Parameter Estimation of Spacecraft Fuel Slosh Model

NASA Technical Reports Server (NTRS)

Gangadharan, Sathya; Sudermann, James; Marlowe, Andrea; Njengam Charles

2004-01-01

Fuel slosh in the upper stages of a spinning spacecraft during launch has been a long standing concern for the success of a space mission. Energy loss through the movement of the liquid fuel in the fuel tank affects the gyroscopic stability of the spacecraft and leads to nutation (wobble) which can cause devastating control issues. The rate at which nutation develops (defined by Nutation Time Constant (NTC can be tedious to calculate and largely inaccurate if done during the early stages of spacecraft design. Pure analytical means of predicting the influence of onboard liquids have generally failed. A strong need exists to identify and model the conditions of resonance between nutation motion and liquid modes and to understand the general characteristics of the liquid motion that causes the problem in spinning spacecraft. A 3-D computerized model of the fuel slosh that accounts for any resonant modes found in the experimental testing will allow for increased accuracy in the overall modeling process. Development of a more accurate model of the fuel slosh currently lies in a more generalized 3-D computerized model incorporating masses, springs and dampers. Parameters describing the model include the inertia tensor of the fuel, spring constants, and damper coefficients. Refinement and understanding the effects of these parameters allow for a more accurate simulation of fuel slosh. The current research will focus on developing models of different complexity and estimating the model parameters that will ultimately provide a more realistic prediction of Nutation Time Constant obtained through simulation.

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.

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

Wang, Yi; Xue, Wei, E-mail: yw366@cam.ac.uk, E-mail: wei.xue@sissa.it

We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experimentsmore » do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.« less

Counting conformal correlators

NASA Astrophysics Data System (ADS)

Kravchuk, Petr; Simmons-Duffin, David

2018-02-01

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

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

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.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

The theory of spherically symmetric thin shells in conformal gravity

NASA Astrophysics Data System (ADS)

Berezin, Victor; Dokuchaev, Vyacheslav; Eroshenko, Yury

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

A distinguishing gravitational property for gravitational equation in higher dimensions

NASA Astrophysics Data System (ADS)

Dadhich, Naresh

2016-03-01

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

Tensor Algebra Library for NVidia Graphics Processing Units

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

Liakh, Dmitry

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

The Spacetime Between Einstein and Kaluza-Klein: Further Explorations

NASA Astrophysics Data System (ADS)

Vuille, Chris

2017-01-01

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

Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory

NASA Astrophysics Data System (ADS)

Hehl, Friedrich W.; Kiefer, Claus

2018-01-01

We perform a short comparison between the local and linear constitutive tensor χ ^{λ ν σ κ } in four-dimensional electrodynamics, the elasticity tensor c^{ijkl} in three-dimensional elasticity theory, and the DeWitt metric G^{abcd} in general relativity, with {a,b,\\ldots =1,2,3}. We find that the DeWitt metric has only six independent components.

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} \

Invariant operators, orthogonal bases and correlators in general tensor models

NASA Astrophysics Data System (ADS)

Diaz, Pablo; Rey, Soo-Jong

2018-07-01

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

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

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

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.

The Dispersion Tensor and Its Unique Minimizer in Hashin-Shtrikman Micro-structures

NASA Astrophysics Data System (ADS)

Bălilescu, Loredana; Conca, Carlos; Ghosh, Tuhin; San Martín, Jorge; Vanninathan, Muthusamy

2018-05-01

In this paper, we introduce a macroscopic quantity, namely the dispersion tensor or the Burnett coefficients in the class of generalized Hashin-Shtrikman micro-structures (Tartar in The general theory of homogenization, volume 7 of Lecture notes of the Unione Matematica Italiana, Springer, Berlin, p 281, 2009). In the case of two-phase materials associated with the periodic Hashin-Shtrikman structures, we settle the issue that the dispersion tensor has a unique minimizer, which is the so called Apollonian-Hashin-Shtrikman micro-structure.

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

PubMed

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

2002-01-01

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

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.

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.

Genten: Software for Generalized Tensor Decompositions v. 1.0.0

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

Phipps, Eric T.; Kolda, Tamara G.; Dunlavy, Daniel

Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.

Entangled scalar and tensor fluctuations during inflation

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

Collins, Hael; Vardanyan, Tereza

2016-11-29

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

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

NASA Astrophysics Data System (ADS)

Lawden, D. F.

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

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.

A Communication-Optimal Framework for Contracting Distributed Tensors

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

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

Tensor contractions are extremely compute intensive generalized matrix multiplication operations encountered in many computational science fields, such as quantum chemistry and nuclear physics. Unlike distributed matrix multiplication, which has been extensively studied, limited work has been done in understanding distributed tensor contractions. In this paper, we characterize distributed tensor contraction algorithms on torus networks. We develop a framework with three fundamental communication operators to generate communication-efficient contraction algorithms for arbitrary tensor contractions. We show that for a given amount of memory per processor, our framework is communication optimal for all tensor contractions. We demonstrate performance and scalability of our frameworkmore » on up to 262,144 cores of BG/Q supercomputer using five tensor contraction examples.« less

Surface‐wave Green’s tensors in the near field

USGS Publications Warehouse

Haney, Matt; Nakahara, Hisashi

2014-01-01

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

On the energy-momentum tensor of light in strong fields: an all optical view of the Abraham-Minkowski controversy

NASA Astrophysics Data System (ADS)

Macleod, Alexander J.; Noble, Adam; Jaroszynski, Dino A.

2017-05-01

The Abraham-Minkowski controversy is the debate surrounding the "correct" form of the energy-momentum tensor of light in a medium. Over a century of theoretical and experimental studies have consistently produced conflicting results, with no consensus being found on how best to describe the influence of a material on the propagation of light. It has been argued that the total energy-momentum tensor for each of the theories, which includes both wave and material components, are equal. The difficulty in separating the full energy-momentum tensor is generally attributed to the fact that one cannot obtain the energy-momentum tensor of the medium for real materials. Non-linear electrodynamics provides an opportunity to approach the debate from an all optical set up, where the role of the medium is replaced by the vacuum under the influence of a strong background field. We derive, from first principles, the general form of the energy-momentum tensor in such theories, and use our results to shed some light on this long standing issue.

Heterotic reduction of Courant algebroid connections and Einstein-Hilbert actions

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Vysoký, Jan

2016-08-01

We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein-Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.

Geometry of Lax pairs: Particle motion and Killing-Yano tensors

NASA Astrophysics Data System (ADS)

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

2013-01-01

A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

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

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

Lipnikov, Konstantin; Shashkov, Mikhail

2011-01-11

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

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.

Development of the Tensoral Computer Language

NASA Technical Reports Server (NTRS)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

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

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.

Anisotropy tensor of the potential model of steady creep

NASA Astrophysics Data System (ADS)

Annin, B. D.; Ostrosablin, N. I.

2014-01-01

The Kelvin approach describing the structure of the generalized Hooke's law is used to analyze the potential model of anisotropic creep of materials. The creep equations of incompressible transversely isotropic, orthotropic materials and those with cubic symmetry are considered. The eigen coefficients of anisotropy and eigen tensors for the anisotropy tensors of these materials are determined.

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.

Audiomagnetotelluric data from Spring, Cave, and Coyote Spring Valleys, Nevada

USGS Publications Warehouse

McPhee, Darcy K.; Chuchel, Bruce A.; Pellerin, Louise

2006-01-01

Audiomagnetotelluric (AMT) data along four profiles in Spring, Cave, and Coyote Spring Valleys are presented here. The AMT method is used to estimate the electrical resistivity of the earth over depth ranges of a few meters to greater than one kilometer. This method is a valuable tool for revealing subsurface structure and stratigraphy within the Basin and Range of eastern Nevada, therefore helping to define the geohydrologic framework in this region. We collected AMT data using the Geometrics StrataGem EH4 system, a four-channel, natural and controlled- source tensor system recording in the range of 10 to 92,000 Hz. To augment the low signal in the natural field, an unpolarized transmitter comprised of two horizontal-magnetic dipoles was used from 1,000 to 70,000 Hz. Profiles were 1.4 - 12.6 km in length with station spacing of 100-400 m. Data were recorded with the electrical (E) field parallel to and perpendicular to the regional geologic strike direction. Station locations and sounding curves, showing apparent resistivity, phase data, and coherency data, are presented here.

Gravitoelectromagnetic analogy based on tidal tensors

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

Costa, L. Filipe O.; Herdeiro, Carlos A. R.

2008-07-15

We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, which makes transparent both the similarities and key differences between the two interactions. The following realizations of the analogy are given. The first one matches linearized gravitational tidal tensors to exact electromagnetic tidal tensors in Minkowski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultrastationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third wemore » show that our approach leads to a two-step exact derivation of Papapetrou's equation describing the force exerted on a spinning test particle. Analogous scalar invariants built from tidal tensors of both theories are also discussed.« less

A geometric description of Maxwell field in a Kerr spacetime

NASA Astrophysics Data System (ADS)

Jezierski, Jacek; Smołka, Tomasz

2016-06-01

We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein-Gordon equation called Fackerell-Ipser equation. Our model is based on conformal Yano-Killing tensor (CYK tensor). We present non-standard properties of CYK tensors in the Kerr spacetime which are useful in electrodynamics.

Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the Rényi entropy of such states and recover the Ryu–Takayanagi formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.

A Brownian dynamics program for the simulation of linear and circular DNA and other wormlike chain polyelectrolytes.

PubMed Central

Klenin, K; Merlitz, H; Langowski, J

1998-01-01

For the interpretation of solution structural and dynamic data of linear and circular DNA molecules in the kb range, and for the prediction of the effect of local structural changes on the global conformation of such DNAs, we have developed an efficient and easy way to set up a program based on a second-order explicit Brownian dynamics algorithm. The DNA is modeled by a chain of rigid segments interacting through harmonic spring potentials for bending, torsion, and stretching. The electrostatics are handled using precalculated energy tables for the interactions between DNA segments as a function of relative orientation and distance. Hydrodynamic interactions are treated using the Rotne-Prager tensor. While maintaining acceptable precision, the simulation can be accelerated by recalculating this tensor only once in a certain number of steps. PMID:9533691

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

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

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

PubMed

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

2014-01-01

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

Fast multipole method using Cartesian tensor in beam dynamic simulation

DOE PAGES

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

2017-03-06

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

A general mass term for bigravity

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

Cusin, Giulia; Durrer, Ruth; Guarato, Pietro

2016-04-01

We introduce a new formalism to study perturbations of Hassan-Rosen bigravity theory, around general backgrounds for the two dynamical metrics. In particular, we derive the general expression for the mass term of the perturbations and we explicitly compute it for cosmological settings. We study tensor perturbations in a specific branch of bigravity using this formalism. We show that the tensor sector is affected by a late-time instability, which sets in when the mass matrix is no longer positive definite.

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

NASA Astrophysics Data System (ADS)

Deser, S.; Franklin, J.

2011-02-01

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

Hydrogen Burning in Low Mass Stars Constrains Scalar-Tensor Theories of Gravity.

PubMed

Sakstein, Jeremy

2015-11-13

The most general scalar-tensor theories of gravity predict a weakening of the gravitational force inside astrophysical bodies. There is a minimum mass for hydrogen burning in stars that is set by the interplay of plasma physics and the theory of gravity. We calculate this for alternative theories of gravity and find that it is always significantly larger than the general relativity prediction. The observation of several low mass red dwarf stars therefore rules out a large class of scalar-tensor gravity theories and places strong constraints on the cosmological parameters appearing in the effective field theory of dark energy.

Multipole analysis in the radiation field for linearized f (R ) gravity with irreducible Cartesian tensors

NASA Astrophysics Data System (ADS)

Wu, Bofeng; Huang, Chao-Guang

2018-04-01

The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.

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.

Generalized Higher Order Orthogonal Iteration for Tensor Learning and Decomposition.

PubMed

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

2016-12-01

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

Tensor gauge condition and tensor field decomposition

NASA Astrophysics Data System (ADS)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

A gravitational energy–momentum and the thermodynamic description of gravity

NASA Astrophysics Data System (ADS)

Acquaviva, G.; Kofroň, D.; Scholtz, M.

2018-05-01

A proposal for the gravitational energy–momentum tensor, known in the literature as the square root of Bel–Robinson tensor (SQBR), is analyzed in detail. Being constructed exclusively from the Weyl part of the Riemann tensor, such tensor encapsulates the geometric properties of free gravitational fields in terms of optical scalars of null congruences: making use of the general decomposition of any energy–momentum tensor, we explore the thermodynamic interpretation of such geometric quantities. While the matter energy–momentum is identically conserved due to Einstein’s field equations, the SQBR is not necessarily conserved and dissipative terms could arise in its vacuum continuity equation. We discuss the possible physical interpretations of such mathematical properties.

Sparse alignment for robust tensor learning.

PubMed

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

2014-10-01

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

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

PubMed

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

2016-11-01

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

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.

Local metrics admitting a principal Killing-Yano tensor with torsion

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Kubizňák, David; Warnick, Claude M.; Yasui, Yukinori

2012-08-01

In this paper we initiate a classification of local metrics admitting the principal Killing-Yano tensor with a skew-symmetric torsion. It is demonstrated that in such spacetimes rank-2 Killing tensors occur naturally and mutually commute. We reduce the classification problem to that of solving a set of partial differential equations, and we present some solutions to these PDEs. In even dimensions, three types of local metrics are obtained: one of them naturally generalizes the torsion-less case while the others occur only when the torsion is present. In odd dimensions, we obtain more varieties of local metrics. The explicit metrics constructed in this paper are not the most general possible admitting the required symmetry; nevertheless, it is demonstrated that they cover a wide variety of solutions of various supergravities, such as the Kerr-Sen black holes of (un-)gauged Abelian heterotic supergravity, the Chong-Cvetic-Lü-Pope black hole solution of five-dimensional minimal supergravity or the Kähler with torsion manifolds. The relation between generalized Killing-Yano tensors and various torsion Killing spinors is also discussed.

Anisotropic mesoscale eddy transport in ocean general circulation models

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

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.

Compact objects in relativistic theories of gravity

NASA Astrophysics Data System (ADS)

Okada da Silva, Hector

2017-05-01

In this dissertation we discuss several aspects of compact objects, i.e. neutron stars and black holes, in relativistic theories of gravity. We start by studying the role of nuclear physics (encoded in the so-called equation of state) in determining the properties of neutron stars in general relativity. We show that low-mass neutron stars are potentially useful astrophysical laboratories that can be used to constrain the properties of the equation of state. More specifically, we show that various bulk properties of these objects, such as their quadrupole moment and tidal deformability, are tightly correlated. Next, we develop a formalism that aims to capture how generic modifications from general relativity affect the structure of neutron stars, as predicted by a broad class of gravity theories, in the spirit of the parametrized post-Newtonian formalism (PPN). Our "post-Tolman-Oppenheimer-Volkoff" formalism provides a toolbox to study both stellar structure and the interior/exterior geometries of static, spherically symmetric relativistic stars. We also apply the formalism to parametrize deviations from general relativity in various astrophysical observables related with neutron stars, including surface redshift, apparent radius, Eddington luminosity. We then turn our attention to what is arguably the most well-motivated and well-investigated generalization of general relativity: scalar-tensor theory. We start by considering theories where gravity is mediated by a single extra scalar degree of freedom (in addition to the metric tensor). An interesting class of scalar-tensor theories passes all experimental tests in the weak-field regime of gravity, yet considerably deviates from general relativity in the strong-field regime in the presence of matter. A common assumption in modeling neutron stars is that the pressure within these object is spatially isotropic. We relax this assumption and examine how pressure anisotropy affects the mass, radius and moment of inertia of slowly rotating neutron stars, both in general relativity and in scalar-tensor gravity. We show that a sufficient amount of pressure anisotropy results in neutron star models whose properties in scalar-tensor theory deviate significantly from their general relativistic counterparts. Moreover, the presence of anisotropy allows these deviations to be considerable even for values of the theory's coupling parameter for which neutron stars in scalar-tensor theory would be otherwise indistinguishable from those in general relativity. Within scalar-tensor theory we also investigate the effects of the scalar field on the crustal torsional oscillations of neutron stars, which have been associated to quasi-periodic oscillations in the X-ray spectra in the aftermath of giant flares. We show that the presence of the scalar field has an influence on the thickness of the stellar crust, and investigate how it affects the oscillation frequencies. Deviations from the predictions of general relativity can be large for certain values of the theory's coupling parameter. However, the influence of the scalar field is degenerate with uncertainties in the equation of state of the star's crust and microphysics effects (electron screening) for values of the coupling allowed by binary pulsar observations. We also derive the stellar structure equations for slowly-rotating neutron stars in a broader class of scalar-tensor theories in which matter and scalar field are coupled through the so-called disformal coupling. We study in great detail how the disformal coupling affects the structure of neutron stars, and we investigate the existence of universal (equation of state-independent) relations connecting the stellar compactness and moment of inertia. In particular, we find that these universal relations can deviate considerably from the predictions of general relativity. (Abstract shortened by ProQuest.).

Proceedings of the Annual DARPA/AFGL Seismic Research Symposium (7th) Held in Colorado Springs, Colorado on 6-8 May 1985

DTIC Science & Technology

1990-11-08

seismograms were calculated for the three fundemental sources needed to construct an arbitrarily oriented dislocation or deviatoric moment tensor...or the first motion approximation method(FMA). Vertical and radial displacements for the three fundemental source terms are shown since each source...significantly interfere with the SV body wave to produce varying levels of distortion of the waveform among the three fundemental sources. Note, for example

Covariant conserved currents for scalar-tensor Horndeski theory

NASA Astrophysics Data System (ADS)

Schmidt, J.; Bičák, J.

2018-04-01

The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity, we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential that leads to the covariantly conserved current in the Branse-Dicke theory.

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

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-09-01

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

Tensor-based Dictionary Learning for Spectral CT Reconstruction

PubMed Central

Zhang, Yanbo; Wang, Ge

2016-01-01

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

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).

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1983-01-01

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

General theories of linear gravitational perturbations to a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

Inference of segmented color and texture description by tensor voting.

PubMed

Jia, Jiaya; Tang, Chi-Keung

2004-06-01

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

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

NASA Astrophysics Data System (ADS)

Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

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.

Beyond-Standard-Model Tensor Interaction and Hadron Phenomenology.

PubMed

Courtoy, Aurore; Baeßler, Stefan; González-Alonso, Martín; Liuti, Simonetta

2015-10-16

We evaluate the impact of recent developments in hadron phenomenology on extracting possible fundamental tensor interactions beyond the standard model. We show that a novel class of observables, including the chiral-odd generalized parton distributions, and the transversity parton distribution function can contribute to the constraints on this quantity. Experimental extractions of the tensor hadronic matrix elements, if sufficiently precise, will provide a, so far, absent testing ground for lattice QCD calculations.

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.

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

PubMed

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

2016-08-01

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

On the energy-momentum tensor in Moyal space

DOE PAGES

Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; ...

2015-06-26

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another starproduct. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gaugemore » fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.« 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.

BOOK REVIEW: Advanced Mechanics and General Relativity Advanced Mechanics and General Relativity

NASA Astrophysics Data System (ADS)

Louko, Jorma

2011-04-01

Joel Franklin's textbook `Advanced Mechanics and General Relativity' comprises two partially overlapping, partially complementary introductory paths into general relativity at advanced undergraduate level. Path I starts with the Lagrangian and Hamiltonian formulations of Newtonian point particle motion, emphasising the action principle and the connection between symmetries and conservation laws. The concepts are then adapted to point particle motion in Minkowski space, introducing Lorentz transformations as symmetries of the action. There follows a focused development of tensor calculus, parallel transport and curvature, using examples from Newtonian mechanics and special relativity, culminating in the field equations of general relativity. The Schwarzschild solution is analysed, including a detailed discussion of the tidal forces on a radially infalling observer. Basics of gravitational radiation are examined, highlighting the similarities to and differences from electromagnetic radiation. The final topics in Path I are equatorial geodesics in Kerr and the motion of a relativistic string in Minkowski space. Path II starts by introducing scalar field theory on Minkowski space as a limit of point masses connected by springs, emphasising the action principle, conservation laws and the energy-momentum tensor. The action principle for electromagnetism is introduced, and the coupling of electromagnetism to a complex scalar field is developed in a detailed and pedagogical fashion. A free symmetric second-rank tensor field on Minkowski space is introduced, and the action principle of general relativity is recovered from coupling the second-rank tensor to its own energy-momentum tensor. Path II then merges with Path I and, supplanted with judicious early selections from Path I, can proceed to the Schwarzschild solution. The choice of material in each path is logical and focused. A notable example in Path I is that Lorentz transformations in Minkowki space are introduced efficiently and with a minimum of fuss, as symmetries of a geodesic action principle. Another example is a similarly efficient and hands-on introduction of Killing vectors. A consequence of this focus is that some perhaps traditional material is omitted. For example, Lorentz contraction appears briefly in the incompatibility discussion of special relativity and Newtonian gravity but is not introduced in a more systematic manner. The style is informal and very readable, with detailed explanations, frequent summaries of what has been achieved and pointers to what is about to follow. There are plenty of examples and some 150 well-chosen exercises, and the author's website hosts relevant Maple sample scripts for tensor manipulations and variational problems. The text conveys an enthusiasm for explaining the subject, frequently reminiscent of the Feynman lectures. The presentation emphasises explicit calculations and examples, largely avoiding technical definitions of abstract mathematical concepts. The author negotiates the challenge between readability and technical accuracy with admirable skill, striking a balance that will be much appreciated by the target audience. For example, the notion of spherical symmetry in curved spacetime is introduced informally as a generalisation of a spherically symmetric vector field in Minkowski space, and spherically symmetric vacuum and electrovacuum solutions are then carefully discussed so that a formal definition of spherical symmetry is not required. A rare instance that may border on oversimplification is the brief discussion of curvature scalars versus spacetime singularities. Towards the end of the book, the text mentions with increasing explicitness that inserting a gauge condition or an ansatz in an action before varying may not always give the correct equations of motion. It would be useful to be more explicit about this point already earlier in the book. In particular, the text refers to the reparametrisation-invariant square root action of a relativistic point particle as being `in proper time parametrisation', while the actual calculations of course impose the proper time condition only in the equation of motion after the action has been varied. Two presentational conventions surprised me. First, the speed of light is throughout kept explicitly as c: might advanced undergraduates appreciate being trusted with geometric units, reinstating c by dimensional analysis when desired? Second, in Minkowski space field theory, the overall coefficient in the action is chosen so that the time derivative term is negative, with the consequence that the Hamiltonian is negative (as explicitly noted in an exercise) and the definition of the energy-momentum tensor must include a minus sign to achieve the usual choice T00 > 0. This convention eliminates some minus signs in the computations with the spin two field: does this computational saving outweigh the adjustment awaiting those who continue with the topic at graduate level? Overall, Franklin's book is an excellent addition to the literature, and its readability and explicitness will be appreciated by the target audience. Should I be teaching an introductory undergraduate class in general relativity in the near future, I would seriously consider this book for the main class text.

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. .

Quasinormal modes, bifurcations, and nonuniqueness of charged scalar-tensor black holes

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

Doneva, Daniela D.; Theoretical Astrophysics, Eberhard-Karls University of Tuebingen, Tuebingen 72076; Yazadjiev, Stoytcho S.

In the present paper, we study the scalar sector of the quasinormal modes of charged general relativistic, static, and spherically symmetric black holes coupled to nonlinear electrodynamics and embedded in a class of scalar-tensor theories. We find that for a certain domain of the parametric space, there exists unstable quasinormal modes. The presence of instabilities implies the existence of scalar-tensor black holes with primary hair that bifurcate from the embedded general relativistic black-hole solutions at critical values of the parameters corresponding to the static zero modes. We prove that such scalar-tensor black holes really exist by solving the full systemmore » of scalar-tensor field equations for the static, spherically symmetric case. The obtained solutions for the hairy black holes are nonunique, and they are in one-to-one correspondence with the bounded states of the potential governing the linear perturbations of the scalar field. The stability of the nonunique hairy black holes is also examined, and we find that the solutions for which the scalar field has zeros are unstable against radial perturbations. The paper ends with a discussion of possible formulations of a new classification conjecture.« less

Trifocal Tensor-Based Adaptive Visual Trajectory Tracking Control of Mobile Robots.

PubMed

Chen, Jian; Jia, Bingxi; Zhang, Kaixiang

2017-11-01

In this paper, a trifocal tensor-based approach is proposed for the visual trajectory tracking task of a nonholonomic mobile robot equipped with a roughly installed monocular camera. The desired trajectory is expressed by a set of prerecorded images, and the robot is regulated to track the desired trajectory using visual feedback. Trifocal tensor is exploited to obtain the orientation and scaled position information used in the control system, and it works for general scenes owing to the generality of trifocal tensor. In the previous works, the start, current, and final images are required to share enough visual information to estimate the trifocal tensor. However, this requirement can be easily violated for perspective cameras with limited field of view. In this paper, key frame strategy is proposed to loosen this requirement, extending the workspace of the visual servo system. Considering the unknown depth and extrinsic parameters (installing position of the camera), an adaptive controller is developed based on Lyapunov methods. The proposed control strategy works for almost all practical circumstances, including both trajectory tracking and pose regulation tasks. Simulations are made based on the virtual experimentation platform (V-REP) to evaluate the effectiveness of the proposed approach.

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.

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.

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

Bespoke analogue space-times: meta-material mimics

NASA Astrophysics Data System (ADS)

Schuster, Sebastian; Visser, Matt

2018-06-01

Modern meta-materials allow one to construct electromagnetic media with almost arbitrary bespoke permittivity, permeability, and magneto-electric tensors. If (and only if) the permittivity, permeability, and magneto-electric tensors satisfy certain stringent compatibility conditions, can the meta-material be fully described (at the wave optics level) in terms of an effective Lorentzian metric—an analogue spacetime. We shall consider some of the standard black-hole spacetimes of primary interest in general relativity, in various coordinate systems, and determine the equivalent meta-material susceptibility tensors in a laboratory setting. In static black hole spacetimes (Schwarzschild and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the horizon. In stationary black hole spacetimes (Kerr and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the ergo-surface.

Extended vector-tensor theories

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

Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Procamore » theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.« less

Generalized Hodge dual for torsion in teleparallel gravity

NASA Astrophysics Data System (ADS)

Huang, Peng; Yuan, Fang-Fang

2016-07-01

For teleparallel gravity in four dimensions, Lucas and Pereira have shown that its action can be constructed via a generalized Hodge dual for torsion tensor. In this paper, we demonstrate that a direct generalization of this approach to other dimensions fails due to the fact that no generalized Hodge dual operator could be given in general dimensions. Furthermore, if one enforces the definition of a generalized Hodge dual to be consistent with the action of teleparallel gravity in general dimensions, the basic identity for any sensible Hodge dual would require an ad hoc definition for the second Hodge dual operation which is totally unexpected. Therefore, we conclude that at least for the torsion tensor, the observation of Lucas and Pereira only applies to four dimensions.

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

Ab initio elastic tensor of cubic Ti0.5Al0.5N alloys: Dependence of elastic constants on size and shape of the supercell model and their convergence

NASA Astrophysics Data System (ADS)

Tasnádi, Ferenc; Odén, M.; Abrikosov, Igor A.

2012-04-01

In this study we discuss the performance of the special quasirandom structure (SQS) method in predicting the elastic properties of B1 (rocksalt) Ti0.5Al0.5N alloy. We use a symmetry-based projection technique, which gives the closest cubic approximate of the elastic tensor and allows us to align the SQSs of different shapes and sizes for a comparison in modeling elastic tensors. We show that the derived closest cubic approximate of the elastic tensor converges faster with respect to SQS size than the elastic tensor itself. That establishes a less demanding computational strategy to achieve convergence for the elastic constants. We determine the cubic elastic constants (Cij) and Zener's type elastic anisotropy (A) of Ti0.5Al0.5N. Optimal supercells, which capture accurately both the configurational disorder and cubic symmetry of elastic tensor, result in C11=447 GPa, C12=158 GPa, and C44=203 GPa with 3% of error and A=1.40 with 6% of error. In addition, we establish the general importance of selecting proper SQS with symmetry arguments to reliably model elasticity of alloys. We suggest the calculation of nine elastic tensor elements: C11, C22, C33, C12, C13, C23, C44, C55, and C66, to analyze the performance of SQSs and predict elastic constants of cubic alloys. The described methodology is general enough to be extended for alloys with other symmetry at arbitrary composition.

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

NASA Technical Reports Server (NTRS)

Avis, L. M.

1976-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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.

Random SU(2) invariant tensors

NASA Astrophysics Data System (ADS)

Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei

2018-04-01

SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n  =  4. In this paper, we show that for n  >  4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.

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

2. GENERAL VIEW FROM SOUTH SHOWING SOUTHWEST AND SOUTHEAST SIDES ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

2. GENERAL VIEW FROM SOUTH SHOWING SOUTHWEST AND SOUTHEAST SIDES AND CLERESTORY ARRANGEMENT - Sulphur Springs Methodist Campground, Sulphur Springs Road (Sulphur Springs), Sulphur Springs, Washington County, TN

Tensor completion for estimating missing values in visual data.

