global MTM is constructed to calculate similarities of entire minutia sets. It makes full use of global compatibility in fingerprints. Proposed method has stronger description ability and better robustness to noise and nonlinearity. Experiments conducted on Fingerprint Verification Competition databases (FVC2002 and FVC2004) demonstrate the effectiveness and the efficiency. PMID:25822489

2PI effective action for the SYK model and tensor field theories

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2018-05-01

We discuss the two-particle irreducible (2PI) effective action for the SYK model and for tensor field theories. For the SYK model the 2PI effective action reproduces the bilocal reformulation of the model without using replicas. In general tensor field theories the 2PI formalism is the only way to obtain a bilocal reformulation of the theory, and as such is a precious instrument for the identification of soft modes and for possible holographic interpretations. We compute the 2PI action for several models, and push it up to fourth order in the 1 /N expansion for the model proposed by Witten in [1], uncovering a one-loop structure in terms of an auxiliary bilocal action.

Normal stress differences and beyond-Navier-Stokes hydrodynamics

NASA Astrophysics Data System (ADS)

Alam, Meheboob; Saha, Saikat

2017-06-01

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

An Ap-Structure with Finslerian Flavor II:. Torsion, Curvature and Other Objects

NASA Astrophysics Data System (ADS)

Wanas, M. I.; Kamal, Mona M.

An absolute parallelism (AP-) space having Finslerian properties is called FAP-space. This FAP-structure is wider than both conventional AP and Finsler structures. In the present work, more geometric objects as curvature and torsion tensors are derived in the context of this structure. Also second order tensors, usually needed for physical applications, are derived and studied. Furthermore, the anti-curvature and the W-tensor are defined for the FAP-structure. Relations between Riemannian, AP, Finsler and FAP structures are given. These relations facilitate comparison between results of applications carried out in the framework of these structures. We hope that the use of the FAP-structure, in applications may throw some light on some of the problems facing geometric field theories.

Electron in higher-dimensional weakly charged rotating black hole spacetimes

NASA Astrophysics Data System (ADS)

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

2013-03-01

We demonstrate separability of the Dirac equation in weakly charged rotating black hole spacetimes in all dimensions. The electromagnetic field of the black hole is described by a test field approximation, with the vector potential proportional to the primary Killing vector field. It is shown that the demonstrated separability can be intrinsically characterized by the existence of a complete set of mutually commuting first-order symmetry operators generated from the principal Killing-Yano tensor. The presented results generalize the results on integrability of charged particle motion and separability of charged scalar field studied in V. P. Frolov and P. Krtous [Phys. Rev. D 83, 024016 (2011)].

Mass-induced instability of SAdS black hole in Einstein-Ricci cubic gravity

NASA Astrophysics Data System (ADS)

Myung, Yun Soo

2018-05-01

We perform the stability analysis of Schwarzschild-AdS (SAdS) black hole in the Einstein-Ricci cubic gravity. It shows that the Ricci tensor perturbations exhibit unstable modes for small black holes. We call this the mass-induced instability of SAdS black hole because the instability of small black holes arises from the massiveness in the linearized Einstein-Ricci cubic gravity, but not a feature of higher-order derivative theory giving ghost states. Also, we point out that the correlated stability conjecture holds for the SAdS black hole by computing the Wald entropy of SAdS black hole in Einstein-Ricci cubic gravity.

Computational tools for Breakthrough Propulsion Physics: State of the art and future prospects

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2000-01-01

To address problems in Breakthrough Propulsion Physics (BPP) one needs sheer computing capabilities. This is because General Relativity and Quantum Field Theory are so mathematically sophisticated that the amount of analytical calculations is prohibitive and one can hardly do all of them by hand. In this paper we make a comparative review of the main tensor calculus capabilities of the three most advanced and commercially available ``symbolic manipulator'' codes: Macsyma, Maple V and Mathematica. We also point out that currently one faces such a variety of different conventions in tensor calculus that it is difficult or impossible to compare results obtained by different scholars in General Relativity and Quantum Field Theory. Mathematical physicists, experimental physicists and engineers have each their own way of customizing tensors, especially by using the different metric signatures, different metric determinant signs, different definitions of the basic Riemann and Ricci tensors, and by adopting different systems of physical units. This chaos greatly hampers progress toward the chief NASA BPP goal: the design of the NASA Warp Drive. It is thus concluded that NASA should put order by establishing international standards in symbolic tensor calculus and enforcing anyone working in BPP to adopt these NASA BPP Standards. .

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Topology in colored tensor models via crystallization theory

NASA Astrophysics Data System (ADS)

Casali, Maria Rita; Cristofori, Paola; Dartois, Stéphane; Grasselli, Luigi

2018-07-01

The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization theory). On the other hand, the core of the paper is to establish results about the topological and geometrical properties of the Gurau-degree (or G-degree) of the represented manifolds, in relation with the motivations coming from physics. In fact, the G-degree appears naturally in higher dimensional tensor models as the quantity driving their 1 / N expansion, exactly as it happens for the genus of surfaces in the two-dimensional matrix model setting. In particular, the G-degree of PL-manifolds is proved to be finite-to-one in any dimension, while in dimension 3 and 4 a series of classification theorems are obtained for PL-manifolds represented by graphs with a fixed G-degree. All these properties have specific relevance in the tensor models framework, showing a direct fruitful interaction between tensor models and discrete geometry, via crystallization theory.

Differences in Gaussian diffusion tensor imaging and non-Gaussian diffusion kurtosis imaging model-based estimates of diffusion tensor invariants in the human brain.

PubMed

Lanzafame, S; Giannelli, M; Garaci, F; Floris, R; Duggento, A; Guerrisi, M; Toschi, N

2016-05-01

An increasing number of studies have aimed to compare diffusion tensor imaging (DTI)-related parameters [e.g., mean diffusivity (MD), fractional anisotropy (FA), radial diffusivity (RD), and axial diffusivity (AD)] to complementary new indexes [e.g., mean kurtosis (MK)/radial kurtosis (RK)/axial kurtosis (AK)] derived through diffusion kurtosis imaging (DKI) in terms of their discriminative potential about tissue disease-related microstructural alterations. Given that the DTI and DKI models provide conceptually and quantitatively different estimates of the diffusion tensor, which can also depend on fitting routine, the aim of this study was to investigate model- and algorithm-dependent differences in MD/FA/RD/AD and anisotropy mode (MO) estimates in diffusion-weighted imaging of human brain white matter. The authors employed (a) data collected from 33 healthy subjects (20-59 yr, F: 15, M: 18) within the Human Connectome Project (HCP) on a customized 3 T scanner, and (b) data from 34 healthy subjects (26-61 yr, F: 5, M: 29) acquired on a clinical 3 T scanner. The DTI model was fitted to b-value =0 and b-value =1000 s/mm(2) data while the DKI model was fitted to data comprising b-value =0, 1000 and 3000/2500 s/mm(2) [for dataset (a)/(b), respectively] through nonlinear and weighted linear least squares algorithms. In addition to MK/RK/AK maps, MD/FA/MO/RD/AD maps were estimated from both models and both algorithms. Using tract-based spatial statistics, the authors tested the null hypothesis of zero difference between the two MD/FA/MO/RD/AD estimates in brain white matter for both datasets and both algorithms. DKI-derived MD/FA/RD/AD and MO estimates were significantly higher and lower, respectively, than corresponding DTI-derived estimates. All voxelwise differences extended over most of the white matter skeleton. Fractional differences between the two estimates [(DKI - DTI)/DTI] of most invariants were seen to vary with the invariant value itself as well as with MK/RK/AK values, indicating substantial anatomical variability of these discrepancies. In the HCP dataset, the median voxelwise percentage differences across the whole white matter skeleton were (nonlinear least squares algorithm) 14.5% (8.2%-23.1%) for MD, 4.3% (1.4%-17.3%) for FA, -5.2% (-48.7% to -0.8%) for MO, 12.5% (6.4%-21.2%) for RD, and 16.1% (9.9%-25.6%) for AD (all ranges computed as 0.01 and 0.99 quantiles). All differences/trends were consistent between the discovery (HCP) and replication (local) datasets and between estimation algorithms. However, the relationships between such trends, estimated diffusion tensor invariants, and kurtosis estimates were impacted by the choice of fitting routine. Model-dependent differences in the estimation of conventional indexes of MD/FA/MO/RD/AD can be well beyond commonly seen disease-related alterations. While estimating diffusion tensor-derived indexes using the DKI model may be advantageous in terms of mitigating b-value dependence of diffusivity estimates, such estimates should not be referred to as conventional DTI-derived indexes in order to avoid confusion in interpretation as well as multicenter comparisons. In order to assess the potential and advantages of DKI with respect to DTI as well as to standardize diffusion-weighted imaging methods between centers, both conventional DTI-derived indexes and diffusion tensor invariants derived by fitting the non-Gaussian DKI model should be separately estimated and analyzed using the same combination of fitting routines.

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

PubMed

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

2008-07-23

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

Estimation of relative order tensors, and reconstruction of vectors in space using unassigned RDC data and its application

NASA Astrophysics Data System (ADS)

Miao, Xijiang; Mukhopadhyay, Rishi; Valafar, Homayoun

2008-10-01

Advances in NMR instrumentation and pulse sequence design have resulted in easier acquisition of Residual Dipolar Coupling (RDC) data. However, computational and theoretical analysis of this type of data has continued to challenge the international community of investigators because of their complexity and rich information content. Contemporary use of RDC data has required a-priori assignment, which significantly increases the overall cost of structural analysis. This article introduces a novel algorithm that utilizes unassigned RDC data acquired from multiple alignment media ( nD-RDC, n ⩾ 3) for simultaneous extraction of the relative order tensor matrices and reconstruction of the interacting vectors in space. Estimation of the relative order tensors and reconstruction of the interacting vectors can be invaluable in a number of endeavors. An example application has been presented where the reconstructed vectors have been used to quantify the fitness of a template protein structure to the unknown protein structure. This work has other important direct applications such as verification of the novelty of an unknown protein and validation of the accuracy of an available protein structure model in drug design. More importantly, the presented work has the potential to bridge the gap between experimental and computational methods of structure determination.

Black holes in vector-tensor theories

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

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic andmore » quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.« less

Tensor Factorization for Precision Medicine in Heart Failure with Preserved Ejection Fraction

PubMed Central

Luo, Yuan; Ahmad, Faraz S.; Shah, Sanjiv J.

2017-01-01

Heart failure with preserved ejection fraction (HFpEF) is a heterogeneous clinical syndrome that may benefit from improved subtyping in order to better characterize its pathophysiology and to develop novel targeted therapies. The United States Precision Medicine Initiative comes amid the rapid growth in quantity and modality of clinical data for HFpEF patients ranging from deep phenotypic to trans-omic data. Tensor factorization, a form of machine learning, allows for the integration of multiple data modalities to derive clinically relevant HFpEF subtypes that may have significant differences in underlying pathophysiology and differential response to therapies. Tensor factorization also allows for better interpretability by supporting dimensionality reduction and identifying latent groups of data for meaningful summarization of both features and disease outcomes. In this narrative review, we analyze the modest literature on the application of tensor factorization to related biomedical fields including genotyping and phenotyping. Based on the cited work including work of our own, we suggest multiple tensor factorization formulations capable of integrating the deep phenotypic and trans-omic modalities of data for HFpEF, or accounting for interactions between genetic variants at different -omic hierarchies. We encourage extensive experimental studies to tackle challenges in applying tensor factorization for precision medicine in HFpEF, including effectively incorporating existing medical knowledge, properly accounting for uncertainty, and efficiently enforcing sparsity for better interpretability. PMID:28116551

Susceptibility Tensor Imaging (STI) of the Brain

PubMed Central

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

2016-01-01

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

Inertial sensor and method of use

NASA Technical Reports Server (NTRS)

Gutierrez, Roman C. (Inventor); Tang, Tony K. (Inventor)

2003-01-01

The inertial sensor of the present invention utilizes a proof mass suspended from spring structures forming a nearly degenerate resonant structure into which a perturbation is introduced, causing a split in frequency of the two modes so that the mode shape become uniquely defined, and to the first order, remains orthogonal. The resonator is provided with a mass or inertia tensor with off-diagonal elements. These off-diagonal elements are large enough to change the mode shape of the two nearly degenerate modes from the original coordinate frame. The spring tensor is then provided with a compensating off-diagonal element, such that the mode shape is again defined in the original coordinate frame. The compensating off-diagonal element in the spring tensor is provided by a biasing voltage that softens certain elements in the spring tensor. Acceleration disturbs the compensation and the mode shape again changes from the original coordinate frame. By measuring the change in the mode shape, the acceleration is measured.

Six dimensional X-ray Tensor Tomography with a compact laboratory setup

NASA Astrophysics Data System (ADS)

Sharma, Y.; Wieczorek, M.; Schaff, F.; Seyyedi, S.; Prade, F.; Pfeiffer, F.; Lasser, T.

2016-09-01

Attenuation based X-ray micro computed tomography (XCT) provides three-dimensional images with micrometer resolution. However, there is a trade-off between the smallest size of the structures that can be resolved and the measurable sample size. In this letter, we present an imaging method using a compact laboratory setup that reveals information about micrometer-sized structures within samples that are several orders of magnitudes larger. We combine the anisotropic dark-field signal obtained in a grating interferometer and advanced tomographic reconstruction methods to reconstruct a six dimensional scattering tensor at every spatial location in three dimensions. The scattering tensor, thus obtained, encodes information about the orientation of micron-sized structures such as fibres in composite materials or dentinal tubules in human teeth. The sparse acquisition schemes presented in this letter enable the measurement of the full scattering tensor at every spatial location and can be easily incorporated in a practical, commercially feasible laboratory setup using conventional X-ray tubes, thus allowing for widespread industrial applications.

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.

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.

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

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

NASA Astrophysics Data System (ADS)

Kornbluth, Mordechai; Marianetti, Chris

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

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

Basak, Anup; Levitas, Valery I.

2018-04-01

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

Tensor Analysis Reveals Distinct Population Structure that Parallels the Different Computational Roles of Areas M1 and V1

PubMed Central

Ryu, Stephen I.; Shenoy, Krishna V.; Cunningham, John P.; Churchland, Mark M.

2016-01-01

Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure—a basic example is the frequency spectrum—and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1) and primary motor cortex (M1). All V1 datasets were ‘simplest’ (there were relatively few degrees of freedom) along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models. PMID:27814353

Quantum games as quantum types

NASA Astrophysics Data System (ADS)

Delbecque, Yannick

In this thesis, we present a new model for higher-order quantum programming languages. The proposed model is an adaptation of the probabilistic game semantics developed by Danos and Harmer [DH02]: we expand it with quantum strategies which enable one to represent quantum states and quantum operations. Some of the basic properties of these strategies are established and then used to construct denotational semantics for three quantum programming languages. The first of these languages is a formalisation of the measurement calculus proposed by Danos et al. [DKP07]. The other two are new: they are higher-order quantum programming languages. Previous attempts to define a denotational semantics for higher-order quantum programming languages have failed. We identify some of the key reasons for this and base the design of our higher-order languages on these observations. The game semantics proposed in this thesis is the first denotational semantics for a lambda-calculus equipped with quantum types and with extra operations which allow one to program quantum algorithms. The results presented validate the two different approaches used in the design of these two new higher-order languages: a first one where quantum states are used through references and a second one where they are introduced as constants in the language. The quantum strategies presented in this thesis allow one to understand the constraints that must be imposed on quantum type systems with higher-order types. The most significant constraint is the fact that abstraction over part of the tensor product of many unknown quantum states must not be allowed. Quantum strategies are a new mathematical model which describes the interaction between classical and quantum data using system-environment dialogues. The interactions between the different parts of a quantum system are described using the rich structure generated by composition of strategies. This approach has enough generality to be put in relation with other work in quantum computing. Quantum strategies could thus be useful for other purposes than the study of quantum programming languages.

