Two formalisms, one renormalized stress-energy tensor

NASA Astrophysics Data System (ADS)

Barceló, C.; Carballo, R.; Garay, L. J.

2012-04-01

We explicitly compare the structure of the renormalized stress-energy tensor of a massless scalar field in a (1+1) curved spacetime as obtained by two different strategies: normal-mode construction of the field operator and one-loop effective action. We pay special attention to where and how the information related to the choice of vacuum state in both formalisms is encoded. By establishing a clear translation map between both procedures, we show that these two potentially different renormalized stress-energy tensors are actually equal, when using vacuum-state choices related by this map. One specific aim of the analysis is to facilitate the comparison of results regarding semiclassical effects in gravitational collapse as obtained within these different formalisms.

One-loop gravitational wave spectrum in de Sitter spacetime

NASA Astrophysics Data System (ADS)

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

2012-08-01

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

Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances

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

Kampf, Karol; Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, 18000 Prague; Novotny, Jiri

2010-06-01

We study in detail various aspects of the renormalization of the spin-1 resonance propagator in the effective field theory framework. First, we briefly review the formalisms for the description of spin-1 resonances in the path integral formulation with the stress on the issue of propagating degrees of freedom. Then we calculate the one-loop 1{sup --} meson self-energy within the resonance chiral theory in the chiral limit using different methods for the description of spin-1 particles, namely, the Proca field, antisymmetric tensor field, and the first-order formalisms. We discuss in detail technical aspects of the renormalization procedure which are inherent tomore » the power-counting nonrenormalizable theory and give a formal prescription for the organization of both the counterterms and one-particle irreducible graphs. We also construct the corresponding propagators and investigate their properties. We show that the additional poles corresponding to the additional one-particle states are generated by loop corrections, some of which are negative norm ghosts or tachyons. We count the number of such additional poles and briefly discuss their physical meaning.« less

One-loop effective actions and higher spins. Part II

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Displacement Fields and Self-Energies of Circular and Polygonal Dislocation Loops in Homogeneous and Layered Anisotropic Solids

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

Gao, Yanfei; Larson, Ben C.

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order -1, we have shown thatmore » the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.« less

Displacement Fields and Self-Energies of Circular and Polygonal Dislocation Loops in Homogeneous and Layered Anisotropic Solids

DOE PAGES

Gao, Yanfei; Larson, Ben C.

2015-06-19

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order -1, we have shown thatmore » the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.« less

Cosmological footprints of loop quantum gravity.

PubMed

Grain, J; Barrau, A

2009-02-27

The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated corrections should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.

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

Ahuatzin, G.; Bautista, I.; Hernandez-Lopez, J. A.

A constant antisymmetric 2-tensor can arise in general relativity with spontaneous symmetry breaking or in field theories formulated in a noncommutative space-time. In this work, the one-loop contribution of a nonstandard WW{gamma} vertex on the flavor violating quark transition q{sub i}{yields}q{sub j}{gamma} is studied in the context of the electroweak Yang-Mills sector extended with a Lorentz-violating constant 2-tensor. An exact analytical expression for the on-shell case is presented. It is found that the loop amplitude is gauge independent, electromagnetic gauge invariant, and free of ultraviolet divergences. The dipolar contribution to the b{yields}s{gamma} transition together with the experimental data on themore » B{yields}X{sub s{gamma}} decay is used to derive the constraint {Lambda}{sub LV}>1.96 TeV on the Lorentz-violating scale.« less

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.

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

Cosmological singularities and bounce in Cartan-Einstein theory

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

Lucat, Stefano; Prokopec, Tomislav, E-mail: s.lucat@students.uu.nl, E-mail: t.prokopec@uu.nl

We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh ( in-in ) formalism. We then apply the renormalized theory to study the dynamics of a collapsing universe that begins inmore » a thermal state and find that—instead of a big crunch singularity—the Universe with torsion undergoes a bounce . We solve the dynamical equations (a) classically (without particle production); (b) including the production of fermions in a fixed background in the Hartree-Fock approximation and (c) including the quantum backreaction of fermions onto the background space-time. In the first and last cases the Universe undergoes a bounce. The production of fermions due to the coupling to a contracting homogeneous background speeds up the bounce, implying that the quantum contributions from fermions is negative, presumably because fermion production contributes negatively to the energy-momentum tensor. When compared with former works on the subject, our treatment is fully microscopic (namely, we treat fermions by solving the corresponding Dirac equations) and quantum (in the sense that we include fermionic loop contributions).« less

Cosmological singularities and bounce in Cartan-Einstein theory

NASA Astrophysics Data System (ADS)

Lucat, Stefano; Prokopec, Tomislav

2017-10-01

We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh (in-in) formalism. We then apply the renormalized theory to study the dynamics of a collapsing universe that begins in a thermal state and find that—instead of a big crunch singularity—the Universe with torsion undergoes a bounce. We solve the dynamical equations (a) classically (without particle production); (b) including the production of fermions in a fixed background in the Hartree-Fock approximation and (c) including the quantum backreaction of fermions onto the background space-time. In the first and last cases the Universe undergoes a bounce. The production of fermions due to the coupling to a contracting homogeneous background speeds up the bounce, implying that the quantum contributions from fermions is negative, presumably because fermion production contributes negatively to the energy-momentum tensor. When compared with former works on the subject, our treatment is fully microscopic (namely, we treat fermions by solving the corresponding Dirac equations) and quantum (in the sense that we include fermionic loop contributions).

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.

Neutrino mass implications for muon decay parameters

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

Erwin, Rebecca J.; Kile, Jennifer; Ramsey-Musolf, Michael J.

2007-02-01

We use the scale of neutrino mass and naturalness considerations to obtain model-independent expectations for the magnitude of possible contributions to muon decay Michel parameters from new physics above the electroweak symmetry-breaking scale. Focusing on Dirac neutrinos, we obtain a complete basis of dimension four and dimension six effective operators that are invariant under the gauge symmetry of the standard model and that contribute to both muon decay and neutrino mass. We show that - in the absence of fine tuning - the most stringent neutrino-mass naturalness bounds on chirality-changing vector operators relevant to muon decay arise from one-loop operatormore » mixing. The bounds we obtain on their contributions to the Michel parameters are 2 orders of magnitude stronger than bounds previously obtained in the literature. In addition, we analyze the implications of one-loop matching considerations and find that the expectations for the size of various scalar and tensor contributions to the Michel parameters are considerably smaller than derived from previous estimates of two-loop operator mixing. We also show, however, that there exist gauge-invariant operators that generate scalar and tensor contributions to muon decay but whose flavor structure allows them to evade neutrino-mass naturalness bounds. We discuss the implications of our analysis for the interpretation of muon-decay experiments.« less

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

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

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

Nonperturbative study of the four gluon vertex

NASA Astrophysics Data System (ADS)

Binosi, D.; Ibañez, D.; Papavassiliou, J.

2014-09-01

In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where "one-loop" diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale p is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all one-particle reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.

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

NASA Astrophysics Data System (ADS)

Garfinkle, David; Glass, E. N.

2013-03-01

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

SANC: the process γγ → ΖΖ

NASA Astrophysics Data System (ADS)

Bardin, D.; Bondarenko, S.; Christova, P.; Kalinovskaya, L.; von Schlippe, W.; Uglov, E.

2017-11-01

The implementation of the process γγ → ΖΖ at the one-loop level within SANC system multichannel approach is considered. The derived one-loop scalar form factors can be used for any cross channel after an appropriate permutation of their arguments-Mandelstam variables s, t, u. To check of the correctness of the results we observe the independence of the scalar form factors on the gauge parameters and the validity of Ward identity (external photon transversality). We present the complete analytical results for the covariant and tensor structures and helicity amplitudes for this process. We make an extensive comparison of our analytical and numerical results with those existing in the literature.

Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals

NASA Astrophysics Data System (ADS)

Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.

2018-04-01

We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

Tensor Spectral Clustering for Partitioning Higher-order Network Structures.

PubMed

Benson, Austin R; Gleich, David F; Leskovec, Jure

2015-01-01

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.

Tensor Spectral Clustering for Partitioning Higher-order Network Structures

PubMed Central

Benson, Austin R.; Gleich, David F.; Leskovec, Jure

2016-01-01

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms. PMID:27812399

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

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.

One-loop effects of a heavy Higgs boson: A functional approach

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

Dittmaier, S.; Grosse-Knetter, C.

1995-11-01

We integrate out the Higgs boson in the electroweak standard model at one loop, assuming that it is very heavy. We construct a low-energy effective Lagrangian, which parametrizes the one-loop effect of the heavy Higgs boson at {O}({ital M}{sup O}{sup -}{sub {ital H}}). Instead of applying conventional diagrammatical techniques, we integrate out the Higgs boson directly in the path integral. {copyright} 1995 American Institute of Physics

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.

Gluon and Wilson loop TMDs for hadrons of spin ≤ 1

NASA Astrophysics Data System (ADS)

Boer, Daniël; Cotogno, Sabrina; van Daal, Tom; Mulders, Piet J.; Signori, Andrea; Zhou, Ya-Jin

2016-10-01

In this paper we consider the parametrizations of gluon transverse momentum dependent (TMD) correlators in terms of TMD parton distribution functions (PDFs). These functions, referred to as TMDs, are defined as the Fourier transforms of hadronic matrix elements of nonlocal combinations of gluon fields. The nonlocality is bridged by gauge links, which have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. For gluons, the specific correlator with one future and one past pointing gauge link is, in the limit of small x, related to a correlator of a single Wilson loop. We present the parametrization of Wilson loop correlators in terms of Wilson loop TMDs and discuss the relation between these functions and the small- x `dipole' gluon TMDs. This analysis shows which gluon TMDs are leading or suppressed in the small- x limit. We discuss hadronic targets that are unpolarized, vector polarized (relevant for spin-1 /2 and spin-1 hadrons), and tensor polarized (relevant for spin-1 hadrons). The latter are of interest for studies with a future Electron-Ion Collider with polarized deuterons.

Landau singularities and symbology: One- and two-loop MHV amplitudes in SYM theory

DOE PAGES

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia

2016-03-14

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N = 4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. Finally, we observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

Reducing full one-loop amplitudes to scalar integrals at the integrand level

NASA Astrophysics Data System (ADS)

Ossola, Giovanni; Papadopoulos, Costas G.; Pittau, Roberto

2007-02-01

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation.

Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams

NASA Astrophysics Data System (ADS)

Karbstein, Felix; Mosman, Elena A.

2017-12-01

In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Loop corrections to primordial fluctuations from inflationary phase transitions

NASA Astrophysics Data System (ADS)

Wu, Yi-Peng; Yokoyama, Jun'ichi

2018-05-01

We investigate loop corrections to the primordial fluctuations in the single-field inflationary paradigm from spectator fields that experience a smooth transition of their vacuum expectation values. We show that when the phase transition involves a classical evolution effectively driven by a negative mass term from the potential, important corrections to the curvature perturbation can be generated by field perturbations that are frozen outside the horizon by the time of the phase transition, yet the correction to tensor perturbation is naturally suppressed by the spatial derivative couplings between spectator fields and graviton. At one-loop level, the dominant channel for the production of primordial fluctuations comes from a pair-scattering of free spectator fields that decay into the curvature perturbations, and this decay process is only sensitive to field masses comparable to the Hubble scale of inflation.

Perturbative quantum gravity as a double copy of gauge theory.

PubMed

Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

2010-08-06

In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

Fusion of Positive Energy Representations of LSpin(2n)

NASA Astrophysics Data System (ADS)

Toledano-Laredo, V.

2004-09-01

Building upon the Jones-Wassermann program of studying Conformal Field Theory using operator algebraic tools, and the work of A. Wassermann on the loop group of LSU(n) (Invent. Math. 133 (1998), 467-538), we give a solution to the problem of fusion for the loop group of Spin(2n). Our approach relies on the use of A. Connes' tensor product of bimodules over a von Neumann algebra to define a multiplicative operation (Connes fusion) on the (integrable) positive energy representations of a given level. The notion of bimodules arises by restricting these representations to loops with support contained in an interval I of the circle or its complement. We study the corresponding Grothendieck ring and show that fusion with the vector representation is given by the Verlinde rules. The computation rests on 1) the solution of a 6-parameter family of Knizhnik-Zamolodchikhov equations and the determination of its monodromy, 2) the explicit construction of the primary fields of the theory, which allows to prove that they define operator-valued distributions and 3) the algebraic theory of superselection sectors developed by Doplicher-Haag-Roberts.

One-loop pseudo-Goldstone masses in the minimal S O (10 ) Higgs model

NASA Astrophysics Data System (ADS)

Gráf, Lukáš; Malinský, Michal; Mede, Timon; Susič, Vasja

2017-04-01

We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal renormalizable nonsupersymmetric S O (10 ) Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic 45 ⊕126 variant in which the rank is reduced by a vacuum expectation value of the 5-index antisymmetric self-dual tensor, we provide a thorough analysis of the corresponding Coleman-Weinberg one-loop effective potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons transforming as (1, 3, 0) and (8, 1, 0) under the standard model (SM) gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree level. The effective potential tedium is compared to that encountered in the previously studied 45 ⊕16 S O (10 ) Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.

Rational first integrals of geodesic equations and generalised hidden symmetries

NASA Astrophysics Data System (ADS)

Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro

2016-10-01

We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson-O’Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four-dimensions, by using the Maciejewski-Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing-Yano tensors.

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.

Contribution of the polarization moments of different rank to the integral CPT signal

NASA Astrophysics Data System (ADS)

Taskova, E.; Alipieva, E.; Todorov, G.

2016-01-01

In the present work we investigate the relation of the polarization moments having different ranks with the tensor components which form the observable integral CPT signal, in the presence of a stray magnetic field. A numerical experiment with parameters close to the real ones is performed, using a program based on the irreducible tensor operator formalism1. The integral fluorescent signal is calculated for the non-polarized fluorescence at different laser power excitation. Detailed analysis of the numerical solutions for all tensor components which describe population and alignment allows visualizing the dynamics of their behavior in dependence on the experimental geometry and laboratory magnetic field B'. The dependence of population f00, longitudinal f02 and transverse f22 alignment in the presence of transverse magnetic field is investigated. The shape and sign of the resonance change with laser power.

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.

Bloch-Nordsieck thermometers: one-loop exponentiation in finite temperature QED

NASA Astrophysics Data System (ADS)

Gupta, Sourendu; Indumathi, D.; Mathews, Prakash; Ravindran, V.

1996-02-01

We study the scattering of hard external particles in a heat bath in a real-time formalism for finite temperature QED. We investigate the distribution of the 4-momentum difference of initial and final hard particles in a fully covariant manner when the scale of the process, Q, is much larger than the temperature, T. Our computations are valid for all T subject to this constraint. We exponentiate the leading infra-red term at one-loop order through a resummation of soft (thermal) photon emissions and absorptions. For T > 0, we find that tensor structures arise which are not present at T = 0. These cant' thermal signatures. As a result, external particles can serve as thermometers introduced into the heat bath. We investigate the phase space origin of log( Q/ m) and log ( Q/ T) teens.

Extending the Universal One-Loop Effective Action: heavy-light coefficients

DOE PAGES

Ellis, Sebastian A. R.; Quevillon, Jérémie; You, Tevong; ...

2017-08-16

The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can also be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recently-developed covariant diagram technique to extend the UOLEAmore » to include heavy-light terms which retain the same universal structure as the previously-derived heavy-only terms. As an example of its application, we integrate out a heavy singlet scalar with a linear coupling to a light doublet Higgs. The extension presented here is a first step towards completing the UOLEA to incorporate all possible structures encountered in a covariant derivative expansion of the one-loop path integral.« less

Extending the Universal One-Loop Effective Action: heavy-light coefficients

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

Ellis, Sebastian A. R.; Quevillon, Jérémie; You, Tevong

The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can also be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recently-developed covariant diagram technique to extend the UOLEAmore » to include heavy-light terms which retain the same universal structure as the previously-derived heavy-only terms. As an example of its application, we integrate out a heavy singlet scalar with a linear coupling to a light doublet Higgs. The extension presented here is a first step towards completing the UOLEA to incorporate all possible structures encountered in a covariant derivative expansion of the one-loop path integral.« less

Digital Filters for Digital Phase-locked Loops

NASA Technical Reports Server (NTRS)

Simon, M.; Mileant, A.

1985-01-01

An s/z hybrid model for a general phase locked loop is proposed. The impact of the loop filter on the stability, gain margin, noise equivalent bandwidth, steady state error and time response is investigated. A specific digital filter is selected which maximizes the overall gain margin of the loop. This filter can have any desired number of integrators. Three integrators are sufficient in order to track a phase jerk with zero steady state error at loop update instants. This filter has one zero near z = 1.0 for each integrator. The total number of poles of the filter is equal to the number of integrators plus two.