PubMed

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

2013-01-01

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

Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

Dvoeglazov, V. V.

Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.

Hidden symmetries in Sasaki-Einstein geometries

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

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.

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

NASA Astrophysics Data System (ADS)

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

2004-03-01

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

Generalized Rainich conditions, generalized stress-energy conditions, and the Hawking-Ellis classification

NASA Astrophysics Data System (ADS)

Martín–Moruno, Prado; Visser, Matt

2017-11-01

The (generalized) Rainich conditions are algebraic conditions which are polynomial in the (mixed-component) stress-energy tensor. As such they are logically distinct from the usual classical energy conditions (NEC, WEC, SEC, DEC), and logically distinct from the usual Hawking-Ellis (Segré-Plebański) classification of stress-energy tensors (type I, type II, type III, type IV). There will of course be significant inter-connections between these classification schemes, which we explore in the current article. Overall, we shall argue that it is best to view the (generalized) Rainich conditions as a refinement of the classical energy conditions and the usual Hawking-Ellis classification.

Geo-electrical and geological strikes of the Mount Lamongan geothermal area, East Java, Indonesia – preliminary results

NASA Astrophysics Data System (ADS)

Nugraheni, L. R.; Niasari, S. W.; Nukman, M.

2018-04-01

Geothermal manifestations located in the Tiris, Mount Lamongan, Probolinggo, consist of warm springs. These warm springs have temperature from 35° until 45°C. Tiris fault has NW-SE dominant orientation, similar to some lineaments of maars and cinder cones around Mount Lamongan. The Mount Lamongan geothermal area is situated between Bromo and Argapura volcanoes. This study aims to map the geo-electrical and geological strikes in the study area. Phase tensor analysis has been performed in this study to determine geo-electrical strike of study area. Geological field campaign has been conducted to measure geological strikes. Then, orientation of geo-electrical strike was compared to geological strike. The result presents that the regional geological strike of study area is NW-SE while the orientation of geo-electrical strike is N-S.

7. GENERAL VIEW OF INTERIOR OF MEETINGHOUSE FROM SOUTHEAST SHOWING ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

7. GENERAL VIEW OF INTERIOR OF MEETINGHOUSE FROM SOUTHEAST SHOWING CLERESTORY ARRANGEMENT AND SUPPORT SYSTEM - Sulphur Springs Methodist Campground, Sulphur Springs Road (Sulphur Springs), Sulphur Springs, Washington County, TN

Relative-observer definition of the Simon tensor

NASA Astrophysics Data System (ADS)

Bini, Donato; Geralico, Andrea

2018-05-01

The definition of the Simon tensor, originally given only in Kerr spacetime and associated with the static family of observers, is generalized to any spacetime and to any possible observer family. Such generalization is obtained by a standard ‘3  +  1’ splitting of the Bianchi identities, which are rewritten here as a ‘balance equation’ between various spatial fields, associated with the kinematical properties of the observer congruence and representing the spacetime curvature.

On the initial conditions of scalar and tensor fluctuations in f(R,φ ) gravity

NASA Astrophysics Data System (ADS)

Cheraghchi, S.; Shojai, F.

2018-05-01

We have considered the perturbation equations governing the growth of fluctuations during inflation in generalized scalar tensor theory f(R,φ ). We have found that the scalar metric perturbations at very early times are negligible compared to the scalar field perturbation, just like general relativity. At sufficiently early times, when the physical momentum of perturbation mode, q / a is much larger than the Hubble parameter H, i.e. q/a≫ H, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov-Sasaki equation. Then a similar procedure is performed for the case of tensor metric perturbation. As an example of the generalized Mukhanov-Sasaki equation and its initial condition, we have proposed a power-law functional form as f(R,φ )=f_0 R^m φ ^n and obtained an exact inflationary solution. In this background, then we have discussed how the scalar and tensor fluctuations grow.

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.

Why did Einstein reject the November tensor in 1912-1913, only to come back to it in November 1915?

NASA Astrophysics Data System (ADS)

Weinstein, Galina

2018-05-01

The question of Einstein's rejection of the November tensor is re-examined in light of conflicting answers by several historians. I discuss these conflicting conjectures in view of three questions that should inform our thinking: Why did Einstein reject the November tensor in 1912, only to come back to it in 1915? Why was it hard for Einstein to recognize that the November tensor is a natural generalization of Newton's law of gravitation? Why did it take him three years to realize that the November tensor is not incompatible with Newton's law? I first briefly describe Einstein's work in the Zurich Notebook. I then discuss a number of interpretive conjectures formulated by historians and what may be inferred from them. Finally, I offer a new combined conjecture that answers the above questions.

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

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

NASA Technical Reports Server (NTRS)

Jongen, T.; Gatski, T. B.

1997-01-01

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

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.

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

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

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

g-Tensor determination from single-crystal ESR data

NASA Astrophysics Data System (ADS)

Byrn, Marianne P.; Strouse, Charles E.

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

A Simple Method for Calculating Clebsch-Gordan Coefficients

ERIC Educational Resources Information Center

Klink, W. H.; Wickramasekara, S.

2010-01-01

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

General perspective view of the Spring Creek Bridge, view looking ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

General perspective view of the Spring Creek Bridge, view looking southeast. - Spring Creek Bridge, Spanning Spring Creek at Milepoint 253.98 on Oregon to California Highway (US Route 97), Chiloquin, Klamath County, OR

General perspective view of the Spring Creek Bridge, view looking ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

General perspective view of the Spring Creek Bridge, view looking northwest. - Spring Creek Bridge, Spanning Spring Creek at Milepoint 253.98 on Oregon to California Highway (US Route 97), Chiloquin, Klamath County, OR

General perspective view of the Spring Creek Bridge, view looking ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

General perspective view of the Spring Creek Bridge, view looking east. - Spring Creek Bridge, Spanning Spring Creek at Milepoint 253.98 on Oregon to California Highway (US Route 97), Chiloquin, Klamath County, OR

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.

Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

PubMed

Guérin, T; Dean, D S

2015-12-01

We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

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.

Tensor models, Kronecker coefficients and permutation centralizer algebras

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

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

Spacetime encodings. III. Second order Killing tensors

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

Brink, Jeandrew

2010-01-15

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

Cosmology in beyond-generalized Proca theories

NASA Astrophysics Data System (ADS)

Nakamura, Shintaro; Kase, Ryotaro; Tsujikawa, Shinji

2017-05-01

The beyond-generalized Proca theories are the extension of second-order massive vector-tensor theories (dubbed generalized Proca theories) with two transverse vector modes and one longitudinal scalar besides two tensor polarizations. Even with this extension, the propagating degrees of freedom remain unchanged on the isotropic cosmological background without an Ostrogradski instability. We study the cosmology in beyond-generalized Proca theories by paying particular attention to the dynamics of late-time cosmic acceleration and resulting observational consequences. We derive conditions for avoiding ghosts and instabilities of tensor, vector, and scalar perturbations and discuss viable parameter spaces in concrete models allowing the dark energy equation of state smaller than -1 . The propagation speeds of those perturbations are subject to modifications beyond the domain of generalized Proca theories. There is a mixing between scalar and matter sound speeds, but such a mixing is suppressed during most of the cosmic expansion history without causing a new instability. On the other hand, we find that derivative interactions arising in beyond-generalized Proca theories give rise to important modifications to the cosmic growth history. The growth rate of matter perturbations can be compatible with the redshift-space distortion data due to the realization of gravitational interaction weaker than that in generalized Proca theories. Thus, it is possible to distinguish the dark energy model in beyond-generalized Proca theories from the counterpart in generalized Proca theories as well as from the Λ CDM model.

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

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

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

2012-10-15

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

Separability of black holes in string theory

NASA Astrophysics Data System (ADS)

Keeler, Cynthia; Larsen, Finn

2012-10-01

We analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We construct a conformal Killing-Stackel tensor for a general class of black holes with four independent charges, then identify two-charge configurations where enhancement to an exact Killing-Stackel tensor is possible. We show that further enhancement to a conserved Killing-Yano tensor is possible only for the special case of Kerr-Newman black holes. We construct natural null congruences for all these black holes and use the results to show that only the Kerr-Newman black holes are algebraically special in the sense of Petrov. Modifying the asymptotic behavior by the subtraction procedure that induces an exact SL(2)2 also preserves only the conformal Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black hole possesses a conformal Killing-Stackel tensor but has no further enhancements.

Hand-waving and interpretive dance: an introductory course on tensor networks

NASA Astrophysics Data System (ADS)

Bridgeman, Jacob C.; Chubb, Christopher T.

2017-06-01

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes. These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases using tensor networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states. The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/quantum information. For each lecture, several problems are given, with worked solutions in an ancillary file.

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

A defect in holographic interpretations of tensor networks

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Potentials for transverse trace-free tensors

NASA Astrophysics Data System (ADS)

Conboye, Rory; Murchadha, Niall Ó.

2014-04-01

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

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

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis; Deruelle, Nathalie

2017-06-01

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

Projective mappings and dimensions of vector spaces of three types of Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature

NASA Astrophysics Data System (ADS)

Mikeš, Josef; Stepanov, Sergey; Hinterleitner, Irena

2012-07-01

In our paper we have determined the dimension of the space of conformal Killing-Yano tensors and the dimensions of its two subspaces of closed conformal Killing-Yano and Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature. This result is a generalization of well known results on sharp upper bounds of the dimensions of the vector spaces of conformal Killing-Yano, Killing-Yano and concircular vector fields on pseudo Riemannian manifolds of constant curvature.

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.

Unified Stress Tensor of the Hydration Water Layer

NASA Astrophysics Data System (ADS)

Kim, Bongsu; Kim, QHwan; Kwon, Soyoung; An, Sangmin; Lee, Kunyoung; Lee, Manhee; Jhe, Wonho

2013-12-01

We present the general stress tensor of the ubiquitous hydration water layer (HWL), based on the empirical hydration force, by combining the elasticity and hydrodynamics theories. The tapping and shear component of the tensor describe the elastic and damping properties of the HWL, respectively, in good agreement with experiments. In particular, a unified understanding of HWL dynamics provides the otherwise unavailable intrinsic parameters of the HWL, which offer additional but unexplored aspects to the supercooled liquidity of the confined HWL. Our results may allow deeper insight on systems where the HWL is critical.

Unified stress tensor of the hydration water layer.

PubMed

Kim, Bongsu; Kim, Qhwan; Kwon, Soyoung; An, Sangmin; Lee, Kunyoung; Lee, Manhee; Jhe, Wonho

2013-12-13

We present the general stress tensor of the ubiquitous hydration water layer (HWL), based on the empirical hydration force, by combining the elasticity and hydrodynamics theories. The tapping and shear component of the tensor describe the elastic and damping properties of the HWL, respectively, in good agreement with experiments. In particular, a unified understanding of HWL dynamics provides the otherwise unavailable intrinsic parameters of the HWL, which offer additional but unexplored aspects to the supercooled liquidity of the confined HWL. Our results may allow deeper insight on systems where the HWL is critical.

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

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

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

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

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

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo

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

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.

Anisotropic Mesoscale Eddy Transport in Ocean General Circulation Models

NASA Astrophysics Data System (ADS)

Reckinger, S. J.; Fox-Kemper, B.; Bachman, S.; Bryan, F.; Dennis, J.; Danabasoglu, G.

2014-12-01

Modern climate models are limited to coarse-resolution representations of large-scale ocean circulation that rely on parameterizations for mesoscale eddies. The effects of eddies are typically introduced by relating subgrid eddy fluxes to the resolved gradients of buoyancy or other tracers, where the proportionality is, in general, governed by an eddy transport tensor. The symmetric part of the tensor, which represents the diffusive effects of mesoscale eddies, is universally treated isotropically in general circulation models. Thus, only a single parameter, namely the eddy diffusivity, is used at each spatial and temporal location to impart the influence of mesoscale eddies on the resolved flow. However, the diffusive processes that the parameterization approximates, such as shear dispersion, potential vorticity barriers, oceanic turbulence, and instabilities, typically have strongly anisotropic characteristics. Generalizing the eddy diffusivity tensor for anisotropy extends the number of parameters to three: a major diffusivity, a minor diffusivity, and the principal axis of alignment. The Community Earth System Model (CESM) with the anisotropic eddy parameterization is used to test various choices for the newly introduced parameters, which are motivated by observations and the eddy transport tensor diagnosed from high resolution simulations. Simply setting the ratio of major to minor diffusivities to a value of five globally, while aligning the major axis along the flow direction, improves biogeochemical tracer ventilation and reduces global temperature and salinity biases. These effects can be improved even further by parameterizing the anisotropic transport mechanisms in the ocean.

Shingle Springs Band of Miwok Indians/Shingle Springs Rancheria: Express Fuel General Air Quality Permit Application

EPA Pesticide Factsheets

Shingle Springs Rancheria/Shingle Springs Band of Miwok Indians/Express Fuel Request for Coverage under the General Air Quality Permit for New or Modified Minor Source Gasoline Dispensing Facilities in Indian Country within California.

Closed system of coupling effects in generalized thermo-elastoplasticity

NASA Astrophysics Data System (ADS)

Śloderbach, Z.

2016-05-01

In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such materials as rocks, soils, concretes and in some metalic materials. In this paper not only the usual postulate of existence of a dissipation qupotential (the Gyarmati postulate) is used to derive the velocity equation. The plastic flow constitutive equations have the character of non-associated flow laws even when the Gyarmati postulate is assumed. In general formulation, the plastic strain rate tensor is normal to the surface of the generalized function of plastic flow defined in the the space of internal thermodynamic forces Π but is not normal to the yield surface. However, in general formulation and after the use the Gyarmati postulate, the direction of the sum of the plastic strain rate tensor and the coupled elastic strain rate tensor is normal to the yield surface.

Scale invariance, conformality, and generalized free fields

DOE PAGES

Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar; ...

2016-02-16

This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum fi eld theories with scale invariance but not conformal invariance. We present an important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen that is the trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unlessmore » the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Finally, despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.« less

Solar System constraints on massless scalar-tensor gravity with positive coupling constant upon cosmological evolution of the scalar field

NASA Astrophysics Data System (ADS)

Anderson, David; Yunes, Nicolás

2017-09-01

Scalar-tensor theories of gravity modify general relativity by introducing a scalar field that couples nonminimally to the metric tensor, while satisfying the weak-equivalence principle. These theories are interesting because they have the potential to simultaneously suppress modifications to Einstein's theory on Solar System scales, while introducing large deviations in the strong field of neutron stars. Scalar-tensor theories can be classified through the choice of conformal factor, a scalar that regulates the coupling between matter and the metric in the Einstein frame. The class defined by a Gaussian conformal factor with a negative exponent has been studied the most because it leads to spontaneous scalarization (i.e. the sudden activation of the scalar field in neutron stars), which consequently leads to large deviations from general relativity in the strong field. This class, however, has recently been shown to be in conflict with Solar System observations when accounting for the cosmological evolution of the scalar field. We here study whether this remains the case when the exponent of the conformal factor is positive, as well as in another class of theories defined by a hyperbolic conformal factor. We find that in both of these scalar-tensor theories, Solar System tests are passed only in a very small subset of coupling parameter space, for a large set of initial conditions compatible with big bang nucleosynthesis. However, while we find that it is possible for neutron stars to scalarize, one must carefully select the coupling parameter to do so, and even then, the scalar charge is typically 2 orders of magnitude smaller than in the negative-exponent case. Our study suggests that future work on scalar-tensor gravity, for example in the context of tests of general relativity with gravitational waves from neutron star binaries, should be carried out within the positive coupling parameter class.

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

PubMed

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

2017-07-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Affine theory of gravitation

NASA Astrophysics Data System (ADS)

Popławski, Nikodem

2014-01-01

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

The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

NASA Astrophysics Data System (ADS)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

2018-04-01

The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

Strong Constraints on Cosmological Gravity from GW170817 and GRB 170817A

NASA Astrophysics Data System (ADS)

Baker, T.; Bellini, E.; Ferreira, P. G.; Lagos, M.; Noller, J.; Sawicki, I.

2017-12-01

The detection of an electromagnetic counterpart (GRB 170817A) to the gravitational-wave signal (GW170817) from the merger of two neutron stars opens a completely new arena for testing theories of gravity. We show that this measurement allows us to place stringent constraints on general scalar-tensor and vector-tensor theories, while allowing us to place an independent bound on the graviton mass in bimetric theories of gravity. These constraints severely reduce the viable range of cosmological models that have been proposed as alternatives to general relativistic cosmology.

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

PubMed

Raju, Suvrat

2011-03-04

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

The 1/ N Expansion of Tensor Models Beyond Perturbation Theory

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2014-09-01

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.

Fake conformal symmetry in unimodular gravity

NASA Astrophysics Data System (ADS)

Oda, Ichiro

2016-08-01

We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry vanish exactly as in conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences in Einstein's general relativity, conformally invariant scalar-tensor gravity, and the Weyl-transverse gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing.

White matter structure in loneliness: preliminary findings from diffusion tensor imaging.

PubMed

Tian, Yin; Liang, Shanshan; Yuan, Zhen; Chen, Sifan; Xu, Peng; Yao, Dezhong

2014-08-06

A pilot study was carried out to determine individual differences in perceived loneliness using diffusion tensor imaging. To the best of our knowledge, this is the first preliminary diffusion tensor imaging evidence that the ventral attention network, generally activated by attentional reorienting, was also related to loneliness. Image reconstruction results indicated significantly decreased fractional anisotropy of white matter fibers and that associated nodes of the ventral attention network are highly correlated with increased loneliness ratings. By providing evidence on the structural level, our findings suggested that attention-reorienting capabilities play an important role in shaping an individual's loneliness.

Estimates of green tensors for certain boundary value problems

NASA Technical Reports Server (NTRS)

Solonnikov, V.

1988-01-01

Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.

Implementing the sine transform of fermionic modes as a tensor network

NASA Astrophysics Data System (ADS)

Epple, Hannes; Fries, Pascal; Hinrichsen, Haye

2017-09-01

Based on the algebraic theory of signal processing, we recursively decompose the discrete sine transform of the first kind (DST-I) into small orthogonal block operations. Using a diagrammatic language, we then second-quantize this decomposition to construct a tensor network implementing the DST-I for fermionic modes on a lattice. The complexity of the resulting network is shown to scale as 5/4 n logn (not considering swap gates), where n is the number of lattice sites. Our method provides a systematic approach of generalizing Ferris' spectral tensor network for nontrivial boundary conditions.

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.

Scalar-tensor theory of gravitation with negative coupling constant

NASA Technical Reports Server (NTRS)

Smalley, L. L.; Eby, P. B.

1976-01-01

The possibility of a Brans-Dicke scalar-tensor gravitation theory with a negative coupling constant is considered. The admissibility of a negative-coupling theory is investigated, and a simplified cosmological solution is obtained which allows a negative derivative of the gravitation constant. It is concluded that a Brans-Dicke theory with a negative coupling constant can be a viable alternative to general relativity and that a large negative value for the coupling constant seems to bring the original scalar-tensor theory into close agreement with perihelion-precession results in view of recent observations of small solar oblateness.

Moment tensor inversion of ground motion from mining-induced earthquakes, Trail Mountain, Utah

USGS Publications Warehouse

Fletcher, Joe B.; McGarr, A.

2005-01-01

A seismic network was operated in the vicinity of the Trail Mountain mine, central Utah, from the summer of 2000 to the spring of 2001 to investigate the seismic hazard to a local dam from mining-induced events that we expect to be triggered by future coal mining in this area. In support of efforts to develop groundmotion prediction relations for this situation, we inverted ground-motion recordings for six mining-induced events to determine seismic moment tensors and then to estimate moment magnitudes M for comparison with the network coda magnitudes Mc. Six components of the tensor were determined, for an assumed point source, following the inversion method of McGarr (1992a), which uses key measurements of amplitude from obvious features of the displacement waveforms. When the resulting moment tensors were decomposed into implosive and deviatoric components, we found that four of the six events showed a substantial volume reduction, presumably due to coseismic closure of the adjacent mine openings. For these four events, the volume reduction ranges from 27% to 55% of the shear component (fault area times average slip). Radiated seismic energy, computed from attenuation-corrected body-wave spectra, ranged from 2.4 ?? 105 to 2.4 ?? 106 J for events with M from 1.3 to 1.8, yielding apparent stresses from 0.02 to 0.06 MPa. The energy released for each event, approximated as the product of volume reduction and overburden stress, when compared with the corresponding seismic energies, revealed seismic efficiencies ranging from 0.5% to 7%. The low apparent stresses are consistent with the shallow focal depths of 0.2 to 0.6 km and rupture in a low stress/low strength regime compared with typical earthquake source regions at midcrustal depths.

New insights on the matter-gravity coupling paradigm.

PubMed

Delsate, Térence; Steinhoff, Jan

2012-07-13

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

Size, shape, and diffusivity of a single Debye-Hückel polyelectrolyte chain in solution.

PubMed

Soysa, W Chamath; Dünweg, B; Prakash, J Ravi

2015-08-14

Brownian dynamics simulations of a coarse-grained bead-spring chain model, with Debye-Hückel electrostatic interactions between the beads, are used to determine the root-mean-square end-to-end vector, the radius of gyration, and various shape functions (defined in terms of eigenvalues of the radius of gyration tensor) of a weakly charged polyelectrolyte chain in solution, in the limit of low polymer concentration. The long-time diffusivity is calculated from the mean square displacement of the centre of mass of the chain, with hydrodynamic interactions taken into account through the incorporation of the Rotne-Prager-Yamakawa tensor. Simulation results are interpreted in the light of the Odjik, Skolnick, Fixman, Khokhlov, and Khachaturian blob scaling theory (Everaers et al., Eur. Phys. J. E 8, 3 (2002)) which predicts that all solution properties are determined by just two scaling variables-the number of electrostatic blobs X and the reduced Debye screening length, Y. We identify three broad regimes, the ideal chain regime at small values of Y, the blob-pole regime at large values of Y, and the crossover regime at intermediate values of Y, within which the mean size, shape, and diffusivity exhibit characteristic behaviours. In particular, when simulation results are recast in terms of blob scaling variables, universal behaviour independent of the choice of bead-spring chain parameters, and the number of blobs X, is observed in the ideal chain regime and in much of the crossover regime, while the existence of logarithmic corrections to scaling in the blob-pole regime leads to non-universal behaviour.

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

Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar

This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum fi eld theories with scale invariance but not conformal invariance. We present an important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen that is the trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unlessmore » the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Finally, despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.« less

Computer Tensor Codes to Design the War Drive

NASA Astrophysics Data System (ADS)

Maccone, C.

To address problems in Breakthrough Propulsion Physics (BPP) and design the Warp Drive one needs sheer computing capabilities. This is because General Relativity (GR) and Quantum Field Theory (QFT) 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. 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 GR and QFT. Mathematical physicists, experimental physicists and engineers have each their own way of customizing tensors, especially by using 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 design of the Warp Drive. It is thus suggested that NASA would be a suitable organization to establish standards in symbolic tensor calculus and anyone working in BPP should adopt these standards. Alternatively other institutions, like CERN in Europe, might consider the challenge of starting the preliminary implementation of a Universal Tensor Code to design the Warp Drive.

Atomic-batched tensor decomposed two-electron repulsion integrals

NASA Astrophysics Data System (ADS)

Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove

2017-04-01

We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.

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

USGS Publications Warehouse

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

2003-01-01

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

Atomic-batched tensor decomposed two-electron repulsion integrals.

PubMed

Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove

2017-04-07

We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.

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

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

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

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.

Theoretical frameworks for testing relativistic gravity. IV - A compendium of metric theories of gravity and their post-Newtonian limits.

NASA Technical Reports Server (NTRS)

Ni, W.-T.

1972-01-01

Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.

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

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

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

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

11. GENERAL VIEW OF MEN'S BATH HALL. Hot Springs ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

11. GENERAL VIEW OF MEN'S BATH HALL. - Hot Springs National Park, Bathhouse Row, Fordyce Bathhouse: Mechanical & Piping Systems, State Highway 7, 1 mile north of U.S. Highway 70, Hot Springs, Garland County, AR

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic (Bianchi Type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley (RS) improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.

Null conformal Killing-Yano tensors and Birkhoff theorem

NASA Astrophysics Data System (ADS)

Ferrando, Joan Josep; Sáez, Juan Antonio

2016-04-01

We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similarities and differences with the recently studied non null case (Ferrando and Sáez in Gen Relativ Gravit 47:1911, 2015). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.

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.

Symmetry classes of the anisotropy tensors of quasielastic materials and a generalized Kelvin approach

NASA Astrophysics Data System (ADS)

Ostrosablin, N. I.

2017-05-01

The anisotropy matrices (tensors) of quasielastic (Cauchy-elastic) materials were obtained for all classes of crystallographic symmetries in explicit form. The fourth-rank anisotropy tensors of such materials do not have the main symmetry, in which case the anisotropy matrix is not symmetric. As a result of introducing various bases in the space of symmetric stress and strain tensors, the linear relationship between stresses and strains is represented in invariant form similar to the form in which generalized Hooke's law is written for the case of anisotropic hyperelastic materials and contains six positive Kelvin eigen moduli. It is shown that the introduction of modified rotation-induced deformation in the strain space can cause a transition to the symmetric anisotropy matrix observed in the case of hyperelasticity. For the case of transverse isotropy, there are examples of determination of the Kelvin eigen moduli and eigen bases and the rotation matrix in the strain space. It is shown that there is a possibility of existence of quasielastic media with a skew-symmetric anisotropy matrix with no symmetric part. Some techniques for the experimental testing of the quasielasticity model are proposed.

Generalized second law of thermodynamics in f(R,T) theory of gravity

NASA Astrophysics Data System (ADS)

Momeni, D.; Moraes, P. H. R. S.; Myrzakulov, R.

2016-07-01

We present a study of the generalized second law of thermodynamics in the scope of the f(R,T) theory of gravity, with R and T representing the Ricci scalar and trace of the energy-momentum tensor, respectively. From the energy-momentum tensor equation for the f(R,T)=R+f(T) case, we calculate the form of the geometric entropy in such a theory. Then, the generalized second law of thermodynamics is quantified and some relations for its obedience in f(R,T) gravity are presented. Those relations depend on some cosmological quantities, as the Hubble and deceleration parameters, and also on the form of f(T).