High-order perturbations of a spherical collapsing star

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

Brizuela, David; Martin-Garcia, Jose M.; Sperhake, Ulrich

2010-11-15

A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006); D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 76, 024004 (2007)]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations.more » For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.« less

Holographic bulk reconstruction with α' corrections

NASA Astrophysics Data System (ADS)

Roy, Shubho R.; Sarkar, Debajyoti

2017-10-01

We outline a holographic recipe to reconstruct α' corrections to anti-de Sitter (AdS) (quantum) gravity from an underlying CFT in the strictly planar limit (N →∞ ). Assuming that the boundary CFT can be solved in principle to all orders of the 't Hooft coupling λ , for scalar primary operators, the λ-1 expansion of the conformal dimensions can be mapped to higher curvature corrections of the dual bulk scalar field action. Furthermore, for the metric perturbations in the bulk, the AdS /CFT operator-field isomorphism forces these corrections to be of the Lovelock type. We demonstrate this by reconstructing the coefficient of the leading Lovelock correction, also known as the Gauss-Bonnet term in a bulk AdS gravity action using the expression of stress-tensor two-point function up to subleading order in λ-1.

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.

An Introduction to Tensors for Students of Physics and Engineering

NASA Technical Reports Server (NTRS)

Kolecki, Joseph C.

2002-01-01

Tensor analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way throughout the various formalisms. Prior to taking that class, I had spent many years "playing" on my own with tensors. I found the going to be tremendously difficult but was able, over time, to back out some physical and geometrical considerations that helped to make the subject a little more transparent. Today, it is sometimes hard not to think in terms of tensors and their associated concepts. This article, prompted and greatly enhanced by Marlos Jacob, whom I've met only by e-mail, is an attempt to record those early notions concerning tensors. It is intended to serve as a bridge from the point where most undergraduate students "leave off" in their studies of mathematics to the place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and higher vector products. The reader must be prepared to do some mathematics and to think. For those students who wish to go beyond this humble start, I can only recommend my professor's wisdom: find the rhythm in the mathematics and you will fare pretty well.

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.

Observable tensor-to-scalar ratio and secondary gravitational wave background

NASA Astrophysics Data System (ADS)

Chatterjee, Arindam; Mazumdar, Anupam

2018-03-01

In this paper we will highlight how a simple vacuum energy dominated inflection-point inflation can match the current data from cosmic microwave background radiation, and predict large primordial tensor to scalar ratio, r ˜O (10-3-10-2), with observable second order gravitational wave background, which can be potentially detectable from future experiments, such as DECi-hertz Interferometer Gravitational wave Observatory (DECIGO), Laser Interferometer Space Antenna (eLISA), cosmic explorer (CE), and big bang observatory (BBO).

Nanosecond electric modification of order parameters

NASA Astrophysics Data System (ADS)

Borshch, Volodymyr

In this Dissertation, we study a nanosecond electro-optic response of a nematic liquid crystal in a geometry where an applied electric field E modifies the tensor order parameter but does not change the orientation of the optic axis (director N̂). We use nematics with negative dielectric anisotropy with the electric field applied perpendicularly to N̂. The field changes the dielectric tensor at optical frequencies (optic tensor), due to the following mechanisms: (a) nanosecond creation of biaxial orientational order; (b) uniaxial modification of the orientational order that occurs over the timescales of tens of nanoseconds, and (c) quenching of director fluctuations with a wide range of characteristic times up to milliseconds. We develop a model to describe the dynamics of all three mechanisms. We design the experimental conditions to selectively suppress the contributions from the quenching of director fluctuations (c) and from the biaxial order effect (a) and thus, separate the contributions of the three mechanisms in the electro-optic response. As a result, the experimental data can be well fitted with the model parameters. The analysis provides a rather detailed physical picture of how the liquid crystal responds to a strong electric field, E ˜ 108 V/m, on a timescale of nanoseconds. This work provides a useful guide in the current search of the biaxial nematic phase. Namely, the temperature dependence of the biaxial susceptibility allows one to estimate the temperature of the potential uniaxial-to-biaxial phase transition. An analysis of the quenching of director fluctuations indicates that on a timescale of nanoseconds, the classic model with constant viscoelastic material parameters might reach its limit of validity. The effect of nanosecond electric modification of the order parameter (NEMOP) can be used in applications in which one needs to achieve ultrafast (nanosecond) changes of optical characteristics, such as birefringence.

Spin-1/2 kagome XXZ model in a field: Competition between lattice nematic and solid orders

NASA Astrophysics Data System (ADS)

Kshetrimayum, Augustine; Picot, Thibaut; Orús, Román; Poilblanc, Didier

2016-12-01

We study numerically the spin-1/2 XXZ model in a field on an infinite kagome lattice. We use different algorithms based on infinite projected entangled pair states (iPEPSs) for this, namely, (i) an approach with simplex tensors and a 9-site unit cell, and (ii) an approach based on coarse-graining three spins in the kagome lattice and mapping it to a square-lattice model with local and nearest-neighbor interactions, with the usual PEPS tensors, 6- and 12-site unit cells. Similarly to our previous calculation at the SU(2)-symmetric point (Heisenberg Hamiltonian), for any anisotropy from the Ising limit to the XY limit, we also observe the emergence of magnetization plateaus as a function of the magnetic field, at mz=1/3 using 6-, 9-, and 12-site PEPS unit cells, and at mz=1/9 ,5/9 , and 7/9 using a 9-site PEPS unit cell, the latter setup being able to accommodate √{3 }×√{3 } solid order. We also find that, at mz=1/3 , (lattice) nematic and √{3 }×√{3 } VBC-order states are degenerate within the accuracy of the nine-site simplex method, for all anisotropy. The 6- and 12-site coarse-grained PEPS methods produce almost-degenerate nematic and 1 ×2 VBC-solid orders. We also find that, within our accuracy, the six-site coarse-grained PEPS method gives slightly lower energies, which can be explained by the larger amount of entanglement this approach can handle, even in cases where the PEPS unit cell is not commensurate with the expected ground-state unit cell. Furthermore, we do not observe chiral spin liquid behaviors at and close to the XY point, as has been recently proposed. Our results are the first tensor network investigations of the XXZ model in a field and reveal the subtle competition between nearby magnetic orders in numerical simulations of frustrated quantum antiferromagnets, as well as the delicate interplay between energy optimization and symmetry in tensor network numerical simulations.

Magma flow recorded by magmatic and magnetic fabrics in a shallow granitic pluton: La Gloria Pluton, central Chile

NASA Astrophysics Data System (ADS)

Payacán, I. J.; Gutiérrez, F. J.; Gelman, S. E.; Bachmann, O.; Parada, M. A.

2013-12-01

To better understand the dynamics of a small, shallow, silicic magma reservoir, magmatic and magnetic (AMS) fabrics are compared in samples obtained from La Gloria Pluton (LGP), a 10 Ma granitic intrusion located in southern Andes. The magnetic fabric of LGP, mainly given by magnetite, is characterized by oblate shapes. Magnetic lineations have a NW trend with subhorizontal dip, following the main pluton elongation, while magnetic foliation planes have dips varying gradually from vertical at the walls to subhorizontal toward the center and the roof of the pluton. On the basis of numerical simulations, magnetic fabric was interpreted to represent the shear record induced by magmatic convection along solidification fronts as the reservoir reached its rheological locking point. Magmatic fabric (mineral orientation) was determined on 12 samples along the pluton. Three mutually orthogonal thin sections were produced for each sample, perpendicular to the AMS tensor axes. Size and orientation of individual crystals were obtained by image analysis. A 2-D tensor for two mineral groups (plagioclase and amphibole+biotitie) was defined in each mineral plane projecting the crystal lengths on the main crystal orientation (given by Bingham statistics). A 3-D magmatic fabric tensor was obtained. In order to compare the magmatic and magnetic fabrics, magmatic anisotropy parameters were defined similar to the AMS tensors. Magmatic fabric and anisotropy parameter values vary depending on the location inside the pluton: (1) Samples located at the borders exhibit vertical foliations and lineations with a NW trend, similar to the magnetic fabric tensors and higher anisotropy values for plagioclase than amphibole+biotite,; (2) samples located at the center of the LGP commonly present subvertical foliations/lineations, which differ from the magnetic fabric, and higher magmatic anisotropy degree values for amphibole+biotite than plagioclase. Based on numerical simulations of the fluid dynamics of the LGP and the different aspect ratio of minerals, we interpret that both the magnetic and magmatic fabrics represent the shear pattern produced along solidification fronts due to rheological locking during late-stage of magma cooling. It is interesting to note that while the magmatic fabric records vertical convection patterns in the core of the pluton, in agreement with predictions from numerical simulations, the magnetic fabric does not, probably because shear rate values are too low. Acknowledgments. This research has been developed by the FONDECYT N°11100241 and PBCT-PDA07 projects granted by CONICYT (Chilean National Commission for Science and Technology). I.P. is supported by CONICYT magister grant N°22130729. We thank to FONDAP N°15090013 for supporting during the congress.

The spectral expansion of the elasticity random field

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

Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

2014-12-10

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

Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models

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

Felice, Antonio De; Tsujikawa, Shinji, E-mail: antoniod@nu.ac.th, E-mail: shinji@rs.kagu.tus.ac.jp

2012-02-01

In the Horndeski's most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter space in which the ghosts and Laplacian instabilities are absent and we numerically confirmmore » that such models are indeed cosmologically viable.« less

Neutron stars in Horndeski gravity

NASA Astrophysics Data System (ADS)

Maselli, Andrea; Silva, Hector O.; Minamitsuji, Masato; Berti, Emanuele

2016-06-01

Horndeski's theory of gravity is the most general scalar-tensor theory with a single scalar whose equations of motion contain at most second-order derivatives. A subsector of Horndeski's theory known as "Fab Four" gravity allows for dynamical self-tuning of the quantum vacuum energy, and therefore it has received particular attention in cosmology as a possible alternative to the Λ CDM model. Here we study compact stars in Fab Four gravity, which includes as special cases general relativity ("George"), Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories with a nonminimal coupling with the Einstein tensor ("John"), and theories involving the double-dual of the Riemann tensor ("Paul"). We generalize and extend previous results in theories of the John class and were not able to find realistic compact stars in theories involving the Paul class.

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.

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

NASA Astrophysics Data System (ADS)

Ujj, Laszlo

2018-06-01

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

Fokker-Planck electron diffusion caused by an obliquely propagating electromagnetic wave packet of narrow bandwidth

NASA Technical Reports Server (NTRS)

Hizanidis, Kyriakos

1989-01-01

The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker-Planck-Kolmogorov (FPK) approach. The wavepacket consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second-order parts with respect to the relative bandwidth. The zeroth-order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second-order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.

[Assessment of motor and sensory pathways of the brain using diffusion-tensor tractography in children with cerebral palsy].

PubMed

Memedyarov, A M; Namazova-Baranova, L S; Ermolina, Y V; Anikin, A V; Maslova, O I; Karkashadze, M Z; Klochkova, O A

2014-01-01

Diffusion tensor tractography--a new method of magnetic resonance imaging, that allows to visualize the pathways of the brain and to study their structural-functional state. The authors investigated the changes in motor and sensory pathways of brain in children with cerebral palsy using routine magnetic resonance imaging and diffusion-tensor tractography. The main group consisted of 26 patients with various forms of cerebral palsy and the comparison group was 25 people with normal psychomotor development (aged 2 to 6 years) and MR-picture of the brain. Magnetic resonance imaging was performed on the scanner with the induction of a magnetic field of 1,5 Tesla. Coefficients of fractional anisotropy and average diffusion coefficient estimated in regions of the brain containing the motor and sensory pathways: precentral gyrus, posterior limb of the internal capsule, thalamus, posterior thalamic radiation and corpus callosum. Statistically significant differences (p < 0.05) values of fractional anisotropy and average diffusion coefficient in patients with cerebral palsy in relation to the comparison group. All investigated regions, the coefficients of fractional anisotropy in children with cerebral palsy were significantly lower, and the average diffusion coefficient, respectively, higher. These changes indicate a lower degree of ordering of the white matter tracts associated with damage and subsequent development of gliosis of varying severity in children with cerebral palsy. It is shown that microstructural damage localized in both motor and sensory tracts that plays a leading role in the development of the clinical picture of cerebral palsy.

Holographic spin networks from tensor network states

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder; McMahon, Nathan A.; Brennen, Gavin K.

2018-01-01

In the holographic correspondence of quantum gravity, a global on-site symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary on-site symmetries can be gauged within the formalism of the multiscale renormalization ansatz (MERA), in light of the ongoing discussion between tensor networks and holography. We describe how to "lift" the MERA representation of the ground state of a generic one dimensional (1D) local Hamiltonian, which has a global on-site symmetry, to a dual quantum state of a 2D "bulk" lattice on which the symmetry appears gauged. The 2D bulk state decomposes in terms of spin network states, which label a basis in the gauge-invariant sector of the bulk lattice. This decomposition is instrumental to obtain expectation values of gauge-invariant observables in the bulk, and also reveals that the bulk state is generally entangled between the gauge and the remaining ("gravitational") bulk degrees of freedom that are not fixed by the symmetry. We present numerical results for ground states of several 1D critical spin chains to illustrate that the bulk entanglement potentially depends on the central charge of the underlying conformal field theory. We also discuss the possibility of emergent topological order in the bulk using a simple example, and also of emergent symmetries in the nongauge (gravitational) sector in the bulk. More broadly, our holographic model translates the MERA, a tensor network state, to a superposition of spin network states, as they appear in lattice gauge theories in one higher dimension.