Perturbative calculations in space-time having extra dimensions: The 6D single axial box anomaly

NASA Astrophysics Data System (ADS)

Fonseca, M. V. S.; Dallabona, G.; Battistel, O. A.

2014-11-01

A detailed investigation about the 6D single axial box anomalous amplitude is presented. The superficial degree of divergence involved, in the one-loop perturbative calculations, is quadratic and the corresponding theory is nonrenormalizable. In spite of this, we show that the phenomenon of anomaly can be clearly characterized in a completely analogous way as that of 4D single axial triangle anomaly. The required calculations are made within the context of a novel calculational strategy where the amplitudes are not modified in intermediary steps. Divergent integrals are, in fact, not really solved. Adequate representations for the internal propagators are adopted according to the degree of divergence involved, so that when the last Feynman rule is taken (integration over the loop momentum) all the dependence on the internal (arbitrary) momenta are placed only in finite integrals. In the divergent structures emerging, no physical parameter is present and such objects are not really integrated. Only very general properties are assumed for such quantities which are universal (all space-time dimensions). The consistency of the perturbative calculations fixes some relations among the divergent integrals so that all the potentially ambiguous terms can be automatically removed. In spite of the absence of ambiguities, the emerging results allow us to give a clear and transparent description of the anomaly. The present investigation confirms the point of view stated by the same prescription for the well-known 2D axial-vector (AV) two-point and 4D single (AVV) and triple (AAA) axial-vector anomalies: the anomalous amplitudes need not be assumed as ambiguous quantities to allow an adequate description of the anomalies. We show also that a surprising, but natural, connection between the coupling of fermions with a pseudoscalar tensor field is found. In addition, we show that the crucial mathematical aspects of the problem are deeply related to a recently arisen controversy involving the evaluation of the Higgs Boson decay and the question of unicity in the dimensional regularization.

Application of the Feynman-tree theorem together with BCFW recursion relations

NASA Astrophysics Data System (ADS)

Maniatis, M.

2018-03-01

Recently, it has been shown that on-shell scattering amplitudes can be constructed by the Feynman-tree theorem combined with the BCFW recursion relations. Since the BCFW relations are restricted to tree diagrams, the preceding application of the Feynman-tree theorem is essential. In this way, amplitudes can be constructed by on-shell and gauge-invariant tree amplitudes. Here, we want to apply this method to the electron-photon vertex correction. We present all the single, double, and triple phase-space tensor integrals explicitly and show that the sum of amplitudes coincides with the result of the conventional calculation of a virtual loop correction.

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

Foreign exchange market as a lattice gauge theory

NASA Astrophysics Data System (ADS)

Young, K.

1999-10-01

A simple model of the foreign exchange market is exactly a lattice gauge theory. Exchange rates are the exponentials of gauge potentials defined on spatial links while interest rates are related to gauge potentials on temporal links. Arbitrage opportunities are given by nonzero values of the gauge-invariant field tensor or curvature defined on closed loops. Arbitrage opportunities involving cross-rates at one time are "magnetic fields," while arbitrage opportunities involving future contracts are "electric fields."

The Value of Neurosurgical and Intraoperative Magnetic Resonance Imaging and Diffusion Tensor Imaging Tractography in Clinically Integrated Neuroanatomy Modules: A Cross-Sectional Study

ERIC Educational Resources Information Center

Familiari, Giuseppe; Relucenti, Michela; Heyn, Rosemarie; Baldini, Rossella; D'Andrea, Giancarlo; Familiari, Pietro; Bozzao, Alessandro; Raco, Antonino

2013-01-01

Neuroanatomy is considered to be one of the most difficult anatomical subjects for students. To provide motivation and improve learning outcomes in this area, clinical cases and neurosurgical images from diffusion tensor imaging (DTI) tractographies produced using an intraoperative magnetic resonance imaging apparatus (MRI/DTI) were presented and…

Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology

NASA Astrophysics Data System (ADS)

Elizaga Navascués, Beatriz; Martín de Blas, Daniel; Mena Marugán, Guillermo A.

2018-02-01

Loop quantum cosmology has recently been applied in order to extend the analysis of primordial perturbations to the Planck era and discuss the possible effects of quantum geometry on the cosmic microwave background. Two approaches to loop quantum cosmology with admissible ultraviolet behavior leading to predictions that are compatible with observations are the so-called hybrid and dressed metric approaches. In spite of their similarities and relations, we show in this work that the effective equations that they provide for the evolution of the tensor and scalar perturbations are somewhat different. When backreaction is neglected, the discrepancy appears only in the time-dependent mass term of the corresponding field equations. We explain the origin of this difference, arising from the distinct quantization procedures. Besides, given the privileged role that the big bounce plays in loop quantum cosmology, e.g. as a natural instant of time to set initial conditions for the perturbations, we also analyze the positivity of the time-dependent mass when this bounce occurs. We prove that the mass of the tensor perturbations is positive in the hybrid approach when the kinetic contribution to the energy density of the inflaton dominates over its potential, as well as for a considerably large sector of backgrounds around that situation, while this mass is always nonpositive in the dressed metric approach. Similar results are demonstrated for the scalar perturbations in a sector of background solutions that includes the kinetically dominated ones; namely, the mass then is positive for the hybrid approach, whereas it typically becomes negative in the dressed metric case. More precisely, this last statement is strictly valid when the potential is quadratic for values of the inflaton mass that are phenomenologically favored.

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.

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.

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

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE PAGES

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

2018-03-20

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

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

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

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

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

Ward identities and combinatorics of rainbow tensor models

NASA Astrophysics Data System (ADS)

Itoyama, H.; Mironov, A.; Morozov, A.

2017-06-01

We discuss the notion of renormalization group (RG) completion of non-Gaussian Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in application to the matrix and tensor models. With the example of the simplest non-trivial RGB tensor theory (Aristotelian rainbow), we introduce a few methods, which allow one to connect calculations in the tensor models to those in the matrix models. As a byproduct, we obtain some new factorization formulas and sum rules for the Gaussian correlators in the Hermitian and complex matrix theories, square and rectangular. These sum rules describe correlators as solutions to finite linear systems, which are much simpler than the bilinear Hirota equations and the infinite Virasoro recursion. Search for such relations can be a way to solving the tensor models, where an explicit integrability is still obscure.

From Loops to Trees By-passing Feynman's Theorem

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

Catani, Stefano; Gleisberg, Tanju; Krauss, Frank

2008-04-22

We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts. The duality relation is realized by a modification of the customary + i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write in a Lorentz covariant form, compensates for the absence of multiple cut contributions that appear in the Feynman Tree Theorem. The duality relation can be applied to generic one-loop quantities in any relativistic, local and unitary field theories. It is suitable for applications to the analytical calculation of one-loop scattering amplitudes, and to the numerical evaluationmore » of cross-sections at next-to-leading order.« less

Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

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

Dixon, Lance J.; /SLAC; Drummond, James M.

2012-02-15

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parametersmore » uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.« less

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.

T -odd correlations in polarized top quark decays in the sequential decay t (↑)→Xb+W+(→ℓ++νℓ) and in the quasi-three-body decay t (↑)→ Xb+ℓ++νℓ

NASA Astrophysics Data System (ADS)

Fischer, M.; Groote, S.; Körner, J. G.

2018-05-01

We identify the T -odd structure functions that appear in the description of polarized top quark decays in the sequential decay t (↑)→Xb+W+(→ℓ++νℓ) (two structure functions) and the quasi-three-body decay t (↑)→X b+ℓ++νℓ (one structure function). A convenient measure of the magnitude of the T -odd structure functions is the contribution of the imaginary part Im gR of the right-chiral tensor coupling gR to the T -odd structure functions which we work out. Contrary to the case of QCD, the NLO electroweak corrections to polarized top quark decays admit absorptive one-loop vertex contributions. We analytically calculate the imaginary parts of the relevant four electroweak one-loop triangle vertex diagrams and determine their contributions to the T -odd helicity structure functions that appear in the description of polarized top quark decays.

EFTofPNG: a package for high precision computation with the effective field theory of post-Newtonian gravity

NASA Astrophysics Data System (ADS)

Levi, Michele; Steinhoff, Jan

2017-12-01

We present a novel public package ‘EFTofPNG’ for high precision computation in the effective field theory of post-Newtonian (PN) gravity, including spins. We created this package in view of the timely need to publicly share automated computation tools, which integrate the various types of physics manifested in the expected increasing influx of gravitational wave (GW) data. Hence, we created a free and open source package, which is self-contained, modular, all-inclusive, and accessible to the classical gravity community. The ‘EFTofPNG’ Mathematica package also uses the power of the ‘xTensor’ package, suited for complicated tensor computation, where our coding also strategically approaches the generic generation of Feynman contractions, which is universal to all perturbation theories in physics, by efficiently treating n-point functions as tensors of rank n. The package currently contains four independent units, which serve as subsidiaries to the main one. Its final unit serves as a pipeline chain for the obtainment of the final GW templates, and provides the full computation of derivatives and physical observables of interest. The upcoming ‘EFTofPNG’ package version 1.0 should cover the point mass sector, and all the spin sectors, up to the fourth PN order, and the two-loop level. We expect and strongly encourage public development of the package to improve its efficiency, and to extend it to further PN sectors, and observables useful for the waveform modelling.

The Epstein–Glaser causal approach to the light-front QED{sub 4}. II: Vacuum polarization tensor

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

Bufalo, R., E-mail: rodrigo.bufalo@helsinki.fi; Instituto de Física Teórica; Pimentel, B.M., E-mail: pimentel@ift.unesp.br

2014-12-15

In this work we show how to construct the one-loop vacuum polarization for light-front QED{sub 4} in the framework of the perturbative causal theory. Usually, in the canonical approach, it is considered for the fermionic propagator the so-called instantaneous term, but it is known in the literature that this term is controversial because it can be omitted by computational reasons; for instance, by compensation or vanishing by dimensional regularization. In this work we propose a solution to this paradox. First, in the Epstein–Glaser causal theory, it is shown that the fermionic propagator does not have instantaneous term, and with thismore » propagator we calculate the one-loop vacuum polarization, from this calculation it follows the same result as those obtained by the standard approach, but without reclaiming any extra assumptions. Moreover, since the perturbative causal theory is defined in the distributional framework, we can also show the reason behind our obtaining the same result whether we consider or not the instantaneous fermionic propagator term. - Highlights: • We develop the Epstein–Glaser causal approach for light-front field theory. • We evaluate in detail the vacuum polarization at one-loop for the light-front QED. • We discuss the subtle issues of the Instantaneous part of the fermionic propagator in the light-front. • We evaluate the vacuum polarization at one-loop for the light-front QED with the Instantaneous fermionic part.« less

Conformal anomaly of generalized form factors and finite loop integrals

NASA Astrophysics Data System (ADS)

Chicherin, Dmitry; Sokatchev, Emery

2018-04-01

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an ℓ-loop integral is a 2nd-order differential equation whose right-hand side is an (ℓ - 1)-loop integral. It could serve as a new useful tool to find/test analytic expressions for conformal integrals. We illustrate this point with several examples of known integrals. We propose a new differential equation for the four-dimensional scalar double box.

A systematic and efficient method to compute multi-loop master integrals

NASA Astrophysics Data System (ADS)

Liu, Xiao; Ma, Yan-Qing; Wang, Chen-Yu

2018-04-01

We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems with arbitrary kinematic configurations. Numerical tests show that our method can not only achieve results with high precision, but also be much faster than the only existing systematic method sector decomposition. As a by product, we find a new strategy to compute scalar one-loop integrals without reducing them to master integrals.

Manifesting enhanced cancellations in supergravity: integrands versus integrals

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

Bern, Zvi; Enciso, Michael; Parra-Martinez, Julio

2017-05-25

We have found examples of `enhanced ultraviolet cancellations' with no known standard-symmetry explanation in a variety of supergravity theories. Furthermore, by examining one- and two-loop examples in four- and five-dimensional half-maximal supergravity, we argue that enhanced cancellations in general cannot be exhibited prior to integration. In light of this, we explore reorganizations of integrands into parts that are manifestly finite and parts that have poor power counting but integrate to zero due to integral identities. At two loops we find that in the large loop-momentum limit the required integral identities follow from Lorentz and SL(2) relabeling symmetry. We carry outmore » a nontrivial check at four loops showing that the identities generated in this way are a complete set. We propose that at L loops the combination of Lorentz and SL(L) symmetry is sufficient for displaying enhanced cancellations when they happen, whenever the theory is known to be ultraviolet finite up to (L - 1) loops.« less

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

DOE PAGES

Peng, Bo; Kowalski, Karol

2017-01-25

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

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

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

Peng, Bo; Kowalski, Karol

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

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

NASA Astrophysics Data System (ADS)

Batista, Carlos

2015-04-01

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

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

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

Peng, Bo; Kowalski, Karol

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

Scalar-tensor linear inflation

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

Artymowski, Michał; Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee

2017-04-01

We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead tomore » linear inflation in the strong coupling limit.« less

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

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

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

Phenomenological implications of a predictive formulation of the Nambu-Jona-Lasinio model having tensor couplings and isospin symmetry breaking terms

NASA Astrophysics Data System (ADS)

Battistel, O. A.; Pimenta, T. H.; Dallabona, G.

2016-10-01

In the present work we consider the phenomenological consequences of a predictive formulation of the Nambu-Jona-Lasinio (NJL) model at the one loop level of perturbative calculations. The investigation reported here can be considered as an extension of previously made ones on the same issue. In the study made in this work we have included vector and tensor couplings, simultaneously, as well as S U (2 ) isospin symmetry breaking terms. As a consequence of the last ingredient mentioned, there are different masses in the model amplitudes. In spite of this, within the context of the adopted procedure, we verify that it is possible to eliminate unphysical dependencies on the arbitrary choices for the routing of internal lines momenta as well as Ward identities violating contributions and scale ambiguous terms, from the corresponding one loop amplitudes, through the simple and universal Consistency Relations. The total content of divergence of the amplitudes is reduced to only two basic divergent objects. They are related to two inputs of the model in a way that, due to their scale properties, an unique arbitrariness remains. However, due to the critical condition found in the mechanism which generates the constituent quark mass, within our approach, this arbitrariness is also removed turning the model predictive in the sense that its phenomenological consequences is not dependent in possible choices made in intermediary steps of the calculations, as occurs in usual treatments. In this scenario, we investigate the most typical static properties of the scalar, pseudoscalar, vector and axial-vector mesons at low-energy. Special attention is given to the consequences of the S U (2 ) isospin symmetry breaking for the phenomenological predictions. The implications of the tensor couplings for the model observables, which can be considered an original contribution of the present work, at the level of the content and not only in the form, is analyzed in a detailed way. The found values are in good accordance with the expectations and are globally consistent, having the obvious advantage that the predictions are not dependent in parameters aliens to the model Lagrangian as occurs in traditional approaches based in regularizations.

Reformulations of Yang–Mills theories with space–time tensor fields

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

Guo, Zhi-Qiang, E-mail: gzhqedu@gmail.com

2016-01-15

We provide the reformulations of Yang–Mills theories in terms of gauge invariant metric-like variables in three and four dimensions. The reformulations are used to analyze the dimension two gluon condensate and give gauge invariant descriptions of gluon polarization. In three dimensions, we obtain a non-zero dimension two gluon condensate by one loop computation, whose value is similar to the square of photon mass in the Schwinger model. In four dimensions, we obtain a Lagrangian with the dual property, which shares the similar but different property with the dual superconductor scenario. We also make discussions on the effectiveness of one loopmore » approximation.« less

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

NASA Astrophysics Data System (ADS)

Boettcher, Igor; Herbut, Igor F.

2018-02-01

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

Local recovery of lithospheric stress tensor from GOCE gravitational tensor

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi

2017-04-01

The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

N =4 supergravity next-to-maximally-helicity-violating six-point one-loop amplitude

NASA Astrophysics Data System (ADS)

Dunbar, David C.; Perkins, Warren B.

2016-12-01

We construct the six-point, next-to-maximally-helicity-violating one-loop amplitude in N =4 supergravity using unitarity and recursion. The use of recursion requires the introduction of rational descendants of the cut-constructible pieces of the amplitude and the computation of the nonstandard factorization terms arising from the loop integrals.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

BRST Exactness of Stress-Energy Tensors

NASA Astrophysics Data System (ADS)

Miyata, Hideo; Sugimoto, Hiroshi

BRST commutators in the topological conformal field theories obtained by twisting N=2 theories are evaluated explicitly. By our systematic calculations of the multiple integrals which contain screening operators, the BRST exactness of the twisted stress-energy tensors is deduced for classical simple Lie algebras and general level k. We can see that the paths of integrations do not affect the result, and further, the N=2 coset theories are obtained by deleting two simple roots with Kac-label 1 from the extended Dynkin diagram; in other words, by not performing the integrations over the variables corresponding to the two simple roots of Kac-Moody algebras. It is also shown that a series of N=1 theories are generated in the same way by deleting one simple root with Kac-label 2.