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

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

NASA Astrophysics Data System (ADS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Afrough, M.; Agarwal, B.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allen, G.; Allocca, A.; Altin, P. A.; Amato, A.; Ananyeva, A.; Anderson, S. B.; Anderson, W. G.; Angelova, S. V.; Antier, S.; Appert, S.; Arai, K.; Araya, M. C.; Areeda, J. S.; Arnaud, N.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Atallah, D. V.; Aufmuth, P.; Aulbert, C.; AultONeal, K.; Austin, C.; Avila-Alvarez, A.; Babak, S.; Bacon, P.; Bader, M. K. M.; Bae, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Banagiri, S.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barkett, K.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Bawaj, M.; Bayley, J. C.; Bazzan, M.; Bécsy, B.; Beer, C.; Bejger, M.; Belahcene, I.; Bell, A. S.; Berger, B. K.; Bergmann, G.; Bero, J. J.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Billman, C. R.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Biscoveanu, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blackman, J.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Bode, N.; Boer, M.; Bogaert, G.; Bohe, A.; Bondu, F.; Bonilla, E.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bossie, K.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Broida, J. E.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brunett, S.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cabero, M.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T. A.; Calloni, E.; Camp, J. B.; Canepa, M.; Canizares, P.; Cannon, K. C.; Cao, H.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Carney, M. F.; Diaz, J. Casanueva; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerdá-Durán, P.; Cerretani, G.; Cesarini, E.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chase, E.; Chassande-Mottin, E.; Chatterjee, D.; Cheeseboro, B. D.; Chen, H. Y.; Chen, X.; Chen, Y.; Cheng, H.-P.; Chia, H.; Chincarini, A.; Chiummo, A.; Chmiel, T.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, A. J. K.; Chua, S.; Chung, A. K. W.; Chung, S.; Ciani, G.; Ciolfi, R.; Cirelli, C. E.; Cirone, A.; Clara, F.; Clark, J. A.; Clearwater, P.; Cleva, F.; Cocchieri, C.; Coccia, E.; Cohadon, P.-F.; Cohen, D.; Colla, A.; Collette, C. G.; Cominsky, L. R.; Constancio, M.; Conti, L.; Cooper, S. J.; Corban, P.; Corbitt, T. R.; Cordero-Carrión, I.; Corley, K. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, E.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Covas, P. B.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Creighton, J. D. E.; Creighton, T. D.; Cripe, J.; Crowder, S. G.; Cullen, T. J.; Cumming, A.; Cunningham, L.; Cuoco, E.; Canton, T. Dal; Dálya, G.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Dasgupta, A.; Da Silva Costa, C. F.; Dattilo, V.; Dave, I.; Davier, M.; Davis, D.; Daw, E. J.; Day, B.; De, S.; DeBra, D.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Demos, N.; Denker, T.; Dent, T.; De Pietri, R.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; De Rossi, C.; DeSalvo, R.; de Varona, O.; Devenson, J.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Girolamo, T.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Renzo, F.; Doctor, Z.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Dorrington, I.; Douglas, R.; Dovale Álvarez, M.; Downes, T. P.; Drago, M.; Dreissigacker, C.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dupej, P.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Eisenstein, R. A.; Essick, R. C.; Estevez, D.; Etienne, Z. B.; Etzel, T.; Evans, M.; Evans, T. M.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Farinon, S.; Farr, B.; Farr, W. M.; Fauchon-Jones, E. J.; Favata, M.; Fays, M.; Fee, C.; Fehrmann, H.; Feicht, J.; Fejer, M. M.; Fernandez-Galiana, A.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Finstad, D.; Fiori, I.; Fiorucci, D.; Fishbach, M.; Fisher, R. P.; Fitz-Axen, M.; Flaminio, R.; Fletcher, M.; Fong, H.; Font, J. A.; Forsyth, P. W. F.; Forsyth, S. S.; Fournier, J.-D.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fries, E. M.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H.; Gadre, B. U.; Gaebel, S. M.; Gair, J. R.; Gammaitoni, L.; Ganija, M. R.; Gaonkar, S. G.; Garcia-Quiros, C.; Garufi, F.; Gateley, B.; Gaudio, S.; Gaur, G.; Gayathri, V.; Gehrels, N.; Gemme, G.; Genin, E.; Gennai, A.; George, D.; George, J.; Gergely, L.; Germain, V.; Ghonge, S.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glover, L.; Goetz, E.; Goetz, R.; Gomes, S.; Goncharov, B.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Grado, A.; Graef, C.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Gretarsson, E. M.; Groot, P.; Grote, H.; Grunewald, S.; Gruning, P.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Halim, O.; Hall, B. R.; Hall, E. D.; Hamilton, E. Z.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hannuksela, O. A.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hinderer, T.; Hoak, D.; Hofman, D.; Holt, K.; Holz, D. E.; Hopkins, P.; Horst, C.; Hough, J.; Houston, E. A.; Howell, E. J.; Hreibi, A.; Hu, Y. M.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Indik, N.; Inta, R.; Intini, G.; Isa, H. N.; Isac, J.-M.; Isi, M.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Junker, J.; Kalaghatgi, C. V.; Kalogera, V.; Kamai, B.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Kapadia, S. J.; Karki, S.; Karvinen, K. S.; Kasprzack, M.; Katolik, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kawabe, K.; Kéfélian, F.; Keitel, D.; Kemball, A. J.; Kennedy, R.; Kent, C.; Key, J. S.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, Chunglee; Kim, J. C.; Kim, K.; Kim, W.; Kim, W. S.; Kim, Y.-M.; Kimbrell, S. J.; King, E. J.; King, P. J.; Kinley-Hanlon, M.; Kirchhoff, R.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Knowles, T. D.; Koch, P.; Koehlenbeck, S. M.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Krämer, C.; Kringel, V.; Królak, A.; Kuehn, G.; Kumar, P.; Kumar, R.; Kumar, S.; Kuo, L.; Kutynia, A.; Kwang, S.; Lackey, B. D.; Lai, K. H.; Landry, M.; Lang, R. N.; Lange, J.; Lantz, B.; Lanza, R. K.; Lartaux-Vollard, A.; Lasky, P. D.; Laxen, M.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, H. W.; Lee, K.; Lehmann, J.; Lenon, A.; Leonardi, M.; Leroy, N.; Letendre, N.; Levin, Y.; Li, T. G. F.; Linker, S. D.; Littenberg, T. B.; Liu, J.; Lo, R. K. L.; Lockerbie, N. A.; London, L. T.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lousto, C. O.; Lovelace, G.; Lück, H.; Lumaca, D.; Lundgren, A. P.; Lynch, R.; Ma, Y.; Macas, R.; Macfoy, S.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña Hernandez, I.; Magaña-Sandoval, F.; Magaña Zertuche, L.; Magee, R. M.; Majorana, E.; Maksimovic, I.; Man, N.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markakis, C.; Markosyan, A. S.; Markowitz, A.; Maros, E.; Marquina, A.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Mason, K.; Massera, E.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Mastrogiovanni, S.; Matas, A.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McCuller, L.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McNeill, L.; McRae, T.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Mehmet, M.; Meidam, J.; Mejuto-Villa, E.; Melatos, A.; Mendell, G.; Mercer, R. A.; Merilh, E. L.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Metzdorff, R.; Meyers, P. M.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, A. L.; Miller, B. B.; Miller, J.; Millhouse, M.; Milovich-Goff, M. C.; Minazzoli, O.; Minenkov, Y.; Ming, J.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moffa, D.; Moggi, A.; Mogushi, K.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mours, B.; Mow-Lowry, C. M.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Muñiz, E. A.; Muratore, M.; Murray, P. G.; Napier, K.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Neilson, J.; Nelemans, G.; Nelson, T. J. N.; Nery, M.; Neunzert, A.; Nevin, L.; Newport, J. M.; Newton, G.; Ng, K. K. Y.; Nguyen, T. T.; Nichols, D.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Noack, A.; Nocera, F.; Nolting, D.; North, C.; Nuttall, L. K.; Oberling, J.; O'Dea, G. D.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Okada, M. A.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; Ormiston, R.; Ortega, L. F.; O'Shaughnessy, R.; Ossokine, S.; Ottaway, D. J.; Overmier, H.; Owen, B. J.; Pace, A. E.; Page, J.; Page, M. A.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, Howard; Pan, Huang-Wei; Pang, B.; Pang, P. T. H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Parida, A.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patil, M.; Patricelli, B.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perez, C. J.; Perreca, A.; Perri, L. M.; Pfeiffer, H. P.; Phelps, M.; Piccinni, O. J.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pirello, M.; Pitkin, M.; Poe, M.; Poggiani, R.; Popolizio, P.; Porter, E. K.; Post, A.; Powell, J.; Prasad, J.; Pratt, J. W. W.; Pratten, G.; Predoi, V.; Prestegard, T.; Prijatelj, M.; Principe, M.; Privitera, S.; Prodi, G. A.; Prokhorov, L. G.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rajan, C.; Rajbhandari, B.; Rakhmanov, M.; Ramirez, K. E.; Ramos-Buades, A.; Rapagnani, P.; Raymond, V.; Razzano, M.; Read, J.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Ren, W.; Reyes, S. D.; Ricci, F.; Ricker, P. M.; Rieger, S.; Riles, K.; Rizzo, M.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romel, C. L.; Romie, J. H.; Rosińska, D.; Ross, M. P.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Rutins, G.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Sakellariadou, M.; Salconi, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sampson, L. M.; Sanchez, E. J.; Sanchez, L. E.; Sanchis-Gual, N.; Sandberg, V.; Sanders, J. R.; Sassolas, B.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Scheel, M.; Scheuer, J.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schulte, B. W.; Schutz, B. F.; Schwalbe, S. G.; Scott, J.; Scott, S. M.; Seidel, E.; Sellers, D.; Sengupta, A. S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Shaddock, D. A.; Shaffer, T. J.; Shah, A. A.; Shahriar, M. S.; Shaner, M. B.; Shao, L.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sieniawska, M.; Sigg, D.; Silva, A. D.; Singer, L. P.; Singh, A.; Singhal, A.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, B.; Smith, J. R.; Smith, R. J. E.; Somala, S.; Son, E. J.; Sonnenberg, J. A.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Spencer, A. P.; Srivastava, A. K.; Staats, K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stevenson, S. P.; Stone, R.; Stops, D. J.; Strain, K. A.; Stratta, G.; Strigin, S. E.; Strunk, A.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sunil, S.; Suresh, J.; Sutton, P. J.; Swinkels, B. L.; Szczepańczyk, M. J.; Tacca, M.; Tait, S. C.; Talbot, C.; Talukder, D.; Tanner, D. B.; Tao, D.; Tápai, M.; Taracchini, A.; Tasson, J. D.; Taylor, J. A.; Taylor, R.; Tewari, S. V.; Theeg, T.; Thies, F.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Toland, K.; Tonelli, M.; Tornasi, Z.; Torres-Forné, A.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trinastic, J.; Tringali, M. C.; Trozzo, L.; Tsang, K. W.; Tse, M.; Tso, R.; Tsukada, L.; Tsuna, D.; Tuyenbayev, D.; Ueno, K.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; Van Den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Varma, V.; Vass, S.; Vasúth, M.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Venugopalan, G.; Verkindt, D.; Vetrano, F.; Viceré, A.; Viets, A. D.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walet, R.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, J. Z.; Wang, W. H.; Wang, Y. F.; Ward, R. L.; Warner, J.; Was, M.; Watchi, J.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Wen, L.; Wessel, E. K.; Weßels, P.; Westerweck, J.; Westphal, T.; Wette, K.; Whelan, J. T.; Whiting, B. F.; Whittle, C.; Wilken, D.; Williams, D.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Woehler, J.; Wofford, J.; Wong, K. W. K.; Worden, J.; Wright, J. L.; Wu, D. S.; Wysocki, D. M.; Xiao, S.; Yamamoto, H.; Yancey, C. C.; Yang, L.; Yap, M. J.; Yazback, M.; Yu, Hang; Yu, Haocun; Yvert, M.; ZadroŻny, A.; Zanolin, M.; Zelenova, T.; Zendri, J.-P.; Zevin, M.; Zhang, L.; Zhang, M.; Zhang, T.; Zhang, Y.-H.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, S. J.; Zhu, X. J.; Zucker, M. E.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration

2018-05-01

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58 ×10-8 , Ω0V<6.35 ×10-8 , and Ω0S<1.08 ×10-7 at a reference frequency f0=25 Hz .

Lectures on gravitation

NASA Astrophysics Data System (ADS)

Das, Ashok

1. Basics of geometry and relativity. 1.1. Two dimensional geometry. 1.2. Inertial and gravitational masses. 1.3. Relativity -- 2. Relativistic dynamics. 2.1. Relativistic point particle. 2.2. Current and charge densities. 2.3. Maxwell's equations in the presence of sources. 2.4. Motion of a charged particle in EM field. 2.5. Energy-momentum tensor. 2.6. Angular momentum -- 3. Principle of general covariance. 3.1. Principle of equivalence. 3.2. Principle of general covariance. 3.3. Tensor densities -- 4. Affine connection and covariant derivative. 4.1. Parallel transport of a vector. 4.2. Christoffel symbol. 4.3. Covariant derivative of contravariant tensors. 4.4. Metric compatibility. 4.5. Covariant derivative of covariant and mixed tensors. 4.6. Electromagnetic analogy. 4.7. Gradient, divergence and curl -- 5. Geodesic equation. 5.1. Covariant differentiation along a curve. 5.2. Curvature from derivatives. 5.3. Parallel transport along a closed curve. 5.4. Geodesic equation. 5.5. Derivation of geodesic equation from a Lagrangian -- 6. Applications of the geodesic equation. 6.1. Geodesic as representing gravitational effect. 6.2. Rotating coordinate system and the Coriolis force. 6.3. Gravitational red shift. 6.4. Twin paradox and general covariance. 6.5. Other equations in the presence of gravitation -- 7. Curvature tensor and Einstein's equation. 7.1. Curvilinear coordinates versus gravitational field. 7.2. Definition of an inertial coordinate frame. 7.3. Geodesic deviation. 7.4. Properties of the curvature tensor. 7.5. Einstein's equation. 7.6. Cosmological constant. 7.7. Initial value problem. 7.8. Einstein's equation from an action -- 8. Schwarzschild solution. 8.1. Line element. 8.2. Connection. 8.3. Solution of the Einstein equation. 8.4. Properties of the Schwarzschild solution. 8.5. Isotropic coordinates -- 9. Tests of general relativity. 9.1. Radar echo experiment. 9.2. Motion of a particle in a Schwarzschild background. 9.3. Motion of light rays in a Schwarzschild background. 9.4. Perihelion advance of Mercury -- 10. Black holes. 10.1. Singularities of the metric. 10.2. Singularities of the Schwarzschild metric. 10.3. Black holes -- 11. Cosmological models and the big bang theory. 11.1. Homogeneity and isotropy. 11.2. Different models of the universe. 11.3. Hubble's law. 11.4. Evolution equation. 11.5. Big bang theory and blackbody radiation.

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 Cartesian parametrization for the numerical analysis of material instability

DOE PAGES

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; ...

2016-02-25

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

A Cartesian parametrization for the numerical analysis of material instability

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

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

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.

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.

Neutron star solutions with curvature induced scalarization in the extended Gauss-Bonnet scalar-tensor theories

NASA Astrophysics Data System (ADS)

Doneva, Daniela D.; Yazadjiev, Stoytcho S.

2018-04-01

In the present paper we study models of neutron stars in a class of extended scalar-tensor Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is exited only in the strong curvature regime. We show that in the framework of the ESTGB theories under consideration there exist new neutron star solutions which are formed via spontaneous scalarization of the general relativistic neutron stars. In contrast to the spontaneous scalarization in the standard scalar-tensor theories which is induced by the presence of matter, in our case the scalarization is induced by the spacetime curvature.

Long-Lived Inverse Chirp Signals from Core-Collapse in Massive Scalar-Tensor Gravity

NASA Astrophysics Data System (ADS)

Sperhake, Ulrich; Moore, Christopher J.; Rosca, Roxana; Agathos, Michalis; Gerosa, Davide; Ott, Christian D.

2017-11-01

This Letter considers stellar core collapse in massive scalar-tensor theories of gravity. The presence of a mass term for the scalar field allows for dramatic increases in the radiated gravitational wave signal. There are several potential smoking gun signatures of a departure from general relativity associated with this process. These signatures could show up within existing LIGO-Virgo searches.

Geometrization of the Dirac theory of the electron

NASA Technical Reports Server (NTRS)

Fock, V.

1977-01-01

Using the concept of parallel displacement of a half vector, the Dirac equations are generally written in invariant form. The energy tensor is formed and both the macroscopic and quantum mechanic equations of motion are set up. The former have the usual form: divergence of the energy tensor equals the Lorentz force and the latter are essentially identical with those of the geodesic line.

Electrical impedance tomography in anisotropic media with known eigenvectors

NASA Astrophysics Data System (ADS)

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

2011-06-01

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

Forces in General Relativity

ERIC Educational Resources Information Center

Ridgely, Charles T.

2010-01-01

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

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.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

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

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

IIB supergravity and the E 6(6) covariant vector-tensor hierarchy

DOE PAGES

Ciceri, Franz; de Wit, Bernard; Varela, Oscar

2015-04-20

IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional ‘dual graviton’. The invariant E 6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions formore » the USp(8) covariant fermion fields. Implications are further discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.« less

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

Semi-inclusive charged-current neutrino-nucleus reactions

DOE PAGES

Moreno, O.; Donnelly, T. W.; Van Orden, J. W.; ...

2014-07-17

The general, universal formalism for semi-inclusive charged-current (anti)neutrino-nucleus reactions is given for studies of any hadronic system, namely, either nuclei or the nucleon itself. The detailed developments are presented with the former in mind and are further specialized to cases where the final-state charged lepton and an ejected nucleon are presumed to be detected. General kinematics for such processes are summarized and then explicit expressions are developed for the leptonic and hadronic tensors involved and for the corresponding responses according to the usual charge, longitudinal and transverse projections, keeping finite the masses of all particles involved. In the case ofmore » the hadronic responses, general symmetry principles are invoked to determine which contributions can occur. As a result, the general leptonic-hadronic tensor contraction is given as well as the cross section for the process.« less

On the origin independence of the Verdet tensor†

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

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

PubMed

Carmichael, Owen; Sakhanenko, Lyudmila

2015-05-15

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

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

PubMed Central

Carmichael, Owen; Sakhanenko, Lyudmila

2015-01-01

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

Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

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.

Modelling Dynamic Behaviour and Spall Failure of Aluminium Alloy AA7010

NASA Astrophysics Data System (ADS)

Ma'at, N.; Nor, M. K. Mohd; Ismail, A. E.; Kamarudin, K. A.; Jamian, S.; Ibrahim, M. N.; Awang, M. K.

2017-10-01

A finite strain constitutive model to predict the dynamic deformation behaviour of Aluminium Alloy 7010 including shockwaves and spall failure is developed in this work. The important feature of this newly hyperelastic-plastic constitutive formulation is a new Mandel stress tensor formulated using new generalized orthotropic pressure. This tensor is combined with a shock equation of state (EOS) and Grady spall failure. The Hill’s yield criterion is adopted to characterize plastic orthotropy by means of the evolving structural tensors that is defined in the isoclinic configuration. This material model was developed and integration into elastic and plastic parts. The elastic anisotropy is taken into account through the newly stress tensor decomposition of a generalized orthotropic pressure. Plastic anisotropy is considered through yield surface and an isotropic hardening defined in a unique alignment of deviatoric plane within the stress space. To test its ability to describe shockwave propagation and spall failure, the new material model was implemented into the LLNL-DYNA3D code of UTHM’s. The capability of this newly constitutive model were compared against published experimental data of Plate Impact Test at 234m/s, 450m/s and 895m/s impact velocities. A good agreement is obtained between experimental and simulation in each test.

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

Exact solutions to quadratic gravity

NASA Astrophysics Data System (ADS)

Pravda, V.; Pravdová, A.; Podolský, J.; Švarc, R.

2017-04-01

Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one nonlinear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

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.

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.

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.

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background.

PubMed

Abbott, B P; Abbott, R; Abbott, T D; Acernese, F; Ackley, K; Adams, C; Adams, T; Addesso, P; Adhikari, R X; Adya, V B; Affeldt, C; Afrough, M; Agarwal, B; Agathos, M; Agatsuma, K; Aggarwal, N; Aguiar, O D; Aiello, L; Ain, A; Ajith, P; Allen, B; Allen, G; Allocca, A; Altin, P A; Amato, A; Ananyeva, A; Anderson, S B; Anderson, W G; Angelova, S V; Antier, S; Appert, S; Arai, K; Araya, M C; Areeda, J S; Arnaud, N; Ascenzi, S; Ashton, G; Ast, M; Aston, S M; Astone, P; Atallah, D V; Aufmuth, P; Aulbert, C; AultONeal, K; Austin, C; Avila-Alvarez, A; Babak, S; Bacon, P; Bader, M K M; Bae, S; Baker, P T; Baldaccini, F; Ballardin, G; Ballmer, S W; Banagiri, S; Barayoga, J C; Barclay, S E; Barish, B C; Barker, D; Barkett, K; Barone, F; Barr, B; Barsotti, L; Barsuglia, M; Barta, D; Bartlett, J; Bartos, I; Bassiri, R; Basti, A; Batch, J C; Bawaj, M; Bayley, J C; Bazzan, M; Bécsy, B; Beer, C; Bejger, M; Belahcene, I; Bell, A S; Berger, B K; Bergmann, G; Bero, J J; Berry, C P L; Bersanetti, D; Bertolini, A; Betzwieser, J; Bhagwat, S; Bhandare, R; Bilenko, I A; Billingsley, G; Billman, C R; Birch, J; Birney, R; Birnholtz, O; Biscans, S; Biscoveanu, S; Bisht, A; Bitossi, M; Biwer, C; Bizouard, M A; Blackburn, J K; Blackman, J; Blair, C D; Blair, D G; Blair, R M; Bloemen, S; Bock, O; Bode, N; Boer, M; Bogaert, G; Bohe, A; Bondu, F; Bonilla, E; Bonnand, R; Boom, B A; Bork, R; Boschi, V; Bose, S; Bossie, K; Bouffanais, Y; Bozzi, A; Bradaschia, C; Brady, P R; Branchesi, M; Brau, J E; Briant, T; Brillet, A; Brinkmann, M; Brisson, V; Brockill, P; Broida, J E; Brooks, A F; Brown, D A; Brown, D D; Brunett, S; Buchanan, C C; Buikema, A; Bulik, T; Bulten, H J; Buonanno, A; Buskulic, D; Buy, C; Byer, R L; Cabero, M; Cadonati, L; Cagnoli, G; Cahillane, C; Calderón Bustillo, J; Callister, T A; Calloni, E; Camp, J B; Canepa, M; Canizares, P; Cannon, K C; Cao, H; Cao, J; Capano, C D; Capocasa, E; Carbognani, F; Caride, S; Carney, M F; Diaz, J Casanueva; Casentini, C; Caudill, S; Cavaglià, M; Cavalier, F; Cavalieri, R; Cella, G; Cepeda, C B; Cerdá-Durán, P; Cerretani, G; Cesarini, E; Chamberlin, S J; Chan, M; Chao, S; Charlton, P; Chase, E; Chassande-Mottin, E; Chatterjee, D; Cheeseboro, B D; Chen, H Y; Chen, X; Chen, Y; Cheng, H-P; Chia, H; Chincarini, A; Chiummo, A; Chmiel, T; Cho, H S; Cho, M; Chow, J H; Christensen, N; Chu, Q; Chua, A J K; Chua, S; Chung, A K W; Chung, S; Ciani, G; Ciolfi, R; Cirelli, C E; Cirone, A; Clara, F; Clark, J A; Clearwater, P; Cleva, F; Cocchieri, C; Coccia, E; Cohadon, P-F; Cohen, D; Colla, A; Collette, C G; Cominsky, L R; Constancio, M; Conti, L; Cooper, S J; Corban, P; Corbitt, T R; Cordero-Carrión, I; Corley, K R; Cornish, N; Corsi, A; Cortese, S; Costa, C A; Coughlin, E; Coughlin, M W; Coughlin, S B; Coulon, J-P; Countryman, S T; Couvares, P; Covas, P B; Cowan, E E; Coward, D M; Cowart, M J; Coyne, D C; Coyne, R; Creighton, J D E; Creighton, T D; Cripe, J; Crowder, S G; Cullen, T J; Cumming, A; Cunningham, L; Cuoco, E; Canton, T Dal; Dálya, G; Danilishin, S L; D'Antonio, S; Danzmann, K; Dasgupta, A; Da Silva Costa, C F; Dattilo, V; Dave, I; Davier, M; Davis, D; Daw, E J; Day, B; De, S; DeBra, D; Degallaix, J; De Laurentis, M; Deléglise, S; Del Pozzo, W; Demos, N; Denker, T; Dent, T; De Pietri, R; Dergachev, V; De Rosa, R; DeRosa, R T; De Rossi, C; DeSalvo, R; de Varona, O; Devenson, J; Dhurandhar, S; Díaz, M C; Di Fiore, L; Di Giovanni, M; Di Girolamo, T; Di Lieto, A; Di Pace, S; Di Palma, I; Di Renzo, F; Doctor, Z; Dolique, V; Donovan, F; Dooley, K L; Doravari, S; Dorrington, I; Douglas, R; Dovale Álvarez, M; Downes, T P; Drago, M; Dreissigacker, C; Driggers, J C; Du, Z; Ducrot, M; Dupej, P; Dwyer, S E; Edo, T B; Edwards, M C; Effler, A; Eggenstein, H-B; Ehrens, P; Eichholz, J; Eikenberry, S S; Eisenstein, R A; Essick, R C; Estevez, D; Etienne, Z B; Etzel, T; Evans, M; Evans, T M; Factourovich, M; Fafone, V; Fair, H; Fairhurst, S; Fan, X; Farinon, S; Farr, B; Farr, W M; Fauchon-Jones, E J; Favata, M; Fays, M; Fee, C; Fehrmann, H; Feicht, J; Fejer, M M; Fernandez-Galiana, A; Ferrante, I; Ferreira, E C; Ferrini, F; Fidecaro, F; Finstad, D; Fiori, I; Fiorucci, D; Fishbach, M; Fisher, R P; Fitz-Axen, M; Flaminio, R; Fletcher, M; Fong, H; Font, J A; Forsyth, P W F; Forsyth, S S; Fournier, J-D; Frasca, S; Frasconi, F; Frei, Z; Freise, A; Frey, R; Frey, V; Fries, E M; Fritschel, P; Frolov, V V; Fulda, P; Fyffe, M; Gabbard, H; Gadre, B U; Gaebel, S M; Gair, J R; Gammaitoni, L; Ganija, M R; Gaonkar, S G; Garcia-Quiros, C; Garufi, F; Gateley, B; Gaudio, S; Gaur, G; Gayathri, V; Gehrels, N; Gemme, G; Genin, E; Gennai, A; George, D; George, J; Gergely, L; Germain, V; Ghonge, S; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S; Giaime, J A; Giardina, K D; Giazotto, A; Gill, K; Glover, L; Goetz, E; Goetz, R; Gomes, S; Goncharov, B; González, G; Gonzalez Castro, J M; Gopakumar, A; Gorodetsky, M L; Gossan, S E; Gosselin, M; Gouaty, R; Grado, A; Graef, C; Granata, M; Grant, A; Gras, S; Gray, C; Greco, G; Green, A C; Gretarsson, E M; Groot, P; Grote, H; Grunewald, S; Gruning, P; Guidi, G M; Guo, X; Gupta, A; Gupta, M K; Gushwa, K E; Gustafson, E K; Gustafson, R; Halim, O; Hall, B R; Hall, E D; Hamilton, E Z; Hammond, G; Haney, M; Hanke, M M; Hanks, J; Hanna, C; Hannam, M D; Hannuksela, O A; Hanson, J; Hardwick, T; Harms, J; Harry, G M; Harry, I W; Hart, M J; Haster, C-J; Haughian, K; Healy, J; Heidmann, A; Heintze, M C; Heitmann, H; Hello, P; Hemming, G; Hendry, M; Heng, I S; Hennig, J; Heptonstall, A W; Heurs, M; Hild, S; Hinderer, T; Hoak, D; Hofman, D; Holt, K; Holz, D E; Hopkins, P; Horst, C; Hough, J; Houston, E A; Howell, E J; Hreibi, A; Hu, Y M; Huerta, E A; Huet, D; Hughey, B; Husa, S; Huttner, S H; Huynh-Dinh, T; Indik, N; Inta, R; Intini, G; Isa, H N; Isac, J-M; Isi, M; Iyer, B R; Izumi, K; Jacqmin, T; Jani, K; Jaranowski, P; Jawahar, S; Jiménez-Forteza, F; Johnson, W W; Jones, D I; Jones, R; Jonker, R J G; Ju, L; Junker, J; Kalaghatgi, C V; Kalogera, V; Kamai, B; Kandhasamy, S; Kang, G; Kanner, J B; Kapadia, S J; Karki, S; Karvinen, K S; Kasprzack, M; Katolik, M; Katsavounidis, E; Katzman, W; Kaufer, S; Kawabe, K; Kéfélian, F; Keitel, D; Kemball, A J; Kennedy, R; Kent, C; Key, J S; Khalili, F Y; Khan, I; Khan, S; Khan, Z; Khazanov, E A; Kijbunchoo, N; Kim, Chunglee; Kim, J C; Kim, K; Kim, W; Kim, W S; Kim, Y-M; Kimbrell, S J; King, E J; King, P J; Kinley-Hanlon, M; Kirchhoff, R; Kissel, J S; Kleybolte, L; Klimenko, S; Knowles, T D; Koch, P; Koehlenbeck, S M; Koley, S; Kondrashov, V; Kontos, A; Korobko, M; Korth, W Z; Kowalska, I; Kozak, D B; Krämer, C; Kringel, V; Królak, A; Kuehn, G; Kumar, P; Kumar, R; Kumar, S; Kuo, L; Kutynia, A; Kwang, S; Lackey, B D; Lai, K H; Landry, M; Lang, R N; Lange, J; Lantz, B; Lanza, R K; Lartaux-Vollard, A; Lasky, P D; Laxen, M; Lazzarini, A; Lazzaro, C; Leaci, P; Leavey, S; Lee, C H; Lee, H K; Lee, H M; Lee, H W; Lee, K; Lehmann, J; Lenon, A; Leonardi, M; Leroy, N; Letendre, N; Levin, Y; Li, T G F; Linker, S D; Littenberg, T B; Liu, J; Lo, R K L; Lockerbie, N A; London, L T; Lord, J E; Lorenzini, M; Loriette, V; Lormand, M; Losurdo, G; Lough, J D; Lousto, C O; Lovelace, G; Lück, H; Lumaca, D; Lundgren, A P; Lynch, R; Ma, Y; Macas, R; Macfoy, S; Machenschalk, B; MacInnis, M; Macleod, D M; Magaña Hernandez, I; Magaña-Sandoval, F; Magaña Zertuche, L; Magee, R M; Majorana, E; Maksimovic, I; Man, N; Mandic, V; Mangano, V; Mansell, G L; Manske, M; Mantovani, M; Marchesoni, F; Marion, F; Márka, S; Márka, Z; Markakis, C; Markosyan, A S; Markowitz, A; Maros, E; Marquina, A; Martelli, F; Martellini, L; Martin, I W; Martin, R M; Martynov, D V; Mason, K; Massera, E; Masserot, A; Massinger, T J; Masso-Reid, M; Mastrogiovanni, S; Matas, A; Matichard, F; Matone, L; Mavalvala, N; Mazumder, N; McCarthy, R; McClelland, D E; McCormick, S; McCuller, L; McGuire, S C; McIntyre, G; McIver, J; McManus, D J; McNeill, L; McRae, T; McWilliams, S T; Meacher, D; Meadors, G D; Mehmet, M; Meidam, J; Mejuto-Villa, E; Melatos, A; Mendell, G; Mercer, R A; Merilh, E L; Merzougui, M; Meshkov, S; Messenger, C; Messick, C; Metzdorff, R; Meyers, P M; Miao, H; Michel, C; Middleton, H; Mikhailov, E E; Milano, L; Miller, A L; Miller, B B; Miller, J; Millhouse, M; Milovich-Goff, M C; Minazzoli, O; Minenkov, Y; Ming, J; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moffa, D; Moggi, A; Mogushi, K; Mohan, M; Mohapatra, S R P; Montani, M; Moore, C J; Moraru, D; Moreno, G; Morriss, S R; Mours, B; Mow-Lowry, C M; Mueller, G; Muir, A W; Mukherjee, Arunava; Mukherjee, D; Mukherjee, S; Mukund, N; Mullavey, A; Munch, J; Muñiz, E A; Muratore, M; Murray, P G; Napier, K; Nardecchia, I; Naticchioni, L; Nayak, R K; Neilson, J; Nelemans, G; Nelson, T J N; Nery, M; Neunzert, A; Nevin, L; Newport, J M; Newton, G; Ng, K K Y; Nguyen, T T; Nichols, D; Nielsen, A B; Nissanke, S; Nitz, A; Noack, A; Nocera, F; Nolting, D; North, C; Nuttall, L K; Oberling, J; O'Dea, G D; Ogin, G H; Oh, J J; Oh, S H; Ohme, F; Okada, M A; Oliver, M; Oppermann, P; Oram, Richard J; O'Reilly, B; Ormiston, R; Ortega, L F; O'Shaughnessy, R; Ossokine, S; Ottaway, D J; Overmier, H; Owen, B J; Pace, A E; Page, J; Page, M A; Pai, A; Pai, S A; Palamos, J R; Palashov, O; Palomba, C; Pal-Singh, A; Pan, Howard; Pan, Huang-Wei; Pang, B; Pang, P T H; Pankow, C; Pannarale, F; Pant, B C; Paoletti, F; Paoli, A; Papa, M A; Parida, A; Parker, W; Pascucci, D; Pasqualetti, A; Passaquieti, R; Passuello, D; Patil, M; Patricelli, B; Pearlstone, B L; Pedraza, M; Pedurand, R; Pekowsky, L; Pele, A; Penn, S; Perez, C J; Perreca, A; Perri, L M; Pfeiffer, H P; Phelps, M; Piccinni, O J; Pichot, M; Piergiovanni, F; Pierro, V; Pillant, G; Pinard, L; Pinto, I M; Pirello, M; Pitkin, M; Poe, M; Poggiani, R; Popolizio, P; Porter, E K; Post, A; Powell, J; Prasad, J; Pratt, J W W; Pratten, G; Predoi, V; Prestegard, T; Prijatelj, M; Principe, M; Privitera, S; Prodi, G A; Prokhorov, L G; Puncken, O; Punturo, M; Puppo, P; Pürrer, M; Qi, H; Quetschke, V; Quintero, E A; Quitzow-James, R; Raab, F J; Rabeling, D S; Radkins, H; Raffai, P; Raja, S; Rajan, C; Rajbhandari, B; Rakhmanov, M; Ramirez, K E; Ramos-Buades, A; Rapagnani, P; Raymond, V; Razzano, M; Read, J; Regimbau, T; Rei, L; Reid, S; Reitze, D H; Ren, W; Reyes, S D; Ricci, F; Ricker, P M; Rieger, S; Riles, K; Rizzo, M; Robertson, N A; Robie, R; Robinet, F; Rocchi, A; Rolland, L; Rollins, J G; Roma, V J; Romano, J D; Romano, R; Romel, C L; Romie, J H; Rosińska, D; Ross, M P; Rowan, S; Rüdiger, A; Ruggi, P; Rutins, G; Ryan, K; Sachdev, S; Sadecki, T; Sadeghian, L; Sakellariadou, M; Salconi, L; Saleem, M; Salemi, F; Samajdar, A; Sammut, L; Sampson, L M; Sanchez, E J; Sanchez, L E; Sanchis-Gual, N; Sandberg, V; Sanders, J R; Sassolas, B; Saulson, P R; Sauter, O; Savage, R L; Sawadsky, A; Schale, P; Scheel, M; Scheuer, J; Schmidt, J; Schmidt, P; Schnabel, R; Schofield, R M S; Schönbeck, A; Schreiber, E; Schuette, D; Schulte, B W; Schutz, B F; Schwalbe, S G; Scott, J; Scott, S M; Seidel, E; Sellers, D; Sengupta, A S; Sentenac, D; Sequino, V; Sergeev, A; Shaddock, D A; Shaffer, T J; Shah, A A; Shahriar, M S; Shaner, M B; Shao, L; Shapiro, B; Shawhan, P; Sheperd, A; Shoemaker, D H; Shoemaker, D M; Siellez, K; Siemens, X; Sieniawska, M; Sigg, D; Silva, A D; Singer, L P; Singh, A; Singhal, A; Sintes, A M; Slagmolen, B J J; Smith, B; Smith, J R; Smith, R J E; Somala, S; Son, E J; Sonnenberg, J A; Sorazu, B; Sorrentino, F; Souradeep, T; Spencer, A P; Srivastava, A K; Staats, K; Staley, A; Steinke, M; Steinlechner, J; Steinlechner, S; Steinmeyer, D; Stevenson, S P; Stone, R; Stops, D J; Strain, K A; Stratta, G; Strigin, S E; Strunk, A; Sturani, R; Stuver, A L; Summerscales, T Z; Sun, L; Sunil, S; Suresh, J; Sutton, P J; Swinkels, B L; Szczepańczyk, M J; Tacca, M; Tait, S C; Talbot, C; Talukder, D; Tanner, D B; Tao, D; Tápai, M; Taracchini, A; Tasson, J D; Taylor, J A; Taylor, R; Tewari, S V; Theeg, T; Thies, F; Thomas, E G; Thomas, M; Thomas, P; Thorne, K A; Thrane, E; Tiwari, S; Tiwari, V; Tokmakov, K V; Toland, K; Tonelli, M; Tornasi, Z; Torres-Forné, A; Torrie, C I; Töyrä, D; Travasso, F; Traylor, G; Trinastic, J; Tringali, M C; Trozzo, L; Tsang, K W; Tse, M; Tso, R; Tsukada, L; Tsuna, D; Tuyenbayev, D; Ueno, K; Ugolini, D; Unnikrishnan, C S; Urban, A L; Usman, S A; Vahlbruch, H; Vajente, G; Valdes, G; van Bakel, N; van Beuzekom, M; van den Brand, J F J; Van Den Broeck, C; Vander-Hyde, D C; van der Schaaf, L; van Heijningen, J V; van Veggel, A A; Vardaro, M; Varma, V; Vass, S; Vasúth, M; Vecchio, A; Vedovato, G; Veitch, J; Veitch, P J; Venkateswara, K; Venugopalan, G; Verkindt, D; Vetrano, F; Viceré, A; Viets, A D; Vinciguerra, S; Vine, D J; Vinet, J-Y; Vitale, S; Vo, T; Vocca, H; Vorvick, C; Vyatchanin, S P; Wade, A R; Wade, L E; Wade, M; Walet, R; Walker, M; Wallace, L; Walsh, S; Wang, G; Wang, H; Wang, J Z; Wang, W H; Wang, Y F; Ward, R L; Warner, J; Was, M; Watchi, J; Weaver, B; Wei, L-W; Weinert, M; Weinstein, A J; Weiss, R; Wen, L; Wessel, E K; Weßels, P; Westerweck, J; Westphal, T; Wette, K; Whelan, J T; Whiting, B F; Whittle, C; Wilken, D; Williams, D; Williams, R D; Williamson, A R; Willis, J L; Willke, B; Wimmer, M H; Winkler, W; Wipf, C C; Wittel, H; Woan, G; Woehler, J; Wofford, J; Wong, K W K; Worden, J; Wright, J L; Wu, D S; Wysocki, D M; Xiao, S; Yamamoto, H; Yancey, C C; Yang, L; Yap, M J; Yazback, M; Yu, Hang; Yu, Haocun; Yvert, M; Zadrożny, A; Zanolin, M; Zelenova, T; Zendri, J-P; Zevin, M; Zhang, L; Zhang, M; Zhang, T; Zhang, Y-H; Zhao, C; Zhou, M; Zhou, Z; Zhu, S J; Zhu, X J; Zucker, M E; Zweizig, J