Experience-Related Structural Changes of Degenerated Occipital White Matter in Late-Blind Humans – A Diffusion Tensor Imaging Study

PubMed Central

Dietrich, Susanne; Hertrich, Ingo; Kumar, Vinod; Ackermann, Hermann

2015-01-01

Late-blind humans can learn to understand speech at ultra-fast syllable rates (ca. 20 syllables/s), a capability associated with hemodynamic activation of the central-visual system. Thus, the observed functional cross-modal recruitment of occipital cortex might facilitate ultra-fast speech processing in these individuals. To further elucidate the structural prerequisites of this skill, diffusion tensor imaging (DTI) was conducted in late-blind subjects differing in their capability of understanding ultra-fast speech. Fractional anisotropy (FA) was determined as a quantitative measure of the directionality of water diffusion, indicating fiber tract characteristics that might be influenced by blindness as well as the acquired perceptual skills. Analysis of the diffusion images revealed reduced FA in late-blind individuals relative to sighted controls at the level of the optic radiations at either side and the right-hemisphere dorsal thalamus (pulvinar). Moreover, late-blind subjects showed significant positive correlations between FA and the capacity of ultra-fast speech comprehension within right-hemisphere optic radiation and thalamus. Thus, experience-related structural alterations occurred in late-blind individuals within visual pathways that, presumably, are linked to higher order frontal language areas. PMID:25830371

Low-dose dynamic myocardial perfusion CT image reconstruction using pre-contrast normal-dose CT scan induced structure tensor total variation regularization

NASA Astrophysics Data System (ADS)

Gong, Changfei; Han, Ce; Gan, Guanghui; Deng, Zhenxiang; Zhou, Yongqiang; Yi, Jinling; Zheng, Xiaomin; Xie, Congying; Jin, Xiance

2017-04-01

Dynamic myocardial perfusion CT (DMP-CT) imaging provides quantitative functional information for diagnosis and risk stratification of coronary artery disease by calculating myocardial perfusion hemodynamic parameter (MPHP) maps. However, the level of radiation delivered by dynamic sequential scan protocol can be potentially high. The purpose of this work is to develop a pre-contrast normal-dose scan induced structure tensor total variation regularization based on the penalized weighted least-squares (PWLS) criteria to improve the image quality of DMP-CT with a low-mAs CT acquisition. For simplicity, the present approach was termed as ‘PWLS-ndiSTV’. Specifically, the ndiSTV regularization takes into account the spatial-temporal structure information of DMP-CT data and further exploits the higher order derivatives of the objective images to enhance denoising performance. Subsequently, an effective optimization algorithm based on the split-Bregman approach was adopted to minimize the associative objective function. Evaluations with modified dynamic XCAT phantom and preclinical porcine datasets have demonstrated that the proposed PWLS-ndiSTV approach can achieve promising gains over other existing approaches in terms of noise-induced artifacts mitigation, edge details preservation, and accurate MPHP maps calculation.

Single-shot spiral imaging enabled by an expanded encoding model: Demonstration in diffusion MRI.

PubMed

Wilm, Bertram J; Barmet, Christoph; Gross, Simon; Kasper, Lars; Vannesjo, S Johanna; Haeberlin, Max; Dietrich, Benjamin E; Brunner, David O; Schmid, Thomas; Pruessmann, Klaas P

2017-01-01

The purpose of this work was to improve the quality of single-shot spiral MRI and demonstrate its application for diffusion-weighted imaging. Image formation is based on an expanded encoding model that accounts for dynamic magnetic fields up to third order in space, nonuniform static B 0 , and coil sensitivity encoding. The encoding model is determined by B 0 mapping, sensitivity mapping, and concurrent field monitoring. Reconstruction is performed by iterative inversion of the expanded signal equations. Diffusion-tensor imaging with single-shot spiral readouts is performed in a phantom and in vivo, using a clinical 3T instrument. Image quality is assessed in terms of artefact levels, image congruence, and the influence of the different encoding factors. Using the full encoding model, diffusion-weighted single-shot spiral imaging of high quality is accomplished both in vitro and in vivo. Accounting for actual field dynamics, including higher orders, is found to be critical to suppress blurring, aliasing, and distortion. Enhanced image congruence permitted data fusion and diffusion tensor analysis without coregistration. Use of an expanded signal model largely overcomes the traditional vulnerability of spiral imaging with long readouts. It renders single-shot spirals competitive with echo-planar readouts and thus deploys shorter echo times and superior readout efficiency for diffusion imaging and further prospective applications. Magn Reson Med 77:83-91, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Irreversibility and higher-spin conformal field theory

NASA Astrophysics Data System (ADS)

Anselmi, Damiano

2000-08-01

I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.

Characterization and correction of eddy-current artifacts in unipolar and bipolar diffusion sequences using magnetic field monitoring.

PubMed

Chan, Rachel W; von Deuster, Constantin; Giese, Daniel; Stoeck, Christian T; Harmer, Jack; Aitken, Andrew P; Atkinson, David; Kozerke, Sebastian

2014-07-01

Diffusion tensor imaging (DTI) of moving organs is gaining increasing attention but robust performance requires sequence modifications and dedicated correction methods to account for system imperfections. In this study, eddy currents in the "unipolar" Stejskal-Tanner and the velocity-compensated "bipolar" spin-echo diffusion sequences were investigated and corrected for using a magnetic field monitoring approach in combination with higher-order image reconstruction. From the field-camera measurements, increased levels of second-order eddy currents were quantified in the unipolar sequence relative to the bipolar diffusion sequence while zeroth and linear orders were found to be similar between both sequences. Second-order image reconstruction based on field-monitoring data resulted in reduced spatial misalignment artifacts and residual displacements of less than 0.43 mm and 0.29 mm (in the unipolar and bipolar sequences, respectively) after second-order eddy-current correction. Results demonstrate the need for second-order correction in unipolar encoding schemes but also show that bipolar sequences benefit from second-order reconstruction to correct for incomplete intrinsic cancellation of eddy-currents. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Simultaneous tensor decomposition and completion using factor priors.

PubMed

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

2014-03-01

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

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.

Flexoelectricity from density-functional perturbation theory

NASA Astrophysics Data System (ADS)

Stengel, Massimiliano

2013-11-01

We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wave vector q around the Γ (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q we recover Martin's theory of piezoelectricity [Martin, Phys. Rev. B 5, 1607 (1972)], thus providing an alternative derivation thereof. To put our derivations on firm theoretical grounds, we perform a thorough analysis of the nonanalytic behavior of the dynamical matrix and other response functions in a vicinity of Γ. Based on this analysis, we find that there is an ambiguity in the specification of the “zero macroscopic field” condition in the flexoelectric case; such arbitrariness can be related to an analytic band-structure term, in close analogy to the theory of deformation potentials. As a by-product, we derive a rigorous generalization of the Cochran-Cowley formula [Cochran and Cowley, J. Phys. Chem. Solids 23, 447 (1962)] to higher orders in q. This can be of great utility in building reliable atomistic models of electromechanical phenomena, as well as for improving the accuracy of the calculation of phonon dispersion curves. Finally, we discuss the physical interpretation of the various contributions to the flexoelectric response, either in the static or dynamic regime, and we relate our findings to earlier theoretical works on the subject.

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.

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

NASA Astrophysics Data System (ADS)

Luminari, Nicola; Airiau, Christophe; Bottaro, Alessandro

2017-11-01

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

Aspects of the Antisymmetric Tensor Field

NASA Astrophysics Data System (ADS)

Lahiri, Amitabha

1991-02-01

With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.

The simplicial Ricci tensor

NASA Astrophysics Data System (ADS)

Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

2011-08-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

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

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

Bryce, David L.; Wasylishen, Roderick E.

2002-06-21

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Multi-linear sparse reconstruction for SAR imaging based on higher-order SVD

NASA Astrophysics Data System (ADS)

Gao, Yu-Fei; Gui, Guan; Cong, Xun-Chao; Yang, Yue; Zou, Yan-Bin; Wan, Qun

2017-12-01

This paper focuses on the spotlight synthetic aperture radar (SAR) imaging for point scattering targets based on tensor modeling. In a real-world scenario, scatterers usually distribute in the block sparse pattern. Such a distribution feature has been scarcely utilized by the previous studies of SAR imaging. Our work takes advantage of this structure property of the target scene, constructing a multi-linear sparse reconstruction algorithm for SAR imaging. The multi-linear block sparsity is introduced into higher-order singular value decomposition (SVD) with a dictionary constructing procedure by this research. The simulation experiments for ideal point targets show the robustness of the proposed algorithm to the noise and sidelobe disturbance which always influence the imaging quality of the conventional methods. The computational resources requirement is further investigated in this paper. As a consequence of the algorithm complexity analysis, the present method possesses the superiority on resource consumption compared with the classic matching pursuit method. The imaging implementations for practical measured data also demonstrate the effectiveness of the algorithm developed in this paper.

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.

Uniqueness of First Order Post-Newtonian Collinear Solutions for Three-Body Problem under a Scalar-Tensor Theory

NASA Astrophysics Data System (ADS)

Cao, Wei-Guang; Zhou, Tian-Yi; Xie, Yi

2017-10-01

As a continuing investigation of an earlier work that establishes the collinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness up to the first order post-Newtonian approximation. With the help of observed bounds on the scalar field in the Solar System, we show that the seventh-order polynomial equation determining the distance ratio among the three masses has either one or three positive roots. However, in the case with three positive roots, it is found that two positive roots break down the slow-motion condition for the post-Newtonian approximation so that only one positive root is physically valid. The resulting uniqueness suggests that the locations of the three masses are very close to their Newtonian positions with post-Newtonian corrections of general relativity and the scalar field. We also prove that, in the framework of the scalar-tensor theory, the angular velocity of the collinear configuration is always less than the Newtonian one when all other parameters are fixed. These results are valid only for three-body systems where upper-bounds on the scalar field are compatible with those of the Solar System. Supported by the National Natural Science Foundation of China under Grant Nos. 11573015 and J1210039, and the Innovation Training Project for Undergraduates of Nanjing University, China

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

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

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

1993-01-01

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

Multivariate Hermite interpolation on scattered point sets using tensor-product expo-rational B-splines

NASA Astrophysics Data System (ADS)

Dechevsky, Lubomir T.; Bang, Børre; Laksa˚, Arne; Zanaty, Peter

2011-12-01

At the Seventh International Conference on Mathematical Methods for Curves and Surfaces, To/nsberg, Norway, in 2008, several new constructions for Hermite interpolation on scattered point sets in domains in Rn,n∈N, combined with smooth convex partition of unity for several general types of partitions of these domains were proposed in [1]. All of these constructions were based on a new type of B-splines, proposed by some of the authors several years earlier: expo-rational B-splines (ERBS) [3]. In the present communication we shall provide more details about one of these constructions: the one for the most general class of domain partitions considered. This construction is based on the use of two separate families of basis functions: one which has all the necessary Hermite interpolation properties, and another which has the necessary properties of a smooth convex partition of unity. The constructions of both of these two bases are well-known; the new part of the construction is the combined use of these bases for the derivation of a new basis which enjoys having all above-said interpolation and unity partition properties simultaneously. In [1] the emphasis was put on the use of radial basis functions in the definitions of the two initial bases in the construction; now we shall put the main emphasis on the case when these bases consist of tensor-product B-splines. This selection provides two useful advantages: (A) it is easier to compute higher-order derivatives while working in Cartesian coordinates; (B) it becomes clear that this construction becomes a far-going extension of tensor-product constructions. We shall provide 3-dimensional visualization of the resulting bivariate bases, using tensor-product ERBS. In the main tensor-product variant, we shall consider also replacement of ERBS with simpler generalized ERBS (GERBS) [2], namely, their simplified polynomial modifications: the Euler Beta-function B-splines (BFBS). One advantage of using BFBS instead of ERBS is the simplified computation, since BFBS are piecewise polynomial, which ERBS are not. One disadvantage of using BFBS in the place of ERBS in this construction is that the necessary selection of the degree of BFBS imposes constraints on the maximal possible multiplicity of the Hermite interpolation.

Conformal supergravity in five dimensions: new approach and applications

NASA Astrophysics Data System (ADS)

Butter, Daniel; Kuzenko, Sergei M.; Novak, Joseph; Tartaglino-Mazzucchelli, Gabriele

2015-02-01

We develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the conformal superspace introduced is that it reduces to the super-conformal tensor calculus (formulated in the early 2000's) upon gauging away a number of superfluous fields. On the other hand, a different gauge fixing reduces our formulation to the SU(2) superspace of arXiv:0802.3953, which is suitable to describe the most general off-shell supergravity-matter couplings. Using the conformal superspace approach, we show how to reproduce practically all off-shell constructions derived so far, including he supersymmetric extensions of R 2 terms, thus demonstrating the power of our formulation. Furthermore, we construct for the first time a supersymmetric completion of the Ricci tensor squared term using the standard Weyl multiplet coupled to an off-shell vector multiplet. In addition, we present several procedures to generate higher-order off-shell invariants in supergravity, including higher-derivative ones. The covariant projective multiplets proposed in arXiv:0802.3953 are lifted to conformal superspace, and a manifestly superconformal action principle is given. We also introduce unconstrained prepotentials for the vector multiplet, the multiplet (i.e., the linear multiplet without central charge) and multiplets, with n = 0 , 1 , . . . Superform formulations are given for the BF action and the non-abelian Chern-Simons action. Finally, we describe locally supersymmetric theories with gauged central charge in conformal superspace.

A finite element beam propagation method for simulation of liquid crystal devices.

PubMed

Vanbrabant, Pieter J M; Beeckman, Jeroen; Neyts, Kristiaan; James, Richard; Fernandez, F Anibal

2009-06-22

An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell's equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.

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.

Effects of motion and b-matrix correction for high resolution DTI with short-axis PROPELLER-EPI

PubMed Central

Aksoy, Murat; Skare, Stefan; Holdsworth, Samantha; Bammer, Roland

2010-01-01

Short-axis PROPELLER-EPI (SAP-EPI) has been proven to be very effective in providing high-resolution diffusion-weighted and diffusion tensor data. The self-navigation capabilities of SAP-EPI allow one to correct for motion, phase errors, and geometric distortion. However, in the presence of patient motion, the change in the effective diffusion-encoding direction (i.e. the b-matrix) between successive PROPELLER ‘blades’ can decrease the accuracy of the estimated diffusion tensors, which might result in erroneous reconstruction of white matter tracts in the brain. In this study, we investigate the effects of alterations in the b-matrix as a result of patient motion on the example of SAP-EPI DTI and eliminate these effects by incorporating our novel single-step non-linear diffusion tensor estimation scheme into the SAP-EPI post-processing procedure. Our simulations and in-vivo studies showed that, in the presence of patient motion, correcting the b-matrix is necessary in order to get more accurate diffusion tensor and white matter pathway reconstructions. PMID:20222149

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

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

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

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.

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.

The role of electron heat flux in guide-field magnetic reconnection

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

Hesse, Michael; Kuznetsova, Masha; Birn, Joachim

2004-12-01

A combination of analytical theory and particle-in-cell simulations are employed in order to investigate the electron dynamics near and at the site of guide field magnetic reconnection. A detailed analysis of the contributions to the reconnection electric field shows that both bulk inertia and pressure-based quasiviscous processes are important for the electrons. Analytic scaling demonstrates that conventional approximations for the electron pressure tensor behavior in the dissipation region fail, and that heat flux contributions need to be accounted for. Based on the evolution equation of the heat flux three tensor, which is derived in this paper, an approximate form ofmore » the relevant heat flux contributions to the pressure tensor is developed, which reproduces the numerical modeling result reasonably well. Based on this approximation, it is possible to develop a scaling of the electron current layer in the central dissipation region. It is shown that the pressure tensor contributions become important at the scale length defined by the electron Larmor radius in the guide magnetic field.« less

Surfing gravitational waves: can bigravity survive growing tensor modes?

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

Amendola, Luca; Könnig, Frank; Martinelli, Matteo

The theory of bigravity offers one of the simplest possibilities to describe a massive graviton while having self-accelerating cosmological solutions without a cosmological constant. However, it has been shown recently that bigravity is affected by early-time fast growing modes on the tensor sector. Here we argue that we can only trust the linear analysis up to when perturbations are in the linear regime and use a cut-off to stop the growing of the metric perturbations. This analysis, although more consistent, still leads to growing tensor modes that are unacceptably large for the theory to be compatible with measurements of themore » cosmic microwave background (CMB), both in temperature and polarization spectra. In order to suppress the growing modes and make the model compatible with CMB spectra, we find it necessary to either fine-tune the initial conditions, modify the theory or set the cut-off for the tensor perturbations of the second metric much lower than unity. Initial conditions such that the growing mode is sufficiently suppresed can be achieved in scenarios in which inflation ends at the GeV scale.« less

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.

Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks

DOE PAGES

Park, Jong-Kyu; Logan, Nikolas C.

2017-03-01

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

Weak deflection gravitational lensing for photons coupled to Weyl tensor in a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Cao, Wei-Guang; Xie, Yi

2018-03-01

Beyond the Einstein-Maxwell model, electromagnetic field might couple with gravitational field through the Weyl tensor. In order to provide one of the missing puzzles of the whole physical picture, we investigate weak deflection lensing for photons coupled to the Weyl tensor in a Schwarzschild black hole under a unified framework that is valid for its two possible polarizations. We obtain its coordinate-independent expressions for all observables of the geometric optics lensing up to the second order in the terms of ɛ which is the ratio of the angular gravitational radius to angular Einstein radius of the lens. These observables include bending angle, image position, magnification, centroid and time delay. The contributions of such a coupling on some astrophysical scenarios are also studied. We find that, in the cases of weak deflection lensing on a star orbiting the Galactic Center Sgr A*, Galactic microlensing on a star in the bulge and astrometric microlensing by a nearby object, these effects are beyond the current limits of technology. However, measuring the variation of the total flux of two weak deflection lensing images caused by the Sgr A* might be a promising way for testing such a coupling in the future.

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

DTIC Science & Technology

2015-04-01

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

ELATE: an open-source online application for analysis and visualization of elastic tensors

NASA Astrophysics Data System (ADS)

Gaillac, Romain; Pullumbi, Pluton; Coudert, François-Xavier

2016-07-01

We report on the implementation of a tool for the analysis of second-order elastic stiffness tensors, provided with both an open-source Python module and a standalone online application allowing the visualization of anisotropic mechanical properties. After describing the software features, how we compute the conventional elastic constants and how we represent them graphically, we explain our technical choices for the implementation. In particular, we focus on why a Python module is used to generate the HTML web page with embedded Javascript for dynamical plots.

Computer transformation of partial differential equations into any coordinate system

NASA Technical Reports Server (NTRS)

Sullivan, R. D.

1977-01-01

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

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

DOE PAGES

Song, Chenchen; Martinez, Todd J.

2017-08-29

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

Compactly supported linearised observables in single-field inflation

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

Fröob, Markus B.; Higuchi, Atsushi; Hack, Thomas-Paul, E-mail: mbf503@york.ac.uk, E-mail: thomas-paul.hack@itp.uni-leipzig.de, E-mail: atsushi.higuchi@york.ac.uk

We investigate the gauge-invariant observables constructed by smearing the graviton and inflaton fields by compactly supported tensors at linear order in general single-field inflation. These observables correspond to gauge-invariant quantities that can be measured locally. In particular, we show that these observables are equivalent to (smeared) local gauge-invariant observables such as the linearised Weyl tensor, which have better infrared properties than the graviton and inflaton fields. Special cases include the equivalence between the compactly supported gauge-invariant graviton observable and the smeared linearised Weyl tensor in Minkowski and de Sitter spaces. Our results indicate that the infrared divergences in the tensormore » and scalar perturbations in single-field inflation have the same status as in de Sitter space and are both a gauge artefact, in a certain technical sense, at tree level.« less

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

NASA Technical Reports Server (NTRS)

Howard, J. C.

1975-01-01

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

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).

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

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-10-01

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

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

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

Song, Chenchen; Martinez, Todd J.

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

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).

The incompressible Rindler fluid versus the Schwarzschild-AdS fluid

NASA Astrophysics Data System (ADS)

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

2013-02-01

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

Classical Dynamics of Fullerenes

NASA Astrophysics Data System (ADS)

Sławianowski, Jan J.; Kotowski, Romuald K.

2017-06-01

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

Excitation basis for (3+1)d topological phases

NASA Astrophysics Data System (ADS)

Delcamp, Clement

2017-12-01

We consider an exactly solvable model in 3+1 dimensions, based on a finite group, which is a natural generalization of Kitaev's quantum double model. The corresponding lattice Hamiltonian yields excitations located at torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded by two tori which supports states satisfying a higher-dimensional version of Ocneanu's tube algebra. This defines an algebraic structure extending the Drinfel'd double. Its irreducible representations, labeled by two fluxes and one charge, characterize the torus-excitations. The tensor product of such representations is introduced in order to construct a basis for (3+1)d gauge models which relies upon the fusion of the defect excitations. This basis is defined on manifolds of the form Σ × S_1 , with Σ a two-dimensional Riemann surface. As such, our construction is closely related to dimensional reduction from (3+1)d to (2+1)d topological orders.

Topics in Higher-Derivative Supergravity and N = 2 Yang-Mills Theories

NASA Astrophysics Data System (ADS)

Hindawi, Ahmed Abdel-Ati

1997-09-01

In Part I of the thesis we discuss higher-derivative theories of gravity. We start by discussing the field content of quadratic higher-derivative gravity, together with a new example of a massless spin-two field consistently coupled to gravity. The full quadratic gravity theory is shown to be equivalent to a canonical second-order theory of a massive scalar field, a massive spin-two symmetric tensor field and gravity. It is shown that flat-space is the only stable vacuum, and that the spin-two field around it is always ghost-like. We give a procedure for exhibiting the new propagating degrees of freedom in a generic higher-derivative gravity, at the full non-linear level. We show that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. In Part II of the thesis we extend our investigations to the realm of supergravity. We consider the general form of quadratic (1, 1) supergravity in two dimensions. It is demonstrated that the theory possesses stable vacua with vanishing cosmological constant which spontaneously break supersymmetry. We then consider higher-derivative N=1 supergravity in four dimensions. We construct two classes of higher-derivative supergravity theories. They are found to be equivalent to Einstein supergravity coupled to one or two chiral superfields and have a rich vacuum structure. It is demonstrated that theories of the second class can possess a stable vacuum with vanishing cosmological constant that spontaneously breaks supersymmetry. We then proceed to show how spontaneous supersymmetry breaking in the vacuum state of higher-derivative supergravity is transmitted, as explicit soft supersymmetry-breaking terms, to the effective Lagrangian of the standard electroweak model. In Part III we use central charge superspace to give a geometrical construction of the N=2 Abelian vector-tensor multiplet consisting, under N=1 supersymmetry, of one vector and one linear multiplet. We derive the component field supersymmetry and central charge transformations, and show that there is a super-Lagrangian, the higher components of which are all total derivatives, allowing us to construct superfield and component actions.

Higher order terms in the inflation potential and the lower bound on the tensor to scalar ratio r

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

Destri, C., E-mail: Claudio.Destri@mib.infn.it; Vega, H.J. de, E-mail: devega@lpthe.jussieu.fr; Observatoire de Paris, LERMA, Laboratoire Associe au CNRS UMR 8112, 61, Avenue de l'Observatoire, 75014 Paris

Research Highlights: > In Ginsburg-Landau (G-L) approach data favors new inflation over chaotic inflation. > n{sub s} and r fall inside a universal banana-shaped region in G-L new inflation. > The banana region for the observed value n{sub s}=0.964 implies 0.021 Fermion condensate inflaton potential is a double well in the G-L class. - Abstract: The MCMC analysis of the CMB + LSS data in the context of the Ginsburg-Landau approach to inflation indicated that the fourth degree double-well inflaton potential in new inflation gives an excellent fit of the present CMB and LSS data. This provided a lowermore » bound for the ratio r of the tensor to scalar fluctuations and as most probable value r {approx_equal} 0.05, within reach of the forthcoming CMB observations. In this paper we systematically analyze the effects of arbitrarily higher order terms in the inflaton potential on the CMB observables: spectral index n{sub s} and ratio r. Furthermore, we compute in close form the inflaton potential dynamically generated when the inflaton field is a fermion condensate in the inflationary universe. This inflaton potential turns out to belong to the Ginsburg-Landau class too. The theoretical values in the (n{sub s}, r) plane for all double well inflaton potentials in the Ginsburg-Landau approach (including the potential generated by fermions) fall inside a universal banana-shaped region B. The upper border of the banana-shaped region B is given by the fourth order double-well potential and provides an upper bound for the ratio r. The lower border of B is defined by the quadratic plus an infinite barrier inflaton potential and provides a lower bound for the ratio r. For example, the current best value of the spectral index n{sub s} = 0.964, implies r is in the interval: 0.021 < r < 0.053. Interestingly enough, this range is within reach of forthcoming CMB observations.« less

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

PubMed

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

2015-04-21

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

Finding the chiral gravitational wave background of an axion-S U (2 ) inflationary model using CMB observations and laser interferometers

NASA Astrophysics Data System (ADS)

Thorne, Ben; Fujita, Tomohiro; Hazumi, Masashi; Katayama, Nobuhiko; Komatsu, Eiichiro; Shiraishi, Maresuke

2018-02-01

A detection of B-mode polarization of the cosmic microwave background (CMB) anisotropies would confirm the presence of a primordial gravitational wave background (GWB). In the inflation paradigm, this would be an unprecedented probe of the energy scale of inflation as it is directly proportional to the power spectrum of the GWB. However, similar tensor perturbations can be produced by the matter fields present during inflation, breaking the simple relationship between energy scale and the tensor-to-scalar ratio r . It is therefore important to find ways of distinguishing between the generation mechanisms of the GWB. Without doing a full model selection, we analyze the detectability of a new axion-S U (2 ) gauge field model by calculating the signal-to-noise ratio of future CMB and interferometer observations sensitive to the chirality of the tensor spectrum. We forecast the detectability of the resulting CMB temperature and B-mode (TB) or E-mode and B-mode (EB) cross-correlation by the LiteBIRD satellite, considering the effects of residual foregrounds, gravitational lensing, and assess the ability of such an experiment to jointly detect primordial TB and EB spectra and self-calibrate its polarimeter. We find that LiteBIRD will be able to detect the chiral signal for r*>0.03 , with r* denoting the tensor-to-scalar ratio at the peak scale, and that the maximum signal-to-noise ratio for r*<0.07 is ˜2 . We go on to consider an advanced stage of a LISA-like mission, which is designed to be sensitive to the intensity and polarization of the GWB. We find that such experiments would complement CMB observations as they would be able to detect the chirality of the GWB with high significance on scales inaccessible to the CMB. We conclude that CMB two-point statistics are limited in their ability to distinguish this model from a conventional vacuum fluctuation model of GWB generation, due to the fundamental limits on their sensitivity to parity violation. In order to test the predictions of such a model as compared to vacuum fluctuations, it will be necessary to test deviations from the self-consistency relation or use higher order statistics to leverage the non-Gaussianity of the model. On the other hand, in the case of a spectrum peaked at very small scales inaccessible to the CMB, a highly significant detection could be made using space-based laser interferometers.

Super-Laplacians and their symmetries

NASA Astrophysics Data System (ADS)

Howe, P. S.; Lindström, U.

2017-05-01

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

A 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.

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

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

NASA Astrophysics Data System (ADS)

Silbermann, C. B.; Ihlemann, J.

2016-03-01

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

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

Solid-state (127)I NMR and GIPAW DFT study of metal iodides and their hydrates: structure, symmetry, and higher-order quadrupole-induced effects.

PubMed

Widdifield, Cory M; Bryce, David L

2010-10-14

Central-transition (127)I solid-state nuclear magnetic resonance (SSNMR) spectra are presented for several anhydrous group 2 metal iodides (MgI(2), CaI(2), SrI(2), and BaI(2)), hydrates (BaI(2)·2H(2)O and SrI(2)·6H(2)O), and CdI(2) (4H polytype). Variable offset cumulative spectrum data acquisition coupled with echo pulse sequences and an 'ultrahigh' applied field of 21.1 T were usually suitable to acquire high-quality spectra. Spectral analysis revealed iodine-127 nuclear quadrupole coupling constants (C(Q)((127)I)) ranging in magnitude from 43.5 (CaI(2)) to 214 MHz (one site in SrI(2)). For very large C(Q), analytical second-order perturbation theory could not be used to reliably extract chemical shifts and a treatment which includes quadrupolar effects exactly was required (Bain, A. D. Mol. Phys. 2003, 101, 3163). Differences between second-order and exact modeling allowed us to observe 'higher-order' quadrupole-induced effects for the first time. This finding will have implications for the interpretation of SSNMR spectra of quadrupolar nuclei with large quadrupole moments. In favorable situations (i.e., C(Q)((127)I) < 120 MHz), measurements were also performed at 11.75 T which when combined with the 21.1 T data allowed us to measure iodine chemical shift (CS) tensor spans in the range from 60 (BaI(2)·2H(2)O) to 300 ppm (one site in BaI(2)). These measurements represent the first complete characterizations (i.e., electric field gradient and CS tensors as well as their relative orientation) of noncubic iodide sites using (127)I SSNMR. In select cases, the SSNMR data are supported with (127)I NQR measurements. We also summarize a variety of trends in the halogen SSNMR parameters for group 2 metal halides. Gauge-including projector-augmented wave DFT computations are employed to complement the experimental observations, to predict potential structures for the two hydrates, and to highlight the sensitivity of C(Q)((127)I) to minute structural changes, which has potential applications in NMR crystallography.

On the construction of a ground truth framework for evaluating voxel-based diffusion tensor MRI analysis methods.

PubMed

Van Hecke, Wim; Sijbers, Jan; De Backer, Steve; Poot, Dirk; Parizel, Paul M; Leemans, Alexander

2009-07-01

Although many studies are starting to use voxel-based analysis (VBA) methods to compare diffusion tensor images between healthy and diseased subjects, it has been demonstrated that VBA results depend heavily on parameter settings and implementation strategies, such as the applied coregistration technique, smoothing kernel width, statistical analysis, etc. In order to investigate the effect of different parameter settings and implementations on the accuracy and precision of the VBA results quantitatively, ground truth knowledge regarding the underlying microstructural alterations is required. To address the lack of such a gold standard, simulated diffusion tensor data sets are developed, which can model an array of anomalies in the diffusion properties of a predefined location. These data sets can be employed to evaluate the numerous parameters that characterize the pipeline of a VBA algorithm and to compare the accuracy, precision, and reproducibility of different post-processing approaches quantitatively. We are convinced that the use of these simulated data sets can improve the understanding of how different diffusion tensor image post-processing techniques affect the outcome of VBA. In turn, this may possibly lead to a more standardized and reliable evaluation of diffusion tensor data sets of large study groups with a wide range of white matter altering pathologies. The simulated DTI data sets will be made available online (http://www.dti.ua.ac.be).

Tensor renormalization group methods for spin and gauge models

NASA Astrophysics Data System (ADS)

Zou, Haiyuan

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

Methodological improvements in voxel-based analysis of diffusion tensor images: applications to study the impact of apolipoprotein E on white matter integrity.