An Integrated Tensorial Approach for Quantifying Porous, Fractured Rocks

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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.

A non-planar two-loop three-point function beyond multiple polylogarithms

NASA Astrophysics Data System (ADS)

von Manteuffel, Andreas; Tancredi, Lorenzo

2017-06-01

We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for t\\overline{t} production and γγ production in gluon fusion through a massive top-quark loop. All subtopology integrals can be written in terms of multiple polylogarithms over an irrational alphabet and we employ a new method for the integration of the differential equations which does not rely on the rationalization of the latter. The top topology integrals, instead, in spite of the absence of a massive three-particle cut, cannot be evaluated in terms of multiple polylogarithms and require the introduction of integrals over complete elliptic integrals and polylogarithms. We provide one-fold integral representations for the solutions and continue them analytically to all relevant regions of the phase space in terms of real functions, extracting all imaginary parts explicitly. The numerical evaluation of our expressions becomes straightforward in this way.

Characterization facility for magneto-optic media and systems

NASA Technical Reports Server (NTRS)

Mansuripur, M.; Fu, H.; Gadetsky, S.; Sugaya, S.; Wu, T. H.; Zambuto, J.; Gerber, R.; Goodman, T.; Erwin, J. K.

1993-01-01

Objectives of this research are: (1) to measure the hysteresis loop, Kerr rotation angle, anisotropy energy profile, Hall voltage, and magnetoresistance of thin-film magneto-optic media using our loop-tracer; (2) measure the wavelength-dependence of the Kerr rotation angle, Theta(sub k), and ellipticity, epsilon(sub k), for thin-film media using our magneto-optic Kerr spectrometer (MOKS); (3) measure the dielectric tensor of thin-film and multilayer samples using our variable-angle magneto-optic ellipsometer (VAMOE); (4) measure the hysteresis loop, coercivity, remanent magnetization, saturation magnetization, and anisotropy energy constant for thin film magnetic media using vibrating sample magnetometry; (5) observe small magnetic domains and investigate their interaction with defects using magnetic force microscopy; (6) perform static read/write/erase experiments on thin-film magneto-optic media using our static test station; (7) integrate the existing models of magnetization, magneto-optic effects, coercivity, and anisotropy in an interactive and user-friendly environment, and analyze the characterization data obtained in the various experiments, using this modeling package; (8) measure focusing- and tracking-error signals on a static testbed, determine the 'feedthrough' for various focusing schemes, investigate the effects of polarization and birefringence, and compare the results with diffraction-based calculations; and (9) measure the birefringence of optical disk substrates using two variable angle ellipsometers.

The trispectrum in the Effective Field Theory of Large Scale Structure

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

Bertolini, Daniele; Schutz, Katelin; Solon, Mikhail P.

2016-06-01

We compute the connected four point correlation function (the trispectrum in Fourier space) of cosmological density perturbations at one-loop order in Standard Perturbation Theory (SPT) and the Effective Field Theory of Large Scale Structure (EFT of LSS). This paper is a companion to our earlier work on the non-Gaussian covariance of the matter power spectrum, which corresponds to a particular wavenumber configuration of the trispectrum. In the present calculation, we highlight and clarify some of the subtle aspects of the EFT framework that arise at third order in perturbation theory for general wavenumber configurations of the trispectrum. We consistently incorporatemore » vorticity and non-locality in time into the EFT counterterms and lay out a complete basis of building blocks for the stress tensor. We show predictions for the one-loop SPT trispectrum and the EFT contributions, focusing on configurations which have particular relevance for using LSS to constrain primordial non-Gaussianity.« less

Pre-inflationary universe in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Zhu, Tao; Wang, Anzhong; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin

2017-10-01

The evolutions of the flat Friedmann-Lemaître-Robertson-Walker universe and its linear perturbations are studied systematically in the dressed metric approach of loop quantum cosmology. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating: bouncing, transition and slow-roll inflation. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential-dominated case such a universality is lost. It is because of this universality that the linear perturbations are also independent of the inflationary models and obtained exactly. During the transition phase, the evolutions of the background and its linear perturbations are found explicitly, and then matched to the ones given in the other two phases. Hence, once the initial conditions are imposed, the linear scalar and tensor perturbations will be uniquely determined. Considering two different sets of initial conditions, one imposed during the contracting phase and the other at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the preinflationary dynamics, the scalar and tensor power spectra become scale dependent. By comparing our results with the Planck 2015 data, we find constraints on the total number of e -folds since the bounce, in order to be consistent with current observations.

Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory

NASA Astrophysics Data System (ADS)

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

2012-07-01

Many approximations have been developed to help deal with the O(N4) growth of the electron repulsion integral (ERI) tensor, where N is the number of one-electron basis functions used to represent the electronic wavefunction. Of these, the density fitting (DF) approximation is currently the most widely used despite the fact that it is often incapable of altering the underlying scaling of computational effort with respect to molecular size. We present a method for exploiting sparsity in three-center overlap integrals through tensor decomposition to obtain a low-rank approximation to density fitting (tensor hypercontraction density fitting or THC-DF). This new approximation reduces the 4th-order ERI tensor to a product of five matrices, simultaneously reducing the storage requirement as well as increasing the flexibility to regroup terms and reduce scaling behavior. As an example, we demonstrate such a scaling reduction for second- and third-order perturbation theory (MP2 and MP3), showing that both can be carried out in O(N4) operations. This should be compared to the usual scaling behavior of O(N5) and O(N6) for MP2 and MP3, respectively. The THC-DF technique can also be applied to other methods in electronic structure theory, such as coupled-cluster and configuration interaction, promising significant gains in computational efficiency and storage reduction.

Renormalization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point

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

Sturm, C.; Soni, A.; Aoki, Y.

2009-07-01

We extend the Rome-Southampton regularization independent momentum-subtraction renormalization scheme (RI/MOM) for bilinear operators to one with a nonexceptional, symmetric subtraction point. Two-point Green's functions with the insertion of quark bilinear operators are computed with scalar, pseudoscalar, vector, axial-vector and tensor operators at one-loop order in perturbative QCD. We call this new scheme RI/SMOM, where the S stands for 'symmetric'. Conversion factors are derived, which connect the RI/SMOM scheme and the MS scheme and can be used to convert results obtained in lattice calculations into the MS scheme. Such a symmetric subtraction point involves nonexceptional momenta implying a lattice calculation withmore » substantially suppressed contamination from infrared effects. Further, we find that the size of the one-loop corrections for these infrared improved kinematics is substantially decreased in the case of the pseudoscalar and scalar operator, suggesting a much better behaved perturbative series. Therefore it should allow us to reduce the error in the determination of the quark mass appreciably.« less

Observational constraints on loop quantum cosmology.

PubMed

Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji

2011-11-18

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

Mixed heavy–light matching in the Universal One-Loop Effective Action

DOE PAGES

Ellis, Sebastian A. R.; Quevillon, Jérémie; You, Tevong; ...

2016-11-10

Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass dependence encapsulated in the universal coefficients. In this study we show that it can account for loops of mixed heavy–light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintaining the universal structure ofmore » the effective action, which we illustrate using the example of integrating out a heavy electroweak triplet scalar coupling to a light Higgs doublet. Finally we also identify new structures that were previously neglected in the universal results.« less

Two-loop renormalization of the quark propagator in the light-cone gauge

NASA Astrophysics Data System (ADS)

Williams, James Daniel

The divergent parts of the five two-loop quark self- energy diagrams of quantum chromodynamics are evaluated in the noncovariant light-cone gauge. Most of the Feynman integrals are computed by means of the powerful matrix integration method, originally developed for the author's Master's thesis. From the results of the integrations, it is shown how to renormalize the quark mass and wave function in such a way that the effective quark propagator is rendered finite at two-loop order. The required counterterms turn out to be local functions of the quark momentum, due to cancellation of the nonlocal divergent parts of the two-loop integrals with equal and opposite contributions from one-loop counterterm subtraction diagrams. The final form of the counterterms is seen to be consistent with the renormalization framework proposed by Bassetto, Dalbosco, and Soldati, in which all noncovariant divergences are absorbed into the wave function normalizations. It also turns out that the mass renormalization d m is the same in the light-cone gauge as it is in a general covariant gauge, at least up to two-loop order.

Vacuum fluctuations of the supersymmetric field in curved background

NASA Astrophysics Data System (ADS)

Bilić, Neven; Domazet, Silvije; Guberina, Branko

2012-01-01

We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants.

On the asymptotic states and the quantum S matrix of the η-deformed AdS 5 × S 5 superstring

DOE PAGES

Engelund, Oluf Tang; Roiban, Radu

2015-03-31

We investigate the worldsheet S matrix of string theory in η-deformed AdS 5 × S 5. By computing the six-point tree-level S matrix we explicitly show that there is no particle production at this level, as required by the classical integrability of the theory. At one and two loops we show that integrability requires that the classical two-particle states be redefined in a non-local and η-dependent way. This is a significant departure from the undeformed theory which is probably related to the quantum group symmetry of the worldsheet theory. We use generalized unitarity to carry out the loop calculations andmore » identify a set of integrals that allow us to give a two-loop Feynman integral representation of the logarithmic terms of the two-loop S matrix. We finally also discuss aspects of the calculation of the two-loop rational terms.« less

Lattice corrections to the quark quasidistribution at one loop

DOE PAGES

Carlson, Carl E.; Freid, Michael

2017-05-12

Here, we calculate radiative corrections to the quark quasidistribution in lattice perturbation theory at one loop to leading orders in the lattice spacing. We also consider one-loop corrections in continuum Euclidean space. We find that the infrared behavior of the corrections in Euclidean and Minkowski space are different. Furthermore, we explore features of momentum loop integrals and demonstrate why loop corrections from the lattice perturbation theory and Euclidean continuum do not correspond with their Minkowski brethren, and comment on a recent suggestion for transcending the differences in the results. Finally, we examine the role of the lattice spacing a andmore » of the r parameter in the Wilson action in these radiative corrections.« less

Lattice corrections to the quark quasidistribution at one loop

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

Carlson, Carl E.; Freid, Michael

Here, we calculate radiative corrections to the quark quasidistribution in lattice perturbation theory at one loop to leading orders in the lattice spacing. We also consider one-loop corrections in continuum Euclidean space. We find that the infrared behavior of the corrections in Euclidean and Minkowski space are different. Furthermore, we explore features of momentum loop integrals and demonstrate why loop corrections from the lattice perturbation theory and Euclidean continuum do not correspond with their Minkowski brethren, and comment on a recent suggestion for transcending the differences in the results. Finally, we examine the role of the lattice spacing a andmore » of the r parameter in the Wilson action in these radiative corrections.« 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., 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

Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

PubMed

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

2007-01-01

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

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.

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.

Principle of Magnetodynamics for Composite Magnetic Pole

NASA Astrophysics Data System (ADS)

Animalu, Alexander

2014-03-01

It is shown in this paper that geometry provides the key to the new magnetodynamics principle of operation of the machine (invented by Dr. Ezekiel Izuogu) which has an unexpected feature of driving a motor with static magnetic field. Essentially, because an array of like magnetic poles of the machine is arranged in a half circular array of a cylindrical geometry, the array creates a non-pointlike magnet pole that may be represented by a ``magnetic current loop'' at the position of the pivot of the movable arm. As a result, in three-dimensional space, it is possible to characterize the symmetry of the stator magnetic field B and the magnetic current loop J as a cube-hexagon system by a 6-vector (J,B) (with J.B ≠0) comprising a 4x4 antisymmetric tensor analogous to the conventional electric and magnetic 6-vector (E,B) (with E.B ≠0) comprising the 4x4 antisymmetric tensor of classical electrodynamics The implications are discussed. Supported by International Centre for Basic Research, Abuja, Nigeria.

Spin-dependent μ → e conversion

DOE PAGES

Cirigliano, Vincenzo; Davidson, Sacha; Kuno, Yoshitaka

2017-05-22

The experimental sensitivity to μ→e conversion on nuclei is expected to improve by four orders of magnitude in coming years. Here, we consider the impact of μ→e flavour-changing tensor and axial-vector four-fermion operators which couple to the spin of nucleons. Such operators, which have not previously been considered, contribute to μ→e conversion in three ways: in nuclei with spin they mediate a spin-dependent transition; in all nuclei they contribute to the coherent (A 2-enhanced) spin-independent conversion via finite recoil effects and via loop mixing with dipole, scalar, and vector operators. Furthermore, we estimate the spin-dependent rate in Aluminium (the targetmore » of the upcoming COMET and Mu2e experiments), show that the loop effects give the greatest sensitivity to tensor and axial-vector operators involving first-generation quarks, and discuss the complementarity of the spin-dependent and independent contributions to μ→e conversion.« less

Spin-dependent μ → e conversion

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

Cirigliano, Vincenzo; Davidson, Sacha; Kuno, Yoshitaka

The experimental sensitivity to μ→e conversion on nuclei is expected to improve by four orders of magnitude in coming years. Here, we consider the impact of μ→e flavour-changing tensor and axial-vector four-fermion operators which couple to the spin of nucleons. Such operators, which have not previously been considered, contribute to μ→e conversion in three ways: in nuclei with spin they mediate a spin-dependent transition; in all nuclei they contribute to the coherent (A 2-enhanced) spin-independent conversion via finite recoil effects and via loop mixing with dipole, scalar, and vector operators. Furthermore, we estimate the spin-dependent rate in Aluminium (the targetmore » of the upcoming COMET and Mu2e experiments), show that the loop effects give the greatest sensitivity to tensor and axial-vector operators involving first-generation quarks, and discuss the complementarity of the spin-dependent and independent contributions to μ→e conversion.« less

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.

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

Super-integrable Calogero-type systems admit maximal number of Poisson structures

NASA Astrophysics Data System (ADS)

Gonera, C.; Nutku, Y.

2001-07-01

We present a general scheme for constructing the Poisson structure of super-integrable dynamical systems of which the rational Calogero-Moser system is the most interesting one. This dynamical system is 2 N-dimensional with 2 N-1 first integrals and our construction yields 2 N-1 degenerate Poisson tensors that each admit 2( N-1) Casimirs. Our results are quite generally applicable to all super-integrable systems and form an alternative to the traditional bi-Hamiltonian approach.

Signs and stability in higher-derivative gravity

NASA Astrophysics Data System (ADS)

Narain, Gaurav

2018-02-01

Perturbatively renormalizable higher-derivative gravity in four space-time dimensions with arbitrary signs of couplings has been considered. Systematic analysis of the action with arbitrary signs of couplings in Lorentzian flat space-time for no-tachyons, fixes the signs. Feynman + i𝜖 prescription for these signs further grants necessary convergence in path-integral, suppressing the field modes with large action. This also leads to a sensible wick rotation where quantum computation can be performed. Running couplings for these sign of parameters make the massive tensor ghost innocuous leading to a stable and ghost-free renormalizable theory in four space-time dimensions. The theory has a transition point arising from renormalization group (RG) equations, where the coefficient of R2 diverges without affecting the perturbative quantum field theory (QFT). Redefining this coefficient gives a better handle over the theory around the transition point. The flow equations push the flow of parameters across the transition point. The flow beyond the transition point is analyzed using the one-loop RG equations which shows that the regime beyond the transition point has unphysical properties: there are tachyons, the path-integral loses positive definiteness, Newton’s constant G becomes negative and large, and perturbative parameters become large. These shortcomings indicate a lack of completeness beyond the transition point and need of a nonperturbative treatment of the theory beyond the transition point.

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

Symmetric Topological Phases and Tensor Network States

NASA Astrophysics Data System (ADS)

Jiang, Shenghan

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

Loop quantum cosmology scalar field models

NASA Astrophysics Data System (ADS)

Kleidis, K.; Oikonomou, V. K.

In this work, we use the Loop Quantum Cosmology (LQC) modified scalar-tensor reconstruction techniques in order to investigate how bouncing and inflationary cosmologies can be realized. With regard to the inflationary cosmologies, we shall be interested in realizing the intermediate inflation and the Type IV singular inflation, while with regard to bouncing cosmologies, we shall realize the superbounce and the symmetric bounce. In all the cases, we shall find the kinetic term of the LQC holonomy corrected scalar-tensor theory and the corresponding scalar potential. In addition, we shall include a study of the effective Equation of State (EoS), emphasizing at the early- and late-time eras. As we demonstrate, in some cases it is possible to have a nearly de Sitter EoS at the late-time era, a result that could be interpreted as the description of a late-time acceleration era. Also, in all cases we shall examine the dynamical stability of the LQC holonomy corrected scalar-tensor theory, and we shall confront the results with those coming from the corresponding classical dynamical stability theory. The most appealing cosmological scenario is that of a Type IV singular inflationary scenario, in which the singularity may occur at the late-time era. As we demonstrate, for this model, during the dark energy era, a transition from non-phantom to a phantom dark energy era occurs.