2018-05-18

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω_{0}^{T}<5.58×10^{-8}, Ω_{0}^{V}<6.35×10^{-8}, and Ω_{0}^{S}<1.08×10^{-7} at a reference frequency f_{0}=25  Hz.

Eshelby's problem of non-elliptical inclusions

NASA Astrophysics Data System (ADS)

Zou, Wennan; He, Qichang; Huang, Mojia; Zheng, Quanshui

2010-03-01

The Eshelby problem consists in determining the strain field of an infinite linearly elastic homogeneous medium due to a uniform eigenstrain prescribed over a subdomain, called inclusion, of the medium. The salient feature of Eshelby's solution for an ellipsoidal inclusion is that the strain tensor field inside the latter is uniform. This uniformity has the important consequence that the solution to the fundamental problem of determination of the strain field in an infinite linearly elastic homogeneous medium containing an embedded ellipsoidal inhomogeneity and subjected to remote uniform loading can be readily deduced from Eshelby's solution for an ellipsoidal inclusion upon imposing appropriate uniform eigenstrains. Based on this result, most of the existing micromechanics schemes dedicated to estimating the effective properties of inhomogeneous materials have been nevertheless applied to a number of materials of practical interest where inhomogeneities are in reality non-ellipsoidal. Aiming to examine the validity of the ellipsoidal approximation of inhomogeneities underlying various micromechanics schemes, we first derive a new boundary integral expression for calculating Eshelby's tensor field (ETF) in the context of two-dimensional isotropic elasticity. The simple and compact structure of the new boundary integral expression leads us to obtain the explicit expressions of ETF and its average for a wide variety of non-elliptical inclusions including arbitrary polygonal ones and those characterized by the finite Laurent series. In light of these new analytical results, we show that: (i) the elliptical approximation to the average of ETF is valid for a convex non-elliptical inclusion but becomes inacceptable for a non-convex non-elliptical inclusion; (ii) in general, the Eshelby tensor field inside a non-elliptical inclusion is quite non-uniform and cannot be replaced by its average; (iii) the substitution of the generalized Eshelby tensor involved in various micromechanics schemes by the average Eshelby tensor for non-elliptical inhomogeneities is in general inadmissible.

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.)

Scalar-tensor extension of the ΛCDM model

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

Algoner, W.C.; Velten, H.E.S.; Zimdahl, W., E-mail: w.algoner@cosmo-ufes.org, E-mail: velten@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br

2016-11-01

We construct a cosmological scalar-tensor-theory model in which the Brans-Dicke type scalar Φ enters the effective (Jordan-frame) Hubble rate as a simple modification of the Hubble rate of the ΛCDM model. This allows us to quantify differences between the background dynamics of scalar-tensor theories and general relativity (GR) in a transparent and observationally testable manner in terms of one single parameter. Problems of the mapping of the scalar-field degrees of freedom on an effective fluid description in a GR context are discused. Data from supernovae, the differential age of old galaxies and baryon acoustic oscillations are shown to strongly limitmore » potential deviations from the standard model.« less

Theory of the Maxwell pressure tensor and the tension in a water bridge.

PubMed

Widom, A; Swain, J; Silverberg, J; Sivasubramanian, S; Srivastava, Y N

2009-07-01

A water bridge refers to an experimental "flexible cable" made up of pure de-ionized water, which can hang across two supports maintained with a sufficiently large voltage difference. The resulting electric fields within the de-ionized water flexible cable maintain a tension that sustains the water against the downward force of gravity. A detailed calculation of the water bridge tension will be provided in terms of the Maxwell pressure tensor in a dielectric fluid medium. General properties of the dielectric liquid pressure tensor are discussed along with unusual features of dielectric fluid Bernoulli flows in an electric field. The "frictionless" Bernoulli flow is closely analogous to that of a superfluid.

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.

Effective field theory of statistical anisotropies for primordial bispectrum and gravitational waves

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

Rostami, Tahereh; Karami, Asieh; Firouzjahi, Hassan, E-mail: t.rostami@ipm.ir, E-mail: karami@ipm.ir, E-mail: firouz@ipm.ir

2017-06-01

We present the effective field theory studies of primordial statistical anisotropies in models of anisotropic inflation. The general action in unitary gauge is presented to calculate the leading interactions between the gauge field fluctuations, the curvature perturbations and the tensor perturbations. The anisotropies in scalar power spectrum and bispectrum are calculated and the dependence of these anisotropies to EFT couplings are presented. In addition, we calculate the statistical anisotropy in tensor power spectrum and the scalar-tensor cross correlation. Our EFT approach incorporates anisotropies generated in models with non-trivial speed for the gauge field fluctuations and sound speed for scalar perturbationsmore » such as in DBI inflation.« less

Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

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

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

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

The structure and Gel'fand patterns inherent in the Heisenberg supergenerator algebra of dual Liouville-space ||kq{K-tilde.}(k1 - kn)[lambda- tilde],scriptn>> tensors and the Cayley algebra of scalar invariants over a (k1 - kn) field

NASA Astrophysics Data System (ADS)

Temme, F. P.

1991-06-01

For many-body spin cluster problems, dual-symmetry recoupled tensors over Liouville space provide suitable bases for a generalized torque formalism using the Sn-adapted density operator in which to discuss NMR and related techniques. The explicit structure of such tensors is considered in the context of the Cayley algebra of scalar invariants over a field, specified by the inner ki rank labels of the Tkq(kl-kn)s. The pertinence of both lexical combinatorial architectures over inner rank sets and SU2 propagative topologies in specifying the structure of dual recoupling tensors is considered in the context of the Sn partitional aspects of spin clusters. The form of Heisenberg superoperator generators whose algebra underlies the Gel'fand pattern algebra of SU(2) and SU(2)×Sn tensor bases over Liouville space is presented together with both the related s-boson algebras and a description of the associated {||2k 0>>} pattern sets of CF29H carrier space under the appropriate symmetry. These concepts are correlated with recent work on SU(2)×Sn induced symmetry hierarchies over Liouville spin space. The pertinence of this theoretical work to an understanding of multiquantum NMR in Liouville space formalisms is stressed in a discussion of the nature of pathways for intracluster J coupling, which also gives a valuable physical insight into the nature of coherence transfer in more general spin-1/2 systems.

50 CFR 92.30 - General overview of regulations.

Code of Federal Regulations, 2013 CFR

2013-10-01

... Governing Subsistence Harvest § 92.30 General overview of regulations. These regulations establish a spring... hunting regulations in the Federal Register in the spring for seasons beginning September 1 of that year... 92.39 provide for the annual harvest of migratory birds and their eggs during spring and summer for...

50 CFR 92.30 - General overview of regulations.

Code of Federal Regulations, 2014 CFR

2014-10-01

... Governing Subsistence Harvest § 92.30 General overview of regulations. These regulations establish a spring... hunting regulations in the Federal Register in the spring for seasons beginning September 1 of that year... 92.39 provide for the annual harvest of migratory birds and their eggs during spring and summer for...

The Dependence of the Spring Constant in the Linear Range on Spring Parameters

ERIC Educational Resources Information Center

Khotimah, Siti Nurul; Viridi, Sparisoma; Widayani; Khairurrijal

2011-01-01

In basic physics laboratories, springs are normally used to determine both spring constants and the Earth's gravitational acceleration. Students generally do not notice that the spring constant is not a universal constant, but depends on the spring parameters. This paper shows and verifies that the spring constant in the linear range is inversely…

Wedge and spring assembly for securing coils in electromagnets and dynamoelectric machines

DOEpatents

Lindner, Melvin; Cottingham, James G.

1996-03-12

A wedge and spring assembly for use in electromagnets or dynamoelectric machines having a housing with an axis therethrough and a plurality of coils supported on salient poles that extend radially inward from the housing toward the housing axis to define a plurality of interpole spaces. The wedge and spring assembly includes a nonmagnetic retainer spring and a nonmagnetic wedge. The retainer spring is formed to fit into one of the interpole spaces, and has juxtaposed ends defining between them a slit extending in a direction generally parallel to the housing axis. The wedge for insertion into the slit provides an outwardly directed force on respective portions of the juxtaposed ends to expand the slit so that respective portions of the retainer spring engage areas of the coils adjacent thereto, thereby resiliently holding the coils against their respective salient poles. The retainer spring is generally triangular shaped to fit within the interpole space, and the wedge is generally T-shaped.

Wedge and spring assembly for securing coils in electromagnets and dynamoelectric machines

DOEpatents

Lindner, M.; Cottingham, J.G.

1996-03-12

A wedge and spring assembly for use in electromagnets or dynamoelectric machines is disclosed having a housing with an axis therethrough and a plurality of coils supported on salient poles that extend radially inward from the housing toward the housing axis to define a plurality of interpole spaces. The wedge and spring assembly includes a nonmagnetic retainer spring and a nonmagnetic wedge. The retainer spring is formed to fit into one of the interpole spaces, and has juxtaposed ends defining between them a slit extending in a direction generally parallel to the housing axis. The wedge for insertion into the slit provides an outwardly directed force on respective portions of the juxtaposed ends to expand the slit so that respective portions of the retainer spring engage areas of the coils adjacent thereto, thereby resiliently holding the coils against their respective salient poles. The retainer spring is generally triangular shaped to fit within the interpole space, and the wedge is generally T-shaped. 6 figs.

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

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

The mathematical formulation of a generalized Hooke's law for blood vessels.

PubMed

Zhang, Wei; Wang, Chong; Kassab, Ghassan S

2007-08-01

It is well known that the stress-strain relationship of blood vessels is highly nonlinear. To linearize the relationship, the Hencky strain tensor is generalized to a logarithmic-exponential (log-exp) strain tensor to absorb the nonlinearity. A quadratic nominal strain potential is proposed to derive the second Piola-Kirchhoff stresses by differentiating the potential with respect to the log-exp strains. The resulting constitutive equation is a generalized Hooke's law. Ten material constants are needed for the three-dimensional orthotropic model. The nondimensional constant used in the log-exp strain definition is interpreted as a nonlinearity parameter. The other nine constants are the elastic moduli with respect to the log-exp strains. In this paper, the proposed linear stress-strain relation is shown to represent the pseudoelastic Fung model very well.

1. photocopy of postcard (from Glenwood Springs Lodge & Pool, ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. photocopy of postcard (from Glenwood Springs Lodge & Pool, Inc., Date unknown) Photographer unknown, Date unknown GENERAL VIEW OF LODGE, HOT SPRINGS POOL AND ENVIRONS - Hot Springs Lodge, Garfield County, CO

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

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

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

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

Tensor network state correspondence and holography

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

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

Seismicity and stress transfer studies in eastern California and Nevada: Implications for earthquake sources and tectonics

NASA Astrophysics Data System (ADS)

Ichinose, Gene Aaron

The source parameters for eastern California and western Nevada earthquakes are estimated from regionally recorded seismograms using a moment tensor inversion. We use the point source approximation and fit the seismograms, at long periods. We generated a moment tensor catalog for Mw > 4.0 since 1997 and Mw > 5.0 since 1990. The catalog includes centroid depths, seismic moments, and focal mechanisms. The regions with the most moderate sized earthquakes in the last decade were in aftershock zones located in Eureka Valley, Double Spring Flat, Coso, Ridgecrest, Fish Lake Valley, and Scotty's Junction. The remaining moderate size earthquakes were distributed across the region. The 1993 (Mw 6.0) Eureka Valley earthquake occurred in the Eastern California Shear Zone. Careful aftershock relocations were used to resolve structure from aftershock clusters. The mainshock appears to rupture along the western side of the Last Change Range along a 30° to 60° west dipping fault plane, consistent with previous geodetic modeling. We estimate the source parameters for aftershocks at source-receiver distances less than 20 km using waveform modeling. The relocated aftershocks and waveform modeling results do not indicate any significant evidence of low angle faulting (dips > 30°. The results did reveal deformation along vertical faults within the hanging-wall block, consistent with observed surface rupture along the Saline Range above the dipping fault plane. The 1994 (Mw 5.8) Double Spring Flat earthquake occurred along the eastern Sierra Nevada between overlapping normal faults. Aftershock migration and cross fault triggering occurred in the following two years, producing seventeen Mw > 4 aftershocks The source parameters for the largest aftershocks were estimated from regionally recorded seismograms using moment tensor inversion. We estimate the source parameters for two moderate sized earthquakes which occurred near Reno, Nevada, the 1995 (Mw 4.4) Border Town, and the 1998 (Mw 4.7) Incline Village Earthquakes. We test to see how such stress interactions affected a cluster of six large earthquakes (Mw 6.6 to 7.5) between 1915 to 1954 within the Central Nevada Seismic Belt. We compute the static stress changes for these earthquake using dislocation models based on the location and amount of surface rupture. (Abstract shortened by UMI.)

Quantum incompatibility of channels with general outcome operator algebras

NASA Astrophysics Data System (ADS)

Kuramochi, Yui

2018-04-01

A pair of quantum channels is said to be incompatible if they cannot be realized as marginals of a single channel. This paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input space and with general outcome operator algebras. We define a compatibility relation for such channels by identifying the composite outcome space as the maximal (projective) C*-tensor product of outcome algebras. We show theorems that characterize this compatibility relation in terms of the concatenation and conjugation of channels, generalizing the recent result for channels with quantum outcome spaces. These results are applied to the positive operator valued measures (POVMs) by identifying each of them with the corresponding quantum-classical (QC) channel. We also give a characterization of the maximality of a POVM with respect to the post-processing preorder in terms of the conjugate channel of the QC channel. We consider another definition of compatibility of normal channels by identifying the composite outcome space with the normal tensor product of the outcome von Neumann algebras. We prove that for a given normal channel, the class of normally compatible channels is upper bounded by a special class of channels called tensor conjugate channels. We show the inequivalence of the C*- and normal compatibility relations for QC channels, which originates from the possibility and impossibility of copying operations for commutative von Neumann algebras in C*- and normal compatibility relations, respectively.

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.

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

Yetter-Drinfeld modules for Hom-bialgebras

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

Makhlouf, Abdenacer, E-mail: Abdenacer.Makhlouf@uha.fr; Panaite, Florin, E-mail: Florin.Panaite@imar.ro

The aim of this paper is to define and study Yetter-Drinfeld modules over Hom-bialgebras, a generalized version of bialgebras obtained by modifying the algebra and coalgebra structures by a homomorphism. Yetter-Drinfeld modules over a Hom-bialgebra with bijective structure map provide solutions of the Hom-Yang-Baxter equation. The category H/HYD of Yetter-Drinfeld modules with bijective structure maps over a Hom-bialgebra H with bijective structure map can be organized, in two different ways, as a quasi-braided pre-tensor category. If H is quasitriangular (respectively, coquasitriangular) the first (respectively, second) quasi-braided pre-tensor category H/HYD contains, as a quasi-braided pre-tensor subcategory, the category of modules (respectively,more » comodules) with bijective structure maps over H.« less

Quantum Max-flow/Min-cut

NASA Astrophysics Data System (ADS)

Cui, Shawn X.; Freedman, Michael H.; Sattath, Or; Stong, Richard; Minton, Greg

2016-06-01

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts of the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.

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.

A Generalization of the Einstein-Maxwell Equations

NASA Astrophysics Data System (ADS)

Cotton, Fredrick

2016-03-01

The proposed modifications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor and (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two auxiliary fields which describe the particle structure. The additional curvature terms couple both to particle solutions and to electromagnetic and gravitational wave solutions. http://sites.google.com/site/fwcotton/em-30.pdf

Effects of viscous pressure on warm inflationary generalized cosmic Chaplygin gas model

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

Sharif, M.; Saleem, Rabia, E-mail: msharif.math@pu.edu.pk, E-mail: rabiasaleem1988@yahoo.com

This paper is devoted to study the effects of bulk viscous pressure on an inflationary generalized cosmic Chaplygin gas model using FRW background. The matter contents of the universe are assumed to be inflaton and imperfect fluid. We evaluate inflaton fields, potentials and entropy density for variable as well as constant dissipation and bulk viscous coefficients in weak as well as high dissipative regimes during intermediate era. In order to discuss inflationary perturbations, we evaluate entropy density, scalar (tensor) power spectra, their corresponding spectral indices, tensor-scalar ratio and running of spectral index in terms of inflaton which are constrained usingmore » recent Planck, WMAP7 and Bicep2 probes.« less

Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds

NASA Astrophysics Data System (ADS)

Roth, Julien

2010-06-01

We give spinorial characterizations of isometrically immersed surfaces into three-dimensional homogeneous manifolds with four-dimensional isometry group in terms of the existence of a particular spinor field. This generalizes works by Friedrich for R3 and Morel for S3 and H3. The main argument is the interpretation of the energy-momentum tensor of such a spinor field as the second fundamental form up to a tensor depending on the structure of the ambient space.

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

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2013-02-01

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

Utility of the CS and IOS approximations for calculating generalized phenomenological cross sections in atom-diatom systems

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

Fitz, D.E.; Kouri, D.J.; Liu, W.K.

1982-04-01

The calculation of shear viscosity and thermal conductivity coefficients in the presence of a magnetic field requires the accurate calculation of several types of generalized phenomenological cross sections in which velocity and angular momentum tensors are coupled with the orbital and rotational motion of the system. These cross sections are then averaged over energy in a fashion appropriate for the phenomenon of interest. The coupled states (CS) and/or infinite order sudden (IOS) approximations have been used to calculate several such cross sections for systems such as He-HCl, He-CO, He-H/sub 2/, HD-Ne, Ar-N/sub 2/, and Ne-H/sub 2/. Excellent results are obtainedmore » compared with close-coupled methods for cross sections which are symmetric in tensor index, especially in the CS approximation, and these results are not very sensitive to the choice of orbital wave parameter. On the other hand, the cross sections which are asymmetric in tensor index are much more sensitive to interference effects and are unsatisfactory in many cases.« less

On the `simple' form of the gravitational action and the self-interacting graviton

NASA Astrophysics Data System (ADS)

Tomboulis, E. T.

2017-09-01

The so-called ΓΓ-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General Relativity as a theory of the self-interacting graviton. A straightforward but general method of converting to a covariant formulation by the introduction of a reference metric is given. It is used to recast the Einstein field equation as the equation of motion of a spin-2 particle interacting with the canonical energy-momentum tensor symmetrized by the standard Belinfante method applicable to any field carrying nonzero spin. This represents the graviton field equation in a form complying with the precepts of standard field theory. It is then shown how representations based on other, at face value completely unrelated definitions of energy-momentum (pseudo)tensors are all related by the addition of appropriate superpotential terms. Specifically, the superpotentials are explicitly constructed which connect to: i) the common definition consisting simply of the nonlinear part of the Einstein tensor; ii) the Landau-Lifshitz definition.

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.

Emergent symmetries in the canonical tensor model

NASA Astrophysics Data System (ADS)

Obster, Dennis; Sasakura, Naoki

2018-04-01

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

Weyl geometry

NASA Astrophysics Data System (ADS)

Wheeler, James T.

2018-07-01

We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature tensor is the conformally invariant part of the Riemann curvature, and shows the explicit change in the Ricci and Schouten tensors required to insure conformal invariance. We include a proof of the well-known condition for the existence of a conformal transformation to a Ricci-flat spacetime. We generalize this to a derivation of the condition for the existence of a conformal transformation to a spacetime satisfying the Einstein equation with matter sources. Then, enlarging the symmetry from Poincaré to Weyl, we develop the Cartan structure equations of Weyl geometry, the form of the curvature tensor and its relationship to the Riemann curvature of the corresponding Riemannian geometry. We present a simple theory of Weyl-covariant gravity based on a curvature-linear action, and show that it is conformally equivalent to general relativity. This theory is invariant under local dilatations, but not the full conformal group.

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

PubMed

Cheng, Jian; Basser, Peter J

2018-01-01

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

A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions

NASA Astrophysics Data System (ADS)

Rahmouni, A.; Beidouri, Z.; Benamar, R.