PubMed

Newlander, Shawn M; Chu, Alan; Sinha, Usha S; Lu, Po H; Bartzokis, George

2014-02-01

To identify regional differences in apparent diffusion coefficient (ADC) and fractional anisotropy (FA) using customized preprocessing before voxel-based analysis (VBA) in 14 normal subjects with the specific genes that decrease (apolipoprotein [APO] E ε2) and that increase (APOE ε4) the risk of Alzheimer's disease. Diffusion tensor images (DTI) acquired at 1.5 Tesla were denoised with a total variation tensor regularization algorithm before affine and nonlinear registration to generate a common reference frame for the image volumes of all subjects. Anisotropic and isotropic smoothing with varying kernel sizes was applied to the aligned data before VBA to determine regional differences between cohorts segregated by allele status. VBA on the denoised tensor data identified regions of reduced FA in APOE ε4 compared with the APOE ε2 healthy older carriers. The most consistent results were obtained using the denoised tensor and anisotropic smoothing before statistical testing. In contrast, isotropic smoothing identified regional differences for small filter sizes alone, emphasizing that this method introduces bias in FA values for higher kernel sizes. Voxel-based DTI analysis can be performed on low signal to noise ratio images to detect subtle regional differences in cohorts using the proposed preprocessing techniques. Copyright © 2013 Wiley Periodicals, Inc.

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.

Possibilities of inversion of satellite third-order gravitational tensor onto gravity anomalies: a case study for central Europe

NASA Astrophysics Data System (ADS)

Pitoňák, Martin; Šprlák, Michal; Tenzer, Robert

2017-05-01

We investigate a numerical performance of four different schemes applied to a regional recovery of the gravity anomalies from the third-order gravitational tensor components (assumed to be observable in the future) synthetized at the satellite altitude of 200 km above the mean sphere. The first approach is based on applying a regional inversion without modelling the far-zone contribution or long-wavelength support. In the second approach we separate integral formulas into two parts, that is, the effects of the third-order disturbing tensor data within near and far zones. Whereas the far-zone contribution is evaluated by using existing global geopotential model (GGM) with spectral weights given by truncation error coefficients, the near-zone contribution is solved by applying a regional inversion. We then extend this approach for a smoothing procedure, in which we remove the gravitational contributions of the topographic-isostatic and atmospheric masses. Finally, we apply the remove-compute-restore (r-c-r) scheme in order to reduce the far-zone contribution by subtracting the reference (long-wavelength) gravity field, which is computed for maximum degree 80. We apply these four numerical schemes to a regional recovery of the gravity anomalies from individual components of the third-order gravitational tensor as well as from their combinations, while applying two different levels of a white noise. We validated our results with respect to gravity anomalies evaluated at the mean sphere from EGM2008 up to the degree 250. Not surprisingly, better fit in terms of standard deviation (STD) was attained using lower level of noise. The worst results were gained applying classical approach, STD values of our solution from Tzzz are 1.705 mGal (noise value with a standard deviation 0.01 × 10 - 15m - 1s - 2) and 2.005 mGal (noise value with a standard deviation 0.05 × 10 - 15m - 1s - 2), while the superior from r-c-r up to the degree 80, STD fit of gravity anomalies from Tzzz with respect to the same counterpart from EGM2008 is 0.510 mGal (noise value with a standard deviation 0.01 × 10 - 15m - 1s - 2) and 1.190 mGal (noise value with a standard deviation 0.05 × 10 - 15m - 1s - 2).

Tensor Network Wavefunctions for Topological Phases

NASA Astrophysics Data System (ADS)

Ware, Brayden Alexander

The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for intrinsically fermionic topological phases, i.e. topological phases contructed out of fermions with a nontrivial response to fermion parity defects. A zero correlation length wavefunction and a commuting projector Hamiltonian that realizes this wavefunction as its ground state are constructed. Using an appropriate generalization of the minimally entangled states method for extraction of topological order from the ground states on a torus to the intrinsically fermionic case, we fully characterize the corresponding topological order as Ising x (px - ipy). We argue that this phase can be captured using fermionic tensor networks, expanding the applicability of tensor network methods.

No-Go Theorem for Nonstandard Explanations of the τ →KSπ ντ C P Asymmetry

NASA Astrophysics Data System (ADS)

Cirigliano, Vincenzo; Crivellin, Andreas; Hoferichter, Martin

2018-04-01

The C P asymmetry in τ →KSπ ντ , as measured by the BABAR collaboration, differs from the standard model prediction by 2.8 σ . Most nonstandard interactions do not allow for the required strong phase needed to produce a nonvanishing C P asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least 2 orders of magnitude due to Watson's final-state-interaction theorem. Furthermore, we find that the strength of the relevant C P -violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and D - D ¯ mixing. These observations together imply that it is extremely difficult to explain the current τ →KSπ ντ measurement in terms of physics beyond the standard model originating in the ultraviolet.

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.

Intrinsic Viscosity of Dendrimers via Equilibrium Molecular Dynamics

NASA Astrophysics Data System (ADS)

Drew, Phil; Adolf, David

2004-03-01

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

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

Computations of the chirality-sensitive effect induced by an antisymmetric indirect spin–spin coupling

NASA Astrophysics Data System (ADS)

Garbacz, Piotr

2018-05-01

Results of quantum mechanical computations of the antisymmetric part of the indirect spin-spin coupling tensor, ?, performed using the coupled-cluster method, the second-order polarisation propagator approximation, and the density functional theory for 25 molecules and nearly 100 spin-spin couplings are reported. These results are used for an estimation of the magnitude of the recently proposed liquid-state nuclear magnetic resonance chirality-sensitive effect, which allows to determine the molecular chirality directly, i.e. without the need for the application of any chiral agent. The following were found: (i) the antisymmetry J⋆ is usually larger for the coupling between spins separated by two chemical bonds in comparison with the coupling through one bond, (ii) promising samples are those which contain fluorine, and (iii) the antisymmetry of the spin-spin coupling tensor is of the order of a few hertz for commercially available chemical compounds. Therefore, the relevant property of the experiment, the pseudoscalar Jc, for them is of the order of 1 nHz m/V.

Nature of the tensor order in Cd 2 Re 2 O 7

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

Di Matteo, S.; Norman, M. R.

The pyrochlore metal Cd 2Re 2O 7 has been recently investigated by second-harmonic generation (SHG) reflectivity. In this paper, we develop a general formalism that allows for the identification of the relevant tensor components of the SHG from azimuthal scans. We demonstrate that the secondary order parameter identified by SHG at the structural phase transition is the x 2 - y 2 component of the axial toroidal quadrupole. This differs from the 3z 2 - r 2 symmetry of the atomic displacements associated with the I4m2 crystal structure that was previously thought to be its origin. Within the same formalism,more » we suggest that the primary order parameter detected in the SHG experiment is the 3z 2 - r 2 component of the magnetic quadrupole. We discuss the general mechanism driving the phase transition in our proposed framework, and suggest experiments, particularly resonant x-ray scattering ones, that could clarify this issue.« less

Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

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

Thingna, Juzar; Wang, Jian-Sheng; Haenggi, Peter

A novel scheme for the steady state solution of the standard Redfield quantum master equation is developed which yields agreement with the exact result for the corresponding reduced density matrix up to second order in the system-bath coupling strength. We achieve this objective by use of an analytic continuation of the off-diagonal matrix elements of the Redfield solution towards its diagonal limit. Notably, our scheme does not require the provision of yet higher order relaxation tensors. Testing this modified method for a heat bath consisting of a collection of harmonic oscillators we assess that the system relaxes towards its correctmore » coupling-dependent, generalized quantum Gibbs state in second order. We numerically compare our formulation for a damped quantum harmonic system with the nonequilibrium Green's function formalism: we find good agreement at low temperatures for coupling strengths that are even larger than expected from the very regime of validity of the second-order Redfield quantum master equation. Yet another advantage of our method is that it markedly reduces the numerical complexity of the problem; thus, allowing to study efficiently large-sized system Hilbert spaces.« less

Leith diffusion model for homogeneous anisotropic turbulence

DOE PAGES

Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan

2017-06-01

Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numericalmore » simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.« less

More on the tensor response of the QCD vacuum to an external magnetic field

NASA Astrophysics Data System (ADS)

Gorsky, A.; Kopnin, P. N.; Krikun, A.; Vainshtein, A.

2012-04-01

In this paper we discuss a few issues concerning the magnetic susceptibility of the quark condensate and the Son-Yamamoto anomaly matching equation. It is shown that the Son-Yamamoto relation in the IR implies a nontrivial interplay between the kinetic and Wess-Zumino-Witten terms in the chiral Lagrangian. It is also demonstrated that in a holographic framework an external magnetic field triggers mixing between scalar and tensor fields. Accounting for this, one may calculate the magnetic susceptibility of the quark condensate to all orders in the magnetic field.

Solution of Einsteins Equation for Deformation of a Magnetized Neutron Star

NASA Astrophysics Data System (ADS)

Rizaldy, R.; Sulaksono, A.

2018-04-01

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

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

PubMed

Nguyen, Thanh-Son; Selinger, Jonathan V

2017-09-01

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

On the Landau-de Gennes Elastic Energy of a Q-Tensor Model for Soft Biaxial Nematics

NASA Astrophysics Data System (ADS)

Mucci, Domenico; Nicolodi, Lorenzo

2017-12-01

In the Landau-de Gennes theory of liquid crystals, the propensities for alignments of molecules are represented at each point of the fluid by an element Q of the vector space S_0 of 3× 3 real symmetric traceless matrices, or Q-tensors. According to Longa and Trebin (1989), a biaxial nematic system is called soft biaxial if the tensor order parameter Q satisfies the constraint tr(Q^2) = {const}. After the introduction of a Q-tensor model for soft biaxial nematic systems and the description of its geometric structure, we address the question of coercivity for the most common four-elastic-constant form of the Landau-de Gennes elastic free-energy (Iyer et al. 2015) in this model. For a soft biaxial nematic system, the tensor field Q takes values in a four-dimensional sphere S^4_ρ of radius ρ ≤ √{2/3} in the five-dimensional space S_0 with inner product < Q, P > = tr(QP). The rotation group it{SO}(3) acts orthogonally on S_0 by conjugation and hence induces an action on S^4_ρ \\subset {S}_0. This action has generic orbits of codimension one that are diffeomorphic to an eightfold quotient S^3/H of the unit three-sphere S^3, where H={± 1, ± i, ± j, ± k} is the quaternion group, and has two degenerate orbits of codimension two that are diffeomorphic to the projective plane RP^2. Each generic orbit can be interpreted as the order parameter space of a constrained biaxial nematic system and each singular orbit as the order parameter space of a constrained uniaxial nematic system. It turns out that S^4_ρ is a cohomogeneity one manifold, i.e., a manifold with a group action whose orbit space is one-dimensional. Another important geometric feature of the model is that the set Σ _ρ of diagonal Q-tensors of fixed norm ρ is a (geodesic) great circle in S^4_ρ which meets every orbit of S^4_ρ orthogonally and is then a section for S^4_ρ in the sense of the general theory of canonical forms. We compute necessary and sufficient coercivity conditions for the elastic energy by exploiting the it{SO}(3)-invariance of the elastic energy (frame-indifference), the existence of the section Σ _ρ for S^4_ρ , and the geometry of the model, which allow us to reduce to a suitable invariant problem on (an arc of) Σ _ρ . Our approach can ultimately be seen as an application of the general method of reduction of variables, or cohomogeneity method.

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

Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de; Reeb, David, E-mail: reeb.qit@gmail.com

We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transposemore » bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task.« less

An implanted 8-channel array coil for high-resolution macaque MRI at 3T

PubMed Central

Janssens, T.; Keil, B.; Farivar, R.; McNab, J.A.; Polimeni, J. R.; Gerits, A.; Arsenault, J.T.; Wald, L. L.; Vanduffel, W.

2012-01-01

An 8-channel receive coil array was constructed and implanted adjacent to the skull in a male rhesus monkey in order to improve the sensitivity of (functional) brain imaging. The permanent implant was part of an acrylic headpost assembly and only the coil element loop wires were implanted. The tuning, matching, and preamplifier circuitry was connected via a removable external assembly. Signal-to-noise ratio (SNR) and noise amplification for parallel imaging were compared to a single-, 4-, and 8-channel external receive-only coil routinely used for macaque fMRI. In vivo measurements showed significantly improved SNR within the brain for the implanted versus the external coils. Within a region-of-interest covering the cerebral cortex, we observed a 5.4-, 3.6-fold, and 3.4-fold increase in SNR compared to the external single-, 4-, and 8-channel coil, respectively. In the center of the brain, the implanted array maintained a 2.4×, 2.5×, and 2.1× higher SNR, respectively compared to the external coils. The array performance was evaluated for anatomical, diffusion tensor and functional brain imaging. This study suggests that a stable implanted phased-array coil can be used in macaque MRI to substantially increase the spatial resolution for anatomical, diffusion tensor, and functional imaging. PMID:22609793

The Full Ward-Takahashi Identity for Colored Tensor Models

NASA Astrophysics Data System (ADS)

Pérez-Sánchez, Carlos I.

2018-03-01

Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank- D interactions including, but not restricted to, all melonic φ^4 -vertices—to wit, solely those quartic vertices that can lead to dominant spherical contributions in the large- N expansion—the aforementioned boundary graphs are shown to be precisely all (possibly disconnected) vertex-bipartite regularly edge- D-colored graphs. The concept of CTM-compatible boundary-graph automorphism is introduced and an auxiliary graph calculus is developed. With the aid of these constructs, certain U (∞)-invariance of the path integral measure is fully exploited in order to derive a strong Ward-Takahashi Identity for CTMs with a symmetry-breaking kinetic term. For the rank-3 φ^4 -theory, we get the exact integral-like equation for the 2-point function. Similarly, exact equations for higher multipoint functions can be readily obtained departing from this full Ward-Takahashi identity. Our results hold for some Group Field Theories as well. Altogether, our non-perturbative approach trades some graph theoretical methods for analytical ones. We believe that these tools can be extended to tensorial SYK-models.

Penalized weighted least-squares approach for multienergy computed tomography image reconstruction via structure tensor total variation regularization.

PubMed

Zeng, Dong; Gao, Yuanyuan; Huang, Jing; Bian, Zhaoying; Zhang, Hua; Lu, Lijun; Ma, Jianhua

2016-10-01

Multienergy computed tomography (MECT) allows identifying and differentiating different materials through simultaneous capture of multiple sets of energy-selective data belonging to specific energy windows. However, because sufficient photon counts are not available in each energy window compared with that in the whole energy window, the MECT images reconstructed by the analytical approach often suffer from poor signal-to-noise and strong streak artifacts. To address the particular challenge, this work presents a penalized weighted least-squares (PWLS) scheme by incorporating the new concept of structure tensor total variation (STV) regularization, which is henceforth referred to as 'PWLS-STV' for simplicity. Specifically, the STV regularization is derived by penalizing higher-order derivatives of the desired MECT images. Thus it could provide more robust measures of image variation, which can eliminate the patchy artifacts often observed in total variation (TV) regularization. Subsequently, an alternating optimization algorithm was adopted to minimize the objective function. Extensive experiments with a digital XCAT phantom and meat specimen clearly demonstrate that the present PWLS-STV algorithm can achieve more gains than the existing TV-based algorithms and the conventional filtered backpeojection (FBP) algorithm in terms of both quantitative and visual quality evaluations. Copyright © 2016 Elsevier Ltd. All rights reserved.

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging.