Scalar Contribution to the Graviton Self-Energy During Inflation

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

Park, Sohyun

2012-01-01

We use dimensional regularization to evaluate the one loop contribution to the graviton self-energy from a massless, minimally coupled scalar on a locally de Sitter background. For noncoincident points our result agrees with the stress tensor correlators obtained recently by Perez-Nadal, Roura and Verdaguer. We absorb the ultraviolet divergences using the R 2 and C 2 counterterms first derived by ’t Hooft and Veltman, and we take the D = 4 limit of the finite remainder. The renormalized result is expressed as the sum of two transverse, 4th order differential operators acting on nonlocal, de Sitter invariant structure functions. Inmore » this form it can be used to quantum-correct the linearized Einstein equations so that one can study how the inflationary production of infrared scalars affects the propagation of dynamical gravitons and the force of gravity. We have seen that they have no effect on the propagation of dynamical gravitons. Our computation motivates a conjecture for the first correction to the vacuum state wave functional of gravitons. We comment as well on performing the same analysis for the more interesting contribution from inflationary gravitons, and on inferring one loop corrections to the force of gravity.« less

Hidden Symmetries in String Theory

NASA Astrophysics Data System (ADS)

Chervonyi, Iurii

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

Chemical looping integration with a carbon dioxide gas purification unit

DOEpatents

Andrus, Jr., Herbert E.; Jukkola, Glen D.; Thibeault, Paul R.; Liljedahl, Gregory N.

2017-01-24

A chemical looping system that contains an oxidizer and a reducer is in fluid communication with a gas purification unit. The gas purification unit has at least one compressor, at least one dryer; and at least one distillation purification system; where the gas purification unit is operative to separate carbon dioxide from other contaminants present in the flue gas stream; and where the gas purification unit is operative to recycle the contaminants to the chemical looping system in the form of a vent gas that provides lift for reactants in the reducer.

Anomaly free cosmological perturbations with generalised holonomy correction in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Han, Yu; Liu, Molin

2018-05-01

In the spatially flat case of loop quantum cosmology, the connection is usually replaced by the holonomy in effective theory. In this paper, instead of the standard scheme, we use a generalised, undetermined function to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction in the form of , then we derive the gauge-invariant equations of motion of the scalar, tensor and vector perturbations and study the inflationary power spectra with generalised holonomy correction.

Shrunk loop theorem for the topology probabilities of closed Brownian (or Feynman) paths on the twice punctured plane

NASA Astrophysics Data System (ADS)

Giraud, O.; Thain, A.; Hannay, J. H.

2004-02-01

The shrunk loop theorem proved here is an integral identity which facilitates the calculation of the relative probability (or probability amplitude) of any given topology that a free, closed Brownian (or Feynman) path of a given 'duration' might have on the twice punctured plane (plane with two marked points). The result is expressed as a 'scattering' series of integrals of increasing dimensionality based on the maximally shrunk version of the path. Physically, this applies in different contexts: (i) the topology probability of a closed ideal polymer chain on a plane with two impassable points, (ii) the trace of the Schrödinger Green function, and thence spectral information, in the presence of two Aharonov-Bohm fluxes and (iii) the same with two branch points of a Riemann surface instead of fluxes. Our theorem starts from the Stovicek scattering expansion for the Green function in the presence of two Aharonov-Bohm flux lines, which itself is based on the famous Sommerfeld one puncture point solution of 1896 (the one puncture case has much easier topology, just one winding number). Stovicek's expansion itself can supply the results at the expense of choosing a base point on the loop and then integrating it away. The shrunk loop theorem eliminates this extra two-dimensional integration, distilling the topology from the geometry.

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

Tronconi, Alessandro, E-mail: Alessandro.Tronconi@bo.infn.it

We study the constraints imposed by the requirement of Asymptotic Safety on a class of inflationary models with an inflaton field non-minimally coupled to the Ricci scalar. The critical surface in the space of theories is determined by the improved renormalization group flow which takes into account quantum corrections beyond the one loop approximation. The combination of constraints deriving from Planck observations and those from theory puts severe bounds on the values of the parameters of the model and predicts a quite large tensor to scalar ratio. We finally comment on the dependence of the results on the definition ofmore » the infrared energy scale which parametrises the running on the critical surface.« less

New method of computing the contributions of graphs without lepton loops to the electron anomalous magnetic moment in QED

NASA Astrophysics Data System (ADS)

Volkov, Sergey

2017-11-01

This paper presents a new method of numerical computation of the mass-independent QED contributions to the electron anomalous magnetic moment which arise from Feynman graphs without closed electron loops. The method is based on a forestlike subtraction formula that removes all ultraviolet and infrared divergences in each Feynman graph before integration in Feynman-parametric space. The integration is performed by an importance sampling Monte-Carlo algorithm with the probability density function that is constructed for each Feynman graph individually. The method is fully automated at any order of the perturbation series. The results of applying the method to 2-loop, 3-loop, 4-loop Feynman graphs, and to some individual 5-loop graphs are presented, as well as the comparison of this method with other ones with respect to Monte Carlo convergence speed.

Introduction to Vector Field Visualization

NASA Technical Reports Server (NTRS)

Kao, David; Shen, Han-Wei

2010-01-01

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

Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysis.

PubMed

Kondic, L; Kramár, M; Pugnaloni, Luis A; Carlevaro, C Manuel; Mischaikow, K

2016-06-01

In the companion paper [Pugnaloni et al., Phys. Rev. E 93, 062902 (2016)10.1103/PhysRevE.93.062902], we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components, related to force chains, and loops), to describe the force networks in tapped systems of disks and pentagons. In the present work, we focus on the use of persistence analysis, which allows us to describe these networks in much more detail. This approach allows us not only to describe but also to quantify the differences between the force networks in different realizations of a system, in different parts of the considered domain, or in different systems. We show that persistence analysis clearly distinguishes the systems that are very difficult or impossible to differentiate using other means. One important finding is that the differences in force networks between disks and pentagons are most apparent when loops are considered: the quantities describing properties of the loops may differ significantly even if other measures (properties of components, Betti numbers, force PDFs, or the stress tensor) do not distinguish clearly or at all the investigated systems.

Optical fiber loops and helices: tools for integrated photonic device characterization and microfluidic trapping

NASA Astrophysics Data System (ADS)

Ren, Yundong; Zhang, Rui; Ti, Chaoyang; Liu, Yuxiang

2016-09-01

Tapered optical fibers can deliver guided light into and carry light out of micro/nanoscale systems with low loss and high spatial resolution, which makes them ideal tools in integrated photonics and microfluidics. Special geometries of tapered fibers are desired for probing monolithic devices in plane as well as optical manipulation of micro particles in fluids. However, for many specially shaped tapered fibers, it remains a challenge to fabricate them in a straightforward, controllable, and repeatable way. In this work, we fabricated and characterized two special geometries of tapered optical fibers, namely fiber loops and helices, that could be switched between one and the other. The fiber loops in this work are distinct from previous ones in terms of their superior mechanical stability and high optical quality factors in air, thanks to a post-annealing process. We experimentally measured an intrinsic optical quality factor of 32,500 and a finesse of 137 from a fiber loop. A fiber helix was used to characterize a monolithic cavity optomechanical device. Moreover, a microfluidic "roller coaster" was demonstrated, where microscale particles in water were optically trapped and transported by a fiber helix. Tapered fiber loops and helices can find various applications ranging from on-the-fly characterization of integrated photonic devices to particle manipulation and sorting in microfluidics.

Basin Characterisation by Means of Joint Inversion of Electromagnetic Geophysical Data, Borehole Data and Multivariate Statistical Methods: The Loop Head Peninsula, Western Ireland, Case Study

NASA Astrophysics Data System (ADS)

Campanya, J. L.; Ogaya, X.; Jones, A. G.; Rath, V.; McConnell, B.; Haughton, P.; Prada, M.

2016-12-01

The Science Foundation Ireland funded project IRECCSEM project (www.ireccsem.ie) aims to evaluate Ireland's potential for onshore carbon sequestration in saline aquifers by integrating new electromagnetic geophysical data with existing geophysical and geological data. One of the objectives of this component of IRECCSEM is to characterise the subsurface beneath the Loop Head Peninsula (part of Clare Basin, Co. Clare, Ireland), and identify major electrical resistivity structures that can guide an interpretation of the carbon sequestration potential of this area. During the summer of 2014, a magnetotelluric (MT) survey was carried out on the Loop Head Peninsula, and data from a total of 140 sites were acquired, including audio-magnetotelluric (AMT), and broadband magnetotelluric (BBMT). The dataset was used to generate shallow three-dimensional (3-D) electrical resistivity models constraining the subsurface to depths of up to 3.5 km. The three-dimensional (3-D) joint inversions were performed using three different types of electromagnetic data: MT impedance tensor (Z), geomagnetic transfer functions (T), and inter-station horizontal magnetic transfer-functions (H). The interpretation of the results was complemented with second-derivative models of the resulting electrical resistivity models, and a quantitative comparison with borehole data using multivariate statistical methods. Second-derivative models were used to define the main interfaces between the geoelectrical structures, facilitating superior comparison with geological and seismic results, and also reducing the influence of the colour scale when interpreting the results. Specific analysis was performed to compare the extant borehole data with the electrical resistivity model, identifying those structures that are better characterised by the resistivity model. Finally, the electrical resistivity model was also used to propagate some of the physical properties measured in the borehole, when a good relation was possible between the different types of data. The final results were compared with independent geological and geophysical data for a high-quality interpretation.

Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals

DOE PAGES

Schmittfull, Marcel; Vlah, Zvonimir

2016-11-28

Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve this is to model nonlinear scales perturbatively. Unfortunately, this involves high-dimensional loop integrals that are cumbersome to evaluate. Here, trying to simplify this, we show how two-loop (next-to-next-to-leading order) corrections to the density power spectrum can be reduced to low-dimensional, radial integrals. Many of those can be evaluated with a one-dimensional fast Fourier transform, which is significantly faster than the five-dimensional Monte-Carlo integrals thatmore » are needed otherwise. The general idea of this fast fourier transform perturbation theory method is to switch between Fourier and position space to avoid convolutions and integrate over orientations, leaving only radial integrals. This reformulation is independent of the underlying shape of the initial linear density power spectrum and should easily accommodate features such as those from baryonic acoustic oscillations. We also discuss how to account for halo bias and redshift space distortions.« less

Towards a phase diagram for spin foams

NASA Astrophysics Data System (ADS)

Delcamp, Clement; Dittrich, Bianca

2017-11-01

One of the most pressing issues for loop quantum gravity and spin foams is the construction of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for three-dimensional lattice gauge models including spin foams. This scheme is based on the concept of decorated tensor networks, which have been introduced recently. Here we develop an algorithm applicable to gauge theories with non-Abelian groups, which for the first time allows for the application of tensor network coarse-graining techniques to proper spin foams. The procedure deals efficiently with the large redundancy of degrees of freedom resulting from gauge invariance. The algorithm is applied to 3D spin foams defined on a cubical lattice which, in contrast to a proper triangulation, allows for non-trivial simplicity constraints. This mimics the construction of spin foams for 4D gravity. For lattice gauge models based on a finite group we use the algorithm to obtain phase diagrams, encoding the continuum limit of a wide range of these models. We find phase transitions for various families of models carrying non-trivial simplicity constraints.

Energy theorem for (2+1)-dimensional gravity.

NASA Astrophysics Data System (ADS)

Menotti, P.; Seminara, D.

1995-05-01

We prove a positive energy theorem in (2+1)-dimensional gravity for open universes and any matter energy-momentum tensor satisfying the dominant energy condition. We consider on the space-like initial value surface a family of widening Wilson loops and show that the energy-momentum of the enclosed subsystem is a future directed time-like vector whose mass is an increasing function of the loop, until it reaches the value 1/4G corresponding to a deficit angle of 2π. At this point the energy-momentum of the system evolves, depending on the nature of a zero norm vector appearing in the evolution equations, either into a time-like vector of a universe which closes kinematically or into a Gott-like universe whose energy momentum vector, as first recognized by Deser, Jackiw, and 't Hooft (1984) is space-like. This treatment generalizes results obtained by Carroll, Fahri, Guth, and Olum (1994) for a system of point-like spinless particle, to the most general form of matter whose energy-momentum tensor satisfies the dominant energy condition. The treatment is also given for the anti-de Sitter (2+1)-dimensional gravity.

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.

Topology-driven phase transitions in the classical monomer-dimer-loop model.

PubMed

Li, Sazi; Li, Wei; Chen, Ziyu

2015-06-01

In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product state technique to contract the partition function TN, and determine the thermodynamic properties with high accuracy. In this monomer-dimer-loop model, we find a second-order phase transition between a trivial monomer-condensation and a loop-condensation (LC) phase, which cannot be distinguished by any local order parameter, while nevertheless the two phases have distinct topological properties. In the LC phase, we find two degenerate dominating eigenvalues in the transfer-matrix spectrum, as well as a nonvanishing (nonlocal) string order parameter, both of which identify the topological ergodicity breaking in the LC phase and can serve as the order parameter for detecting the phase transitions.

One- and two-center ETF-integrals of first order in relativistic calculation of NMR parameters

NASA Astrophysics Data System (ADS)

Slevinsky, R. M.; Temga, T.; Mouattamid, M.; Safouhi, H.

2010-06-01

The present work focuses on the analytical and numerical developments of first-order integrals involved in the relativistic calculation of the shielding tensor using exponential-type functions as a basis set of atomic orbitals. For the analytical development, we use the Fourier integral transformation and practical properties of spherical harmonics and the Rayleigh expansion of the plane wavefunctions. The Fourier transforms of the operators were derived in previous work and they are used for analytical development. In both the one- and two-center integrals, Cauchy's residue theorem is used in the final developments of the analytical expressions, which are shown to be accurate to machine precision.

Floating Loop System For Cooling Integrated Motors And Inverters Using Hot Liquid Refrigerant

DOEpatents

Hsu, John S [Oak Ridge, TN; Ayers, Curtis W [Kingston, TN; Coomer, Chester [Knoxville, TN; Marlino, Laura D [Oak Ridge, TN

2006-02-07

A floating loop vehicle component cooling and air-conditioning system having at least one compressor for compressing cool vapor refrigerant into hot vapor refrigerant; at least one condenser for condensing the hot vapor refrigerant into hot liquid refrigerant by exchanging heat with outdoor air; at least one floating loop component cooling device for evaporating the hot liquid refrigerant into hot vapor refrigerant; at least one expansion device for expanding the hot liquid refrigerant into cool liquid refrigerant; at least one air conditioning evaporator for evaporating the cool liquid refrigerant into cool vapor refrigerant by exchanging heat with indoor air; and piping for interconnecting components of the cooling and air conditioning system.

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.

Diagram reduction in problem of critical dynamics of ferromagnets: 4-loop approximation

NASA Astrophysics Data System (ADS)

Adzhemyan, L. Ts; Ivanova, E. V.; Kompaniets, M. V.; Vorobyeva, S. Ye

2018-04-01

Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we perform a calculation of the critical exponent z of model A at 4-loop level, where our method allows one to reduce the number of integrals from 66 to 17. The way of constructing the integrand in a Feynman representation of such diagrams is discussed. Integrals were estimated numerically with a sector decomposition technique.