2013-09-01

The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the previously developed models of geometrically nonlinear vibrations of Euler-Bernoulli continuous beams, and multidof system models made of N masses placed at the end of elastic bars connected by linear spiral springs, presenting the beam flexural rigidity. The validation of the new model via the analysis of the convergence conditions of the nonlinear frequencies obtained by the N-dof system, when N increases, and those obtained in previous works using a continuous description of the beam. In addition to the above points, the models developed in the present work, may constitute, in our opinion, a good illustration, from the didactic point of view, of the origin of the geometrical nonlinearity induced by large transverse vibration amplitudes of constrained continuous beams, which may appear as a Pythagorean Theorem effect. The first step of the work presented here was the formulation of the problem of nonlinear vibrations of the discrete system shown in Fig. 1 in terms of the semi-analytical method, denoted as SAA, developed in the early 90's by Benamar and coauthors [3], and discussed for example in [6,7]. This method has been applied successfully to various types of geometrically nonlinear problems of structural dynamics [1-3,6-8,10-12] and the objective here was to use it in order to develop a flexible discrete nonlinear model which may be useful for presenting in further works geometrically nonlinear vibrations of real beams with discontinuities in the mass, the section, or the stiffness distributions. The purpose in the present work was restricted to developing and validating the model, via comparison of the obtained dependence of the resonance frequencies of such a system on the amplitude of vibration, with the results obtained previously by continuous beams nonlinear models. In the SAA method, the dynamic system under consideration is described by the mass matrix [M], the rigidity matrix [K], and the nonlinear rigidity matrix [B], which depends on the amplitude of vibration, and involves a fourth-order nonlinearity tensor bijkl. Details are given below, corresponding to the definition of the tensors mentioned above. The analogy between the classical continuous Euler-Bernoulli model of beams and the present discrete model is developed, leading to the expressions for the equivalent spiral and axial stiffness, in terms of the continuous beam geometrical and mechanical characteristics. Some numerical results are also given, showing the amplitude dependence of the frequencies on the amplitude of vibration, and compared to the backbone curves obtained previously by the continuous nonlinear classical beam theory, presented for example in [3,5,8,15-22]. A convergence study is performed by increasing the number of masses and bars, showing a good convergence to the theoretical values of continuous beams.

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

PubMed

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

2017-01-01

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

Predicting the patterns of change in spring onset and false springs in China during the twenty-first century

NASA Astrophysics Data System (ADS)

Zhu, Likai; Meng, Jijun; Li, Feng; You, Nanshan

2017-10-01

Spring onset has generally shifted earlier in China over the past several decades in response to the warming climate. However, future changes in spring onset and false springs, which will have profound effects on ecosystems, are still not well understood. Here, we used the extended form of the Spring Indices model (SI-x) to project changes in the first leaf and first bloom dates, and predicted false springs for the historical (1950-2005) and future (2006-2100) periods based on the downscaled daily maximum/minimum temperatures under two emission scenarios from 21 General Circulation Models (GCMs) of the Coupled Model Intercomparison Project Phase 5 (CMIP5). On average, first leaf and first bloom in China were projected to occur 21 and 23 days earlier, respectively, by the end of the twenty-first century in the Representative Concentration Pathway (RCP) 8.5 scenario. Areas with greater earlier shifts in spring onset were in the warm temperate zone, as well as the north and middle subtropical zones of China. Early false spring risk increased rapidly in the warm temperate and north subtropical zones, while that declined in the cold temperate zone. Relative to early false spring risk, late false spring risk showed a common increase with smaller magnitude in the RCP 8.5 scenario but might cause greater damage to ecosystems because plants tend to become more vulnerable to the later occurrence of a freeze event. We conclude that future climate warming will continue to cause earlier occurrence of spring onset in general, but might counterintuitively increase plant damage risk in natural and agricultural systems of the warm temperate and subtropical China.

Predicting the patterns of change in spring onset and false springs in China during the twenty-first century.

PubMed

Zhu, Likai; Meng, Jijun; Li, Feng; You, Nanshan

2017-10-28

Spring onset has generally shifted earlier in China over the past several decades in response to the warming climate. However, future changes in spring onset and false springs, which will have profound effects on ecosystems, are still not well understood. Here, we used the extended form of the Spring Indices model (SI-x) to project changes in the first leaf and first bloom dates, and predicted false springs for the historical (1950-2005) and future (2006-2100) periods based on the downscaled daily maximum/minimum temperatures under two emission scenarios from 21 General Circulation Models (GCMs) of the Coupled Model Intercomparison Project Phase 5 (CMIP5). On average, first leaf and first bloom in China were projected to occur 21 and 23 days earlier, respectively, by the end of the twenty-first century in the Representative Concentration Pathway (RCP) 8.5 scenario. Areas with greater earlier shifts in spring onset were in the warm temperate zone, as well as the north and middle subtropical zones of China. Early false spring risk increased rapidly in the warm temperate and north subtropical zones, while that declined in the cold temperate zone. Relative to early false spring risk, late false spring risk showed a common increase with smaller magnitude in the RCP 8.5 scenario but might cause greater damage to ecosystems because plants tend to become more vulnerable to the later occurrence of a freeze event. We conclude that future climate warming will continue to cause earlier occurrence of spring onset in general, but might counterintuitively increase plant damage risk in natural and agricultural systems of the warm temperate and subtropical China.

Somatosensory attunement to the rigid body laws.

PubMed

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

2001-01-01

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

FLRW Cosmology from Yang-Mills Gravity

NASA Astrophysics Data System (ADS)

Katz, Daniel

2013-04-01

We extend to basic cosmology the subject of Yang-Mills gravity - a theory of gravity based on local translational gauge invariance in flat spacetime. It has been shown that this particular gauge invariance leads to tensor factors in the macroscopic limit of the equations of motion of particles which plays the same role as the metric tensor of General Relativity. The assumption that this ``effective metric" tensor takes on the standard FLRW form is our starting point. Equations analogous to the Friedman equations are derived and then solved in closed form for the three special cases of a universe dominated by 1) matter, 2) radiation, and 3) dark energy. We find that the solutions for the scale factor are similar to, but distinct from, those found in the corresponding GR based treatment.

Practical Considerations for Using Constant Force Springs in Space-Based Mechanisms

NASA Technical Reports Server (NTRS)

Williams, R. Brett; Fisher, Charles D.; Gallon, John C.

2013-01-01

Mechanical springs are a common element in mechanism from all walks of life; cars, watches, appliances, and many others. These springs generally exhibit a linear relationship between force and deflection. In small mechanisms, deflections are small so the variation in spring force between one position and another are generally small and do not influence the design or functionality of the device. However, as the spacecraft industry drives towards larger, deployable satellites, the distances a spring or springs must function over can become considerable so much so that the structural integrity of the device may be impacted. As such, an increasingly common mechanism element is the constant force spring- one that provides a constant force regardless of deflection. These elements are commonly in the conceptual design phase to deal with system-level large deflections, but in the detailed design or integration test phase they can pose significant implementation issues. This article addresses some of the detailed issues in order for these constant force springs to be properly designed into space systems.

Mass Function of Galaxy Clusters in Relativistic Inhomogeneous Cosmology

NASA Astrophysics Data System (ADS)

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

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

Nonthermal springs of Utah

USGS Publications Warehouse

Mundorff, J.C.

1971-01-01

Data are presented for about 4,500 nonthermal springs that discharge in the State of Utah. Most major springs having discharge of several cubic feet per second or more are in or near mountain ranges or plateaus where precipitation is much greater than in other parts of the State. The largest instantaneous discharge observed at any spring was 314 cfs at Mammoth Spring in southwestern Utah.  Discharges exceeding 200 cfs have been observed at Swan Creek Spring in extreme northern Utah, and discharges of 200 cfs have been reported for Big Brush Creek Spring in northeastern Utah. Maximum discharges generally are during or within a few weeks after the main period of snowmelt, which is usually from late April to the middle of June.The largest springs generally discharge form or very near carbonate rocks in which solution channels and fractures are numerous or from areas of porous or fractured volcanic rocks. Most nonthermal springs in Utah probably are variable springs – that is, their variability of discharge exceeds 100 percent.Most of the major springs discharge water that contains less than 500 ppm (parts per million) of dissolved solids, and most of the water is of the calcium bicarbonate type. Water from springs is used for domestic, municipal, irrigation, livestock, mining, and industrial purposes.

Polymer Fluid Dynamics: Continuum and Molecular Approaches.

PubMed

Bird, R B; Giacomin, A J

2016-06-07

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

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

PubMed

Peng, Bo; Kowalski, Karol

2017-09-12

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

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.

49 CFR 236.12 - Spring switch signal protection; where required.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 49 Transportation 4 2014-10-01 2014-10-01 false Spring switch signal protection; where required... Rules and Instructions: All Systems General § 236.12 Spring switch signal protection; where required. Signal protection shall be provided for facing and trailing movements through spring switch within...

49 CFR 236.12 - Spring switch signal protection; where required.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 49 Transportation 4 2011-10-01 2011-10-01 false Spring switch signal protection; where required... Rules and Instructions: All Systems General § 236.12 Spring switch signal protection; where required. Signal protection shall be provided for facing and trailing movements through spring switch within...

49 CFR 236.12 - Spring switch signal protection; where required.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 49 Transportation 4 2012-10-01 2012-10-01 false Spring switch signal protection; where required... Rules and Instructions: All Systems General § 236.12 Spring switch signal protection; where required. Signal protection shall be provided for facing and trailing movements through spring switch within...

49 CFR 236.12 - Spring switch signal protection; where required.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 49 Transportation 4 2013-10-01 2013-10-01 false Spring switch signal protection; where required... Rules and Instructions: All Systems General § 236.12 Spring switch signal protection; where required. Signal protection shall be provided for facing and trailing movements through spring switch within...

49 CFR 236.12 - Spring switch signal protection; where required.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 49 Transportation 4 2010-10-01 2010-10-01 false Spring switch signal protection; where required... Rules and Instructions: All Systems General § 236.12 Spring switch signal protection; where required. Signal protection shall be provided for facing and trailing movements through spring switch within...

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

We first introduced a linear stationary equation with a quadratic operator in ∂x and ∂y, then a linear evolution equation is given by N-order polynomials of eigenfunctions. As applications, by taking N=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

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.

Quantum Max-flow/Min-cut

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

Cui, Shawn X., E-mail: xingshan@math.ucsb.edu; Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052; Freedman, Michael H., E-mail: michaelf@microsoft.com

2016-06-15

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts ofmore » the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.« less

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2018-03-01

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group approach, H/H2-matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). We show that the hierarchically resolved many-body tensors can reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram consisting of a finite number of arbitrary-order tensors, e.g. an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we suggest an additional approximation to further reduce the computational complexity of higher order coupled-cluster equations, i.e. equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.

The Model of Educational Reconstruction--A Powerful Strategy to Teach for Conceptual Development in Physical Geography: The Case of Water Springs

ERIC Educational Resources Information Center

Reinfried, Sibylle; Aeschbacher, Urs; Kienzler, Peter M.; Tempelmann, Sebastian

2015-01-01

Springs are an important hydrological concept because springs form an interface between underground and surface sub-systems of the hydrological cycle. Furthermore, springs are important suppliers of drinking water but are at risk today due to numerous anthropogenic interferences. The general knowledge of springs and their formation is usually…

49 CFR 236.14 - Spring switch signal protection; requirements.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 49 Transportation 4 2012-10-01 2012-10-01 false Spring switch signal protection; requirements. 236... Rules and Instructions: All Systems General § 236.14 Spring switch signal protection; requirements. (a... track signaled for movements in only one direction through a spring switch in automatic block signal...

49 CFR 236.14 - Spring switch signal protection; requirements.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 49 Transportation 4 2010-10-01 2010-10-01 false Spring switch signal protection; requirements. 236... Rules and Instructions: All Systems General § 236.14 Spring switch signal protection; requirements. (a... track signaled for movements in only one direction through a spring switch in automatic block signal...

49 CFR 236.14 - Spring switch signal protection; requirements.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 49 Transportation 4 2011-10-01 2011-10-01 false Spring switch signal protection; requirements. 236... Rules and Instructions: All Systems General § 236.14 Spring switch signal protection; requirements. (a... track signaled for movements in only one direction through a spring switch in automatic block signal...

75 FR 28302 - American Food and Vending Spring Hill, TN; Notice of Negative Determination Regarding Application...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-05-20

... Spring Hill, TN; Notice of Negative Determination Regarding Application for Reconsideration By... negative determination applicable to workers and former workers at American Food and Vending, Spring Hill... eligible for TAA because they are service workers who provided services to General Motors, Spring Hill...

49 CFR 236.14 - Spring switch signal protection; requirements.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 49 Transportation 4 2013-10-01 2013-10-01 false Spring switch signal protection; requirements. 236... Rules and Instructions: All Systems General § 236.14 Spring switch signal protection; requirements. (a... track signaled for movements in only one direction through a spring switch in automatic block signal...

49 CFR 236.14 - Spring switch signal protection; requirements.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 49 Transportation 4 2014-10-01 2014-10-01 false Spring switch signal protection; requirements. 236... Rules and Instructions: All Systems General § 236.14 Spring switch signal protection; requirements. (a... track signaled for movements in only one direction through a spring switch in automatic block signal...

Tensor network states and algorithms in the presence of a global SU(2) symmetry

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder; Vidal, Guifre

2012-11-01

The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g., with a given particle number or spin), to ensure the exact preservation of total charge, and to significantly reduce computational costs. Compared to the case of a generic tensor network, the practical implementation of symmetries in the MPS is simplified by the fact that tensors only have three indices (they are trivalent, just as the Clebsch-Gordan coefficients of the symmetry group) and are organized as a one-dimensional array of tensors, without closed loops. Instead, a more complex tensor network, one where tensors have a larger number of indices and/or a more elaborate network structure, requires a more general treatment. In two recent papers, namely, (i) [Singh, Pfeifer, and Vidal, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.050301 82, 050301 (2010)] and (ii) [Singh, Pfeifer, and Vidal, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.115125 83, 115125 (2011)], we described how to incorporate a global internal symmetry into a generic tensor network algorithm based on decomposing and manipulating tensors that are invariant under the symmetry. In (i) we considered a generic symmetry group G that is compact, completely reducible, and multiplicity free, acting as a global internal symmetry. Then, in (ii) we described the implementation of Abelian group symmetries in much more detail, considering a U(1) symmetry (e.g., conservation of global particle number) as a concrete example. In this paper, we describe the implementation of non-Abelian group symmetries in great detail. For concreteness, we consider an SU(2) symmetry (e.g., conservation of global quantum spin). Our formalism can be readily extended to more exotic symmetries associated with conservation of total fermionic or anyonic charge. As a practical demonstration, we describe the SU(2)-invariant version of the multiscale entanglement renormalization ansatz and apply it to study the low-energy spectrum of a quantum spin chain with a global SU(2) symmetry.

Robotic Online Path Planning on Point Cloud.

PubMed

Liu, Ming

2016-05-01

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

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.

Optimizing Tensor Contraction Expressions for Hybrid CPU-GPU Execution

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

Ma, Wenjing; Krishnamoorthy, Sriram; Villa, Oreste

2013-03-01

Tensor contractions are generalized multidimensional matrix multiplication operations that widely occur in quantum chemistry. Efficient execution of tensor contractions on Graphics Processing Units (GPUs) requires several challenges to be addressed, including index permutation and small dimension-sizes reducing thread block utilization. Moreover, to apply the same optimizations to various expressions, we need a code generation tool. In this paper, we present our approach to automatically generate CUDA code to execute tensor contractions on GPUs, including management of data movement between CPU and GPU. To evaluate our tool, GPU-enabled code is generated for the most expensive contractions in CCSD(T), a key coupledmore » cluster method, and incorporated into NWChem, a popular computational chemistry suite. For this method, we demonstrate speedup over a factor of 8.4 using one GPU (instead of one core per node) and over 2.6 when utilizing the entire system using hybrid CPU+GPU solution with 2 GPUs and 5 cores (instead of 7 cores per node). Finally, we analyze the implementation behavior on future GPU systems.« less

GENERAL PERSPECTIVE VIEW OF NORTHWEST SIDE FROM NORTH SHOWING SPRING ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

GENERAL PERSPECTIVE VIEW OF NORTHWEST SIDE FROM NORTH SHOWING SPRING HOUSE IN FOREGROUND AND SMOKE HOUSE TO LEFT OF MAIN HOUSE WITH WOOD SHED TO THE REAR - Lakeside, 20 North Main Street, Yardley, Bucks County, PA

Generalized reduced rank latent factor regression for high dimensional tensor fields, and neuroimaging-genetic applications

PubMed Central

Tao, Chenyang; Nichols, Thomas E.; Hua, Xue; Ching, Christopher R.K.; Rolls, Edmund T.; Thompson, Paul M.; Feng, Jianfeng

2017-01-01

We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches. PMID:27666385

Functional Generalized Additive Models.

PubMed

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

2014-01-01

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

FLRW Cosmology from Yang-Mills Gravity with Translational Gauge Symmetry

NASA Astrophysics Data System (ADS)

Katz, Daniel

2013-03-01

We extend to basic cosmology the subject of Yang-Mills gravity — a theory of gravity based on local translational gauge invariance in flat space-time. It has been shown that this particular gauge invariance leads to tensor factors in the macroscopic limit of the equations of motion of particles which plays the same role as the metric tensor of general relativity (GR). The assumption that this "effective metric" tensor takes on the standard FLRW form is our starting point. Equations analogous to the Friedmann equations are derived and then solved in closed form for the three special cases of a universe dominated by (1) matter, (2) radiation and (3) dark energy. We find that the solutions for the scale factor are similar to, but distinct from, those found in the corresponding GR based treatment.

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

Inevitable inflation in Einstein-Cartan theory with improved energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi Type-1) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density. Shear is not effective in preventing inflation in the ECRS model. The relation between fluid vorticity, torsion, reference axis rotation, and shear ellipsoid precession shows through clearly.

Classical stability of sudden and big rip singularities

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

Barrow, John D.; Lip, Sean Z. W.

2009-08-15

We introduce a general characterization of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar, vector, and tensor perturbations using gauge-invariant perturbation theory. We establish that sudden singularities at which the scale factor, expansion rate, and density are finite are stable except for a set of special parameter values. We also apply our analysis to the stability of Big Rip singularities and find the conditions for their stability against small scalar, vector, and tensor perturbations.

Integrability of geodesics and action-angle variables in Sasaki-Einstein space T^{1,1}

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2016-09-01

We briefly describe the construction of Stäkel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing-Yano tensors of the homogeneous Sasaki-Einstein space T^{1,1}. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed.

Single and double diffractive dissociation and the problem of extraction of the proton-Pomeron cross-section

NASA Astrophysics Data System (ADS)

Petrov, V. A.; Ryutin, R. A.

2016-04-01

Diffractive dissociation processes are analyzed in the framework of covariant reggeization. We have considered the general form of hadronic tensor and its asymptotic behavior for t → 0 in the case of conserved tensor currents before reggeization. Resulting expressions for differential cross-sections of single dissociation (SD) process (pp → pM), double dissociation (DD) (pp → M1M2) and for the proton-Pomeron cross-section are given in detail, and corresponding problems of the approach are discussed.

Vector models and generalized SYK models

DOE PAGES

Peng, Cheng

2017-05-23

Here, we consider the relation between SYK-like models and vector models by studying a toy model where a tensor field is coupled with a vector field. By integrating out the tensor field, the toy model reduces to the Gross-Neveu model in 1 dimension. On the other hand, a certain perturbation can be turned on and the toy model flows to an SYK-like model at low energy. Furthermore, a chaotic-nonchaotic phase transition occurs as the sign of the perturbation is altered. We further study similar models that possess chaos and enhanced reparameterization symmetries.

Temperature dependence of the dielectric tensor of monoclinic Ga2O3 single crystals in the spectral range 1.0-8.5 eV

NASA Astrophysics Data System (ADS)

Sturm, C.; Schmidt-Grund, R.; Zviagin, V.; Grundmann, M.

2017-08-01

The full dielectric tensor of monoclinic Ga2O3 (β-phase) was determined by generalized spectroscopic ellipsometry in the spectral range from 1.0 eV up to 8.5 eV and temperatures in the range from 10 K up to 300 K. By using the oriented dipole approach, the energies and broadenings of the excitonic transitions are determined as a function of the temperature, and the exciton-phonon coupling properties are deduced.

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.

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

A tensor approach to modeling of nonhomogeneous nonlinear systems

NASA Technical Reports Server (NTRS)

Yurkovich, S.; Sain, M.

1980-01-01

Model following control methodology plays a key role in numerous application areas. Cases in point include flight control systems and gas turbine engine control systems. Typical uses of such a design strategy involve the determination of nonlinear models which generate requested control and response trajectories for various commands. Linear multivariable techniques provide trim about these motions; and protection logic is added to secure the hardware from excursions beyond the specification range. This paper reports upon experience in developing a general class of such nonlinear models based upon the idea of the algebraic tensor product.

49 CFR 236.13 - Spring switch; selection of signal control circuits through circuit controller.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 49 Transportation 4 2014-10-01 2014-10-01 false Spring switch; selection of signal control... SYSTEMS, DEVICES, AND APPLIANCES Rules and Instructions: All Systems General § 236.13 Spring switch... facing movements over a main track spring switch shall be selected through the contacts of a switch...

49 CFR 236.13 - Spring switch; selection of signal control circuits through circuit controller.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 49 Transportation 4 2012-10-01 2012-10-01 false Spring switch; selection of signal control... SYSTEMS, DEVICES, AND APPLIANCES Rules and Instructions: All Systems General § 236.13 Spring switch... facing movements over a main track spring switch shall be selected through the contacts of a switch...

49 CFR 236.13 - Spring switch; selection of signal control circuits through circuit controller.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 49 Transportation 4 2013-10-01 2013-10-01 false Spring switch; selection of signal control... SYSTEMS, DEVICES, AND APPLIANCES Rules and Instructions: All Systems General § 236.13 Spring switch... facing movements over a main track spring switch shall be selected through the contacts of a switch...

49 CFR 236.13 - Spring switch; selection of signal control circuits through circuit controller.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 49 Transportation 4 2010-10-01 2010-10-01 false Spring switch; selection of signal control... SYSTEMS, DEVICES, AND APPLIANCES Rules and Instructions: All Systems General § 236.13 Spring switch... facing movements over a main track spring switch shall be selected through the contacts of a switch...

49 CFR 236.13 - Spring switch; selection of signal control circuits through circuit controller.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 49 Transportation 4 2011-10-01 2011-10-01 false Spring switch; selection of signal control... SYSTEMS, DEVICES, AND APPLIANCES Rules and Instructions: All Systems General § 236.13 Spring switch... facing movements over a main track spring switch shall be selected through the contacts of a switch...

Dispersion relations for a general anisotropic distribution function represented as a sum over Legendre polynomials

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

Shaisultanov, Rashid; Eichler, David

2011-03-15

The dielectric tensor is obtained for a general anisotropic distribution function that is represented as a sum over Legendre polynomials. The result is valid over all of k-space. We obtain growth rates for the Weibel instability for some basic examples of distribution functions.

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.

Dispersive transport and symmetry of the dispersion tensor in porous media

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-11-01

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

Einstein's physical strategy, energy conservation, symmetries, and stability: "But Grossmann & I believed that the conservation laws were not satisfied"

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2016-05-01

Recent work on the history of General Relativity by Renn et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911-1914) of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance xμ‧ = Mνμ xν to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom (later called "ghosts" in particle physics). Thus the Entwurf theory fails a 1920s-1930s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics.

International Community Development Statistical Bulletin. Spring 1968 General Edition.

ERIC Educational Resources Information Center

Community Development Foundation, New York, NY.

The Spring 1968 general edition of the International Community Development Statistical Bulletin describes its reporting system based on the International Standard Classification of Community Development Activities and a special project registration and progress form; briefly summarizes overall international data; and presents statistics on…

Second Harmonic Generation of Unpolarized Light

NASA Astrophysics Data System (ADS)

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

2017-11-01

A Mueller tensor mathematical framework was applied for predicting and interpreting the second harmonic generation (SHG) produced with an unpolarized fundamental beam. In deep tissue imaging through SHG and multiphoton fluorescence, partial or complete depolarization of the incident light complicates polarization analysis. The proposed framework has the distinct advantage of seamlessly merging the purely polarized theory based on the Jones or Cartesian susceptibility tensors with a more general Mueller tensor framework capable of handling partial depolarized fundamental and/or SHG produced. The predictions of the model are in excellent agreement with experimental measurements of z -cut quartz and mouse tail tendon obtained with polarized and depolarized incident light. The polarization-dependent SHG produced with unpolarized fundamental allowed determination of collagen fiber orientation in agreement with orthogonal methods based on image analysis. This method has the distinct advantage of being immune to birefringence or depolarization of the fundamental beam for structural analysis of tissues.

Tensor Minkowski Functionals for random fields on the sphere

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

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

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.

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.

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

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

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

2009-06-15

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

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.

Archimedes' Principle in General Coordinates

ERIC Educational Resources Information Center

Ridgely, Charles T.

2010-01-01

Archimedes' principle is well known to state that a body submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body. Herein, Archimedes' principle is derived from first principles by using conservation of the stress-energy-momentum tensor in general coordinates. The resulting expression for the force is…

Relativistic covariance of Ohm's law

NASA Astrophysics Data System (ADS)

Starke, R.; Schober, G. A. H.

2016-04-01

The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor χμ ν relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohm's law, we prove the validity of Ohm's law in every inertial frame. We further use the universal relation between χμ ν and the microscopic conductivity tensor σkℓ to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohm's law.

Variable stiffness torsion springs

NASA Astrophysics Data System (ADS)

Alhorn, Dean C.; Polites, Michael E.

1994-05-01

In a torsion spring the spring action is a result of the relationships between the torque applied in twisting the spring, the angle through which the torsion spring twists, and the modulus of elasticity of the spring material in shear. Torsion springs employed industrially have been strips, rods, or bars, generally termed shafts, capabable of being flexed by twisting their axes. They rely on the variations in shearing forces to furnish an internal restoring torque. In the torsion springs herein the restoring torque is external and therefore independent of the shearing modulus of elasticity of the torsion spring shaft. Also provided herein is a variable stiffness torsion spring. This torsion spring can be so adjusted as to have a given spring constant. Such variable stiffness torsion springs are extremely useful in gimballed payloads such as sensors, telescopes, and electronic devices on such platforms as a space shuttle or a space station.

Variable stiffness torsion springs

NASA Technical Reports Server (NTRS)

Alhorn, Dean C. (Inventor); Polites, Michael E. (Inventor)

1995-01-01

In a torsion spring the spring action is a result of the relationships between the torque applied in twisting the spring, the angle through which the torsion spring twists, and the modulus of elasticity of the spring material in shear. Torsion springs employed industrially have been strips, rods, or bars, generally termed shafts, capabable of being flexed by twisting their axes. They rely on the variations in shearing forces to furnish an internal restoring torque. In the torsion springs herein the restoring torque is external and therefore independent of the shearing modulus of elasticity of the torsion spring shaft. Also provided herein is a variable stiffness torsion spring. This torsion spring can be so adjusted as to have a given spring constant. Such variable stiffness torsion springs are extremely useful in gimballed payloads such as sensors, telescopes, and electronic devices on such platforms as a space shuttle or a space station.

Variable stiffness torsion springs

NASA Astrophysics Data System (ADS)

Alhorn, Dean C.; Polites, Michael E.

1995-08-01

In a torsion spring the spring action is a result of the relationships between the torque applied in twisting the spring, the angle through which the torsion spring twists, and the modulus of elasticity of the spring material in shear. Torsion springs employed industrially have been strips, rods, or bars, generally termed shafts, capabable of being flexed by twisting their axes. They rely on the variations in shearing forces to furnish an internal restoring torque. In the torsion springs herein the restoring torque is external and therefore independent of the shearing modulus of elasticity of the torsion spring shaft. Also provided herein is a variable stiffness torsion spring. This torsion spring can be so adjusted as to have a given spring constant. Such variable stiffness torsion springs are extremely useful in gimballed payloads such as sensors, telescopes, and electronic devices on such platforms as a space shuttle or a space station.

Variable stiffness torsion springs

NASA Technical Reports Server (NTRS)

Alhorn, Dean C. (Inventor); Polites, Michael E. (Inventor)

1994-01-01

In a torsion spring the spring action is a result of the relationships between the torque applied in twisting the spring, the angle through which the torsion spring twists, and the modulus of elasticity of the spring material in shear. Torsion springs employed industrially have been strips, rods, or bars, generally termed shafts, capabable of being flexed by twisting their axes. They rely on the variations in shearing forces to furnish an internal restoring torque. In the torsion springs herein the restoring torque is external and therefore independent of the shearing modulus of elasticity of the torsion spring shaft. Also provided herein is a variable stiffness torsion spring. This torsion spring can be so adjusted as to have a given spring constant. Such variable stiffness torsion springs are extremely useful in gimballed payloads such as sensors, telescopes, and electronic devices on such platforms as a space shuttle or a space station.

Spring water quality and usability in the Mount Cameroon area revealed by hydrogeochemistry.

PubMed

Ako, Andrew Ako; Shimada, Jun; Hosono, Takahiro; Kagabu, Makoto; Ayuk, Akoachere Richard; Nkeng, George Elambo; Eyong, Gloria Eneke Takem; Fouepe Takounjou, Alain L

2012-10-01

Groundwater is the only reliable water resource for drinking, domestic, and agricultural purposes for the people living in the Mount Cameroon area. Hydrogeochemical and R-mode factor analysis were used to identify hydrogeochemical processes controlling spring water quality and assess its usability for the above uses. Main water types in the study area are Ca-Mg-HCO(3) and Na-HCO(3). This study reveals that three processes are controlling the spring water quality. CO(2)-driven silicate weathering and reverse cation exchange are the most important processes affecting the hydrochemistry of the spring waters. While tropical oceanic monsoon chloride-rich/sulfate-rich rainwater seems to affect spring water chemistry at low-altitude areas, strong correlations exist between major ions, dissolved silica and the altitude of springs. In general, the spring waters are suitable for drinking and domestic uses. Total hardness (TH) values indicate a general softness of the waters, which is linked to the development of cardiovascular diseases. Based on Na %, residual sodium carbonate, sodium adsorption ratio, and the USSL classification, the spring waters are considered suitable for irrigation. Though there is wide spread use of chemical fertilizers and intense urban settlements at the lower flanks of the volcano, anthropogenic activities for now seem to have little impact on the spring water quality.