PubMed

Koay, Cheng Guan; Chang, Lin-Ching; Carew, John D; Pierpaoli, Carlo; Basser, Peter J

2006-09-01

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (

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

PubMed

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

2002-04-01

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

Human action recognition based on point context tensor shape descriptor

NASA Astrophysics Data System (ADS)

Li, Jianjun; Mao, Xia; Chen, Lijiang; Wang, Lan

2017-07-01

Motion trajectory recognition is one of the most important means to determine the identity of a moving object. A compact and discriminative feature representation method can improve the trajectory recognition accuracy. This paper presents an efficient framework for action recognition using a three-dimensional skeleton kinematic joint model. First, we put forward a rotation-scale-translation-invariant shape descriptor based on point context (PC) and the normal vector of hypersurface to jointly characterize local motion and shape information. Meanwhile, an algorithm for extracting the key trajectory based on the confidence coefficient is proposed to reduce the randomness and computational complexity. Second, to decrease the eigenvalue decomposition time complexity, a tensor shape descriptor (TSD) based on PC that can globally capture the spatial layout and temporal order to preserve the spatial information of each frame is proposed. Then, a multilinear projection process is achieved by tensor dynamic time warping to map the TSD to a low-dimensional tensor subspace of the same size. Experimental results show that the proposed shape descriptor is effective and feasible, and the proposed approach obtains considerable performance improvement over the state-of-the-art approaches with respect to accuracy on a public action dataset.

Intermolecular shielding contributions studied by modeling the 13C chemical-shift tensors of organic single crystals with plane waves

PubMed Central

Johnston, Jessica C.; Iuliucci, Robbie J.; Facelli, Julio C.; Fitzgerald, George; Mueller, Karl T.

2009-01-01

In order to predict accurately the chemical shift of NMR-active nuclei in solid phase systems, magnetic shielding calculations must be capable of considering the complete lattice structure. Here we assess the accuracy of the density functional theory gauge-including projector augmented wave method, which uses pseudopotentials to approximate the nodal structure of the core electrons, to determine the magnetic properties of crystals by predicting the full chemical-shift tensors of all 13C nuclides in 14 organic single crystals from which experimental tensors have previously been reported. Plane-wave methods use periodic boundary conditions to incorporate the lattice structure, providing a substantial improvement for modeling the chemical shifts in hydrogen-bonded systems. Principal tensor components can now be predicted to an accuracy that approaches the typical experimental uncertainty. Moreover, methods that include the full solid-phase structure enable geometry optimizations to be performed on the input structures prior to calculation of the shielding. Improvement after optimization is noted here even when neutron diffraction data are used for determining the initial structures. After geometry optimization, the isotropic shift can be predicted to within 1 ppm. PMID:19831448

The tensor distribution function.

PubMed

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

2009-01-01

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

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

NASA Astrophysics Data System (ADS)

Jaques, Luís; Pascal, Christophe

2017-09-01

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

High-grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases.

PubMed

Roniotis, Alexandros; Manikis, Georgios C; Sakkalis, Vangelis; Zervakis, Michalis E; Karatzanis, Ioannis; Marias, Kostas

2012-03-01

Glioma, especially glioblastoma, is a leading cause of brain cancer fatality involving highly invasive and neoplastic growth. Diffusive models of glioma growth use variations of the diffusion-reaction equation in order to simulate the invasive patterns of glioma cells by approximating the spatiotemporal change of glioma cell concentration. The most advanced diffusive models take into consideration the heterogeneous velocity of glioma in gray and white matter, by using two different discrete diffusion coefficients in these areas. Moreover, by using diffusion tensor imaging (DTI), they simulate the anisotropic migration of glioma cells, which is facilitated along white fibers, assuming diffusion tensors with different diffusion coefficients along each candidate direction of growth. Our study extends this concept by fully exploiting the proportions of white and gray matter extracted by normal brain atlases, rather than discretizing diffusion coefficients. Moreover, the proportions of white and gray matter, as well as the diffusion tensors, are extracted by the respective atlases; thus, no DTI processing is needed. Finally, we applied this novel glioma growth model on real data and the results indicate that prognostication rates can be improved. © 2012 IEEE

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.

Symmetries, supersymmetries and cohomologies in gauge theories

NASA Astrophysics Data System (ADS)

Bǎbǎlîc, Elena-Mirela

2009-12-01

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

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.

Vortex lattices and defect-mediated viscosity reduction in active liquids

NASA Astrophysics Data System (ADS)

Slomka, Jonasz; Dunkel, Jorn

2016-11-01

Generic pattern-formation and viscosity-reduction mechanisms in active fluids are investigated using a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present exact analytical solutions including stress-free vortex lattices and introduce a computational framework that allows the efficient treatment of previously intractable higher-order shear boundary conditions. Large-scale parameter scans identify the conditions for spontaneous flow symmetry breaking, defect-mediated low-viscosity phases and negative-viscosity states amenable to energy harvesting in confined suspensions. The theory uses only generic assumptions about the symmetries and long-wavelength structure of active stress tensors, suggesting that inviscid phases may be achievable in a broad class of non-equilibrium fluids by tuning confinement geometry and pattern scale selection.

Geometry-dependent viscosity reduction in sheared active fluids

NASA Astrophysics Data System (ADS)

Słomka, Jonasz; Dunkel, Jörn

2017-04-01

We investigate flow pattern formation and viscosity reduction mechanisms in active fluids by studying a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present exact analytical solutions including stress-free vortex lattices and introduce a computational framework that allows the efficient treatment of higher-order shear boundary conditions. Large-scale parameter scans identify the conditions for spontaneous flow symmetry breaking, geometry-dependent viscosity reduction, and negative-viscosity states amenable to energy harvesting in confined suspensions. The theory uses only generic assumptions about the symmetries and long-wavelength structure of active stress tensors, suggesting that inviscid phases may be achievable in a broad class of nonequilibrium fluids by tuning confinement geometry and pattern scale selection.

Additively manufactured metallic pentamode meta-materials

NASA Astrophysics Data System (ADS)

Hedayati, R.; Leeflang, A. M.; Zadpoor, A. A.

2017-02-01

Mechanical metamaterials exhibit unusual mechanical properties that originate from their topological design. Pentamode metamaterials are particularly interesting because they could be designed to possess any thermodynamically admissible elasticity tensor. In this study, we additively manufacture the metallic pentamode metamaterials from a biocompatible and mechanically strong titanium alloy (Ti-6Al-4V) using an energy distribution method developed for the powder bed fusion techniques. The mechanical properties of the developed materials were a few orders of magnitude higher than those of the similar topologies fabricated previously from polymers. Moreover, the elastic modulus and yield stress of the presented pentamode metamaterials were decoupled from their relative density, meaning that the metallic meta-biomaterials with independently tailored elastic and mass transport (permeability) properties could be designed for tissue regeneration purposes.

Hyperbolic geometry of cosmological attractors

NASA Astrophysics Data System (ADS)

Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik

2015-08-01

Cosmological α attractors give a natural explanation for the spectral index ns of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r , consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial role of the hyperbolic geometry of the Poincaré disk or half plane in the supergravity construction. These geometries are isometric under Möbius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kähler potential frame that explicitly preserves this symmetry, enabling the inflaton to be light. Moreover, we include higher-order curvature deformations, which can stabilize a direction orthogonal to the inflationary trajectory. We illustrate this new framework by stabilizing the single superfield α attractors.

The simplest non-minimal matter-geometry coupling in the f( R, T) cosmology

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Sahoo, P. K.

2017-07-01

f( R, T) gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar R and the trace of the energy-momentum tensor T. In this way, f( R, T) models are capable of describing a non-minimal coupling between geometry (through terms in R) and matter (through terms in T). In this article we construct a cosmological model from the simplest non-minimal matter-geometry coupling within the f( R, T) gravity formalism, by means of an effective energy-momentum tensor, given by the sum of the usual matter energy-momentum tensor with a dark energy contribution, with the latter coming from the matter-geometry coupling terms. We apply the energy conditions to our solutions in order to obtain a range of values for the free parameters of the model which yield a healthy and well-behaved scenario. For some values of the free parameters which are submissive to the energy conditions application, it is possible to predict a transition from a decelerated period of the expansion of the universe to a period of acceleration (dark energy era). We also propose further applications of this particular case of the f( R, T) formalism in order to check its reliability in other fields, rather than cosmology.

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.

Generalized minimal principle for rotor filaments.

PubMed

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

2015-05-01

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

Mesoscopic model for the viscosities of nematic liquid crystals.

PubMed

Chrzanowska, A; Kröger, M; Sellers, S

1999-10-01

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

Broad diphoton resonance at the TeV? Not alone

NASA Astrophysics Data System (ADS)

Roig, Pablo; Sanz-Cillero, Juan José

2016-11-01

The hint for a possible resonance in the diphoton channel with mass of 750 GeV disappeared in the data presented at ICHEP'16 by ATLAS and CMS. However, the diphoton final state remains as one of the golden channels for new physics discoveries at the TeV scale in the LHC experiments. This motivates us to analyze model independently the implications of an O (TeV ) bump in the γ γ final state. By means of forward sum rules for γ γ scattering, we show that a spin-zero resonance with mass of the order of the TeV and a sizable γ γ partial width—-of the order of a few GeV—must be accompanied by higher-spin resonances with JR≥2 with similar properties, as expected in strongly coupled extensions of the Standard Model or, alternatively, in higher-dimensional deconstructed duals. Furthermore, independently of whether the putative O (TeV ) candidate is a scalar or a tensor, the large contribution to the forward sum rules in the referred scenario implies the presence of states in the spectrum with JR≥2 , these high-spin particles being a manifestation of new extra dimensions or composite states of a new strong sector.

Collective Modes in a Trapped Gas from Second-Order Hydrodynamics

NASA Astrophysics Data System (ADS)

Lewis, William; Romatschke, Paul

Navier-Stokes equations are often used to analyze collective oscillations and expansion dynamics of strongly interacting quantum gases. However, their use, for example, in precision determination of transport properties such as the ratio shear viscosity to entropy density (η / s) in strongly interacting Fermi gases problematic. Second-order hydrodynamics addresses this by promoting the viscous stress tensor to a hydrodynamic variable relaxing to the Navier-Stokes form on a timescale τπ. We derive frequencies, damping rates, and spatial structure of collective oscillations up to the decapole mode of a harmonically trapped gas in this framework. We find damping of higher-order modes (i.e. beyond quadrupolar) exhibits greater sensitivity to shear viscosity. Thus measurement of the hexapolar mode, for example, may lead to a stronger experimental constraint on η / s . Additionally, we find ``non-hydrodynamic'' modes not contained in a Navier-Stokes description. We calculate excitation amplitudes of non-hydrodynamic modes demonstrating they should be observable. Non-hydrodynamic modes may have implications for the hydrodynamization timescale, the existence of quasi-particles, and universal transport behavior in strongly interacting quantum fluids.

Brans-Dicke Galileon and the variational principle

NASA Astrophysics Data System (ADS)

Quiros, Israel; García-Salcedo, Ricardo; Gonzalez, Tame; Horta-Rangel, F. Antonio; Saavedra, Joel

2016-09-01

This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with cubic self-interaction. This is a modification of the Brans-Dicke theory by the addition of a term in the Lagrangian which is non-linear in the derivatives of the scalar field: it contains second-order derivatives. This is the basis of the so-called Brans-Dicke Galileon. We pay special attention to the variational principle and to the algebraic details of the derivation. It is shown how higher order derivatives of the fields appearing in the intermediate computations cancel out leading to second order motion equations. The reader will find useful tips for the derivation of the field equations of modifications of general relativity such as the scalar-tensor theories and f(R) theories, by means of the (stationary action) variational principle. The content of this paper is particularly recommended to those graduate and postgraduate students who are interested in the study of the mentioned modifications of general relativity.

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Markley, F. Landis

1990-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Stress modeling in colloidal dispersions undergoing non-viscometric flows

NASA Astrophysics Data System (ADS)

Dolata, Benjamin; Zia, Roseanna

2017-11-01

We present a theoretical study of the stress tensor for a colloidal dispersion undergoing non-viscometric flow. In such flows, the non-homogeneous suspension stress depends on not only the local average total stresslet-the sum of symmetric first moments of both the hydrodynamic traction and the interparticle force-but also on the average quadrupole, octupole, and higher-order moments. To compute the average moments, we formulate a six dimensional Smoluchowski equation governing the microstructural evolution of a suspension in an arbitrary fluid velocity field. Under the conditions of rheologically slow flow, where the Brownian relaxation of the particles is much faster than the spatiotemporal evolution of the flow, the Smoluchowski equation permits asymptotic solution, revealing a suspension stress that follows a second-order fluid constitutive model. We obtain a reciprocal theorem and utilize it to show that all constitutive parameters of the second-order fluid model may be obtained from two simpler linear-response problems: a suspension undergoing simple shear and a suspension undergoing isotropic expansion. The consequences of relaxing the assumption of rheologically slow flow, including the appearance of memory and microcontinuum behaviors, are discussed.

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Baritzhack, Itzhack Y.; Markley, F. Landis

1988-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Foundations of Tensor Analysis for Students of Physics and Engineering With an Introduction to the Theory of Relativity

NASA Technical Reports Server (NTRS)

Kolecki, Joseph C.

2005-01-01

Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.

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.)

General equilibrium second-order hydrodynamic coefficients for free quantum fields

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

f(R)-gravity from Killing tensors

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos

2016-04-01

We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.

New classes of modified teleparallel gravity models

NASA Astrophysics Data System (ADS)

Bahamonde, Sebastian; Böhmer, Christian G.; Krššák, Martin

2017-12-01

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion f (Tax ,Tten ,Tvec), where Tax ,Tten and Tvec are squares of the axial, tensor and vector components of torsion, respectively. This is the most general (well-motivated) second order teleparallel theory of gravity that can be constructed from the torsion tensor. Different particular second order theories can be recovered from this theory such as new general relativity, conformal teleparallel gravity or f (T) gravity. Additionally, the boundary term B which connects the Ricci scalar with the torsion scalar via R = - T + B can also be incorporated into the action. By performing a conformal transformation, it is shown that the two unique theories which have an Einstein frame are either the teleparallel equivalent of general relativity or f (- T + B) = f (R) gravity, as expected.

Kinematics of velocity and vorticity correlations in turbulent flow

NASA Technical Reports Server (NTRS)

Bernard, P. S.

1983-01-01

The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.

Failure of geometric electromagnetism in the adiabatic vector Kepler problem

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

Anglin, J.R.; Schmiedmayer, J.

2004-02-01

The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire's magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this 'vector Kepler problem' has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential ('geometric electromagnetism') fails to predict themore » precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a 1/r{sup 3} singularity which is an artifact of the adiabatic approximation.« less

First order augmentation to tensor voting for boundary inference and multiscale analysis in 3D.

PubMed

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

2004-05-01

Most computer vision applications require the reliable detection of boundaries. In the presence of outliers, missing data, orientation discontinuities, and occlusion, this problem is particularly challenging. We propose to address it by complementing the tensor voting framework, which was limited to second order properties, with first order representation and voting. First order voting fields and a mechanism to vote for 3D surface and volume boundaries and curve endpoints in 3D are defined. Boundary inference is also useful for a second difficult problem in grouping, namely, automatic scale selection. We propose an algorithm that automatically infers the smallest scale that can preserve the finest details. Our algorithm then proceeds with progressively larger scales to ensure continuity where it has not been achieved. Therefore, the proposed approach does not oversmooth features or delay the handling of boundaries and discontinuities until model misfit occurs. The interaction of smooth features, boundaries, and outliers is accommodated by the unified representation, making possible the perceptual organization of data in curves, surfaces, volumes, and their boundaries simultaneously. We present results on a variety of data sets to show the efficacy of the improved formalism.

Alterations to the relativistic Love-Franey model and their application to inelastic scattering

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

Zeile, J.R.