MELiSSA Pilot Plant: A facility for ground demonstration of a closed life support system

NASA Astrophysics Data System (ADS)

Godia, Francesc; Fossen, Arnaud; Peiro, Enrique; Gerbi, Olivier; Dussap, Gilles; Leys, Natalie; Arnau, Carolina; Milian, Ernest

MELiSSA (Micro Ecological Life Support System Alternative) is an international collaborative effort focused on the development of a Life Support System for long-term Space missions. The goals of the MELiSSA loop are the recovery of food, water and oxygen from wastes, i.e. CO2 and organic wastes, using light as a source of energy. It is conceived as a series of compartments, each one performing a specific function within this cycle, inspired in the terrestrial ecological systems. Each one of the compartments is colonized with specific bacteria or higher plants depending on its dedicated function. Therefore, its design and operational conditions should guarantee that only a given specific biological activity takes place in each compartment. Moreover, this has to be done in a controlled manner, both at the subsystems level (i.e., compartments) and at the overall system level (i.e., complete loop). In order to achieve the complete operation of such a Closed Ecological System, in a first step each compartment has to be developed at individual level, and its operation demonstrated under its associated control law. In a second step, the complete loop needs to be integrated by the connection of the different compartments in the gas, loop and solid phases. An extensive demonstration of MELiSSA loop under terrestrial conditions is a mandatory step in the process of its adaptation to space. This is the main goal of the MPP. The demonstration scenario for the MPP is the respiration equivalent of a human being, and production of 20 percent of the diet of one person. To serve this goal, the different compartments of the MELiSSA loop have been designed and sized at the pilot scale level, and further characterized. Nowadays, the focus of the MELiSSA Pilot Plant is on the integration of its compartments. To this end, the integration challenge is concentrated in three compartments devoted to the following functions: nitrification (Compartment 3, an axenic co-culture of Nitrosomonas europaea and Nitrobacter winogradskyi), edible biomass and oxygen production (Compartment 4a, an axenic co-culture of Arthrospira platensis) and oxygen consumers (Compartment 5, rats isolator). The presentation will focus on all the necessary elements to achieve this integration, particularly in the start-up of continuous operation of the bioreactors and on the key challenges addressed in the integration of the gas phase of two compartments, 4a and 5, one producing O2 and one consuming it. The design of the integration conditions to ensure the functionality of all the elements will also be discussed. Keywords:, MELiSSA, Pilot Plant, Integration, Arthrospira platensis, Nitrosomonas europaea, Nitrobacter winogradskyi

Microstructural white matter tract alteration in Prader-Willi syndrome: A diffusion tensor imaging study.

PubMed

Rice, Lauren J; Lagopoulos, Jim; Brammer, Michael; Einfeld, Stewart L

2017-09-01

Prader-Willi Syndrome (PWS) is a genetic disorder characterized by infantile hypotonia, hyperphagia, hypogonadism, growth hormone deficiency, intellectual disability, and severe emotional and behavioral problems. The brain mechanisms that underpin these disturbances are unknown. Diffusion tensor imaging (DTI) enables in vivo investigation of the microstructural integrity of white matter pathways. To date, only one study has used DTI to examine white matter alterations in PWS. However, that study used selected regions of interest, rather than a whole brain analysis. In the present study, we used diffusion tensor and magnetic resonance (T 1-weighted) imaging to examine microstructural white matter changes in 15 individuals with PWS (17-30 years) and 15 age-and-gender-matched controls. Whole-brain voxel-wise statistical analysis of FA was carried out using tract-based spatial statistics (TBSS). Significantly decreased fractional anisotropy was found localized to the left hemisphere in individuals with PWS within the splenium of the corpus callosum, the internal capsule including the posterior thalamic radiation and the inferior frontal occipital fasciculus (IFOF). Reduced integrity of these white matter pathways in individuals with PWS may relate to orientating attention, emotion recognition, semantic processing, and sensorimotor dysfunction. © 2017 Wiley Periodicals, Inc.

The complete two-loop integrated jet thrust distribution in soft-collinear effective theory

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

von Manteuffel, Andreas; Schabinger, Robert M.; Zhu, Hua Xing

2014-03-01

In this work, we complete the calculation of the soft part of the two-loop integrated jet thrust distribution in e+e- annihilation. This jet mass observable is based on the thrust cone jet algorithm, which involves a veto scale for out-of-jet radiation. The previously uncomputed part of our result depends in a complicated way on the jet cone size, r, and at intermediate stages of the calculation we actually encounter a new class of multiple polylogarithms. We employ an extension of the coproduct calculus to systematically exploit functional relations and represent our results concisely. In contrast to the individual contributions, themore » sum of all global terms can be expressed in terms of classical polylogarithms. Our explicit two-loop calculation enables us to clarify the small r picture discussed in earlier work. In particular, we show that the resummation of the logarithms of r that appear in the previously uncomputed part of the two-loop integrated jet thrust distribution is inextricably linked to the resummation of the non-global logarithms. Furthermore, we find that the logarithms of r which cannot be absorbed into the non-global logarithms in the way advocated in earlier work have coefficients fixed by the two-loop cusp anomalous dimension. We also show that in many cases one can straightforwardly predict potentially large logarithmic contributions to the integrated jet thrust distribution at L loops by making use of analogous contributions to the simpler integrated hemisphere soft function.« less

Leading-Color Fully Differential Two-Loop Soft Corrections to QCD Dipole Showers

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

Dulat, Falko; Höche, Stefan; Prestel, Stefan

We compute the next-to-leading order corrections to soft-gluon radiation differentially in the one-emission phase space. We show that their contribution to the evolution of color dipoles can be obtained in a modified subtraction scheme, such that both one- and two-emission terms are amenable to Monte-Carlo integration. The two-loop cusp anomalous dimension is recovered naturally upon integration over the full phase space. We present two independent implementations of the new algorithm in the two event generators Pythia and Sherpa, and we compare the resulting fully differential simulation to the CMW scheme.

Spacetimes with Killing tensors. [for Einstein-Maxwell fields with certain spinor indices

NASA Technical Reports Server (NTRS)

Hughston, L. P.; Sommers, P.

1973-01-01

The characteristics of the Killing equation and the Killing tensor are discussed. A conformal Killing tensor is of interest inasmuch as it gives rise to a quadratic first integral for null geodesic orbits. The Einstein-Maxwell equations are considered together with the Bianchi identity and the conformal Killing tensor. Two examples for the application of the considered relations are presented, giving attention to the charged Kerr solution and the charged C-metric.

Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction

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

Parrish, Robert M.; Sherrill, C. David, E-mail: sherrill@gatech.edu; Hohenstein, Edward G.

2014-05-14

We apply orbital-weighted least-squares tensor hypercontraction decomposition of the electron repulsion integrals to accelerate the coupled cluster singles and doubles (CCSD) method. Using accurate and flexible low-rank factorizations of the electron repulsion integral tensor, we are able to reduce the scaling of the most vexing particle-particle ladder term in CCSD from O(N{sup 6}) to O(N{sup 5}), with remarkably low error. Combined with a T{sub 1}-transformed Hamiltonian, this leads to substantial practical accelerations against an optimized density-fitted CCSD implementation.

Hall viscosity of a chiral two-orbital superconductor at finite temperatures

NASA Astrophysics Data System (ADS)

Yazdani-Hamid, Meghdad; Shahzamanian, Mohammad Ali

2018-06-01

The Hall viscosity known as the anti-symmetric part of the viscosity fourth-rank tensor. Such dissipationless response which appears for systems with broken time reversal symmetry. We calculate this non-dissipative quantity for a chiral two-orbital superconductor placed in a viscoelastic magnetic field using the linear response theory and apply our calculations to the putative multiband chiral superconductor Sr2RuO4. The chirality origin of a multiband superconductor arises from the interorbital coupling of the superconducting state. This feature leads to the robustness of the Hall viscosity against temperature and impurity effects. We study the temperature effect on the Hall viscosity at the one-loop approximation.

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

Ellis, Sebastian A. R.; Quevillon, Jérémie; You, Tevong

Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass dependence encapsulated in the universal coefficients. In this study we show that it can account for loops of mixed heavy–light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintaining the universal structure ofmore » the effective action, which we illustrate using the example of integrating out a heavy electroweak triplet scalar coupling to a light Higgs doublet. Finally we also identify new structures that were previously neglected in the universal results.« less

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

2018-02-01

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

Vacuum birefringence in strong magnetic fields: (II) Complex refractive index from the lowest Landau level

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

Hattori, Koichi, E-mail: khattori@yonsei.ac.kr; Itakura, Kazunori, E-mail: kazunori.itakura@kek.jp; Department of Particle and Nuclear Studies, Graduate University for Advanced Studies

2013-07-15

We compute the refractive indices of a photon propagating in strong magnetic fields on the basis of the analytic representation of the vacuum polarization tensor obtained in our previous paper. When the external magnetic field is strong enough for the fermion one-loop diagram of the polarization tensor to be approximated by the lowest Landau level, the propagating mode in parallel to the magnetic field is subject to modification: The refractive index deviates from unity and can be very large, and when the photon energy is large enough, the refractive index acquires an imaginary part indicating decay of a photon intomore » a fermion–antifermion pair. We study dependences of the refractive index on the propagating angle and the magnetic-field strength. It is also emphasized that a self-consistent treatment of the equation which defines the refractive index is indispensable for accurate description of the refractive index. This self-consistent treatment physically corresponds to consistently including the effects of back reactions of the distorted Dirac sea in response to the incident photon. -- Highlights: •Vacuum birefringence and photon decay are described by the complex refractive index. •Resummed photon vacuum polarization tensor in the lowest Landau level is used. •Back reactions from the distorted Dirac sea are self-consistently taken into account. •Self-consistent treatment drastically changes structure in photon energy dependence. •Dependences on photon propagation angle and magnetic-field strength are presented.« less

Spinning AdS loop diagrams: two point functions

NASA Astrophysics Data System (ADS)

Giombi, Simone; Sleight, Charlotte; Taronna, Massimo

2018-06-01

We develop a systematic approach to evaluating AdS loop amplitudes with spinning legs based on the spectral (or "split") representation of bulk-to-bulk propagators, which re-expresses loop diagrams in terms of spectral integrals and higher-point tree diagrams. In this work we focus on 2pt one-loop Witten diagrams involving totally symmetric fields of arbitrary mass and integer spin. As an application of this framework, we study the contribution to the anomalous dimension of higher-spin currents generated by bubble diagrams in higher-spin gauge theories on AdS.

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

PubMed Central

Chanraud, Sandra; Zahr, Natalie; Pfefferbaum, Adolf

2010-01-01

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

Tachyon warm inflation with the effects of loop quantum cosmology in the light of Planck 2015

NASA Astrophysics Data System (ADS)

Kamali, Vahid; Basilakos, Spyros; Mehrabi, Ahmad; Motaharfar, Meysam; Massaeli, Erfan

We investigate the observational signatures of quantum cosmology in the Cosmic Microwave Background data provided by Planck collaboration. We apply the warm inflationary paradigm with a tachyon scalar field to the loop quantum cosmology. In this context, we first provide the basic cosmological functions in terms of the tachyon field. We then obtain the slow-roll parameters and the power spectrum of scalar and tensor fluctuations, respectively. Finally, we study the performance of various warm inflationary scenarios against the latest Planck data and we find a family of models which are in agreement with the observations.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Automated Coronal Loop Identification Using Digital Image Processing Techniques

NASA Technical Reports Server (NTRS)

Lee, Jong K.; Gary, G. Allen; Newman, Timothy S.

2003-01-01

The results of a master thesis project on a study of computer algorithms for automatic identification of optical-thin, 3-dimensional solar coronal loop centers from extreme ultraviolet and X-ray 2-dimensional images will be presented. These center splines are proxies of associated magnetic field lines. The project is pattern recognition problems in which there are no unique shapes or edges and in which photon and detector noise heavily influence the images. The study explores extraction techniques using: (1) linear feature recognition of local patterns (related to the inertia-tensor concept), (2) parametric space via the Hough transform, and (3) topological adaptive contours (snakes) that constrains curvature and continuity as possible candidates for digital loop detection schemes. We have developed synthesized images for the coronal loops to test the various loop identification algorithms. Since the topology of these solar features is dominated by the magnetic field structure, a first-order magnetic field approximation using multiple dipoles provides a priori information in the identification process. Results from both synthesized and solar images will be presented.

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.

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

Miyashita, Takenori, E-mail: takenori@med.kagawa-u.ac.jp; Burford, James L.; Hong, Young-Kwon

Highlights: •We newly developed the whole-mount imaging method of the tympanic membrane. •Lymphatic vessel loops were localized around the malleus handle and annulus tympanicus. •In regeneration, abundant lymphatic vessels were observed in the pars tensa. •Site-specific lymphatic vessels may play an important role in the tympanic membrane. -- Abstract: We clarified the localization of lymphatic vessels in the tympanic membrane and proliferation of lymphatic vessels during regeneration after perforation of the tympanic membrane by using whole-mount imaging of the tympanic membrane of Prox1 GFP mice. In the pars tensa, lymphatic vessel loops surrounded the malleus handle and annulus tympanicus. Apartmore » from these locations, lymphatic vessel loops were not observed in the pars tensa in the normal tympanic membrane. Lymphatic vessel loops surrounding the malleus handle were connected to the lymphatic vessel loops in the pars flaccida and around the tensor tympani muscle. Many lymphatic vessel loops were detected in the pars flaccida. After perforation of the tympanic membrane, abundant lymphatic regeneration was observed in the pars tensa, and these regenerated lymphatic vessels extended from the lymphatic vessels surrounding the malleus at day 7. These results suggest that site-specific lymphatic vessels play an important role in the tympanic membrane.« less

Notes on integrable boundary interactions of open SU(4) alternating spin chains

NASA Astrophysics Data System (ADS)

Wu, JunBao

2018-07-01

Ref. [J. High Energy Phys. 1708, 001 (2017)] showed that the planar flavored Ahanory-Bergman-Jafferis-Maldacena (ABJM) theory is integrable in the scalar sector at two-loop order using coordinate Bethe ansatz. A salient feature of this case is that the boundary reflection matrices are anti-diagonal with respect to the chosen basis. In this paper, we relax the coefficients of the boundary terms to be general constants to search for integrable systems among this class. We found that the only integrable boundary interaction at each end of the spin chain aside from the one in ref. [J. High Energy Phys. 1708, 001 (2017)] is the one with vanishing boundary interactions leading to diagonal reflection matrices. We also construct non-supersymmetric planar flavored ABJM theory which leads to trivial boundary interactions at both ends of the open chain from the two-loop anomalous dimension matrix in the scalar sector.

Opto-electronic oscillator: moving toward solutions based on polymer materials

NASA Astrophysics Data System (ADS)

Nguyên, Lâm Duy; Journet, Bernard; Zyss, Joseph

2008-02-01

Optoelectronic oscillators have been studied since many years now, their high spectral purity being one of their most interesting quality for photonics signal processing, communication or radio over fiber systems. One part of the structure is a long fiber optic feedback loop acting as a delay line. Different techniques have been introduced such as multiple loops in order to get very narrow spectral lines and large mode spacing. One of the problems due to long fiber loops is the size and the requirement of temperature control. In order to go toward integrated solutions it is also possible to introduce optical resonators instead of a delay line structure (as for classical electronic oscillators). But such resonators should present very high quality factor. In this paper we demonstrate solutions using resonators based on polymer materials such as PMMA-DCM. Structures such as micro-rings, micro-disks or stadium-shaped resonator have been realized at the laboratory. Quality factor of 6000 have already been achieved leading to an equivalent fiber loop of 19 m for an oscillator at 10 GHz. But it has been already theoretically proved that quality factor greater than one thousand hundred could be obtained. These resonators can be directly implemented with Mach-Zehnder optical modulators based on electro-optic polymer such as PMMA-DR1 leading to integrated solutions. And in the future it should be also possible to add a laser made with polymer material, with a structure as stadium-shape polymer micro-laser. The fully integrated photonic chip is not so far. The last important function to be implemented is the tuning of the oscillation frequency.

Loop vertex expansion for higher-order interactions

NASA Astrophysics Data System (ADS)

Rivasseau, Vincent

2018-05-01

This note provides an extension of the constructive loop vertex expansion to stable interactions of arbitrarily high order, opening the way to many applications. We treat in detail the example of the (\\bar{φ } φ )^p field theory in zero dimension. We find that the important feature to extend the loop vertex expansion is not to use an intermediate field representation, but rather to force integration of exactly one particular field per vertex of the initial action.

Effective field theory dimensional regularization

NASA Astrophysics Data System (ADS)

Lehmann, Dirk; Prézeau, Gary

2002-01-01

A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed.

Self-gravity, Resonances, and Orbital Diffusion in Stellar Disks

NASA Astrophysics Data System (ADS)

Fouvry, Jean-Baptiste; Binney, James; Pichon, Christophe

2015-06-01

Fluctuations in a stellar system's gravitational field cause the orbits of stars to evolve. The resulting evolution of the system can be computed with the orbit-averaged Fokker-Planck equation once the diffusion tensor is known. We present the formalism that enables one to compute the diffusion tensor from a given source of noise in the gravitational field when the system's dynamical response to that noise is included. In the case of a cool stellar disk we are able to reduce the computation of the diffusion tensor to a one-dimensional integral. We implement this formula for a tapered Mestel disk that is exposed to shot noise and find that we are able to explain analytically the principal features of a numerical simulation of such a disk. In particular the formation of narrow ridges of enhanced density in action space is recovered. As the disk's value of Toomre's Q is reduced and the disk becomes more responsive, there is a transition from a regime of heating in the inner regions of the disk through the inner Lindblad resonance to one of radial migration of near-circular orbits via the corotation resonance in the intermediate regions of the disk. The formalism developed here provides the ideal framework in which to study the long-term evolution of all kinds of stellar disks.