Non-perturbative calculation of orbital and spin effects in molecules subject to non-uniform magnetic fields

NASA Astrophysics Data System (ADS)

Sen, Sangita; Tellgren, Erik I.

2018-05-01

External non-uniform magnetic fields acting on molecules induce non-collinear spin densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a general Hartree-Fock method, without any spin constraints, for non-perturbative calculations with finite non-uniform fields. London atomic orbitals are used to ensure faster basis convergence as well as invariance under constant gauge shifts of the magnetic vector potential. The implementation has been applied to investigate the joint orbital and spin response to a field gradient—quantified through the anapole moments—of a set of small molecules. The relative contributions of orbital and spin-Zeeman interaction terms have been studied both theoretically and computationally. Spin effects are stronger and show a general paramagnetic behavior for closed shell molecules while orbital effects can have either direction. Basis set convergence and size effects of anapole susceptibility tensors have been reported. The relation of the mixed anapole susceptibility tensor to chirality is also demonstrated.

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

NASA Astrophysics Data System (ADS)

Kushch, Volodymyr I.; Sevostianov, Igor; Giraud, Albert

2017-11-01

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows.

PubMed

Daivis, Peter J; Todd, B D

2006-05-21

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.

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

PubMed

Hoy, Erik P; Mazziotti, David A

2015-08-14

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

The dynamic generalization of the Eshelby inclusion problem and its static limit

PubMed Central

2016-01-01

The dynamic generalization of the celebrated Eshelby inclusion with transformation strain is the (subsonically) self-similarly expanding ellipsoidal inclusion starting from the zero dimension. The solution of the governing system of partial differential equations was obtained recently by Ni & Markenscoff (In press. J. Mech. Phys. Solids (doi:10.1016/j.jmps.2016.02.025)) on the basis of the Radon transformation, while here an alternative method is presented. In the self-similarly expanding motion, the Eshelby property of constant constrained strain is valid in the interior domain of the expanding ellipsoid where the particle velocity vanishes (lacuna). The dynamic Eshelby tensor is obtained in integral form. From it, the static Eshelby tensor is obtained by a limiting procedure, as the axes' expansion velocities tend to zero and time to infinity, while their product is equal to the length of the static axis. This makes the Eshelby problem the limit of its dynamic generalization. PMID:27493574

Cosmology in generalized Proca theories

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

2016-06-01

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.

Novel symmetries in Weyl-invariant gravity with massive gauge field

NASA Astrophysics Data System (ADS)

Abhinav, K.; Shukla, A.; Panigrahi, P. K.

2016-11-01

The background field method is used to linearize the Weyl-invariant scalar-tensor gravity, coupled with a Stückelberg field. For a generic background metric, this action is found not to be invariant, under both a diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both transformations independently. The Becchi-Rouet-Stora-Tyutin symmetry of scalar-tensor gravity coupled with a Stückelberg-like massive gauge particle, possessing a diffeomorphism and generalized Weyl symmetry, reveals that in both cases negative-norm states with unphysical degrees of freedom do exist. We then show that, by combining diffeomorphism and generalized Weyl symmetries, all the ghost states decouple, thereby removing the unphysical redundancies of the theory. During this process, the scalar field does not represent any dynamic mode, yet modifies the usual harmonic gauge condition through non-minimal coupling with gravity.

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.

Extended Riemannian geometry II: local heterotic double field theory

NASA Astrophysics Data System (ADS)

Deser, Andreas; Heller, Marc Andre; Sämann, Christian

2018-04-01

We continue our exploration of local Double Field Theory (DFT) in terms of symplectic graded manifolds carrying compatible derivations and study the case of heterotic DFT. We start by developing in detail the differential graded manifold that captures heterotic Generalized Geometry which leads to new observations on the generalized metric and its twists. We then give a symplectic pre-N Q-manifold that captures the symmetries and the geometry of local heterotic DFT. We derive a weakened form of the section condition, which arises algebraically from consistency of the symmetry Lie 2-algebra and its action on extended tensors. We also give appropriate notions of twists — which are required for global formulations — and of the torsion and Riemann tensors. Finally, we show how the observed α'-corrections are interpreted naturally in our framework.

Constraining f(R) gravity in solar system, cosmology and binary pulsar systems

NASA Astrophysics Data System (ADS)

Liu, Tan; Zhang, Xing; Zhao, Wen

2018-02-01

The f (R) gravity can be cast into the form of a scalar-tensor theory, and scalar degree of freedom can be suppressed in high-density regions by the chameleon mechanism. In this article, for the general f (R) gravity, using a scalar-tensor representation with the chameleon mechanism, we calculate the parametrized post-Newtonian parameters γ and β, the effective gravitational constant Geff, and the effective cosmological constant Λeff. In addition, for the general f (R) gravity, we also calculate the rate of orbital period decay of the binary system due to gravitational radiation. Then we apply these results to specific f (R) models (Hu-Sawicki model, Tsujikawa model and Starobinsky model) and derive the constraints on the model parameters by combining the observations in solar system, cosmological scales and the binary systems.

Initial conditions for cosmological perturbations

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Gupt, Brajesh

2017-02-01

Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations.

Cosmological singularities in Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Woolgar, Eric

2014-12-01

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

Gauge-origin dependence in electronic g-tensor calculations

NASA Astrophysics Data System (ADS)

Glasbrenner, Michael; Vogler, Sigurd; Ochsenfeld, Christian

2018-06-01

We present a benchmark study on the gauge-origin dependence of the electronic g-tensor using data from unrestricted density functional theory calculations with the spin-orbit mean field ansatz. Our data suggest in accordance with previous studies that g-tensor calculations employing a common gauge-origin are sufficiently accurate for small molecules; however, for extended molecules, the introduced errors can become relevant and significantly exceed the basis set error. Using calculations with the spin-orbit mean field ansatz and gauge-including atomic orbitals as a reference, we furthermore show that the accuracy and reliability of common gauge-origin approaches in larger molecules depends strongly on the locality of the spin density distribution. We propose a new pragmatic ansatz for choosing the gauge-origin which takes the spin density distribution into account and gives reasonably accurate values for molecules with a single localized spin center. For more general cases like molecules with several spatially distant spin centers, common gauge-origin approaches are shown to be insufficient for consistently achieving high accuracy. Therefore the computation of g-tensors using distributed gauge-origin methods like gauge-including atomic orbitals is considered as the ideal approach and is recommended for larger molecular systems.

New Methods For Interpretation Of Magnetic Gradient Tensor Data Using Eigenalysis And The Normalized Source Strength

NASA Astrophysics Data System (ADS)

Clark, D.

2012-12-01

In the future, acquisition of magnetic gradient tensor data is likely to become routine. New methods developed for analysis of magnetic gradient tensor data can also be applied to high quality conventional TMI surveys that have been processed using Fourier filtering techniques, or otherwise, to calculate magnetic vector and tensor components. This approach is, in fact, the only practical way at present to analyze vector component data, as measurements of vector components are seriously afflicted by motion noise, which is not as serious a problem for gradient components. In many circumstances, an optimal approach to extracting maximum information from magnetic surveys would be to combine analysis of measured gradient tensor data with vector components calculated from TMI measurements. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for a number of elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, horizontal line current and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalized source strength (NSS), calculated from the eigenvalues, is a particularly useful rotational invariant that peaks directly over 3D compact sources, 2D compact sources, thin sheets and contacts, and is independent of magnetization direction for these sources (and only very weakly dependent on magnetization direction in general). In combination the NSS and its vector gradient enable estimation of the Euler structural index, thereby constraining source geometry, and determine source locations uniquely. NSS analysis can be extended to other useful models, such as vertical pipes, by calculating eigenvalues of the vertical derivative of the gradient tensor. Once source locations are determined, information of source magnetizations can be obtained by simple linear inversion of measured or calculated vector and/or tensor data. Inversions based on the vector gradient of the NSS over the Tallawang magnetite deposit in central New South Wales obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Inverted magnetizations are consistent with magnetic property measurements on drill core samples from this deposit. Similarly, inversions of calculated tensor data over the Mount Leyshold gold-mineralized porphyry system in Queensland yield good estimates of the centroid location, total magnetic moment and magnetization direction of the magnetite-bearing potassic alteration zone that are consistent with geological and petrophysical information.

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

NASA Astrophysics Data System (ADS)

Lorente, M.; Kramer, P.

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

Tensor network states in time-bin quantum optics

NASA Astrophysics Data System (ADS)

Lubasch, Michael; Valido, Antonio A.; Renema, Jelmer J.; Kolthammer, W. Steven; Jaksch, Dieter; Kim, M. S.; Walmsley, Ian; García-Patrón, Raúl

2018-06-01

The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

Tensor Decompositions for Learning Latent Variable Models

DTIC Science & Technology

2012-12-08

and eigenvectors of tensors is generally significantly more complicated than their matrix counterpart (both algebraically [Qi05, CS11, Lim05] and...The reduction First, let W ∈ Rd×k be a linear transformation such that M2(W,W ) = W M2W = I where I is the k × k identity matrix (i.e., W whitens ...approximate the whitening matrix W ∈ Rd×k from second-moment matrix M2 ∈ Rd×d. To do this, one first multiplies M2 by a random matrix R ∈ Rd×k′ for some k′ ≥ k

Measurement of the β-asymmetry parameter of Cu67 in search for tensor-type currents in the weak interaction

NASA Astrophysics Data System (ADS)

Soti, G.; Wauters, F.; Breitenfeldt, M.; Finlay, P.; Herzog, P.; Knecht, A.; Köster, U.; Kraev, I. S.; Porobic, T.; Prashanth, P. N.; Towner, I. S.; Tramm, C.; Zákoucký, D.; Severijns, N.

2014-09-01

Background: Precision measurements at low energy search for physics beyond the standard model in a way complementary to searches for new particles at colliders. In the weak sector the most general β-decay Hamiltonian contains, besides vector and axial-vector terms, also scalar, tensor, and pseudoscalar terms. Current limits on the scalar and tensor coupling constants from neutron and nuclear β decay are on the level of several percent. Purpose: Extracting new information on tensor coupling constants by measuring the β-asymmetry parameter in the pure Gamow-Teller decay of Cu67, thereby testing the V-A structure of the weak interaction. Method: An iron sample foil into which the radioactive nuclei were implanted was cooled down to mK temperatures in a 3He-4He dilution refrigerator. An external magnetic field of 0.1 T, in combination with the internal hyperfine magnetic field, oriented the nuclei. The anisotropic β radiation was observed with planar high-purity germanium detectors operating at a temperature of about 10 K. An on-line measurement of the β asymmetry of Cu68 was performed as well for normalization purposes. Systematic effects were investigated using geant4 simulations. Results: The experimental value, Ã=0.587(14), is in agreement with the standard model value of 0.5991(2) and is interpreted in terms of physics beyond the standard model. The limits obtained on possible tensor-type charged currents in the weak interaction Hamiltonian are -0.045<(CT+CT')/CA<0.159 (90% C.L.). Conclusions: The obtained limits are comparable to limits from other correlation measurements in nuclear β decay and contribute to further constraining tensor coupling constants.

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

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

Peng, Bo; Kowalski, Karol

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

Hydrodynamic and elastic interactions of sedimenting flexible fibers

NASA Astrophysics Data System (ADS)

Ekiel-Jezewska, Maria L.; Bukowicki, Marek

2017-11-01

Dynamics of flexible micro and nano filaments in fluids is intensively investigated in many laboratories, with a perspective of numerous applications in biology, medicine or modern technology. In the literature, different theoretical models of elastic interactions between flexible fiber segments are applied. The task of this work is to examine the impact of a chosen elastic model on the dynamics of fibers settling in a viscous fluid under low Reynolds number. To this goal, we construct two trumbbells, each made of three beads connected by springs and with a bending resistance, and we describe hydrodynamic interactions of the beads in terms of the Rotne-Prager mobility tensors. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and a fast horizontal attraction of two elastic trumbbells towards a periodic long-lasting orbit. We show that for sufficiently large bending angles, other models of bending interactions can lead to qualitatively and quantitatively different spurious effects. We also demonstrate examples of essential differences between the dynamics of elastic dumbbells and trumbbells. This work was supported in part by Narodowe Centrum Nauki under Grant No. 2014/15/B/ST8/04359.

Comparison of fall and spring planting on strip-mine spoils in the bituminous region of Pennsylvania

Treesearch

Grant Davis

1973-01-01

To evaluate fall versus spring planting of 10 coniferous tree species and 5 hardwood shrub species, experimental plantings were established over a 2-year period on 7 graded strip-mine spoils. In general, initial tree survival was better with spring planting than with fall planting, especially on the more acid sites. Shrubs survived well with both spring and fall...

Radiative corrections from heavy fast-roll fields during inflation

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

Jain, Rajeev Kumar; Sandora, McCullen; Sloth, Martin S., E-mail: jain@cp3.dias.sdu.dk, E-mail: sandora@cp3.dias.sdu.dk, E-mail: sloth@cp3.dias.sdu.dk

2015-06-01

We investigate radiative corrections to the inflaton potential from heavy fields undergoing a fast-roll phase transition. We find that a logarithmic one-loop correction to the inflaton potential involving this field can induce a temporary running of the spectral index. The induced running can be a short burst of strong running, which may be related to the observed anomalies on large scales in the cosmic microwave spectrum, or extend over many e-folds, sustaining an effectively constant running to be searched for in the future. We implement this in a general class of models, where effects are mediated through a heavy messengermore » field sitting in its minimum. Interestingly, within the present framework it is a generic outcome that a large running implies a small field model with a vanishing tensor-to-scalar ratio, circumventing the normal expectation that small field models typically lead to an unobservably small running of the spectral index. An observable level of tensor modes can also be accommodated, but, surprisingly, this requires running to be induced by a curvaton. If upcoming observations are consistent with a small tensor-to-scalar ratio as predicted by small field models of inflation, then the present study serves as an explicit example contrary to the general expectation that the running will be unobservable.« less

Radiative corrections from heavy fast-roll fields during inflation

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

Jain, Rajeev Kumar; Sandora, McCullen; Sloth, Martin S.

2015-06-09

We investigate radiative corrections to the inflaton potential from heavy fields undergoing a fast-roll phase transition. We find that a logarithmic one-loop correction to the inflaton potential involving this field can induce a temporary running of the spectral index. The induced running can be a short burst of strong running, which may be related to the observed anomalies on large scales in the cosmic microwave spectrum, or extend over many e-folds, sustaining an effectively constant running to be searched for in the future. We implement this in a general class of models, where effects are mediated through a heavy messengermore » field sitting in its minimum. Interestingly, within the present framework it is a generic outcome that a large running implies a small field model with a vanishing tensor-to-scalar ratio, circumventing the normal expectation that small field models typically lead to an unobservably small running of the spectral index. An observable level of tensor modes can also be accommodated, but, surprisingly, this requires running to be induced by a curvaton. If upcoming observations are consistent with a small tensor-to-scalar ratio as predicted by small field models of inflation, then the present study serves as an explicit example contrary to the general expectation that the running will be unobservable.« less

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

NASA Astrophysics Data System (ADS)

Zhou, Shuai; Huang, Danian

2015-11-01

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

Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux

NASA Astrophysics Data System (ADS)

Cariglia, Marco

2012-10-01

The Eisenhart-Duval lift allows embedding nonrelativistic theories into a Lorentzian geometrical setting. In this paper we study the lift from the point of view of the Dirac equation and its hidden symmetries. We show that dimensional reduction of the Dirac equation for the Eisenhart-Duval metric in general gives rise to the nonrelativistic Lévy-Leblond equation in lower dimension. We study in detail in which specific cases the lower dimensional limit is given by the Dirac equation, with scalar and vector flux, and the relation between lift, reduction, and the hidden symmetries of the Dirac equation. While there is a precise correspondence in the case of the lower dimensional massive Dirac equation with no flux, we find that for generic fluxes it is not possible to lift or reduce all solutions and hidden symmetries. As a by-product of this analysis, we construct new Lorentzian metrics with special tensors by lifting Killing-Yano and closed conformal Killing-Yano tensors and describe the general conformal Killing-Yano tensor of the Eisenhart-Duval lift metrics in terms of lower dimensional forms. Last, we show how, by dimensionally reducing the higher dimensional operators of the massless Dirac equation that are associated with shared hidden symmetries, it is possible to recover hidden symmetry operators for the Dirac equation with flux.

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

Effect of cosmological evolution on Solar System constraints and on the scalarization of neutron stars in massless scalar-tensor theories

NASA Astrophysics Data System (ADS)

Anderson, David; Yunes, Nicolás; Barausse, Enrico

2016-11-01

Certain scalar-tensor theories of gravity that generalize Jordan-Fierz-Brans-Dicke theory are known to predict nontrivial phenomenology for neutron stars. In these theories, first proposed by Damour and Esposito-Farèse, the scalar field has a standard kinetic term and couples conformally to the matter fields. The weak equivalence principle is therefore satisfied, but scalar effects may arise in strong-field regimes, e.g., allowing for violations of the strong equivalence principle in neutron stars ("spontaneous scalarization") or in sufficiently tight binary neutron-star systems ("dynamical/induced scalarization"). The original scalar-tensor theory proposed by Damour and Esposito-Farèse is in tension with Solar System constraints (for couplings that lead to scalarization), if one accounts for cosmological evolution of the scalar field and no mass term is included in the action. We extend here the conformal coupling of that theory, in order to ascertain if, in this way, Solar System tests can be passed, while retaining a nontrivial phenomenology for neutron stars. We find that, even with this generalized conformal coupling, it is impossible to construct a theory that passes both big bang nucleosynthesis and Solar System constraints, while simultaneously allowing for scalarization in isolated/binary neutron stars.

Dark Energy After GW170817: Dead Ends and the Road Ahead.

PubMed

Ezquiaga, Jose María; Zumalacárregui, Miguel

2017-12-22

Multimessenger gravitational-wave (GW) astronomy has commenced with the detection of the binary neutron star merger GW170817 and its associated electromagnetic counterparts. The almost coincident observation of both signals places an exquisite bound on the GW speed |c_{g}/c-1|≤5×10^{-16}. We use this result to probe the nature of dark energy (DE), showing that a large class of scalar-tensor theories and DE models are highly disfavored. As an example we consider the covariant Galileon, a cosmologically viable, well motivated gravity theory which predicts a variable GW speed at low redshift. Our results eliminate any late-universe application of these models, as well as their Horndeski and most of their beyond Horndeski generalizations. Three alternatives (and their combinations) emerge as the only possible scalar-tensor DE models: (1) restricting Horndeski's action to its simplest terms, (2) applying a conformal transformation which preserves the causal structure, and (3) compensating the different terms that modify the GW speed (to be robust, the compensation has to be independent on the background on which GWs propagate). Our conclusions extend to any other gravity theory predicting varying c_{g} such as Einstein-Aether, Hořava gravity, Generalized Proca, tensor-vector-scalar gravity (TEVES), and other MOND-like gravities.

Dark Energy After GW170817: Dead Ends and the Road Ahead

NASA Astrophysics Data System (ADS)

Ezquiaga, Jose María; Zumalacárregui, Miguel

2017-12-01

Multimessenger gravitational-wave (GW) astronomy has commenced with the detection of the binary neutron star merger GW170817 and its associated electromagnetic counterparts. The almost coincident observation of both signals places an exquisite bound on the GW speed |cg/c -1 |≤5 ×10-16 . We use this result to probe the nature of dark energy (DE), showing that a large class of scalar-tensor theories and DE models are highly disfavored. As an example we consider the covariant Galileon, a cosmologically viable, well motivated gravity theory which predicts a variable GW speed at low redshift. Our results eliminate any late-universe application of these models, as well as their Horndeski and most of their beyond Horndeski generalizations. Three alternatives (and their combinations) emerge as the only possible scalar-tensor DE models: (1) restricting Horndeski's action to its simplest terms, (2) applying a conformal transformation which preserves the causal structure, and (3) compensating the different terms that modify the GW speed (to be robust, the compensation has to be independent on the background on which GWs propagate). Our conclusions extend to any other gravity theory predicting varying cg such as Einstein-Aether, Hořava gravity, Generalized Proca, tensor-vector-scalar gravity (TEVES), and other MOND-like gravities.

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.

Canonical single field slow-roll inflation with a non-monotonic tensor-to-scalar ratio

NASA Astrophysics Data System (ADS)

Germán, Gabriel; Herrera-Aguilar, Alfredo; Hidalgo, Juan Carlos; Sussman, Roberto A.

2016-05-01

We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter epsilon(phi) and its derivatives epsilon'(phi) and epsilon''(phi), thereby extracting general conditions on the tensor-to-scalar ratio r and the running nsk at phiH where the perturbations are produced, some 50-60 e-folds before the end of inflation. We find quite generally that for models where epsilon(phi) develops a maximum, a relatively large r is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter ξ2(phi). To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic epsilon(phi) decreasing during most part of inflation. Since at phiH the slow-roll parameter epsilon(phi) is increasing, we thus require that epsilon(phi) develops a maximum for phi > phiH after which epsilon(phi) decrease to small values where most e-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion Δphie ≡ |phiH-phie| is obtained with a sufficiently thin profile for epsilon(phi) which, however, should not conflict with the second slow-roll parameter η(phi). As a consequence of this analysis we find bounds for Δphie, rH and for the scalar spectral index nsH. Finally we provide examples where these considerations are explicitly realised.

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.

Armored spring-core superconducting cable and method of construction

DOEpatents

McIntyre, Peter M.; Soika, Rainer H.

2002-01-01

An armored spring-core superconducting cable (12) is provided. The armored spring-core superconducting cable (12) may include a spring-core (20), at least one superconducting strand (24) wound onto the spring-core (20), and an armored shell (22) that encases the superconducting strands (24). The spring-core (20) is generally a perforated tube that allows purge gases and cryogenic liquids to be circulated through the armored superconducting cable (12), as well as managing the internal stresses within the armored spring-core superconducting cable (12). The armored shell (22) manages the external stresses of the armored spring-core superconducting cable (12) to protect the fragile superconducting strands (24). The armored spring-core superconducting cable (12) may also include a conductive jacket (34) formed outwardly of the armored shell (22).

Generalized Cartan Calculus in general dimension

DOE PAGES

Wang, Yi -Nan

2015-07-22

We develop the generalized Cartan Calculus for the groups G = SL(2,R) × R +, SL(5,R) and SO(5,5). They are the underlying algebraic structures of d=9,7,6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincar\\'e lemmas in this new differential geometry is also discussed. Lastly, we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

Piezoelectric Nanogenerators for Self-Powered Nanosystems and Nanosensors

DTIC Science & Technology

2013-05-15

mechanical triggering applied onto the nanogenerator. The structure and general working principle of the spring-substrated nanogenerator ( SNG ) are...schematically shown in Fig. 3a–c. Compressive springs with variable sizes were selected as the skeletons of the SNG devices. The helix-shaped spring surface...In the measurement for the output performance of the SNG , one end of the spring was fixed onto a three-dimensional stage; meanwhile a mechanical

Springs, streams, and gas vent on and near Mount Adams volcano, Washington

USGS Publications Warehouse

Nathenson, Manuel; Mariner, Robert H.

2013-01-01

Springs and some streams on Mount Adams volcano have been sampled for chemistry and light stable isotopes of water. Spring temperatures are generally cooler than air temperatures from weather stations at the same elevation. Spring chemistry generally reflects weathering of volcanic rock from dissolved carbon dioxide. Water in some springs and streams has either dissolved hydrothermal minerals or has reacted with them to add sulfate to the water. Some samples appear to have obtained their sulfate from dissolution of gypsum while some probably involve reaction with sulfide minerals such as pyrite. Light stable isotope data for water from springs follow a local meteoric water line, and the variation of isotopes with elevation indicate that some springs have very local recharge and others have water from elevations a few hundred meters higher. No evidence was found for thermal or slightly thermal springs on Mount Adams. A sample from a seeping gas vent on Mount Adams was at ambient temperature, but the gas is similar to that found on other Cascade volcanoes. Helium isotopes are 4.4 times the value in air, indicating that there is a significant component of mantle helium. The lack of fumaroles on Mount Adams and the ambient temperature of the gas indicates that the gas is from a hydrothermal system that is no longer active.

Revised theory of tachyons in general relativity

NASA Astrophysics Data System (ADS)

Schwartz, Charles

2017-08-01

A minus sign is inserted, for good reason, into the formula for the energy-momentum tensor for tachyons. This leads to remarkable theoretical consequences and a plausible explanation for the phenomenon called dark energy in the cosmos.

Conservative 3 + 1 general relativistic variable Eddington tensor radiation transport equations

DOE PAGES

Cardall, Christian Y.; Endeve, Eirik; Mezzacappa, Anthony

2013-05-07

We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. With an eye towards astrophysical applications—such as core-collapse supernovae and compact object mergers—in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles aremore » neutrinos, we pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.« less

Rapidly rotating neutron stars with a massive scalar field—structure and universal relations

NASA Astrophysics Data System (ADS)

Doneva, Daniela D.; Yazadjiev, Stoytcho S.

2016-11-01

We construct rapidly rotating neutron star models in scalar-tensor theories with a massive scalar field. The fact that the scalar field has nonzero mass leads to very interesting results since the allowed range of values of the coupling parameters is significantly broadened. Deviations from pure general relativity can be very large for values of the parameters that are in agreement with the observations. We found that the rapid rotation can magnify the differences several times compared to the static case. The universal relations between the normalized moment of inertia and quadrupole moment are also investigated both for the slowly and rapidly rotating cases. The results show that these relations are still EOS independent up to a large extend and the deviations from pure general relativity can be large. This places the massive scalar-tensor theories amongst the few alternative theories of gravity that can be tested via the universal I-Love-Q relations.

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.

Linear dispersion properties of ring velocity distribution functions

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

Vandas, Marek, E-mail: marek.vandas@asu.cas.cz; Hellinger, Petr; Institute of Atmospheric Physics, AS CR, Bocni II/1401, CZ-14100 Prague

2015-06-15

Linear properties of ring velocity distribution functions are investigated. The dispersion tensor in a form similar to the case of a Maxwellian distribution function, but for a general distribution function separable in velocities, is presented. Analytical forms of the dispersion tensor are derived for two cases of ring velocity distribution functions: one obtained from physical arguments and one for the usual, ad hoc ring distribution. The analytical expressions involve generalized hypergeometric, Kampé de Fériet functions of two arguments. For a set of plasma parameters, the two ring distribution functions are compared. At the parallel propagation with respect to the ambientmore » magnetic field, the two ring distributions give the same results identical to the corresponding bi-Maxwellian distribution. At oblique propagation, the two ring distributions give similar results only for strong instabilities, whereas for weak growth rates their predictions are significantly different; the two ring distributions have different marginal stability conditions.« less

New Class of Quasinormal Modes of Neutron Stars in Scalar-Tensor Gravity

NASA Astrophysics Data System (ADS)

Mendes, Raissa F. P.; Ortiz, Néstor

2018-05-01

Detection of the characteristic spectrum of pulsating neutron stars can be a powerful tool not only to probe the nuclear equation of state but also to test modifications to general relativity. However, the shift in the oscillation spectrum induced by modified theories of gravity is often small and degenerate with our ignorance of the equation of state. In this Letter, we show that the coupling to additional degrees of freedom present in modified theories of gravity can give rise to new families of modes, with no counterpart in general relativity, which could be sufficiently well resolved in frequency space to allow for clear detection. We present a realization of this idea by performing a thorough study of radial oscillations of neutron stars in massless scalar-tensor theories of gravity. We anticipate astrophysical scenarios where the presence of this class of quasinormal modes could be probed with electromagnetic and gravitational wave measurements.

δ M formalism: a new approach to cosmological perturbation theory in anisotropic inflation

NASA Astrophysics Data System (ADS)

Talebian-Ashkezari, A.; Ahmadi, N.; Abolhasani, A. A.

2018-03-01

We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the δ M formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in almost the same way that the so-called δ N formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twin formula, δ N, this new method can substantially reduce the amount of calculations related to the evolution of tensor modes. However, it is not as general as δ N it is a "perturbative" formula and solves the shear only to linear order. In other words, it is restricted to weak shear limit.