The fictitious axial-vector and tensor mesons for the real part of the relativistic Love-Franey interaction are removed. In an attempt to make up for this loss, derivative couplings are used for the {pi} and {rho} mesons. Such derivative couplings require the introduction of axial-vector and tensor contact term corrections. Meson parameters are then fit to free nucleon-nucleon scattering data. The resulting fits are comparable to those of the relativistic Love-Franey model provided that the contact term corrections are included and the fits are weighted over the physically significant quantity of twice the tensor minus the axial-vector Lorentz invariants. Failure tomore » include contact term corrections leads to poor fits at higher energies. The off-shell behavior of this model is then examined by looking at several applications from inelastic proton-nucleus scattering.« less

Nonexotic matter wormholes in a trace of the energy-momentum tensor squared gravity

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Sahoo, P. K.

2018-01-01

Wormholes are tunnels connecting two different points in space-time. In Einstein's general relativity theory, wormholes are expected to be filled by exotic matter, i.e., matter that does not satisfy the energy conditions and may have negative density. We propose, in this paper, the achievement of wormhole solutions with no need for exotic matter. In order to achieve so, we consider a gravity theory that starts from linear and quadratic terms on the trace of the energy-momentum tensor in the gravitational action. We show that by following this formalism, it is possible, indeed, to obtain nonexotic matter wormhole solutions.

Secondary isocurvature perturbations from acoustic reheating

NASA Astrophysics Data System (ADS)

Ota, Atsuhisa; Yamaguchi, Masahide

2018-06-01

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

Torsional Optomechanics of a Levitated Nonspherical Nanoparticle

NASA Astrophysics Data System (ADS)

Hoang, Thai M.; Ma, Yue; Ahn, Jonghoon; Bang, Jaehoon; Robicheaux, F.; Yin, Zhang-Qi; Li, Tongcang

2016-09-01

An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tensor. The torsional vibration frequency can be 1 order of magnitude higher than its center-of-mass motion frequency, which is promising for ground state cooling. We propose a simple yet novel scheme to achieve ground state cooling of its torsional vibration with a linearly polarized Gaussian cavity mode. A levitated nonspherical nanoparticle in vacuum will also be an ultrasensitive nanoscale torsion balance with a torque detection sensitivity on the order of 10-29 N m /√{Hz } under realistic conditions.

Motion of small bodies in classical field theory

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.

2010-04-01

I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body’s composition (and, e.g., black holes are allowed). The worldline “left behind” by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the “Bianchi identity” for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the “monopoles” of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of “chameleon” bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.

On a viable first-order formulation of relativistic viscous fluids and its applications to cosmology

NASA Astrophysics Data System (ADS)

Disconzi, Marcelo M.; Kephart, Thomas W.; Scherrer, Robert J.

We consider a first-order formulation of relativistic fluids with bulk viscosity based on a stress-energy tensor introduced by Lichnerowicz. Choosing a barotropic equation-of-state, we show that this theory satisfies basic physical requirements and, under the further assumption of vanishing vorticity, that the equations of motion are causal, both in the case of a fixed background and when the equations are coupled to Einstein's equations. Furthermore, Lichnerowicz's proposal does not fit into the general framework of first-order theories studied by Hiscock and Lindblom, and hence their instability results do not apply. These conclusions apply to the full-fledged nonlinear theory, without any equilibrium or near equilibrium assumptions. Similarities and differences between the approach explored here and other theories of relativistic viscosity, including the Mueller-Israel-Stewart formulation, are addressed. Cosmological models based on the Lichnerowicz stress-energy tensor are studied. As the topic of (relativistic) viscous fluids is also of interest outside the general relativity and cosmology communities, such as, for instance, in applications involving heavy-ion collisions, we make our presentation largely self-contained.

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.

Limits on tensor coupling from neutron β decay

NASA Astrophysics Data System (ADS)

Pattie, R. W., Jr.; Hickerson, K. P.; Young, A. R.

2013-10-01

Limits on the tensor couplings generating a Fierz interference term b in mixed Gamow-Teller Fermi decays can be derived by combining data from measurements of angular correlation parameters in neutron decay, the neutron lifetime, and GV=GFVud as extracted from measurements of the Ft values from the 0+→0+ superallowed decay data set. These limits are derived by comparing the neutron β-decay rate as predicted in the standard model with the measured decay rate while allowing for the existence of beyond the standard model (BSM) couplings. We analyze limits derived from the electron-neutrino asymmetry a, or the beta asymmetry A, finding that the most stringent limits for CT/CA under the assumption of no right-handed neutrinos is -0.0026

Polarized two-photon photoselection in EGFP: Theory and experiment

NASA Astrophysics Data System (ADS)

Masters, T. A.; Marsh, R. J.; Blacker, T. S.; Armoogum, D. A.; Larijani, B.; Bain, A. J.

2018-04-01

In this work, we present a complete theoretical description of the excited state order created by two-photon photoselection from an isotropic ground state; this encompasses both the conventionally measured quadrupolar (K = 2) and the "hidden" degree of hexadecapolar (K = 4) transition dipole alignment, their dependence on the two-photon transition tensor and emission transition dipole moment orientation. Linearly and circularly polarized two-photon absorption (TPA) and time-resolved single- and two-photon fluorescence anisotropy measurements are used to determine the structure of the transition tensor in the deprotonated form of enhanced green fluorescent protein. For excitation wavelengths between 800 nm and 900 nm, TPA is best described by a single element, almost completely diagonal, two-dimensional (planar) transition tensor whose principal axis is collinear to that of the single-photon S0 → S1 transition moment. These observations are in accordance with assignments of the near-infrared two-photon absorption band in fluorescent proteins to a vibronically enhanced S0 → S1 transition.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

No-Go Theorem for Nonstandard Explanations of the τ → K S π ν τ C P Asymmetry

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

Cirigliano, Vincenzo; Crivellin, Andreas; Hoferichter, Martin

Tmore » he C P asymmetry in τ → K S π ν τ C P , as measured by the BABAR collaboration, differs from the standard model prediction by 2.8 σ . Most nonstandard interactions do not allow for the required strong phase needed to produce a nonvanishing C P asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least 2 orders of magnitude due to Watson’s final-state-interaction theorem. Furthermore, we find that the strength of the relevant C P -violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and D – ¯ D mixing. hese observations together imply that it is extremely difficult to explain the current τ → K S π ν τ C P measurement in terms of physics beyond the standard model originating in the ultraviolet.« less

No-Go Theorem for Nonstandard Explanations of the τ → K S π ν τ C P Asymmetry

DOE PAGES

Cirigliano, Vincenzo; Crivellin, Andreas; Hoferichter, Martin

2018-04-06

Tmore » he C P asymmetry in τ → K S π ν τ C P , as measured by the BABAR collaboration, differs from the standard model prediction by 2.8 σ . Most nonstandard interactions do not allow for the required strong phase needed to produce a nonvanishing C P asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least 2 orders of magnitude due to Watson’s final-state-interaction theorem. Furthermore, we find that the strength of the relevant C P -violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and D – ¯ D mixing. hese observations together imply that it is extremely difficult to explain the current τ → K S π ν τ C P measurement in terms of physics beyond the standard model originating in the ultraviolet.« less

Experimental constraint on quark electric dipole moments

NASA Astrophysics Data System (ADS)

Liu, Tianbo; Zhao, Zhiwen; Gao, Haiyan

2018-04-01

The electric dipole moments (EDMs) of nucleons are sensitive probes of additional C P violation sources beyond the standard model to account for the baryon number asymmetry of the universe. As a fundamental quantity of the nucleon structure, tensor charge is also a bridge that relates nucleon EDMs to quark EDMs. With a combination of nucleon EDM measurements and tensor charge extractions, we investigate the experimental constraint on quark EDMs, and its sensitivity to C P violation sources from new physics beyond the electroweak scale. We obtain the current limits on quark EDMs as 1.27 ×10-24 e .cm for the up quark and 1.17 ×10-24 e .cm for the down quark at the scale of 4 GeV2 . We also study the impact of future nucleon EDM and tensor charge measurements, and show that upcoming new experiments will improve the constraint on quark EDMs by about 3 orders of magnitude leading to a much more sensitive probe of new physics models.

Polarized two-photon photoselection in EGFP: Theory and experiment.

PubMed

Masters, T A; Marsh, R J; Blacker, T S; Armoogum, D A; Larijani, B; Bain, A J

2018-04-07

In this work, we present a complete theoretical description of the excited state order created by two-photon photoselection from an isotropic ground state; this encompasses both the conventionally measured quadrupolar (K = 2) and the "hidden" degree of hexadecapolar (K = 4) transition dipole alignment, their dependence on the two-photon transition tensor and emission transition dipole moment orientation. Linearly and circularly polarized two-photon absorption (TPA) and time-resolved single- and two-photon fluorescence anisotropy measurements are used to determine the structure of the transition tensor in the deprotonated form of enhanced green fluorescent protein. For excitation wavelengths between 800 nm and 900 nm, TPA is best described by a single element, almost completely diagonal, two-dimensional (planar) transition tensor whose principal axis is collinear to that of the single-photon S 0 → S 1 transition moment. These observations are in accordance with assignments of the near-infrared two-photon absorption band in fluorescent proteins to a vibronically enhanced S 0 → S 1 transition.

Metric-affine f (R ,T ) theories of gravity and their applications

NASA Astrophysics Data System (ADS)

Barrientos, E.; Lobo, Francisco S. N.; Mendoza, S.; Olmo, Gonzalo J.; Rubiera-Garcia, D.

2018-05-01

We study f (R ,T ) theories of gravity, where T is the trace of the energy-momentum tensor Tμ ν, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f (R ) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the nonconservation of the energy-momentum tensor, which implies nongeodesic motion and consequently leads to the appearance of an extra force. The weak field limit leads to a modified Poisson equation formally identical to that found in Eddington-inspired Born-Infeld gravity. Furthermore, the coupling of these gravity theories to perfect fluids, electromagnetic, and scalar fields, and their potential applications are discussed.

MULTISCALE TENSOR ANISOTROPIC FILTERING OF FLUORESCENCE MICROSCOPY FOR DENOISING MICROVASCULATURE.

PubMed

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

2015-04-01

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

Tensor to scalar ratio and large scale power suppression from pre-slow roll initial conditions

NASA Astrophysics Data System (ADS)

Lello, Louis; Boyanovsky, Daniel

2014-05-01

We study the corrections to the power spectra of curvature and tensor perturbations and the tensor-to-scalar ratio r in single field slow roll inflation with standard kinetic term due to initial conditions imprinted by a ``fast-roll'' stage prior to slow roll. For a wide range of initial inflaton kinetic energy, this stage lasts only a few e-folds and merges smoothly with slow-roll thereby leading to non-Bunch-Davies initial conditions for modes that exit the Hubble radius during slow roll. We describe a program that yields the dynamics in the fast-roll stage while matching to the slow roll stage in a manner that is independent of the inflationary potentials. Corrections to the power spectra are encoded in a ``transfer function'' for initial conditions Script Tα(k), Script Pα(k) = PBDα(k)Script Tα(k), implying a modification of the ``consistency condition'' for the tensor to scalar ratio at a pivot scale k0: r(k0) = -8nT(k0) [Script TT(k0)/Script TScript R(k0)]. We obtain Script Tα(k) to leading order in a Born approximation valid for modes of observational relevance today. A fit yields Script Tα(k) = 1+Aαk-pcos [2πωk/Hsr+varphiα], with 1.5lesssimplesssim2, ω simeq 1 and Hsr the Hubble scale during slow roll inflation, where curvature and tensor perturbations feature the same p,ω for a wide range of initial conditions. These corrections lead to both a suppression of the quadrupole and oscillatory features in both PR(k) and r(k0) with a period of the order of the Hubble scale during slow roll inflation. The results are quite general and independent of the specific inflationary potentials, depending solely on the ratio of kinetic to potential energy κ and the slow roll parameters epsilonV, ηV to leading order in slow roll. For a wide range of κ and the values of epsilonV ηV corresponding to the upper bounds from Planck, we find that the low quadrupole is consistent with the results from Planck, and the oscillations in r(k0) as a function of k0 could be observable if the modes corresponding to the quadrupole and the pivot scale crossed the Hubble radius very few (2-3) e-folds after the onset of slow roll. We comment on possible impact on the recent BICEP2 results.

On actions for (entangling) surfaces and DCFTs

NASA Astrophysics Data System (ADS)

Armas, Jay; Tarrío, Javier

2018-04-01

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

The cosmic web and the orientation of angular momenta

NASA Astrophysics Data System (ADS)

Libeskind, Noam I.; Hoffman, Yehuda; Knebe, Alexander; Steinmetz, Matthias; Gottlöber, Stefan; Metuki, Ofer; Yepes, Gustavo

2012-03-01

We use a 64 h-1 Mpc dark-matter-only cosmological simulation to examine the large-scale orientation of haloes and substructures with respect to the cosmic web. A web classification scheme based on the velocity shear tensor is used to assign to each halo in the simulation a web type: knot, filament, sheet or void. Using ˜106 haloes that span ˜3 orders of magnitude in mass, the orientation of the halo's spin and the orbital angular momentum of subhaloes with respect to the eigenvectors of the shear tensor is examined. We find that the orbital angular momentum of subhaloes tends to align with the intermediate eigenvector of the velocity shear tensor for all haloes in knots, filaments and sheets. This result indicates that the kinematics of substructures located deep within the virialized regions of a halo is determined by its infall which in turn is determined by the large-scale velocity shear, a surprising result given the virialized nature of haloes. The non-random nature of subhalo accretion is thus imprinted on the angular momentum measured at z= 0. We also find that the haloes' spin axis is aligned with the third eigenvector of the velocity shear tensor in filaments and sheets: the halo spin axis points along filaments and lies in the plane of cosmic sheets.

Aspects of general higher-order gravities

NASA Astrophysics Data System (ADS)

Bueno, Pablo; Cano, Pablo A.; Min, Vincent S.; Visser, Manus R.

2017-02-01

We study several aspects of higher-order gravities constructed from general contractions of the Riemann tensor and the metric in arbitrary dimensions. First, we use the fast-linearization procedure presented in [P. Bueno and P. A. Cano, arXiv:1607.06463] to obtain the equations satisfied by the metric perturbation modes on a maximally symmetric background in the presence of matter and to classify L (Riemann ) theories according to their spectrum. Then, we linearize all theories up to quartic order in curvature and use this result to construct quartic versions of Einsteinian cubic gravity. In addition, we show that the most general cubic gravity constructed in a dimension-independent way and which does not propagate the ghostlike spin-2 mode (but can propagate the scalar) is a linear combination of f (Lovelock ) invariants, plus the Einsteinian cubic gravity term, plus a new ghost-free gravity term. Next, we construct the generalized Newton potential and the post-Newtonian parameter γ for general L (Riemann ) gravities in arbitrary dimensions, unveiling some interesting differences with respect to the four-dimensional case. We also study the emission and propagation of gravitational radiation from sources for these theories in four dimensions, providing a generalized formula for the power emitted. Finally, we review Wald's formalism for general L (Riemann ) theories and construct new explicit expressions for the relevant quantities involved. Many examples illustrate our calculations.

A new global approach to obtain three-dimensional displacement maps by integrating GPS and DInSAR data

NASA Astrophysics Data System (ADS)

Guglielmino, F.; Nunnari, G.; Puglisi, G.; Spata, A.