COBALT: A GN&C Payload for Testing ALHAT Capabilities in Closed-Loop Terrestrial Rocket Flights

NASA Technical Reports Server (NTRS)

Carson, John M., III; Amzajerdian, Farzin; Hines, Glenn D.; O'Neal, Travis V.; Robertson, Edward A.; Seubert, Carl; Trawny, Nikolas

2016-01-01

The COBALT (CoOperative Blending of Autonomous Landing Technology) payload is being developed within NASA as a risk reduction activity to mature, integrate and test ALHAT (Autonomous precision Landing and Hazard Avoidance Technology) systems targeted for infusion into near-term robotic and future human space flight missions. The initial COBALT payload instantiation is integrating the third-generation ALHAT Navigation Doppler Lidar (NDL) sensor, for ultra high-precision velocity plus range measurements, with the passive-optical Lander Vision System (LVS) that provides Terrain Relative Navigation (TRN) global-position estimates. The COBALT payload will be integrated onboard a rocket-propulsive terrestrial testbed and will provide precise navigation estimates and guidance planning during two flight test campaigns in 2017 (one open-loop and closed- loop). The NDL is targeting performance capabilities desired for future Mars and Moon Entry, Descent and Landing (EDL). The LVS is already baselined for TRN on the Mars 2020 robotic lander mission. The COBALT platform will provide NASA with a new risk-reduction capability to test integrated EDL Guidance, Navigation and Control (GN&C) components in closed-loop flight demonstrations prior to the actual mission EDL.

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.

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

Assessment of MRI-Based Marker of Dopaminergic Integrity as a Biological Indicator of Gulf War Illness

DTIC Science & Technology

2016-10-01

including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and...SUBJECT TERMS Gulf war illness; magnetic resonance imaging; dopamine; diffusion tensor imaging 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF...nigra, basal ganglia and cortex as markers of integrity of the nigro-striatal dopaminergic pathway using high resolution diffusion tensor imaging (DTI

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.

Design of a compact static Fourier transform spectrometer in integrated optics based on a leaky loop structure.

PubMed

Martin, Bruno; Morand, Alain; Benech, Pierre; Leblond, Gregory; Blaize, Sylvain; Lerondel, Gilles; Royer, Pascal; Kern, Pierre; Le Coarer, Etienne

2009-01-15

A compact static Fourier transform spectrometer for integrated optics is proposed. It is based on a plane leaky loop structure combined with a plane waveguide. The interference pattern produced in the loop structure leaks outside of it and is guided in the plane waveguide to the photodetector array. This configuration allows one to control the shape of the field pattern at the end of the plane waveguide. A large fringe pattern with a high interference fringe contrast is obtained. A two-dimensional model based on an aperiodic Fourier modal method is used to modelize the coupling between the bent and the plane waveguides, completed with the Helmholtz-Kirchhoff propagation. This concept gives access to plan and compact spectrometers requiring only a single low-cost realization process step. The simulation has been done to realize a spectrometer in glass integrated optics (Deltalambda=6.1 nm at 1500 nm).

Hagedorn Temperature of AdS5/CFT4 via Integrability

NASA Astrophysics Data System (ADS)

Harmark, Troels; Wilhelm, Matthias

2018-02-01

We establish a framework for calculating the Hagedorn temperature of AdS5/CFT4 via integrability. Concretely, we derive the thermodynamic Bethe ansatz equations that yield the Hagedorn temperature of planar N =4 super Yang-Mills theory at any value of the 't Hooft coupling. We solve these equations perturbatively at weak coupling via the associated Y system, confirming the known results at tree level and one-loop order as well as deriving the previously unknown two-loop Hagedorn temperature. Finally, we comment on solving the equations at finite coupling.

Open-loop frequency acquisition for suppressed-carrier biphase signals using one-pole arm filters

NASA Technical Reports Server (NTRS)

Shah, B.; Holmes, J. K.

1991-01-01

Open loop frequency acquisition performance is discussed for suppressed carrier binary phase shift keyed signals in terms of the probability of detecting the carrier frequency offset when the arms of the Costas loop detector have one pole filters. The approach, which does not require symbol timing, uses fast Fourier transforms (FFTs) to detect the carrier frequency offset. The detection probability, which depends on both the 3 dB arm filter bandwidth and the received symbol signal to noise ratio, is derived and is shown to be independent of symbol timing. It is shown that the performance of this technique is slightly better that other open loop acquisition techniques which use integrators in the arms and whose detection performance varies with symbol timing.

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.)

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.

Rigid Body Rate Inference from Attitude Variation

NASA Technical Reports Server (NTRS)

Bar-Itzhack, I. Y.; Harman, Richard R.; Thienel, Julie K.

2006-01-01

In this paper we research the extraction of the angular rate vector from attitude information without differentiation, in particular from quaternion measurements. We show that instead of using a Kalman filter of some kind, it is possible to obtain good rate estimates, suitable for spacecraft attitude control loop damping, using simple feedback loops, thereby eliminating the need for recurrent covariance computation performed when a Kalman filter is used. This considerably simplifies the computations required for rate estimation in gyro-less spacecraft. Some interesting qualities of the Kalman filter gain are explored, proven and utilized. We examine two kinds of feedback loops, one with varying gain that is proportional to the well known Q matrix, which is computed using the measured quaternion, and the other type of feedback loop is one with constant coefficients. The latter type includes two kinds; namely, a proportional feedback loop, and a proportional-integral feedback loop. The various schemes are examined through simulations and their performance is compared. It is shown that all schemes are adequate for extracting the angular velocity at an accuracy suitable for control loop damping.

On the Extraction of Angular Velocity from Attitude Measurements

NASA Technical Reports Server (NTRS)

Bar-Itzhack, I. Y.; Harman, Richard R.; Thienel, Julie K.

2006-01-01

In this paper we research the extraction of the angular rate vector from attitude information without differentiation, in particular from quaternion measurements. We show that instead of using a Kalman filter of some kind, it is possible to obtain good rate estimates, suitable for spacecraft attitude control loop damping, using simple feedback loops, thereby eliminating the need for recurrent covariance computation performed when a Kalman filter is used. This considerably simplifies the computations required for rate estimation in gyro-less spacecraft. Some interesting qualities of the Kalman filter gain are explored, proven and utilized. We examine two kinds of feedback loops, one with varying gain that is proportional to the well known Q matrix, which is computed using the measured quaternion, and the other type of feedback loop is one with constant coefficients. The latter type includes two kinds; namely, a proportional feedback loop, and a proportional-integral feedback loop. The various schemes are examined through simulations and their performance is compared. It is shown that all schemes are adequate for extracting the angular velocity at an accuracy suitable for control loop damping.

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

NASA Astrophysics Data System (ADS)

Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia

2008-11-01

Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).

Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction

NASA Astrophysics Data System (ADS)

Ammari, Habib; Qiu, Lingyun; Santosa, Fadil; Zhang, Wenlong

2017-12-01

In this paper we present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor by integrating magneto-acoutic tomography with data acquired from diffusion tensor imaging. Magneto-acoustic tomography with magnetic induction (MAT-MI) is a hybrid, non-invasive medical imaging technique to produce conductivity images with improved spatial resolution and accuracy. Diffusion tensor imaging (DTI) is also a non-invasive technique for characterizing the diffusion properties of water molecules in tissues. We propose a model for anisotropic conductivity in which the conductivity is proportional to the diffusion tensor. Under this assumption, we propose an optimal control approach for reconstructing the anisotropic electrical conductivity tensor. We prove convergence and Lipschitz type stability of the algorithm and present numerical examples to illustrate its accuracy and feasibility.

The two and three-loop matter bispectrum in perturbation theories

NASA Astrophysics Data System (ADS)

Lazanu, Andrei; Liguori, Michele

2018-04-01

We evaluate for the first time the dark matter bispectrum of large-scale structure at two loops in the Standard Perturbation Theory and at three loops in the Renormalised Perturbation Theory (MPTBREEZE formalism), removing in each case the leading divergences in the integrals in order to make them infrared-safe. We show that the Standard Perturbation Theory at two loops can be employed to model the matter bispectrum further into the quasi-nonlinear regime compared to the one loop, up to kmax ~ 0.1 h/Mpc at z = 0, but without reaching a high level of accuracy. In the case of the MPTBREEZE method, we show that its bispectra decay at smaller and smaller scales with increasing loop order, but with smaller improvements decreases with loop order. At three loops, this model predicts the bispectrum accurately up to scales kmax ~ 0.17 h/Mpc at z = 0 and kmax ~ 0.24 h/Mpc at z = 1.

Exploring the potential of machine learning to break deadlock in convection parameterization

NASA Astrophysics Data System (ADS)

Pritchard, M. S.; Gentine, P.

2017-12-01

We explore the potential of modern machine learning tools (via TensorFlow) to replace parameterization of deep convection in climate models. Our strategy begins by generating a large ( 1 Tb) training dataset from time-step level (30-min) output harvested from a one-year integration of a zonally symmetric, uniform-SST aquaplanet integration of the SuperParameterized Community Atmosphere Model (SPCAM). We harvest the inputs and outputs connecting each of SPCAM's 8,192 embedded cloud-resolving model (CRM) arrays to its host climate model's arterial thermodynamic state variables to afford 143M independent training instances. We demonstrate that this dataset is sufficiently large to induce preliminary convergence for neural network prediction of desired outputs of SP, i.e. CRM-mean convective heating and moistening profiles. Sensitivity of the machine learning convergence to the nuances of the TensorFlow implementation are discussed, as well as results from pilot tests from the neural network operating inline within the SPCAM as a replacement to the (super)parameterization of convection.

Cut and join operator ring in tensor models

NASA Astrophysics Data System (ADS)

Itoyama, H.; Mironov, A.; Morozov, A.

2018-07-01

Recent advancement of rainbow tensor models based on their superintegrability (manifesting itself as the existence of an explicit expression for a generic Gaussian correlator) has allowed us to bypass the long-standing problem seen as the lack of eigenvalue/determinant representation needed to establish the KP/Toda integrability. As the mandatory next step, we discuss in this paper how to provide an adequate designation to each of the connected gauge-invariant operators that form a double coset, which is required to cleverly formulate a tree-algebra generalization of the Virasoro constraints. This problem goes beyond the enumeration problem per se tied to the permutation group, forcing us to introduce a few gauge fixing procedures to the coset. We point out that the permutation-based labeling, which has proven to be relevant for the Gaussian averages is, via interesting complexity, related to the one based on the keystone trees, whose algebra will provide the tensor counterpart of the Virasoro algebra for matrix models. Moreover, our simple analysis reveals the existence of nontrivial kernels and co-kernels for the cut operation and for the join operation respectively that prevent a straightforward construction of the non-perturbative RG-complete partition function and the identification of truly independent time variables. We demonstrate these problems by the simplest non-trivial Aristotelian RGB model with one complex rank-3 tensor, studying its ring of gauge-invariant operators, generated by the keystone triple with the help of four operations: addition, multiplication, cut and join.

One-loop matching and running with covariant derivative expansion

DOE PAGES

Henning, Brian; Lu, Xiaochuan; Murayama, Hitoshi

2018-01-24

We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these “mixed” one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-knownmore » matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of “integrating out” heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.« less

One-loop matching and running with covariant derivative expansion

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

Henning, Brian; Lu, Xiaochuan; Murayama, Hitoshi

We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these “mixed” one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-knownmore » matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of “integrating out” heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.« less

One-loop matching and running with covariant derivative expansion

NASA Astrophysics Data System (ADS)

Henning, Brian; Lu, Xiaochuan; Murayama, Hitoshi

2018-01-01

We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these "mixed" one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-known matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of "integrating out" heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.

Irreversibility and higher-spin conformal field theory

NASA Astrophysics Data System (ADS)

Anselmi, Damiano

2000-08-01

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

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.

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

NASA Astrophysics Data System (ADS)

Brandenburg, John

2012-10-01

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

On the Casimir scaling violation in the cusp anomalous dimension at small angle

NASA Astrophysics Data System (ADS)

Grozin, Andrey; Henn, Johannes; Stahlhofen, Maximilian

2017-10-01

We compute the four-loop n f contribution proportional to the quartic Casimir of the QCD cusp anomalous dimension as an expansion for small cusp angle ϕ. This piece is gauge invariant, violates Casimir scaling, and first appears at four loops. It requires the evaluation of genuine non-planar four-loop Feynman integrals. We present results up to O({φ}^4) . One motivation for our calculation is to probe a recent conjecture on the all-order structure of the cusp anomalous dimension. As a byproduct we obtain the four-loop HQET wave function anomalous dimension for this color structure.

Multi-loop positivity of the planar $$ \\mathcal{N} $$ = 4 SYM six-point amplitude

DOE PAGES

Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.; ...

2017-02-22

We study the six-point NMHV ratio function in planarmore » $$ \\mathcal{N} $$ = 4 SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a “radial” direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.« less

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2013-08-07

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

Hardware in the Loop at Megawatt-Scale Power | Energy Systems Integration

Science.gov Websites

Facility | NREL Hardware in the Loop at Megawatt-Scale Power Hardware in the Loop at Megawatt -Scale Power Hardware-in-the-loop simulation is not new, but the Energy System Integration Facility's -in-the-loop co-simulation. For more information, read the power hardware-in-the-loop factsheet. Text

COBALT CoOperative Blending of Autonomous Landing Technology

NASA Technical Reports Server (NTRS)

Carson, John M. III; Restrepo, Carolina I.; Robertson, Edward A.; Seubert, Carl R.; Amzajerdian, Farzin

2016-01-01

COBALT is a terrestrial test platform for development and maturation of GN&C (Guidance, Navigation and Control) technologies for PL&HA (Precision Landing and Hazard Avoidance). The project is developing a third generation, Langley Navigation Doppler Lidar (NDL) for ultra-precise velocity and range measurements, which will be integrated and tested with the JPL Lander Vision System (LVS) for Terrain Relative Navigation (TRN) position estimates. These technologies together provide navigation that enables controlled precision landing. The COBALT hardware will be integrated in 2017 into the GN&C subsystem of the Xodiac rocket-propulsive Vertical Test Bed (VTB) developed by Masten Space Systems (MSS), and two terrestrial flight campaigns will be conducted: one open-loop (i.e., passive) and one closed-loop (i.e., active).

Development of a Human Brain Diffusion Tensor Template

PubMed Central

Peng, Huiling; Orlichenko, Anton; Dawe, Robert J.; Agam, Gady; Zhang, Shengwei; Arfanakis, Konstantinos

2009-01-01

The development of a brain template for diffusion tensor imaging (DTI) is crucial for comparisons of neuronal structural integrity and brain connectivity across populations, as well as for the development of a white matter atlas. Previous efforts to produce a DTI brain template have been compromised by factors related to image quality, the effectiveness of the image registration approach, the appropriateness of subject inclusion criteria, the completeness and accuracy of the information summarized in the final template. The purpose of this work was to develop a DTI human brain template using techniques that address the shortcomings of previous efforts. Therefore, data containing minimal artifacts were first obtained on 67 healthy human subjects selected from an age-group with relatively similar diffusion characteristics (20–40 years of age), using an appropriate DTI acquisition protocol. Non-linear image registration based on mean diffusion-weighted and fractional anisotropy images was employed. DTI brain templates containing median and mean tensors were produced in ICBM-152 space and made publicly available. The resulting set of DTI templates is characterized by higher image sharpness, provides the ability to distinguish smaller white matter fiber structures, contains fewer image artifacts, than previously developed templates, and to our knowledge, is one of only two templates produced based on a relatively large number of subjects. Furthermore, median tensors were shown to better preserve the diffusion characteristics at the group level than mean tensors. Finally, white matter fiber tractography was applied on the template and several fiber-bundles were traced. PMID:19341801

Development of a human brain diffusion tensor template.

PubMed

Peng, Huiling; Orlichenko, Anton; Dawe, Robert J; Agam, Gady; Zhang, Shengwei; Arfanakis, Konstantinos

2009-07-15

The development of a brain template for diffusion tensor imaging (DTI) is crucial for comparisons of neuronal structural integrity and brain connectivity across populations, as well as for the development of a white matter atlas. Previous efforts to produce a DTI brain template have been compromised by factors related to image quality, the effectiveness of the image registration approach, the appropriateness of subject inclusion criteria, and the completeness and accuracy of the information summarized in the final template. The purpose of this work was to develop a DTI human brain template using techniques that address the shortcomings of previous efforts. Therefore, data containing minimal artifacts were first obtained on 67 healthy human subjects selected from an age-group with relatively similar diffusion characteristics (20-40 years of age), using an appropriate DTI acquisition protocol. Non-linear image registration based on mean diffusion-weighted and fractional anisotropy images was employed. DTI brain templates containing median and mean tensors were produced in ICBM-152 space and made publicly available. The resulting set of DTI templates is characterized by higher image sharpness, provides the ability to distinguish smaller white matter fiber structures, contains fewer image artifacts, than previously developed templates, and to our knowledge, is one of only two templates produced based on a relatively large number of subjects. Furthermore, median tensors were shown to better preserve the diffusion characteristics at the group level than mean tensors. Finally, white matter fiber tractography was applied on the template and several fiber-bundles were traced.