Water-resources data collected in the Devils Hole area, Ash Meadows, Nevada, 1975-76

USGS Publications Warehouse

Hanes, William Toby

1976-01-01

The U.S. Geological Survey collected water-level, spring-flow, and power-consumption data in the Devils Hole area in Nevada from July 1975 through June 1976. The work for this sfurth annual data report was done in cooperation with the National Park Service. Continuous recorders were used to monitor water levels in Devils Hole, three observation wells, and the flow from four springs. Also, monthly readings were made on two wells to help define a general trend of ground-water levels. Monthly meter readings of six electrically powered irrigation wells provided a record of power consumption, which in turn, is an index of the amount of water pumped. The purpose of the work is to observe the effects, if any, of ground-water withdrawals from specified irrigtion wells in the Ash Meadows area on (1) the water level in Devils Hole, and (2) the flow of four springs in the area. Fairbanks Spring and Big Spring, which are in the extreme northern and southern parts of Ash Meadows respectively, show little effect of pumping. An increase in the monthly average flow at Fairbanks Spring in September can be attributed to runoff and surficial recharge in the surrounding area caused by a large cloudburst. Jack Rabbit Spring, which is about 1 mile southwest of the major pumping field, is affected strongly by pumping. Jack Rabbit Spring flowed during the winter months but flowed very infrequently during non-winter months. Point of Rocks Spring had a flow pattern similar to Big Spring and Fairbanks Spring. All the springs had a general increase in flow during the Winter months. (Woodard-USGS)

Homothetic matter collineations of LRS Bianchi type I spacetimes

NASA Astrophysics Data System (ADS)

Hussain, Tahir; Rahim, Waqas

2017-12-01

A complete classification of locally rotationally symmetric (LRS) Bianchi type I spacetimes via homothetic matter collineations (HMCs) is presented. For non-degenerate energy-momentum tensor, a general form of the vector field generating HMCs is found, subject to some integrability conditions. Solving the integrability conditions in different cases, it is found that the LRS Bianchi type I spacetimes admit 6-, 7-, 8-, 10- or 11-dimensional Lie algebra of HMCs. When the energy-momentum tensor is degenerate, two cases give 6 and 11 HMCs, while the remaining cases produce infinite number of HMCs. Some LRS Bianchi type I metrics are provided admitting HMCs.

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.

Nonsingular, big-bounce cosmology from spinor-torsion coupling

NASA Astrophysics Data System (ADS)

Popławski, Nikodem

2012-05-01

The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of general relativity that the affine connection be symmetric by regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. We show that such an interaction averts the unphysical big-bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. This scenario also explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic.

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.

Gravitational Wave Oscillations in Bigravity.

PubMed

Max, Kevin; Platscher, Moritz; Smirnov, Juri

2017-09-15

We derive consistent equations for gravitational wave oscillations in bigravity. In this framework a second dynamical tensor field is introduced in addition to general relativity and coupled such that one massless and one massive linear combination arise. Only one of the two tensors is the physical metric coupling to matter, and thus the basis in which gravitational waves propagate is different from the basis where the wave is produced and detected. Therefore, one should expect-in analogy to neutrino oscillations-to observe an oscillatory behavior. We show for the first time how this behavior arises explicitly, discuss phenomenological implications, and present new limits on the graviton parameter space in bigravity.

ON THE DECOMPOSITION OF STRESS AND STRAIN TENSORS INTO SPHERICAL AND DEVIATORIC PARTS

PubMed Central

Augusti, G.; Martin, J. B.; Prager, W.

1969-01-01

It is well known that Hooke's law for a linearly elastic, isotropic solid may be written in the form of two relations that involve only the spherical or only the deviatoric parts of the tensors of stress and strain. The example of the linearly elastic, transversely isotropic solid is used to show that this decomposition is not, in general, feasible for linearly elastic, anisotropic solids. The discussion is extended to a large class of work-hardening rigid, plastic solids, and it is shown that the considered decomposition can only be achieved for the incompressible solids of this class. PMID:16591754

Natural Strain

NASA Technical Reports Server (NTRS)

Freed, Alan D.

1995-01-01

The purpose of this paper is to present a consistent and thorough development of the strain and strain-rate measures affiliated with Hencky. Natural measures for strain and strain-rate, as I refer to them, are first expressed in terms of of the fundamental body-metric tensors of Lodge. These strain and strain-rate measures are mixed tensor fields. They are mapped from the body to space in both the Eulerian and Lagrangian configurations, and then transformed from general to Cartesian fields. There they are compared with the various strain and strain-rate measures found in the literature. A simple Cartesian description for Hencky strain-rate in the Lagrangian state is obtained.

General Relativity

NASA Astrophysics Data System (ADS)

Hobson, M. P.; Efstathiou, G. P.; Lasenby, A. N.

2006-02-01

1. The spacetime of special relativity; 2. Manifolds and coordinates; 3. Vector calculus on manifolds; 4. Tensor calculus on manifolds; 5. Special relativity revisited; 6. Electromagnetism; 7. The equivalence principle and spacetime curvature; 8. The gravitational field equations; 9. The Schwarzschild geometry; 10. Experimental tests of general relativity; 11. Schwarzschild black holes; 12. Further spherically-symmetric geometries; 13. The Kerr geometry; 14. The Friedmann-Robertson-Walker geometry; 15. Cosmological models; 16. Inflationary cosmology; 17. Linearised general relativity; 18. Gravitational waves; 19. A variational approach to general relativity.

Curved manifolds with conserved Runge-Lenz vectors

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

Ngome, J.-P.

2009-12-15

van Holten's algorithm is used to construct Runge-Lenz-type conserved quantities, induced by Killing tensors, on curved manifolds. For the generalized Taub-Newman-Unti-Tamburino metric, the most general external potential such that the combined system admits a conserved Runge-Lenz-type vector is found. In the multicenter case, the subclass of two-center metric exhibits a conserved Runge-Lenz-type scalar.

Curved manifolds with conserved Runge-Lenz vectors

NASA Astrophysics Data System (ADS)

Ngome, J.-P.

2009-12-01

van Holten's algorithm is used to construct Runge-Lenz-type conserved quantities, induced by Killing tensors, on curved manifolds. For the generalized Taub-Newman-Unti-Tamburino metric, the most general external potential such that the combined system admits a conserved Runge-Lenz-type vector is found. In the multicenter case, the subclass of two-center metric exhibits a conserved Runge-Lenz-type scalar.

Off-shell supergravity in five dimensions and supersymmetric brane world scenarios

NASA Astrophysics Data System (ADS)

Zucker, M.

2003-09-01

We review the construction of off-shell Poincaré supergravity in five dimensions. We describe in detail the minimal multiplet, which is the basic building block, containing the propagating fields of supergravity. All matter multiplets containing (8 + 8) components, being the smallest matter multiplets in five dimensions, are constructed. Using these multiplets the complete tensor calculus for supergravity is developed. As expected it turns out, that there exist three distinct minimal (i.e. containing (48 + 48) field components) off-shell supergravities. The lagrangians for these theories and their gauged variants are given explicitly. These results are used in the second part to develop a tensor calculus on the orbifold . Gauged supergravity on the orbifold with additional cosmological constants at the fixpoints, is constructed. This generalizes the work of Randall-Sundrum to local supersymmetry. The developed tensor calculus is used to extend this model to include matter located at the fixpoints. Chiral and super Yang-Mills multiplets at the fixpoints are considered.

Limit on Tensor Currents from Li 8 β Decay

NASA Astrophysics Data System (ADS)

Sternberg, M. G.; Segel, R.; Scielzo, N. D.; Savard, G.; Clark, J. A.; Bertone, P. F.; Buchinger, F.; Burkey, M.; Caldwell, S.; Chaudhuri, A.; Crawford, J. E.; Deibel, C. M.; Greene, J.; Gulick, S.; Lascar, D.; Levand, A. F.; Li, G.; Pérez Galván, A.; Sharma, K. S.; Van Schelt, J.; Yee, R. M.; Zabransky, B. J.

2015-10-01

In the standard model, the weak interaction is formulated with a purely vector-axial-vector (V -A ) structure. Without restriction on the chirality of the neutrino, the most general limits on tensor currents from nuclear β decay are dominated by a single measurement of the β -ν ¯ correlation in He 6 β decay dating back over a half century. In the present work, the β -ν ¯ -α correlation in the β decay of Li 8 and subsequent α -particle breakup of the Be8 * daughter was measured. The results are consistent with a purely V -A interaction and in the case of couplings to right-handed neutrinos (CT=-CT' ) limits the tensor fraction to |CT/CA|2<0.011 (95.5% C.L.). The measurement confirms the He 6 result using a different nuclear system and employing modern ion-trapping techniques subject to different systematic uncertainties.

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

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

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Julia

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

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

NASA Astrophysics Data System (ADS)

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

1999-11-01

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

Multi-normed spaces based on non-discrete measures and their tensor products

NASA Astrophysics Data System (ADS)

Helemskii, A. Ya.

2018-04-01

Lambert discovered a new type of structures situated, in a sense, between normed spaces and abstract operator spaces. His definition was based on the notion of amplifying a normed space by means of the spaces \\ell_2^n. Later, several mathematicians studied more general structures (`p-multi- normed spaces') introduced by means of the spaces \\ell_p^n, 1≤ p≤∞. We pass from \\ell_p to L_p(X,μ) with an arbitrary measure. This becomes possible in the framework of the non- coordinate approach to the notion of amplification. In the case of a discrete counting measure, this approach is equivalent to the approach in the papers mentioned. Two categories arise. One consists of amplifications by means of an arbitrary normed space, and the other consists of p-convex amplifications by means of L_p(X,μ). Each of them has its own tensor product of objects (the existence of each product is proved by a separate explicit construction). As a final result, we show that the `p-convex' tensor product has an especially transparent form for the minimal L_p-amplifications of L_q-spaces, where q is conjugate to p. Namely, tensoring L_q(Y,ν) and L_q(Z,λ), we obtain L_q(Y× Z, ν×λ).

A Tensor-Product-Kernel Framework for Multiscale Neural Activity Decoding and Control

PubMed Central

Li, Lin; Brockmeier, Austin J.; Choi, John S.; Francis, Joseph T.; Sanchez, Justin C.; Príncipe, José C.

2014-01-01

Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brain's motor and sensory areas, thereby bypassing the body. The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization of the neural system state. However, heterogeneity on data type (spike timing versus continuous amplitude signals) and spatiotemporal scale complicates the model integration of multiscale neural activity. In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity. This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control. For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering. In a sensory stimulation experiment, the tensor-product-kernel decoder outperforms decoders that use only a single neural data type. In addition, an adaptive inverse controller for delivering electrical microstimulation patterns that utilizes the tensor-product kernel achieves promising results in emulating the responses to natural stimulation. PMID:24829569

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.

Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories

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

Banik, Manik, E-mail: manik11ju@gmail.com

Steering is one of the most counter intuitive non-classical features of bipartite quantum system, first noticed by Schrödinger at the early days of quantum theory. On the other hand, measurement incompatibility is another non-classical feature of quantum theory, initially pointed out by Bohr. Recently, Quintino et al. [Phys. Rev. Lett. 113, 160402 (2014)] and Uola et al. [Phys. Rev. Lett. 113, 160403 (2014)] have investigated the relation between these two distinct non-classical features. They have shown that a set of measurements is not jointly measurable (i.e., incompatible) if and only if they can be used for demonstrating Schrödinger-Einstein-Podolsky-Rosen steering. Themore » concept of steering has been generalized for more general abstract tensor product theories rather than just Hilbert space quantum mechanics. In this article, we discuss that the notion of measurement incompatibility can be extended for general probability theories. Further, we show that the connection between steering and measurement incompatibility holds in a border class of tensor product theories rather than just quantum theory.« less

A priori testing of subgrid-scale models for large-eddy simulation of the atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Juneja, Anurag; Brasseur, James G.

1996-11-01

Subgrid-scale models are generally developed assuming homogeneous isotropic turbulence with the filter cutoff lying in the inertial range. In the surface layer and capping inversion regions of the atmospheric boundary layer, the turbulence is strongly anisotropic and, in general, influenced by both buoyancy and shear. Furthermore, the integral scale motions are under-resolved in these regions. Herein we perform direct numerical simulations of shear and buoyancy-generated homogeneous anisotropic turbulence to compute and analyze the actual subgrid-resolved-scale (SGS-RS) dynamics as the filter cutoff moves into the energy-containing scales. These are compared with the SGS-RS dynamics predicted by Smagorinsky-based models with a focus on motivating improved closures. We find that, in general, the underlying assumption of such models, that the anisotropic part of the subgrid stress tensor be aligned with the resolved strain rate tensor, is a poor approximation. Similarly, we find poor alignment between the actual and predicted stress divergence, and find low correlations between the actual and modeled subgrid-scale contribution to the pressure and pressure gradient. Details will be given in the talk.

Cosmology in generalized Proca theories

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

Felice, Antonio De; Mukohyama, Shinji; Heisenberg, Lavinia

2016-06-01

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for themore » absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.« less

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

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.

2016-01-01

Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.

f( R, L m ) gravity

NASA Astrophysics Data System (ADS)

Harko, Tiberiu; Lobo, Francisco S. N.

2010-11-01

We generalize the f( R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert-Einstein Lagrange density are also derived.

Brownian dynamics of wall tethered polymers in shear flow

NASA Astrophysics Data System (ADS)

Lin, Tiras Y.; Saadat, Amir; Kushwaha, Amit; Shaqfeh, Eric S. G.

2017-11-01

The dynamics of a wall tethered polymer in shear flow is studied using Brownian dynamics. Simulations are performed with bead-spring chains, and the effect of hydrodynamic interactions (HI) is incorporated through Blake's tensor with a finite size bead correction. We characterize the configuration of the polymer as a function of the Weissenberg number by investigating the regions the polymer explores in both the flow-gradient and flow-vorticity planes. The fractional extension in the flow direction, the width in the vorticity direction, and the thickness in the gradient direction are reported as well, and these quantities are found to compare favorably with the experimental data of the literature. The cyclic motion of the polymer is demonstrated through analysis of the mean velocity field of the end bead. We characterize the collision process of each bead with the wall as a Poisson process and extract an average wall collision rate, which in general varies along the backbone of the chain. The inclusion of HI with the wall for a tethered polymer is found to reduce the average wall collision rate. We anticipate that results from this work will be directly applicable to, e.g., the design of polymer brushes or the use of DNA for making nanowires in molecular electronics. T.Y.L. is supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

Effective metrics and a fully covariant description of constitutive tensors in electrodynamics

NASA Astrophysics Data System (ADS)

Schuster, Sebastian; Visser, Matt

2017-12-01

Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-) material would provide an analogue space-time model or—vice versa—characterizing which given metric could be modeled with a (meta-) material. While the consistency conditions themselves are by now well known and studied, the form the metric takes once they are satisfied is not. This question is mostly easily answered by keeping the formalisms of the two research fields here in contact as close to each other as possible. While fully covariant formulations of the electrodynamics of media have been around for a long while, they are usually abandoned for (3 +1 )- or six-dimensional formalisms. Here we use the fully unified and fully covariant approach. This enables us even to generalize the consistency conditions for the existence of an effective metric to arbitrary background metrics beyond flat space-time electrodynamics. We also show how the familiar matrices for permittivity ɛ , permeability μ-1, and magnetoelectric effects ζ can be seen as the three independent pieces of the Bel decomposition for the constitutive tensor Za b c d, i.e., the components of an orthogonal decomposition with respect to a given observer with four-velocity Va. Finally, we use the Moore-Penrose pseudoinverse and the closely related pseudodeterminant to then gain the desired reconstruction of the effective metric in terms of the permittivity tensor ɛa b, the permeability tensor [μ-1]a b, and the magnetoelectric tensor ζa b, as an explicit function geff(ɛ ,μ-1,ζ ).

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

PubMed

Li, Zhendong; Liu, Wenjian

2010-08-14

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

Global moment tensor computation at GFZ Potsdam

NASA Astrophysics Data System (ADS)

Saul, J.; Becker, J.; Hanka, W.

2011-12-01

As part of its earthquake information service, GFZ Potsdam has started to provide seismic moment tensor solutions for significant earthquakes world-wide. The software used to compute the moment tensors is a GFZ-Potsdam in-house development, which uses the framework of the software SeisComP 3 (Hanka et al., 2010). SeisComP 3 (SC3) is a software package for seismological data acquisition, archival, quality control and analysis. SC3 is developed by GFZ Potsdam with significant contributions from its user community. The moment tensor inversion technique uses a combination of several wave types, time windows and frequency bands depending on magnitude and station distance. Wave types include body, surface and mantle waves as well as the so-called 'W-Phase' (Kanamori and Rivera, 2008). The inversion is currently performed in the time domain only. An iterative centroid search can be performed independently both horizontally and in depth. Moment tensors are currently computed in a semi-automatic fashion. This involves inversions that are performed automatically in near-real time, followed by analyst review prior to publication. The automatic results are quite often good enough to be published without further improvements, sometimes in less than 30 minutes from origin time. In those cases where a manual interaction is still required, the automatic inversion usually does a good job at pre-selecting those traces that are the most relevant for the inversion, keeping the work required for the analyst at a minimum. Our published moment tensors are generally in good agreement with those published by the Global Centroid-Moment-Tensor (GCMT) project for earthquakes above a magnitude of about Mw 5. Additionally we provide solutions for smaller earthquakes above about Mw 4 in Europe, which are normally not analyzed by the GCMT project. We find that for earthquakes above Mw 6, the most robust automatic inversions can usually be obtained using the W-Phase time window. The GFZ earthquake bulletin is located at http://geofon.gfz-potsdam.de/eqinfo For more information on the SeisComP 3 software visit http://www.seiscomp3.org

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.

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

NASA Astrophysics Data System (ADS)

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

2003-10-01

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

Stability of Horndeski vector-tensor interactions

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

Jiménez, Jose Beltrán; Durrer, Ruth; Heisenberg, Lavinia

2013-10-01

We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds tomore » an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.« less

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

MOG without anomaly

NASA Astrophysics Data System (ADS)

Sepehri, Alireza; Ghaffary, Tooraj; Naimi, Yaghoob

2018-03-01

We obtain the action of Moffat's Modified Gravity (MOG), a scalar-tensor-vector theory of gravitation, by generalizing the Horava-Witten mechanism to fourteen dimensions. We show that the resulting theory is anomaly-free. We propose an extended version of MOG that includes fermionic fields.

Three-Dimensional Orthogonal Co-ordinates

ERIC Educational Resources Information Center

Astin, J.

1974-01-01

A systematic approach to general orthogonal co-ordinates, suitable for use near the end of a beginning vector analysis course, is presented. It introduces students to tensor quantities and shows how equations and quantities needed in classical problems can be determined. (Author/LS)

On the Numerical Solution of the Integral Equation Formulation for Transient Structural Synthesis

DTIC Science & Technology

2014-09-01

stiffness modification. mass ( ) 1 (2.2 ), spring constant ( ) 100 / 6.9 lbm kg lb k N m ft         2) A SDOF mass-spring system with an...externally applied periodic excitation, subjected to a stiffness modification. mass ( ) 1 (2.2 ), spring constant ( ) 100 / 6.9 lbm kg lb k N m ft...spring. mass ( ) 1 (2.2 ), spring constant ( ) 100 / 6.9 lbm kg lb k N m ft         4) A generalized MDOF cantilevered aluminum beam with

Galileons as the scalar analogue of general relativity

NASA Astrophysics Data System (ADS)

Klein, Remko; Ozkan, Mehmet; Roest, Diederik

2016-02-01

We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial alternative to gauge theories (including general relativity). Moreover, it is shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations, similar to the Lovelock gravity theories. Possible extensions are discussed.

Spinning fluids in general relativity

NASA Technical Reports Server (NTRS)

Ray, J. R.; Smalley, L. L.

1982-01-01

General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.

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.

1. Historic American Buildings Survey, Frank C. Brown, Photographer. Spring ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. Historic American Buildings Survey, Frank C. Brown, Photographer. Spring of 1935 (a) Ext-- General view. (from Southeast) - Old Gaol, Vestal Street (moved from original site), Nantucket, Nantucket County, MA

Disformally self-tuning gravity

NASA Astrophysics Data System (ADS)

Emond, William T.; Saffin, Paul M.

2016-03-01

We extend a previous self-tuning analysis of the most general scalar-tensor theory of gravity in four dimensions with second order field equations by considering a generalized coupling to the matter sector. Through allowing a disformal coupling to matter we are able to extend the Fab Four model and construct a new class of theories that are able to tune away the cosmological constant on Friedmann-Lemaitre-Robertson-Walker backgrounds.

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

NASA Technical Reports Server (NTRS)

Smalley, L. L.

1983-01-01

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

Analytical approach on the stiffness of MR fluid filled spring

NASA Astrophysics Data System (ADS)

Sikulskyi, Stanislav; Kim, Daewon

2017-04-01

A solid mechanical spring generally exhibits uniform stiffness. This paper studies a mechanical spring filled with magnetorheological (MR) fluid to achieve controllable stiffness. The hollow spring filled with MR fluid is subjected to a controlled magnetic field in order to change the viscosity of the MR fluid and thereby to change the overall stiffness of the spring. MR fluid is considered as a Bingham viscoplastic linear material in the mathematical model. The goal of this research is to study the feasibility of such spring system by analytically computing the effects of MR fluid on overall spring stiffness. For this purpose, spring mechanics and MR fluid behavior are studied to increase the accuracy of the analysis. Numerical simulations are also performed to generate some assumptions, which simplify calculations in the analytical part. The accuracy of the present approach is validated by comparing the analytical results to previously known experimental results. Overall stiffness variations of the spring are also discussed for different spring designs.

Databases post-processing in Tensoral

NASA Technical Reports Server (NTRS)

Dresselhaus, Eliot

1994-01-01

The Center for Turbulent Research (CTR) post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, introduced in this document and currently existing in prototype form, is the foundation of this effort. Tensoral provides a convenient and powerful protocol to connect users who wish to analyze fluids databases with the authors who generate them. In this document we introduce Tensoral and its prototype implementation in the form of a user's guide. This guide focuses on use of Tensoral for post-processing turbulence databases. The corresponding document - the Tensoral 'author's guide' - which focuses on how authors can make databases available to users via the Tensoral system - is currently unwritten. Section 1 of this user's guide defines Tensoral's basic notions: we explain the class of problems at hand and how Tensoral abstracts them. Section 2 defines Tensoral syntax for mathematical expressions. Section 3 shows how these expressions make up Tensoral statements. Section 4 shows how Tensoral statements and expressions are embedded into other computer languages (such as C or Vectoral) to make Tensoral programs. We conclude with a complete example program.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

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

PubMed

Farrar, Danielle; Budson, Andrew E

2017-04-01

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

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.

Noether symmetries in Gauss-Bonnet-teleparallel cosmology.

PubMed

Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F

2016-01-01

A generalized teleparallel cosmological model, [Formula: see text], containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant [Formula: see text], is studied in the framework of the Noether symmetry approach. As [Formula: see text] gravity, where [Formula: see text] is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, [Formula: see text] contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function [Formula: see text] and to derive exact cosmological solutions.

Quantum gravitational corrections from the Wheeler–DeWitt equation for scalar–tensor theories

NASA Astrophysics Data System (ADS)

Steinwachs, Christian F.; van der Wild, Matthijs L.

2018-07-01

We perform the canonical quantization of a general scalar–tensor theory and derive the first quantum gravitational corrections following from a semiclassical expansion of the Wheeler–DeWitt equation. The non-minimal coupling of the scalar field to gravity induces a derivative coupling between the scalar field and the gravitational degrees of freedom, which prevents a direct application of the expansion scheme. We address this technical difficulty by transforming the theory from the Jordan frame to the Einstein frame. We find that a large non-minimal coupling can have strong effects on the quantum gravitational correction terms. We briefly discuss these effects in the context of the specific model of Higgs inflation.

Relativistic symmetries in the Rosen—Morse potential and tensor interaction using the Nikiforov—Uvarov method

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-04-01

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen—Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ (κ± 1)r-2. In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov—Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.

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

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2018-06-01

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

Influence of spring phenology on seasonal and annual carbon balance in two contrasting New England forests.

PubMed

Richardson, Andrew D; Hollinger, David Y; Dail, D Bryan; Lee, John T; Munger, J William; O'keefe, John

2009-03-01

Spring phenology is thought to exert a major influence on the carbon (C) balance of temperate and boreal ecosystems. We investigated this hypothesis using four spring onset phenological indicators in conjunction with surface-atmosphere CO(2) exchange data from the conifer-dominated Howland Forest and deciduous-dominated Harvard Forest AmeriFlux sites. All phenological measures, including CO(2) source-sink transition dates, could be well predicted on the basis of a simple two-parameter spring warming model, indicating good potential for improving the representation of phenological transitions and their dynamic responsiveness to climate variability in land surface models. The date at which canopy-scale photosynthetic capacity reached a threshold value of 12 micromol m(-2) s(-1) was better correlated with spring and annual flux integrals than were either deciduous or coniferous bud burst dates. For all phenological indicators, earlier spring onset consistently, but not always significantly, resulted in higher gross primary productivity (GPP) and ecosystem respiration (RE) for both seasonal (spring months, April-June) and annual flux integrals. The increase in RE was less than that in GPP; depending on the phenological indicator used, a one-day advance in spring onset increased springtime net ecosystem productivity (NEP) by 2-4 g C m(-2) day(-1). In general, we could not detect significant differences between the two forest types in response to earlier spring, although the response to earlier spring was generally more pronounced for Harvard Forest than for Howland Forest, suggesting that future climate warming may favor deciduous species over coniferous species, at least in this region. The effect of earlier spring tended to be about twice as large when annual rather than springtime flux integrals were considered. This result is suggestive of both immediate and lagged effects of earlier spring onset on ecosystem C cycling, perhaps as a result of accelerated N cycling rates and cascading effects on N uptake, foliar N concentrations and photosynthetic capacity.

The Weyl curvature tensor, Cotton-York tensor and gravitational waves: A covariant consideration

NASA Astrophysics Data System (ADS)

Osano, Bob

1 + 3 covariant approach to cosmological perturbation theory often employs the electric part (Eab), the magnetic part (Hab) of the Weyl tensor or the shear tensor (σab) in a phenomenological description of gravitational waves. The Cotton-York tensor is rarely mentioned in connection with gravitational waves in this approach. This tensor acts as a source for the magnetic part of the Weyl tensor which should not be neglected in studies of gravitational waves in the 1 + 3 formalism. The tensor is only mentioned in connection with studies of “silent model” but even there the connection with gravitational waves is not exhaustively explored. In this study, we demonstrate that the Cotton-York tensor encodes contributions from both electric and magnetic parts of the Weyl tensor and in directly from the shear tensor. In our opinion, this makes the Cotton-York tensor arguably the natural choice for linear gravitational waves in the 1 + 3 covariant formalism. The tensor is cumbersome to work with but that should negate its usefulness. It is conceivable that the tensor would equally be useful in the metric approach, although we have not demonstrated this in this study. We contend that the use of only one of the Weyl tensor or the shear tensor, although phenomenologically correct, leads to loss of information. Such information is vital particularly when examining the contribution of gravitational waves to the anisotropy of an almost-Friedmann-Lamitre-Robertson-Walker (FLRW) universe. The recourse to this loss is the use Cotton-York tensor.

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

PubMed

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

2017-05-01

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

Geometric decomposition of the conformation tensor in viscoelastic turbulence

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Comparison of Estimated Areas Contributing Recharge to Selected Springs in North-Central Florida by Using Multiple Ground-Water Flow Models

USGS Publications Warehouse

Shoemaker, W. Barclay; O'Reilly, Andrew M.; Sepúlveda, Nicasio; Williams, Stanley A.; Motz, Louis H.; Sun, Qing

2004-01-01

Areas contributing recharge to springs are defined in this report as the land-surface area wherein water entering the ground-water system at the water table eventually discharges to a spring. These areas were delineated for Blue Spring, Silver Springs, Alexander Springs, and Silver Glen Springs in north-central Florida using four regional ground-water flow models and particle tracking. As expected, different models predicted different areas contributing recharge. In general, the differences were due to different hydrologic stresses, subsurface permeability properties, and boundary conditions that were used to calibrate each model, all of which are considered to be equally feasible because each model matched its respective calibration data reasonably well. To evaluate the agreement of the models and to summarize results, areas contributing recharge to springs from each model were combined into composite areas. During 1993-98, the composite areas contributing recharge to Blue Spring, Silver Springs, Alexander Springs, and Silver Glen Springs were about 130, 730, 110, and 120 square miles, respectively. The composite areas for all springs remained about the same when using projected 2020 ground-water withdrawals.

Generalized Grueneisen tensor from solid nonlinearity parameters

NASA Technical Reports Server (NTRS)

Cantrell, J. H., Jr.

1980-01-01

Anharmonic effects in solids are often described in terms of generalized Grueneisen parameters which measure the strain dependence of the lattice vibrational frequencies. The relationship between these parameters and the solid nonlinearity parameters measured directly in ultrasonic harmonic generation experiments is derived using an approach valid for normal-mode elastic wave propagation in any crystalline direction. The resulting generalized Grueneisen parameters are purely isentropic in contrast to the Brugger-Grueneisen parameters which are of a mixed thermodynamic state. Experimental data comparing the isentropic generalized Grueneisen parameters and the Brugger-Grueneisen parameters are presented.