2009-04-01

We propose a new technique, based on the elastic theory, to efficiently produce an estimate of three-dimensional surface displacement maps by integrating sparse Global Position System (GPS) measurements of deformations and Differential Interferometric Synthetic Aperture Radar (DInSAR) maps of movements of the Earth's surface. The previous methodologies known in literature, for combining data from GPS and DInSAR surveys, require two steps: the first, in which sparse GPS measurements are interpolated in order to fill in GPS displacements at the DInSAR grid, and the second, to estimate the three-dimensional surface displacement maps by using a suitable optimization technique. One of the advantages of the proposed approach is that both these steps are unified. We propose a linear matrix equation which accounts for both GPS and DInSAR data whose solution provide simultaneously the strain tensor, the displacement field and the rigid body rotation tensor throughout the entire investigated area. The mentioned linear matrix equation is solved by using the Weighted Least Square (WLS) thus assuring both numerical robustness and high computation efficiency. The proposed methodology was tested on both synthetic and experimental data, these last from GPS and DInSAR measurements carried out on Mt. Etna. The goodness of the results has been evaluated by using standard errors. These tests also allow optimising the choice of specific parameters of this algorithm. This "open" structure of the method will allow in the near future to take account of other available data sets, such as additional interferograms, or other geodetic data (e.g. levelling, tilt, etc.), in order to achieve even higher accuracy.

Estimating cosmic velocity fields from density fields and tidal tensors

NASA Astrophysics Data System (ADS)

Kitaura, Francisco-Shu; Angulo, Raul E.; Hoffman, Yehuda; Gottlöber, Stefan

2012-10-01

In this work we investigate the non-linear and non-local relation between cosmological density and peculiar velocity fields. Our goal is to provide an algorithm for the reconstruction of the non-linear velocity field from the fully non-linear density. We find that including the gravitational tidal field tensor using second-order Lagrangian perturbation theory based upon an estimate of the linear component of the non-linear density field significantly improves the estimate of the cosmic flow in comparison to linear theory not only in the low density, but also and more dramatically in the high-density regions. In particular we test two estimates of the linear component: the lognormal model and the iterative Lagrangian linearization. The present approach relies on a rigorous higher order Lagrangian perturbation theory analysis which incorporates a non-local relation. It does not require additional fitting from simulations being in this sense parameter free, it is independent of statistical-geometrical optimization and it is straightforward and efficient to compute. The method is demonstrated to yield an unbiased estimator of the velocity field on scales ≳5 h-1 Mpc with closely Gaussian distributed errors. Moreover, the statistics of the divergence of the peculiar velocity field is extremely well recovered showing a good agreement with the true one from N-body simulations. The typical errors of about 10 km s-1 (1σ confidence intervals) are reduced by more than 80 per cent with respect to linear theory in the scale range between 5 and 10 h-1 Mpc in high-density regions (δ > 2). We also find that iterative Lagrangian linearization is significantly superior in the low-density regime with respect to the lognormal model.

Remarks on turbulent constitutive relations

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Lumley, John L.

1993-01-01

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

Hybrid High-Order methods for finite deformations of hyperelastic materials

NASA Astrophysics Data System (ADS)

Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

2018-01-01

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

Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix

NASA Astrophysics Data System (ADS)

Bharath, H. M.; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

2017-04-01

Topological phases of matter are characterized by topological order parameters that are built using Berry's geometric phase. Berry's phase is the geometric information stored in the overall phase of a quantum state. We show that geometric information is also stored in the second and higher order spin moments of a quantum spin system, captured by a non-abelian geometric phase. The quantum state of a spin-S system is uniquely characterized by its spin moments up to order 2S. The first-order spin moment is the spin vector, and the second-order spin moment represents the spin fluctuation tensor, i.e., the quantum noise matrix. When the spin vector is transported along a loop in the Bloch ball, we show that the quantum noise matrix picks up a geometric phase. Considering spin-1 systems, we formulate this geometric phase as an SO(3) operator. Geometric phases are usually interpreted in terms of the solid angle subtended by the loop at the center. However, solid angles are not well defined for loops that pass through the center. Here, we introduce a generalized solid angle which is well defined for all loops inside the Bloch ball, in terms of which, we interpret the SO(3) geometric phase. This geometric phase can be used to characterize topological spin textures in cold atomic clouds.

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1990-01-01

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

One-loop effective actions and higher spins. Part II

NASA Astrophysics Data System (ADS)

Bonora, L.; Cvitan, M.; Prester, P. Dominis; Giaccari, S.; Štemberga, T.

2018-01-01

In this paper we continue and improve the analysis of the effective actions obtained by integrating out a scalar and a fermion field coupled to external symmetric sources, started in the previous paper. The first subject we study is the geometrization of the results obtained there, that is we express them in terms of covariant Jacobi tensors. The second subject concerns the treatment of tadpoles and seagull terms in order to implement off-shell covariance in the initial model. The last and by far largest part of the paper is a repository of results concerning all two point correlators (including mixed ones) of symmetric currents of any spin up to 5 and in any dimensions between 3 and 6. In the massless case we also provide formulas for any spin in any dimension.

Higher symmetries of the Schrödinger operator in Newton-Cartan geometry

NASA Astrophysics Data System (ADS)

Gundry, James

2017-03-01

We establish several relationships between the non-relativistic conformal symmetries of Newton-Cartan geometry and the Schrödinger equation. In particular we discuss the algebra sch(d) of vector fields conformally-preserving a flat Newton-Cartan spacetime, and we prove that its curved generalisation generates the symmetry group of the covariant Schrödinger equation coupled to a Newtonian potential and generalised Coriolis force. We provide intrinsic Newton-Cartan definitions of Killing tensors and conformal Schrödinger-Killing tensors, and we discuss their respective links to conserved quantities and to the higher symmetries of the Schrödinger equation. Finally we consider the role of conformal symmetries in Newtonian twistor theory, where the infinite-dimensional algebra of holomorphic vector fields on twistor space corresponds to the symmetry algebra cnc(3) on the Newton-Cartan spacetime.

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Influence of Corticospinal Tracts from Higher Order Motor Cortices on Recruitment Curve Properties in Stroke

PubMed Central

Potter-Baker, Kelsey A.; Varnerin, Nicole M.; Cunningham, David A.; Roelle, Sarah M.; Sankarasubramanian, Vishwanath; Bonnett, Corin E.; Machado, Andre G.; Conforto, Adriana B.; Sakaie, Ken; Plow, Ela B.

2016-01-01

Background: Recruitment curves (RCs) acquired using transcranial magnetic stimulation are commonly used in stroke to study physiologic functioning of corticospinal tracts (CST) from M1. However, it is unclear whether CSTs from higher motor cortices contribute as well. Objective: To explore whether integrity of CST from higher motor areas, besides M1, relates to CST functioning captured using RCs. Methods: RCs were acquired for a paretic hand muscle in patients with chronic stroke. Metrics describing gain and overall output of CST were collected. CST integrity was defined by diffusion tensor imaging. For CST emerging from M1 and higher motor areas, integrity (fractional anisotropy) was evaluated in the region of the posterior limb of the internal capsule, the length of CST and in the region of the stroke lesion. Results: We found that output and gain of RC was related to integrity along the length of CST emerging from higher motor cortices but not the M1. Conclusions: Our results suggest that RC parameters in chronic stroke infer function primarily of CST descending from the higher motor areas but not M1. RCs may thus serve as a simple, in-expensive means to assess re-mapping of alternate areas that is generally studied with resource-intensive neuroimaging in stroke. PMID:27013942

Influence of Corticospinal Tracts from Higher Order Motor Cortices on Recruitment Curve Properties in Stroke.

PubMed

Potter-Baker, Kelsey A; Varnerin, Nicole M; Cunningham, David A; Roelle, Sarah M; Sankarasubramanian, Vishwanath; Bonnett, Corin E; Machado, Andre G; Conforto, Adriana B; Sakaie, Ken; Plow, Ela B

2016-01-01

Recruitment curves (RCs) acquired using transcranial magnetic stimulation are commonly used in stroke to study physiologic functioning of corticospinal tracts (CST) from M1. However, it is unclear whether CSTs from higher motor cortices contribute as well. To explore whether integrity of CST from higher motor areas, besides M1, relates to CST functioning captured using RCs. RCs were acquired for a paretic hand muscle in patients with chronic stroke. Metrics describing gain and overall output of CST were collected. CST integrity was defined by diffusion tensor imaging. For CST emerging from M1 and higher motor areas, integrity (fractional anisotropy) was evaluated in the region of the posterior limb of the internal capsule, the length of CST and in the region of the stroke lesion. We found that output and gain of RC was related to integrity along the length of CST emerging from higher motor cortices but not the M1. Our results suggest that RC parameters in chronic stroke infer function primarily of CST descending from the higher motor areas but not M1. RCs may thus serve as a simple, in-expensive means to assess re-mapping of alternate areas that is generally studied with resource-intensive neuroimaging in stroke.

Vacuum polarization effects on flat branes due to a global monopole

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

Bezerra de Mello, E.R.

2006-05-15

In this paper we analyze the vacuum polarization effects associated with a massless scalar field in the higher-dimensional spacetime. Specifically we calculate the renormalized vacuum expectation value of the square of the field, <{phi}{sup 2}(x)>{sub Ren}, induced by a global monopole in the 'braneworld' scenario. In this context the global monopole lives in a n=3-dimensional submanifold of the higher-dimensional (bulk) spacetime, and our universe is represented by a transverse flat (p-1)-dimensional brane. In order to develop this analysis we calculate the general Green function admitting that the scalar field propagates in the bulk. Also a general curvature coupling parameter betweenmore » the field and the geometry is assumed. We explicitly show that the vacuum polarization effects depend crucially on the values attributed to p. We also investigate the general structure of the renormalized vacuum expectation value of the energy-momentum tensor, {sub Ren}, for p=3.« less

Development of a Human Brain Diffusion Tensor Template

PubMed Central

Peng, Huiling; Orlichenko, Anton; Dawe, Robert J.; Agam, Gady; Zhang, Shengwei; Arfanakis, Konstantinos

2009-01-01

The development of a brain template for diffusion tensor imaging (DTI) is crucial for comparisons of neuronal structural integrity and brain connectivity across populations, as well as for the development of a white matter atlas. Previous efforts to produce a DTI brain template have been compromised by factors related to image quality, the effectiveness of the image registration approach, the appropriateness of subject inclusion criteria, the completeness and accuracy of the information summarized in the final template. The purpose of this work was to develop a DTI human brain template using techniques that address the shortcomings of previous efforts. Therefore, data containing minimal artifacts were first obtained on 67 healthy human subjects selected from an age-group with relatively similar diffusion characteristics (20–40 years of age), using an appropriate DTI acquisition protocol. Non-linear image registration based on mean diffusion-weighted and fractional anisotropy images was employed. DTI brain templates containing median and mean tensors were produced in ICBM-152 space and made publicly available. The resulting set of DTI templates is characterized by higher image sharpness, provides the ability to distinguish smaller white matter fiber structures, contains fewer image artifacts, than previously developed templates, and to our knowledge, is one of only two templates produced based on a relatively large number of subjects. Furthermore, median tensors were shown to better preserve the diffusion characteristics at the group level than mean tensors. Finally, white matter fiber tractography was applied on the template and several fiber-bundles were traced. PMID:19341801

Development of a human brain diffusion tensor template.

PubMed

Peng, Huiling; Orlichenko, Anton; Dawe, Robert J; Agam, Gady; Zhang, Shengwei; Arfanakis, Konstantinos

2009-07-15

The development of a brain template for diffusion tensor imaging (DTI) is crucial for comparisons of neuronal structural integrity and brain connectivity across populations, as well as for the development of a white matter atlas. Previous efforts to produce a DTI brain template have been compromised by factors related to image quality, the effectiveness of the image registration approach, the appropriateness of subject inclusion criteria, and the completeness and accuracy of the information summarized in the final template. The purpose of this work was to develop a DTI human brain template using techniques that address the shortcomings of previous efforts. Therefore, data containing minimal artifacts were first obtained on 67 healthy human subjects selected from an age-group with relatively similar diffusion characteristics (20-40 years of age), using an appropriate DTI acquisition protocol. Non-linear image registration based on mean diffusion-weighted and fractional anisotropy images was employed. DTI brain templates containing median and mean tensors were produced in ICBM-152 space and made publicly available. The resulting set of DTI templates is characterized by higher image sharpness, provides the ability to distinguish smaller white matter fiber structures, contains fewer image artifacts, than previously developed templates, and to our knowledge, is one of only two templates produced based on a relatively large number of subjects. Furthermore, median tensors were shown to better preserve the diffusion characteristics at the group level than mean tensors. Finally, white matter fiber tractography was applied on the template and several fiber-bundles were traced.

Anisotropic Developments for Homogeneous Shear Flows

NASA Technical Reports Server (NTRS)

Cambon, Claude; Rubinstein, Robert

2006-01-01

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

Evaluating Small Sphere Limit of the Wang-Yau Quasi-Local Energy

NASA Astrophysics Data System (ADS)

Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung

2018-01-01

In this article, we study the small sphere limit of the Wang-Yau quasi-local energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009, Commun Math Phys 288(3):919-942, 2009). Given a point p in a spacetime N, we consider a canonical family of surfaces approaching p along its future null cone and evaluate the limit of the Wang-Yau quasi-local energy. The evaluation relies on solving an "optimal embedding equation" whose solutions represent critical points of the quasi-local energy. For a spacetime with matter fields, the scenario is similar to that of the large sphere limit found in Chen et al. (Commun Math Phys 308(3):845-863, 2011). Namely, there is a natural solution which is a local minimum, and the limit of its quasi-local energy recovers the stress-energy tensor at p. For a vacuum spacetime, the quasi-local energy vanishes to higher order and the solution of the optimal embedding equation is more complicated. Nevertheless, we are able to show that there exists a solution that is a local minimum and that the limit of its quasi-local energy is related to the Bel-Robinson tensor. Together with earlier work (Chen et al. 2011), this completes the consistency verification of the Wang-Yau quasi-local energy with all classical limits.

Coupled Analysis of In Vitro and Histology Tissue Samples to Quantify Structure-Function Relationship

PubMed Central

Acar, Evrim; Plopper, George E.; Yener, Bülent

2012-01-01

The structure/function relationship is fundamental to our understanding of biological systems at all levels, and drives most, if not all, techniques for detecting, diagnosing, and treating disease. However, at the tissue level of biological complexity we encounter a gap in the structure/function relationship: having accumulated an extraordinary amount of detailed information about biological tissues at the cellular and subcellular level, we cannot assemble it in a way that explains the correspondingly complex biological functions these structures perform. To help close this information gap we define here several quantitative temperospatial features that link tissue structure to its corresponding biological function. Both histological images of human tissue samples and fluorescence images of three-dimensional cultures of human cells are used to compare the accuracy of in vitro culture models with their corresponding human tissues. To the best of our knowledge, there is no prior work on a quantitative comparison of histology and in vitro samples. Features are calculated from graph theoretical representations of tissue structures and the data are analyzed in the form of matrices and higher-order tensors using matrix and tensor factorization methods, with a goal of differentiating between cancerous and healthy states of brain, breast, and bone tissues. We also show that our techniques can differentiate between the structural organization of native tissues and their corresponding in vitro engineered cell culture models. PMID:22479315