Calibrating a tensor magnetic gradiometer using spin data

USGS Publications Warehouse

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

2005-01-01

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

Differential invariants and exact solutions of the Einstein equations

NASA Astrophysics Data System (ADS)

Lychagin, Valentin; Yumaguzhin, Valeriy

2017-06-01

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

Orbits in elementary, power-law galaxy bars - 1. Occurrence and role of single loops

NASA Astrophysics Data System (ADS)

Struck, Curtis

2018-05-01

Orbits in galaxy bars are generally complex, but simple closed loop orbits play an important role in our conceptual understanding of bars. Such orbits are found in some well-studied potentials, provide a simple model of the bar in themselves, and may generate complex orbit families. The precessing, power ellipse (p-ellipse) orbit approximation provides accurate analytic orbit fits in symmetric galaxy potentials. It remains useful for finding and fitting simple loop orbits in the frame of a rotating bar with bar-like and symmetric power-law potentials. Second-order perturbation theory yields two or fewer simple loop solutions in these potentials. Numerical integrations in the parameter space neighbourhood of perturbation solutions reveal zero or one actual loops in a range of such potentials with rising rotation curves. These loops are embedded in a small parameter region of similar, but librating orbits, which have a subharmonic frequency superimposed on the basic loop. These loops and their librating companions support annular bars. Solid bars can be produced in more complex potentials, as shown by an example with power-law indices varying with radius. The power-law potentials can be viewed as the elementary constituents of more complex potentials. Numerical integrations also reveal interesting classes of orbits with multiple loops. In two-dimensional, self-gravitating bars, with power-law potentials, single-loop orbits are very rare. This result suggests that gas bars or oval distortions are unlikely to be long-lived, and that complex orbits or three-dimensional structure must support self-gravitating stellar bars.

Regularization with numerical extrapolation for finite and UV-divergent multi-loop integrals

NASA Astrophysics Data System (ADS)

de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Kapenga, J.; Olagbemi, O.

2018-03-01

We give numerical integration results for Feynman loop diagrams such as those covered by Laporta (2000) and by Baikov and Chetyrkin (2010), and which may give rise to loop integrals with UV singularities. We explore automatic adaptive integration using multivariate techniques from the PARINT package for multivariate integration, as well as iterated integration with programs from the QUADPACK package, and a trapezoidal method based on a double exponential transformation. PARINT is layered over MPI (Message Passing Interface), and incorporates advanced parallel/distributed techniques including load balancing among processes that may be distributed over a cluster or a network/grid of nodes. Results are included for 2-loop vertex and box diagrams and for sets of 2-, 3- and 4-loop self-energy diagrams with or without UV terms. Numerical regularization of integrals with singular terms is achieved by linear and non-linear extrapolation methods.

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

Aortic stiffness is associated with white matter integrity in patients with type 1 diabetes.

PubMed

Tjeerdema, Nathanja; Van Schinkel, Linda D; Westenberg, Jos J; Van Elderen, Saskia G; Van Buchem, Mark A; Smit, Johannes W; Van der Grond, Jeroen; De Roos, Albert

2014-09-01

To assess the association between aortic pulse wave velocity (PWV) as a marker of arterial stiffness and diffusion tensor imaging of brain white matter integrity in patients with type 1 diabetes using advanced magnetic resonance imaging (MRI) technology. Forty-one patients with type 1 diabetes (23 men, mean age 44 ± 12 years, mean diabetes duration 24 ± 13 years) were included. Aortic PWV was assessed using through-plane velocity-encoded MRI. Brain diffusion tensor imaging (DTI) measurements were performed on 3-T MRI. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were calculated for white and grey matter integrity. Pearson correlation and multivariable linear regression analyses including cardiovascular risk factors as covariates were assessed. Multivariable linear regression analyses revealed that aortic PWV is independently associated with white matter integrity FA (β = -0.777, p = 0.008) in patients with type 1 diabetes. This effect was independent of age, gender, mean arterial pressure, body mass index, smoking, duration of diabetes and glycated haemoglobin levels. Aortic PWV was not significantly related to grey matter integrity. Our data suggest that aortic stiffness is independently associated with reduced white matter integrity in patients with type 1 diabetes. Aortic stiffness is associated with brain injury. Aortic stiffness exposes small vessels to high pressure fluctuations and flow. Aortic stiffness is associated with microvascular brain injury in diabetes. This suggests a vascular contribution to early subtle microstructural deficits.

Moment Tensor Inversions of the M1.7+ Earthquakes in Basel. Switzerland Reveal Predominant Shear Dislocations

NASA Astrophysics Data System (ADS)

Guilhem, A.; Walter, F. T.

2013-12-01

We investigate moment tensor solutions of nearly 30 magnitude (M) 1.7+ earthquakes that occurred in Basel, Switzerland during and after the simulation of the geothermal enhanced system between December 2nd and 8th 2006. In 2009, Deichmann and Ernst determined the focal mechanisms for these events using P-wave first-motions. They found clear evidence for double-couple mechanisms with no indications for substantial volumetric changes. This differs from evidences of composite type ruptures (i.e., shearing with isotropic motion) observed in other geothermal environments. Here, we use a similar approach for the computation of the moment tensor inversions to the one used by Guilhem et al. (2012) for M3 earthquakes in Geysers. We use a dataset from strong-motion stations located within 7 km from the epicenters, with data filtered between 0.5 and 3 Hz and integrated twice to displacement. The waveforms are inverted for both deviatoric and full moment tensor solutions. In addition, we perform a network sensitivity test (NSS) by computing 100 million random moment tensors for each event thus testing the sensitivity of the moment tensor solutions. Finally, because the injection of fluids in the ground can promote crack growth generating seismic events, we also compute a crack + double-couple inversion (Minson et al., 2007) for each of the studied earthquakes between December 2006 and May 2007. From this extensive search we find that the results of our different techniques converge. Moment tensor solutions are very similar to the first-motion focal mechanisms of Deichmann and Ernst (2009) and accordingly do not exhibit dominant volumetric changes except for a subset of events, which we discuss in some detail. References: Deichmann, N. and Ernst, J. (2009), Swiss J. Geosc. Guilhem, A., Dreger, D.S., Hutchings, L. J., and Johnson, L. (2012), AGU Fall meeting Minson, S. E., Dreger, D. S., Bürgmann, R., Kanamori, H., Larson, K. M. (2007), J. Geophys. Res.

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

On physical property tensors invariant under line groups.

PubMed

Litvin, Daniel B

2014-03-01

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

Loop series for discrete statistical models on graphs

NASA Astrophysics Data System (ADS)

Chertkov, Michael; Chernyak, Vladimir Y.

2006-06-01

In this paper we present the derivation details, logic, and motivation for the three loop calculus introduced in Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R)). Generating functions for each of the three interrelated discrete statistical models are expressed in terms of a finite series. The first term in the series corresponds to the Bethe-Peierls belief-propagation (BP) contribution; the other terms are labelled by loops on the factor graph. All loop contributions are simple rational functions of spin correlation functions calculated within the BP approach. We discuss two alternative derivations of the loop series. One approach implements a set of local auxiliary integrations over continuous fields with the BP contribution corresponding to an integrand saddle-point value. The integrals are replaced by sums in the complementary approach, briefly explained in Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R)). Local gauge symmetry transformations that clarify an important invariant feature of the BP solution are revealed in both approaches. The individual terms change under the gauge transformation while the partition function remains invariant. The requirement for all individual terms to be nonzero only for closed loops in the factor graph (as opposed to paths with loose ends) is equivalent to fixing the first term in the series to be exactly equal to the BP contribution. Further applications of the loop calculus to problems in statistical physics, computer and information sciences are discussed.

A minimal approach to the scattering of physical massless bosons

NASA Astrophysics Data System (ADS)

Boels, Rutger H.; Luo, Hui

2018-05-01

Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integration-by-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A number of proof-of-concept examples are presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. Dimensional regularisation is employed throughout; different regularisation schemes are worked out explicitly. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, in the introduced approach iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the so-called rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control colour quantum numbers of scattering amplitudes with matter, especially efficient in the adjoint and fundamental representations.

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.

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.

Improving predicted protein loop structure ranking using a Pareto-optimality consensus method.

PubMed

Li, Yaohang; Rata, Ionel; Chiu, See-wing; Jakobsson, Eric

2010-07-20

Accurate protein loop structure models are important to understand functions of many proteins. Identifying the native or near-native models by distinguishing them from the misfolded ones is a critical step in protein loop structure prediction. We have developed a Pareto Optimal Consensus (POC) method, which is a consensus model ranking approach to integrate multiple knowledge- or physics-based scoring functions. The procedure of identifying the models of best quality in a model set includes: 1) identifying the models at the Pareto optimal front with respect to a set of scoring functions, and 2) ranking them based on the fuzzy dominance relationship to the rest of the models. We apply the POC method to a large number of decoy sets for loops of 4- to 12-residue in length using a functional space composed of several carefully-selected scoring functions: Rosetta, DOPE, DDFIRE, OPLS-AA, and a triplet backbone dihedral potential developed in our lab. Our computational results show that the sets of Pareto-optimal decoys, which are typically composed of approximately 20% or less of the overall decoys in a set, have a good coverage of the best or near-best decoys in more than 99% of the loop targets. Compared to the individual scoring function yielding best selection accuracy in the decoy sets, the POC method yields 23%, 37%, and 64% less false positives in distinguishing the native conformation, indentifying a near-native model (RMSD < 0.5A from the native) as top-ranked, and selecting at least one near-native model in the top-5-ranked models, respectively. Similar effectiveness of the POC method is also found in the decoy sets from membrane protein loops. Furthermore, the POC method outperforms the other popularly-used consensus strategies in model ranking, such as rank-by-number, rank-by-rank, rank-by-vote, and regression-based methods. By integrating multiple knowledge- and physics-based scoring functions based on Pareto optimality and fuzzy dominance, the POC method is effective in distinguishing the best loop models from the other ones within a loop model set.

Improving predicted protein loop structure ranking using a Pareto-optimality consensus method

PubMed Central

2010-01-01

Background Accurate protein loop structure models are important to understand functions of many proteins. Identifying the native or near-native models by distinguishing them from the misfolded ones is a critical step in protein loop structure prediction. Results We have developed a Pareto Optimal Consensus (POC) method, which is a consensus model ranking approach to integrate multiple knowledge- or physics-based scoring functions. The procedure of identifying the models of best quality in a model set includes: 1) identifying the models at the Pareto optimal front with respect to a set of scoring functions, and 2) ranking them based on the fuzzy dominance relationship to the rest of the models. We apply the POC method to a large number of decoy sets for loops of 4- to 12-residue in length using a functional space composed of several carefully-selected scoring functions: Rosetta, DOPE, DDFIRE, OPLS-AA, and a triplet backbone dihedral potential developed in our lab. Our computational results show that the sets of Pareto-optimal decoys, which are typically composed of ~20% or less of the overall decoys in a set, have a good coverage of the best or near-best decoys in more than 99% of the loop targets. Compared to the individual scoring function yielding best selection accuracy in the decoy sets, the POC method yields 23%, 37%, and 64% less false positives in distinguishing the native conformation, indentifying a near-native model (RMSD < 0.5A from the native) as top-ranked, and selecting at least one near-native model in the top-5-ranked models, respectively. Similar effectiveness of the POC method is also found in the decoy sets from membrane protein loops. Furthermore, the POC method outperforms the other popularly-used consensus strategies in model ranking, such as rank-by-number, rank-by-rank, rank-by-vote, and regression-based methods. Conclusions By integrating multiple knowledge- and physics-based scoring functions based on Pareto optimality and fuzzy dominance, the POC method is effective in distinguishing the best loop models from the other ones within a loop model set. PMID:20642859

Tensoral for post-processing users and simulation authors

NASA Technical Reports Server (NTRS)

Dresselhaus, Eliot

1993-01-01

The 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, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.

Utilizing a Suited Manikin Test Apparatus and Spacesuit Ventilation Loop to Evaluate Carbon Dioxide Washout

NASA Technical Reports Server (NTRS)

Chullen, Cinda; Conger, Bruce; Korona, Adam; Kanne, Bryan; McMillin, Summer; Norcross, Jason; Jeng, Frank; Swickrath, Mike

2014-01-01

NASA is pursuing technology development of an Advanced Extravehicular Mobility Unit (AEMU) which is an integrated assembly made up of primarily a pressure garment system and a Portable Life Support System (PLSS). The PLSS is further composed of an oxygen subsystem, a ventilation subsystem, and a thermal subsystem. One of the key functions of the ventilation system is to remove and control the carbon dioxide delivered to the crewmember. Carbon dioxide washout is the mechanism by which CO2 levels are controlled within the spacesuit helmet to limit the concentration of CO2 inhaled by the crew member. CO2 washout performance is a critical parameter needed to ensure proper and robust designs that are insensitive to human variabilities in a spacesuit. A Suited Manikin Test Apparatus (SMTA) is being developed to augment testing of the PLSS ventilation loop in order to provide a lower cost and more controlled alternative to human testing. The CO2 removal function is performed by the regenerative Rapid Cycle Amine (RCA) within the PLSS ventilation loop and its performance is evaluated within the integrated SMTA and Ventilation Loop test system. This paper will provide a detailed description of the schematics, test configurations, and hardware components of this integrated system. Results and analysis of testing performed with this integrated system will be presented within this paper.

Utilizing a Suited Manikin Test Apparatus and Space Suit Ventilation Loop to Evaluate Carbon Dioxide Washout

NASA Technical Reports Server (NTRS)

Chullen, Cinda; Conger, Bruce; Korona, Adam; Kanne, Bryan; McMillin, Summer; Paul, Thomas; Norcross, Jason; Alonso, Jesus Delgado; Swickrath, Mike

2015-01-01

NASA is pursuing technology development of an Advanced Extravehicular Mobility Unit (AEMU) which is an integrated assembly made up of primarily a pressure garment system and a portable life support subsystem (PLSS). The PLSS is further composed of an oxygen subsystem, a ventilation subsystem, and a thermal subsystem. One of the key functions of the ventilation system is to remove and control the carbon dioxide (CO2) delivered to the crewmember. Carbon dioxide washout is the mechanism by which CO2 levels are controlled within the space suit helmet to limit the concentration of CO2 inhaled by the crew member. CO2 washout performance is a critical parameter needed to ensure proper and robust designs that are insensitive to human variabilities in a space suit. A suited manikin test apparatus (SMTA) was developed to augment testing of the PLSS ventilation loop in order to provide a lower cost and more controlled alternative to human testing. The CO2 removal function is performed by the regenerative Rapid Cycle Amine (RCA) within the PLSS ventilation loop and its performance is evaluated within the integrated SMTA and Ventilation Loop test system. This paper will provide a detailed description of the schematics, test configurations, and hardware components of this integrated system. Results and analysis of testing performed with this integrated system will be presented within this paper.

Resolution of singularities for multi-loop integrals

NASA Astrophysics Data System (ADS)

Bogner, Christian; Weinzierl, Stefan

2008-04-01

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program. Program summaryProgram title: sector_decomposition Catalogue identifier: AEAG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAG_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.: 47 506 No. of bytes in distributed program, including test data, etc.: 328 485 Distribution format: tar.gz Programming language: C++ Computer: all Operating system: Unix RAM: Depending on the complexity of the problem Classification: 4.4 External routines: GiNaC, available from http://www.ginac.de, GNU scientific library, available from http://www.gnu.org/software/gsl Nature of problem: Computation of divergent multi-loop integrals. Solution method: Sector decomposition. Restrictions: Only limited by the available memory and CPU time. Running time: Depending on the complexity of the problem.

Asymptotic One-Point Functions in Gauge-String Duality with Defects.

PubMed

Buhl-Mortensen, Isak; de Leeuw, Marius; Ipsen, Asger C; Kristjansen, Charlotte; Wilhelm, Matthias

2017-12-29

We take the first step in extending the integrability approach to one-point functions in AdS/dCFT to higher loop orders. More precisely, we argue that the formula encoding all tree-level one-point functions of SU(2) operators in the defect version of N=4 supersymmetric Yang-Mills theory, dual to the D5-D3 probe-brane system with flux, has a natural asymptotic generalization to higher loop orders. The asymptotic formula correctly encodes the information about the one-loop correction to the one-point functions of nonprotected operators once dressed by a simple flux-dependent factor, as we demonstrate by an explicit computation involving a novel object denoted as an amputated matrix product state. Furthermore, when applied to the Berenstein-Maldacena-Nastase vacuum state, the asymptotic formula gives a result for the one-point function which in a certain double-scaling limit agrees with that obtained in the dual string theory up to wrapping order.