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

PubMed Central

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

2013-01-01

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

Thermal field theory and generalized light front quantization

NASA Astrophysics Data System (ADS)

Weldon, H. Arthur

2003-04-01

The dependence of thermal field theory on the surface of quantization and on the velocity of the heat bath is investigated by working in general coordinates that are arbitrary linear combinations of the Minkowski coordinates. In the general coordinates the metric tensor gμν¯ is nondiagonal. The Kubo-Martin-Schwinger condition requires periodicity in thermal correlation functions when the temporal variable changes by an amount -i/(T(g00¯)). Light-front quantization fails since g00¯=0; however, various related quantizations are possible.

Resonant-state expansion for open optical systems: generalization to magnetic, chiral, and bi-anisotropic materials

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Weiss, T.

2018-05-01

The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue equation of the method remains the same, but the matrix elements of the perturbation now contain variations of the permittivity, permeability, and bi-anisotropy tensors. A general normalization of resonant states in terms of the electric and magnetic fields is presented.

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

PubMed

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

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

A complex fermionic tensor model in d dimensions

NASA Astrophysics Data System (ADS)

Prakash, Shiroman; Sinha, Ritam

2018-02-01

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

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

PubMed Central

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

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

PubMed

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

2013-01-01

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

A new formulation of the dispersion tensor in homogeneous porous media

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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.

Large number limit of multifield inflation

NASA Astrophysics Data System (ADS)

Guo, Zhong-Kai

2017-12-01

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

Rapidly rotating neutron stars with a massive scalar field—structure and universal relations

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

Doneva, Daniela D.; Yazadjiev, Stoytcho S., E-mail: daniela.doneva@uni-tuebingen.de, E-mail: yazad@phys.uni-sofia.bg

We construct rapidly rotating neutron star models in scalar-tensor theories with a massive scalar field. The fact that the scalar field has nonzero mass leads to very interesting results since the allowed range of values of the coupling parameters is significantly broadened. Deviations from pure general relativity can be very large for values of the parameters that are in agreement with the observations. We found that the rapid rotation can magnify the differences several times compared to the static case. The universal relations between the normalized moment of inertia and quadrupole moment are also investigated both for the slowly andmore » rapidly rotating cases. The results show that these relations are still EOS independent up to a large extend and the deviations from pure general relativity can be large. This places the massive scalar-tensor theories amongst the few alternative theories of gravity that can be tested via the universal I -Love- Q relations.« less

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

Spherically symmetric conformal gravity and ''gravitational bubbles''

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

Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru

2016-01-01

The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-timesmore » (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.« less

C%2B%2B tensor toolbox user manual.

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

Plantenga, Todd D.; Kolda, Tamara Gibson

2012-04-01

The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

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

2018-03-01

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

Similar Tensor Arrays - A Framework for Storage of Tensor Array Data

NASA Astrophysics Data System (ADS)

Brun, Anders; Martin-Fernandez, Marcos; Acar, Burak; Munoz-Moreno, Emma; Cammoun, Leila; Sigfridsson, Andreas; Sosa-Cabrera, Dario; Svensson, Björn; Herberthson, Magnus; Knutsson, Hans

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

Electromagnetic stress tensor for an amorphous metamaterial medium

NASA Astrophysics Data System (ADS)

Wang, Neng; Wang, Shubo; Ng, Jack

2018-03-01

We analytically and numerically investigated the internal optical forces exerted by an electromagnetic wave inside an amorphous metamaterial medium. We derived, by using the principle of virtual work, the Helmholtz stress tensor, which takes into account the electrostriction effect. Several examples of amorphous media are considered, and different electromagnetic stress tensors, such as the Einstein-Laub tensor and Minkowski tensor, are also compared. It is concluded that the Helmholtz stress tensor is the appropriate tensor for such systems.

Structural Inventory of Great Basin Geothermal Systems and Definition of Favorable Structural Settings

DOE Data Explorer

Faulds, James E.

2013-12-31

Over the course of the entire project, field visits were made to 117 geothermal systems in the Great Basin region. Major field excursions, incorporating visits to large groups of systems, were conducted in western Nevada, central Nevada, northwestern Nevada, northeastern Nevada, east‐central Nevada, eastern California, southern Oregon, and western Utah. For example, field excursions to the following areas included visits of multiple geothermal systems: - Northwestern Nevada: Baltazor Hot Spring, Blue Mountain, Bog Hot Spring, Dyke Hot Springs, Howard Hot Spring, MacFarlane Hot Spring, McGee Mountain, and Pinto Hot Springs in northwest Nevada. - North‐central to northeastern Nevada: Beowawe, Crescent Valley (Hot Springs Point), Dann Ranch (Hand‐me‐Down Hot Springs), Golconda, and Pumpernickel Valley (Tipton Hot Springs) in north‐central to northeast Nevada. - Eastern Nevada: Ash Springs, Chimney Hot Spring, Duckwater, Hiko Hot Spring, Hot Creek Butte, Iverson Spring, Moon River Hot Spring, Moorman Spring, Railroad Valley, and Williams Hot Spring in eastern Nevada. - Southwestern Nevada‐eastern California: Walley’s Hot Spring, Antelope Valley, Fales Hot Springs, Buckeye Hot Springs, Travertine Hot Springs, Teels Marsh, Rhodes Marsh, Columbus Marsh, Alum‐Silver Peak, Fish Lake Valley, Gabbs Valley, Wild Rose, Rawhide‐ Wedell Hot Springs, Alkali Hot Springs, and Baileys/Hicks/Burrell Hot Springs. - Southern Oregon: Alvord Hot Spring, Antelope Hot Spring‐Hart Mountain, Borax Lake, Crump Geyser, and Mickey Hot Spring in southern Oregon. - Western Utah: Newcastle, Veyo Hot Spring, Dixie Hot Spring, Thermo, Roosevelt, Cove Fort, Red Hill Hot Spring, Joseph Hot Spring, Hatton Hot Spring, and Abraham‐Baker Hot Springs. Structural controls of 426 geothermal systems were analyzed with literature research, air photos, google‐Earth imagery, and/or field reviews (Figures 1 and 2). Of the systems analyzed, we were able to determine the structural settings of more than 240 sites. However, we found that many “systems” consisted of little more than a warm or hot well in the central part of a basin. Such “systems” were difficult to evaluate in terms of structural setting in areas lacking in geophysical data. Developed database for structural catalogue in a master spreadsheet. Data components include structural setting, primary fault orientation, presence or absence of Quaternary faulting, reservoir lithology, geothermometry, presence or absence of recent magmatism, and distinguishing blind systems from those that have surface expressions. Reviewed site locations for all 426 geothermal systems– Confirmed and/or relocated spring and geothermal sites based on imagery, maps, and other information for master database. Many systems were mislocated in the original database. In addition, some systems that included several separate springs spread over large areas were divided into two or more distinct systems. Further, all hot wells were assigned names based on their location to facilitate subsequent analyses. We catalogued systems into the following eight major groups, based on the dominant pattern of faulting (Figure 1): - Major normal fault segments (i.e., near displacement maxima). - Fault bends. - Fault terminations or tips. - Step‐overs or relay ramps in normal faults. - Fault intersections. - Accommodation zones (i.e., belts of intermeshing oppositely dipping normal faults), - Displacement transfer zones whereby strike‐slip faults terminate in arrays of normal faults. - Transtensional pull‐aparts. These settings form a hierarchal pattern with respect to fault complexity. - Major normal faults and fault bends are the simplest. - Fault terminations are typically more complex than mid‐segments, as faults commonly break up into multiple strands or horsetail near their ends. - A fault intersection is generally more complex, as it generally contains both multiple fault strands and can include discrete di...

The hydrogeology of urbanization: The lost springs of Washington, D.C., late Tertiary and Quaternary sediments of D.C., and the Baltimore Long Term Ecological Research site (LTER): Chapter

USGS Publications Warehouse

Bhaskar, Aditi; Pavich, Milan J.; Sharp, John M.

2015-01-01

Urbanization is a major process now shaping the environment. This field trip looks at the hydrogeology of the general Washington, D.C., area and focuses on the city's lost springs. Until 150 years ago, springs and shallow dug wells were the main source of drinking water for residents of Washington, D.C. Celebrating the nation's bicentennial, Garnett P. Williams of the U.S. Geological Survey examined changes in water supply and water courses since 1776. He examined old newspaper files to determine the location of the city's springs. This field trip visits sites of some of these springs (few of which are now flowing), discusses the hydrologic impacts of urbanization and the general geological setting, and finishes with the Baltimore Long Term Ecological Research site at Dead Run and its findings. The field trip visits some familiar locations in the Washington, D.C., area, and gives insights into their often hidden hydrologic past and present.

Tensor Toolbox for MATLAB v. 3.0

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

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

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

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia

2018-02-01

Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

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.

Euclidean supersymmetric solutions with the self-dual Weyl tensor

NASA Astrophysics Data System (ADS)

Nozawa, Masato

2017-07-01

We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of N = 2 minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the Przanowski-Tod class with the self-dual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the Przanowski-Tod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another Przanowski-Tod form. This formalism enables us to show that the self-dual Reissner-Nordström-Taub-NUT-AdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the Przanowski-Tod space is conformal to each of the self-dual ambi-toric Kähler metrics. It turns out that three classes of solutions are all reduced to the self-dual Carter family, by virtue of the nondegenerate Killing-Yano tensor.

Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige

2017-10-01

There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here a method is developed to elucidate this fluctuating diffusivity from trajectory data. Time-averaged mean-square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized to a second-order tensor with which both magnitude and orientation fluctuations of the diffusivity can be clearly detected. This method is used to analyze the center-of-mass motion of four fundamental polymer models: the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer. It is found that these models exhibit distinctly different types of magnitude and orientation fluctuations of diffusivity. This is an advantage of the present method over previous ones, such as the ergodicity-breaking parameter and a non-Gaussian parameter, because with either of these parameters it is difficult to distinguish the dynamics of the four polymer models. Also, the present method of a time-averaged MSD tensor could be used to analyze trajectory data obtained in SPT experiments.

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

NASA Astrophysics Data System (ADS)

Ni, Luqun; Markenscoff, Xanthippi

2016-11-01

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

Tensor discriminant color space for face recognition.

PubMed

Wang, Su-Jing; Yang, Jian; Zhang, Na; Zhou, Chun-Guang

2011-09-01

Recent research efforts reveal that color may provide useful information for face recognition. For different visual tasks, the choice of a color space is generally different. How can a color space be sought for the specific face recognition problem? To address this problem, this paper represents a color image as a third-order tensor and presents the tensor discriminant color space (TDCS) model. The model can keep the underlying spatial structure of color images. With the definition of n-mode between-class scatter matrices and within-class scatter matrices, TDCS constructs an iterative procedure to obtain one color space transformation matrix and two discriminant projection matrices by maximizing the ratio of these two scatter matrices. The experiments are conducted on two color face databases, AR and Georgia Tech face databases, and the results show that both the performance and the efficiency of the proposed method are better than those of the state-of-the-art color image discriminant model, which involve one color space transformation matrix and one discriminant projection matrix, specifically in a complicated face database with various pose variations.

Non-lambertian reflectance modeling and shape recovery of faces using tensor splines.

PubMed

Kumar, Ritwik; Barmpoutis, Angelos; Banerjee, Arunava; Vemuri, Baba C

2011-03-01

Modeling illumination effects and pose variations of a face is of fundamental importance in the field of facial image analysis. Most of the conventional techniques that simultaneously address both of these problems work with the Lambertian assumption and thus fall short of accurately capturing the complex intensity variation that the facial images exhibit or recovering their 3D shape in the presence of specularities and cast shadows. In this paper, we present a novel Tensor-Spline-based framework for facial image analysis. We show that, using this framework, the facial apparent BRDF field can be accurately estimated while seamlessly accounting for cast shadows and specularities. Further, using local neighborhood information, the same framework can be exploited to recover the 3D shape of the face (to handle pose variation). We quantitatively validate the accuracy of the Tensor Spline model using a more general model based on the mixture of single-lobed spherical functions. We demonstrate the effectiveness of our technique by presenting extensive experimental results for face relighting, 3D shape recovery, and face recognition using the Extended Yale B and CMU PIE benchmark data sets.

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)

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

Stealth configurations in vector-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Chagoya, Javier; Tasinato, Gianmassimo

2018-01-01

Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.

Experimental and Analytical Determination of the Motion of Hydraulically Operated Valve Stems in Oil Engine Injection Systems

NASA Technical Reports Server (NTRS)

Gelalles, A G; Rothrock, A M

1930-01-01

This research on the pressure variations in the injection system of the N.A.C.A. Spray Photography Equipment and on the effects of these variations on the motion of the timing valve stem was undertaken in connection with the study of fuel injection systems for high-speed oil engines. The methods of analysis of the pressure variations and the general equation for the motion of the spring-loaded stem for the timing valve are applicable to a spring-loaded automatic injection valve, and in general to all hydraulically operated valves. A sample calculation for a spring-loaded automatic injection valve is included.

Diffusion Tensor Image Registration Using Hybrid Connectivity and Tensor Features

PubMed Central

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

2014-01-01

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

Spring break trips as a risk factor for heavy alcohol use among first-year college students.

PubMed

Lee, Christine M; Maggs, Jennifer L; Rankin, Lela A

2006-11-01

Many high school and college students are believed to use spring break vacation to travel to destinations with the intent of engaging in extreme party behaviors, including excessive alcohol use. However, the extent to which spring break travelers' behaviors are more risky than their typical behaviors remains unclear. To assess the impact of spring break as a situational risk factor, we analyzed data collected from 176 first-year college students across 10 weeks using weekly telephone interviews. Using multilevel modeling, we found the following: (1) men, participants in fraternity/sorority organizations, students traveling on spring break trips, and those with higher fun-social alcohol expectancies drank more during the regular semester; (2) alcohol use did not increase during spring break week in general; however, (3) spring break travelers increased their alcohol use during spring break. Spring break trips are a risk factor for escalated alcohol use both during the academic semester and during spring break trips, suggesting that some students may seek out opportunities for excessive alcohol use. Results are discussed in terms of niche selection and prevention implications.

14. Historic American Buildings Survey E. W. Russell, Photographer, May ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

14. Historic American Buildings Survey E. W. Russell, Photographer, May 8, 1936 GENERAL VIEW OF S. ELEVATION (REAR) FROM 3rd STORY REAR PORCH - Spring Hill College, Main Building, Old Shell Road, Spring Hill, Mobile County, AL

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.

Comparison of quality control software tools for diffusion tensor imaging.

PubMed

Liu, Bilan; Zhu, Tong; Zhong, Jianhui

2015-04-01

Image quality of diffusion tensor imaging (DTI) is critical for image interpretation, diagnostic accuracy and efficiency. However, DTI is susceptible to numerous detrimental artifacts that may impair the reliability and validity of the obtained data. Although many quality control (QC) software tools are being developed and are widely used and each has its different tradeoffs, there is still no general agreement on an image quality control routine for DTIs, and the practical impact of these tradeoffs is not well studied. An objective comparison that identifies the pros and cons of each of the QC tools will be helpful for the users to make the best choice among tools for specific DTI applications. This study aims to quantitatively compare the effectiveness of three popular QC tools including DTI studio (Johns Hopkins University), DTIprep (University of North Carolina at Chapel Hill, University of Iowa and University of Utah) and TORTOISE (National Institute of Health). Both synthetic and in vivo human brain data were used to quantify adverse effects of major DTI artifacts to tensor calculation as well as the effectiveness of different QC tools in identifying and correcting these artifacts. The technical basis of each tool was discussed, and the ways in which particular techniques affect the output of each of the tools were analyzed. The different functions and I/O formats that three QC tools provide for building a general DTI processing pipeline and integration with other popular image processing tools were also discussed. Copyright © 2015 Elsevier Inc. All rights reserved.

Inoculum Potential of Fusarium spp. Relates to Tillage and Straw Management in Norwegian Fields of Spring Oats

PubMed Central

Hofgaard, Ingerd S.; Seehusen, Till; Aamot, Heidi U.; Riley, Hugh; Razzaghian, Jafar; Le, Vinh H.; Hjelkrem, Anne-Grete R.; Dill-Macky, Ruth; Brodal, Guro

2016-01-01

The increased occurrence of Fusarium-mycotoxins in Norwegian cereals over the last decade, is thought to be caused by increased inoculum resulting from more cereal residues at the soil surface as a result of reduced tillage practices. In addition, weather conditions have increasingly promoted inoculum development and infection by Fusarium species. The objective of this work was to elucidate the influence of different tillage regimes (autumn plowing; autumn harrowing; spring plowing; spring harrowing) on the inoculum potential (IP) and dispersal of Fusarium spp. in spring oats. Tillage trials were conducted at two different locations in southeast Norway from 2010 to 2012. Oat residues from the previous year’s crop were collected within a week after sowing for evaluation. IP was calculated as the percentage of residues infested with Fusarium spp. multiplied by the proportion of the soil surface covered with residues. Fusarium avenaceum and F. graminearum were the most common Fusarium species recovered from oat residues. The IP of Fusarium spp. was significantly lower in plowed plots compared to those that were harrowed. Plowing in either the autumn or spring resulted in a low IP. Harrowing in autumn was more effective in reducing IP than the spring harrowing, and IP levels for the spring harrowed treatments were generally higher than all other tillage treatments examined. Surprisingly low levels of F. langsethiae were detected in the residues, although this species is a common pathogen of oat in Norway. The percentage of the residues infested with F. avenaceum, F. graminearum, F. culmorum, and F. langsethiae generally related to the quantity of DNA of the respective Fusarium species determined using quantitative PCR (qPCR). Fusarium dispersal, quantified by qPCR analysis of spore trap samples collected at and after heading, generally corresponded to the IP. Fusarium dispersal was also observed to increase after rainy periods. Our findings are in line with the general understanding that plowing is a means to reduce the IP of Fusarium spp. in cereal fields. The main inoculum source for F. langsethiae remains unclear. Our results will be useful in the development of forecasting tools to calculate the risk of Fusarium in cereals. PMID:27148236

Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity

NASA Astrophysics Data System (ADS)

Veraguth, Olivier J.; Wang, Charles H.-T.

2017-10-01

Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field setting the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arbitrary group parameter that requires no further fixing as its present standard form does. Here, we find that this can be naturally realized via conformal frame transformations in scalar-tensor gravity. Such a theory generally incorporates a dynamical scalar gravitational field and reduces to general relativity when the scalar field becomes a pure gauge. In particular, we introduce a conformal Einstein frame in which loop quantization is implemented. We then discuss how different Immirzi parameters under this description may be related by conformal frame transformations and yet share the same quantization having, for example, the same area gaps, modulated by the scalar gravitational field.

Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves

NASA Astrophysics Data System (ADS)

Al Roumi, Fosca; Buchert, Thomas; Wiegand, Alexander

2017-12-01

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of Lagrangian-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the Lagrangian perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to Eulerian background coordinates with truncation of nonlinear terms.

Vainshtein screening in scalar-tensor theories before and after GW170817: Constraints on theories beyond Horndeski

NASA Astrophysics Data System (ADS)

Dima, Alexandru; Vernizzi, Filippo

2018-05-01

Screening mechanisms are essential features of dark energy models mediating a fifth force on large scales. We study the regime of strong scalar field nonlinearities, known as Vainshtein screening, in the most general scalar-tensor theories propagating a single scalar degree of freedom. We first develop an effective approach to parametrize cosmological perturbations beyond linear order for these theories. In the quasistatic limit, the fully nonlinear effective Lagrangian contains six independent terms, one of which starts at cubic order in perturbations. We compute the two gravitational potentials around a spherical body. Outside and near the body, screening reproduces standard gravity, with a modified gravitational coupling. Inside the body, the two potentials are different and depend on the density profile, signalling the breaking of the Vainshtein screening. We provide the most general expressions for these modifications, revising and extending previous results. We apply our findings to show that the combination of the GW170817 event, the Hulse-Taylor pulsar and stellar structure physics, constrain the parameters of these general theories at the level of 10-1, and of Gleyzes-Langlois-Piazza-Vernizzi theories at the level of 10-2.

Generalizations of the classical Yang-Baxter equation and O-operators

NASA Astrophysics Data System (ADS)

Bai, Chengming; Guo, Li; Ni, Xiang

2011-06-01

Tensor solutions (r-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the R-matrix solution of the quantum Yang-Baxter equation, is an important structure appearing in different areas such as integrable systems, symplectic geometry, quantum groups, and quantum field theory. Further study of CYBE led to its interpretation as certain operators, giving rise to the concept of {O}-operators. The O-operators were in turn interpreted as tensor solutions of CYBE by enlarging the Lie algebra [Bai, C., "A unified algebraic approach to the classical Yang-Baxter equation," J. Phys. A: Math. Theor. 40, 11073 (2007)], 10.1088/1751-8113/40/36/007. The purpose of this paper is to extend this study to a more general class of operators that were recently introduced [Bai, C., Guo, L., and Ni, X., "Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras," Commun. Math. Phys. 297, 553 (2010)], 10.1007/s00220-010-0998-7 in the study of Lax pairs in integrable systems. Relations between O-operators, relative differential operators, and Rota-Baxter operators are also discussed.

Preliminary geochemical assessment of water in selected streams, springs, and caves in the Upper Baker and Snake Creek drainages in Great Basin National Park, Nevada, 2009

USGS Publications Warehouse

Paul, Angela P.; Thodal, Carl E.; Baker, Gretchen M.; Lico, Michael S.; Prudic, David E.

2014-01-01

Water in caves, discharging from springs, and flowing in streams in the upper Baker and Snake Creek drainages are important natural resources in Great Basin National Park, Nevada. Water and rock samples were collected from 15 sites during February 2009 as part of a series of investigations evaluating the potential for water resource depletion in the park resulting from the current and proposed groundwater withdrawals. This report summarizes general geochemical characteristics of water samples collected from the upper Baker and Snake Creek drainages for eventual use in evaluating possible hydrologic connections between the streams and selected caves and springs discharging in limestone terrain within each watershed.Generally, water discharging from selected springs in the upper Baker and Snake Creek watersheds is relatively young and, in some cases, has similar chemical characteristics to water collected from associated streams. In the upper Baker Creek drainage, geochemical data suggest possible hydrologic connections between Baker Creek and selected springs and caves along it. The analytical results for water samples collected from Wheelers Deep and Model Caves show characteristics similar to those from Baker Creek, suggesting a hydrologic connection between the creek and caves, a finding previously documented by other researchers. Generally, geochemical evidence does not support a connection between water flowing in Pole Canyon Creek to that in Model Cave, at least not to any appreciable extent. The water sample collected from Rosethorn Spring had relatively high concentrations of many of the constituents sampled as part of this study. This finding was expected as the water from the spring travelled through alluvium prior to being discharged at the surface and, as a result, was provided the opportunity to interact with soil minerals with which it came into contact. Isotopic evidence does not preclude a connection between Baker Creek and the water discharging from Rosethorn Spring. The residence time of water discharging into the caves and from selected springs sampled as part of this study ranged from 10 to 25 years.Within the upper Snake Creek drainage, the results of this study show geochemical similarities between Snake Creek and Outhouse Spring, Spring Creek Spring, and Squirrel Spring Cave. The strontium isotope ratio (87Sr/86Sr) for intrusive rock samples representative of the Snake Creek drainage were similar to carbonate rock samples. The water sample collected from Snake Creek at the pipeline discharge point had lower strontium concentrations than the sample downstream and a similar 87Sr/86Sr value as the carbonate and intrusive rocks. The chemistry of the water sample was considered representative of upstream conditions in Snake Creek and indicates minimal influence of rock dissolution. The results of this study suggest that water discharging from Outlet Spring is not hydrologically connected to Snake Creek but rather is recharged at high altitude(s) within the Snake Creek drainage. These findings for Outlet Spring largely stem from the relatively high specific conductance and chloride concentration, the lightest deuterium (δD) and oxygen-18 (δ18O) values, and the longest calculated residence time (60 to 90 years) relative to any other sample collected as part of this study. With the exception of water sampled from Outlet Spring, the residence time of water discharging into Squirrel Spring Cave and selected springs in the upper Snake Creek drainage was less than 30 years.

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)

Gomes, C.; Bertolami, O.; Rosa, J.G., E-mail: claudio.gomes@fc.up.pt, E-mail: joao.rosa@ua.pt, E-mail: orfeu.bertolami@fc.up.pt

We study inflationary scenarios driven by a scalar field in the presence of a non-minimal coupling between matter and curvature. We show that the Friedmann equation can be significantly modified when the energy density during inflation exceeds a critical value determined by the non-minimal coupling, which in turn may considerably modify the spectrum of primordial perturbations and the inflationary dynamics. In particular, we show that these models are characterised by a consistency relation between the tensor-to-scalar ratio and the tensor spectral index that can differ significantly from the predictions of general relativity. We also give examples of observational predictions formore » some of the most commonly considered potentials and use the results of the Planck collaboration to set limits on the scale of the non-minimal coupling.« less

Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame

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

Fujita, Tomohiro; Gao, Xian; Yokoyama, Jun'ichi, E-mail: tomofuji@stanford.edu, E-mail: gao@th.phys.titech.ac.jp, E-mail: yokoyama@resceu.s.u-tokyo.ac.jp

We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is preserved under the disformal transformation. We also evaluate the primordial spectra for both the gravitational waves and the curvature perturbation, which are invariant under the disformal transformation. Due to the existence of higher spatial derivatives, the quadratic Lagrangian for the tensor modes itself cannot be transformed to the form in the Einstein frame. Nevertheless, there exists a one-parameter family of frames in which themore » spectrum of the gravitational waves takes the standard form in the Einstein frame.« less

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

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

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

2014-10-15

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

Separation of variables in Maxwell equations in Plebański-Demiański spacetime

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Logamediate Inflation in f(T) Teleparallel Gravity

NASA Astrophysics Data System (ADS)

Rezazadeh, Kazem; Abdolmaleki, Asrin; Karami, Kayoomars

2017-02-01

We study logamediate inflation in the context of f(T) teleparallel gravity. f(T)-gravity is a generalization of the teleparallel gravity which is formulated on the Weitzenbock spacetime, characterized by the vanishing curvature tensor (absolute parallelism) and the non-vanishing torsion tensor. We consider an f(T)-gravity model which is sourced by a canonical scalar field. Assuming a power-law f(T) function in the action, we investigate an inflationary universe with a logamediate scale factor. Our results show that, although logamediate inflation is completely ruled out by observational data in the standard inflationary scenario based on Einstein gravity, it can be compatible with the 68% confidence limit joint region of Planck 2015 TT,TE,EE+lowP data in the framework of f(T)-gravity.

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

Rezazadeh, Kazem; Karami, Kayoomars; Abdolmaleki, Asrin, E-mail: rezazadeh86@gmail.com

We study logamediate inflation in the context of f ( T ) teleparallel gravity. f ( T )-gravity is a generalization of the teleparallel gravity which is formulated on the Weitzenbock spacetime, characterized by the vanishing curvature tensor (absolute parallelism) and the non-vanishing torsion tensor. We consider an f ( T )-gravity model which is sourced by a canonical scalar field. Assuming a power-law f ( T ) function in the action, we investigate an inflationary universe with a logamediate scale factor. Our results show that, although logamediate inflation is completely ruled out by observational data in the standard inflationarymore » scenario based on Einstein gravity, it can be compatible with the 68% confidence limit joint region of Planck 2015 TT,TE,EE+lowP data in the framework of f ( T )-gravity.« less

Chaplygin gas inspired scalar fields inflation via well-known potentials

NASA Astrophysics Data System (ADS)

Jawad, Abdul; Butt, Sadaf; Rani, Shamaila

2016-08-01

Brane inflationary universe models in the context of modified Chaplygin gas and generalized cosmic Chaplygin gas are being studied. We develop these models in view of standard scalar and tachyon fields. In both models, the implemented inflationary parameters such as scalar and tensor power spectra, scalar spectral index and tensor to scalar ratio are derived under slow roll approximations. We also use chaotic and exponential potential in high energy limits and discuss the characteristics of inflationary parameters for both potentials. These models are compatible with recent astronomical observations provided by WMAP7{+}9 and Planck data, i.e., ηs=1.027±0.051, 1.009±0.049, 0.096±0.025 and r<0.38, 0.36, 0.11.

Geometric algebra description of polarization mode dispersion, polarization-dependent loss, and Stokes tensor transformations.

PubMed

Soliman, George; Yevick, David; Jessop, Paul

2014-09-01

This paper demonstrates that numerous calculations involving polarization transformations can be condensed by employing suitable geometric algebra formalism. For example, to describe polarization mode dispersion and polarization-dependent loss, both the material birefringence and differential loss enter as bivectors and can be combined into a single symmetric quantity. Their frequency and distance evolution, as well as that of the Stokes vector through an optical system, can then each be expressed as a single compact expression, in contrast to the corresponding Mueller matrix formulations. The intrinsic advantage of the geometric algebra framework is further demonstrated by presenting a simplified derivation of generalized Stokes parameters that include the electric field phase. This procedure simultaneously establishes the tensor transformation properties of these parameters.

17. Historic American Buildings Survey E. W. Russell, Photographer, May ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

17. Historic American Buildings Survey E. W. Russell, Photographer, May 7, 1936 GENERAL VIEW OF PORTICO (OR ARCADE) LOOKING WEST, 1st FLOOR OF ADMINISTRATION BUILDING - Spring Hill College, Main Building, Old Shell Road, Spring Hill, Mobile County, AL

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.