Higher order first integrals, Killing tensors and Killing-Maxwell system

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2012-02-01

Higher order first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach are investigated. The special role of Stackel-Killing and Killing-Yano tensors is pointed out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Another application of the gauge covariant approach is provided by a non relativistic point charge in the field of a Dirac monopole. The corresponding dynamical system possessing a Kepler type symmetry is associated with the Taub-NUT metric using a reduction procedure of symplectic manifolds with symmetries. The reverse of the reduction procedure can be used to investigate higher-dimensional spacetimes admitting Killing tensors.

White matter integrity as a predictor of response to treatment in first episode psychosis.

PubMed

Reis Marques, Tiago; Taylor, Heather; Chaddock, Chris; Dell'acqua, Flavio; Handley, Rowena; Reinders, A A T Simone; Mondelli, Valeria; Bonaccorso, Stefania; Diforti, Marta; Simmons, Andrew; David, Anthony S; Murray, Robin M; Pariante, Carmine M; Kapur, Shitij; Dazzan, Paola

2014-01-01

The integrity of brain white matter connections is central to a patient's ability to respond to pharmacological interventions. This study tested this hypothesis using a specific measure of white matter integrity, and examining its relationship to treatment response using a prospective design in patients within their first episode of psychosis. Diffusion tensor imaging data were acquired in 63 patients with first episode psychosis and 52 healthy control subjects (baseline). Response was assessed after 12 weeks and patients were classified as responders or non-responders according to treatment outcome. At this second time-point, they also underwent a second diffusion tensor imaging scan. Tract-based spatial statistics were used to assess fractional anisotropy as a marker of white matter integrity. At baseline, non-responders showed lower fractional anisotropy than both responders and healthy control subjects (P < 0.05; family-wise error-corrected), mainly in the uncinate, cingulum and corpus callosum, whereas responders were indistinguishable from healthy control subjects. After 12 weeks, there was an increase in fractional anisotropy in both responders and non-responders, positively correlated with antipsychotic exposure. This represents one of the largest, controlled investigations of white matter integrity and response to antipsychotic treatment early in psychosis. These data, together with earlier findings on cortical grey matter, suggest that grey and white matter integrity at the start of treatment is an important moderator of response to antipsychotics. These findings can inform patient stratification to anticipate care needs, and raise the possibility that antipsychotics may restore white matter integrity as part of the therapeutic response.

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

NASA Astrophysics Data System (ADS)

Hashlamoun, Kotaybah; Grillo, Alfio; Federico, Salvatore

2016-10-01

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

Development Specification for the Portable Life Support System (PLSS) Thermal Loop Pump

NASA Technical Reports Server (NTRS)

Anchondo, Ian; Campbell, Colin

2017-01-01

The AEMU Thermal Loop Pump Development Specification establishes the requirements for design, performance, and testing of the Water Pump as part of the Thermal System of the Advanced Portable Life Support System (PLSS). It is envisioned that the Thermal Loop Pump is a positive displacement pump that provides a repeatable volume of flow against a given range of back-pressures provided by the various applications. The intention is to operate the pump at a fixed speed for the given application. The primary system is made up of two identical and redundant pumps of which only one is in operation at given time. The Auxiliary Loop Pump is an identical pump design to the primary pumps but is operated at half the flow rate. Inlet positive pressure to the pumps is provided by the upstream Flexible Supply Assembly (FSA-431 and FSA-531) which are physically located inside the suit volume and pressurized by suit pressure. An integrated relief valve, placed in parallel to the pump's inlet and outlet protects the pump and loop from over-pressurization. An integrated course filter is placed upstream of the pump's inlet to provide filtration and prevent potential debris from damaging the pump.

Decentralized Dimensionality Reduction for Distributed Tensor Data Across Sensor Networks.

PubMed

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

2016-11-01

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

Black holes, hidden symmetries, and complete integrability

NASA Astrophysics Data System (ADS)

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

2017-11-01

The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

Black holes, hidden symmetries, and complete integrability.

PubMed

Frolov, Valeri P; Krtouš, Pavel; Kubizňák, David

2017-01-01

The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

Aerospace applications of SINDA/FLUINT at the Johnson Space Center

NASA Technical Reports Server (NTRS)

Ewert, Michael K.; Bellmore, Phillip E.; Andish, Kambiz K.; Keller, John R.

1992-01-01

SINDA/FLUINT has been found to be a versatile code for modeling aerospace systems involving single or two-phase fluid flow and all modes of heat transfer. Several applications of SINDA/FLUINT are described in this paper. SINDA/FLUINT is being used extensively to model the single phase water loops and the two-phase ammonia loops of the Space Station Freedom active thermal control system (ATCS). These models range from large integrated system models with multiple submodels to very detailed subsystem models. An integrated Space Station ATCS model has been created with ten submodels representing five water loops, three ammonia loops, a Freon loop and a thermal submodel representing the air loop. The model, which has approximately 800 FLUINT lumps and 300 thermal nodes, is used to determine the interaction between the multiple fluid loops which comprise the Space Station ATCS. Several detailed models of the flow-through radiator subsystem of the Space Station ATCS have been developed. One model, which has approximately 70 FLUINT lumps and 340 thermal nodes, provides a representation of the ATCS low temperature radiator array with two fluid loops connected only by conduction through the radiator face sheet. The detailed models are used to determine parameters such as radiator fluid return temperature, fin efficiency, flow distribution and total heat rejection for the baseline design as well as proposed alternate designs. SINDA/FLUINT has also been used as a design tool for several systems using pressurized gasses. One model examined the pressurization and depressurization of the Space Station airlock under a variety of operating conditions including convection with the side walls and internal cooling. Another model predicted the performance of a new generation of manned maneuvering units. This model included high pressure gas depressurization, internal heat transfer and supersonic thruster equations. The results of both models were used to size components, such as the heaters and gas bottles and also to point to areas where hardware testing was needed.

Polyakov loop fluctuations in the presence of external fields

NASA Astrophysics Data System (ADS)

Lo, Pok Man; Szymański, Michał; Redlich, Krzysztof; Sasaki, Chihiro

2018-06-01

We study the implications of the spontaneous and explicit Z(3) center symmetry breaking for the Polyakov loop susceptibilities. To this end, ratios of the susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop are computed within an effective model using a color group integration scheme. We show that the essential features of the lattice QCD results of these ratios can be successfully captured by the effective approach. Furthermore we discuss a novel scaling relation in one of these ratios involving the explicit breaking field, volume, and temperature.

Proposal for a biometrics of the cortical surface: a statistical method for relative surface distance metrics

NASA Astrophysics Data System (ADS)

Bookstein, Fred L.

1995-08-01

Recent advances in computational geometry have greatly extended the range of neuroanatomical questions that can be approached by rigorous quantitative methods. One of the major current challenges in this area is to describe the variability of human cortical surface form and its implications for individual differences in neurophysiological functioning. Existing techniques for representation of stochastically invaginated surfaces do not conduce to the necessary parametric statistical summaries. In this paper, following a hint from David Van Essen and Heather Drury, I sketch a statistical method customized for the constraints of this complex data type. Cortical surface form is represented by its Riemannian metric tensor and averaged according to parameters of a smooth averaged surface. Sulci are represented by integral trajectories of the smaller principal strains of this metric, and their statistics follow the statistics of that relative metric. The diagrams visualizing this tensor analysis look like alligator leather but summarize all aspects of cortical surface form in between the principal sulci, the reliable ones; no flattening is required.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

On volume-source representations based on the representation theorem

NASA Astrophysics Data System (ADS)

Ichihara, Mie; Kusakabe, Tetsuya; Kame, Nobuki; Kumagai, Hiroyuki

2016-01-01

We discuss different ways to characterize a moment tensor associated with an actual volume change of ΔV C , which has been represented in terms of either the stress glut or the corresponding stress-free volume change ΔV T . Eshelby's virtual operation provides a conceptual model relating ΔV C to ΔV T and the stress glut, where non-elastic processes such as phase transitions allow ΔV T to be introduced and subsequent elastic deformation of - ΔV T is assumed to produce the stress glut. While it is true that ΔV T correctly represents the moment tensor of an actual volume source with volume change ΔV C , an explanation as to why such an operation relating ΔV C to ΔV T exists has not previously been given. This study presents a comprehensive explanation of the relationship between ΔV C and ΔV T based on the representation theorem. The displacement field is represented using Green's function, which consists of two integrals over the source surface: one for displacement and the other for traction. Both integrals are necessary for representing volumetric sources, whereas the representation of seismic faults includes only the first term, as the second integral over the two adjacent fault surfaces, across which the traction balances, always vanishes. Therefore, in a seismological framework, the contribution from the second term should be included as an additional surface displacement. We show that the seismic moment tensor of a volume source is directly obtained from the actual state of the displacement and stress at the source without considering any virtual non-elastic operations. A purely mathematical procedure based on the representation theorem enables us to specify the additional imaginary displacement necessary for representing a volume source only by the displacement term, which links ΔV C to ΔV T . It also specifies the additional imaginary stress necessary for representing a moment tensor solely by the traction term, which gives the "stress glut." The imaginary displacement-stress approach clarifies the mathematical background to the classical theory.

Group field theories for all loop quantum gravity

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Ryan, James P.; Thürigen, Johannes

2015-02-01

Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

Counterterm counterexamples

NASA Astrophysics Data System (ADS)

Pope, C. N.; Sohnius, M. F.; Stelle, K. S.

We show that, contrary to previous conjectures, there exist acceptable counterterms for Ricci-flat N = 1 and N = 2 super-symmetric σ-models. In the N = 1 case we present infinite sequences of counterterms, starting from the 7-loop order, that do not vanish for general riemannian Ricci-flat metrics but do vanish when the metric is also Kähler. We then investigate the counterterms for theories with Ricci-flat Kähler metrics (i.e. N = 2 models). Acceptable counterterms must vanish for hyper-Kähler metrics (the N = 4 case), and must respect the principle of universality; i.e. that counterterms to the metric can be expressed without the use of complex structures or other special tensors, which do not exist for general riemannian spaces. We show that a recently proposed 4-loop counterterm for the N = 2 models does indeed satisfy these two conditions, despite the apparent stringency of the universality principle. Hence the finiteness of Ricci-flat N = 1 and N = 2 supersymmetric σ-models seems unlikely to persist beyond the 3-loop order.

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

PubMed Central

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

2009-01-01

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

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

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.

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

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

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

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

ERIC Educational Resources Information Center

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

2010-01-01

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

COBALT: Development of a Platform to Flight Test Lander GN&C Technologies on Suborbital Rockets

NASA Technical Reports Server (NTRS)

Carson, John M., III; Seubert, Carl R.; Amzajerdian, Farzin; Bergh, Chuck; Kourchians, Ara; Restrepo, Carolina I.; Villapando, Carlos Y.; O'Neal, Travis V.; Robertson, Edward A.; Pierrottet, Diego;

Frobenius manifolds and Frobenius algebra-valued integrable systems

NASA Astrophysics Data System (ADS)

Strachan, Ian A. B.; Zuo, Dafeng

2017-06-01

The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved. In this paper, a new theory of Frobenius algebra-valued integrable systems is developed. This is achieved for systems derived from Frobenius manifolds by utilizing the theory of tensor products for such manifolds, as developed by Kaufmann (Int Math Res Not 19:929-952, 1996), Kontsevich and Manin (Inv Math 124: 313-339, 1996). By specializing this construction, using a fixed Frobenius algebra A, one can arrive at such a theory. More generally, one can apply the same idea to construct an A-valued topological quantum field theory. The Hamiltonian properties of two classes of integrable evolution equations are then studied: dispersionless and dispersive evolution equations. Application of these ideas are discussed, and as an example, an A-valued modified Camassa-Holm equation is constructed.

Energy Systems Integration Facility to Transform U.S. Energy Infrastructure

Science.gov Websites

operations center. Fully integrated with hardware-in-the-loop at power capabilities, an experimental hardware- and systems-in-the-loop capability. Hardware-in-the-Loop at Power ESIF Snapshot Cost : $135M 2013 Hardware-in-the-loop simulation is not a new concept, but adding megawatt-scale power takes

Fully probabilistic control design in an adaptive critic framework.

PubMed

Herzallah, Randa; Kárný, Miroslav

2011-12-01

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem; in particular, very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic control algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this paper. Copyright © 2011 Elsevier Ltd. All rights reserved.

The study of Thai stock market across the 2008 financial crisis

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Hexagonalization of correlation functions II: two-particle contributions

NASA Astrophysics Data System (ADS)

Fleury, Thiago; Komatsu, Shota

2018-02-01

In this work, we compute one-loop planar five-point functions in N=4 super-Yang-Mills using integrability. As in the previous work, we decompose the correlation functions into hexagon form factors and glue them using the weight factors which depend on the cross-ratios. The main new ingredient in the computation, as compared to the four-point functions studied in the previous paper, is the two-particle mirror contribution. We develop techniques to evaluate it and find agreement with the perturbative results in all the cases we analyzed. In addition, we consider next-to-extremal four-point functions, which are known to be protected, and show that the sum of one-particle and two-particle contributions at one loop adds up to zero as expected. The tools developed in this work would be useful for computing higher-particle contributions which would be relevant for more complicated quantities such as higher-loop corrections and non-planar correlators.

Cobalt: Development and Maturation of GN&C Technologies for Precision Landing

NASA Technical Reports Server (NTRS)

Carson, John M.; Restrepo, Carolina; Seubert, Carl; Amzajerdian, Farzin

2016-01-01

The CoOperative Blending of Autonomous Landing Technologies (COBALT) instrument is a terrestrial test platform for development and maturation of guidance, navigation and control (GN&C) technologies for precision landing. The project is developing a third-generation Langley Research Center (LaRC) navigation doppler lidar (NDL) for ultra-precise velocity and range measurements, which will be integrated and tested with the Jet Propulsion Laboratory (JPL) lander vision system (LVS) for terrain relative navigation (TRN) position estimates. These technologies together provide precise navigation knowledge that is critical for a controlled and precise touchdown. The COBALT hardware will be integrated in 2017 into the GN&C subsystem of the Xodiac rocket-propulsive vertical test bed (VTB) developed by Masten Space Systems, and two terrestrial flight campaigns will be conducted: one open-loop (i.e., passive) and one closed-loop (i.e., active).

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.

Effective action for stochastic partial differential equations

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

Hochberg, David; Centro de Astrobiologia, INTA, Carratera Ajalvir, Km. 4, 28850 Torrejon, Madrid,; Molina-Paris, Carmen

Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. SPDEs are used for models of turbulence, pattern formation, and the structural development of the universe itself. It is reasonably well known that certain SPDEs can be manipulated to be equivalent to (nonquantum) field theories that nevertheless exhibit deep and important relationships with quantum field theory. In this paper we systematically extend these ideas: We set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important tomore » realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these nonquantum field theories are fully interacting. The limitation to one loop is not as serious as might be supposed: Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues. The limitation to one loop does, however, offer marked technical advantages: Because at one loop almost any field theory can be rendered finite using zeta function technology, we can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the Becchi-Rouet-Stora-Tyutin formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ''direct approach'' is the SPDE analog of canonical quantization using physical fields). After setting up the general formalism for the characteristic functional (partition function), we show how to define the effective action to all loops, and then focus on the one-loop effective action and its specialization to constant fields: the effective potential. The physical interpretation of the effective action and effective potential for SPDEs is addressed and we show that key features carry over from QFT to the case of SPDEs. An important result is that the amplitude of the two-point function governing the noise acts as the loop-counting parameter and is the analog of Planck's constant ({Dirac_h}/2{pi}) in this SPDE context. We derive a general expression for the one-loop effective potential of an arbitrary SPDE subject to translation-invariant Gaussian noise, and compare this with the one-loop potential for QFT. (c) 1999 The American Physical Society.« less

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

PubMed

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

2018-02-28

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

FAST TRACK COMMUNICATION Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

NASA Astrophysics Data System (ADS)

Senovilla, José M. M.

2010-11-01

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved.

Observational constraints on transverse gravity: A generalization of unimodular gravity

NASA Astrophysics Data System (ADS)

Lopez-Villarejo, J. J.

2010-04-01

We explore the hypothesis that the set of symmetries enjoyed by the theory that describes gravity is not the full group of diffeomorphisms (Diff(M)), as in General Relativity, but a maximal subgroup of it (TransverseDiff(M)), with its elements having a jacobian equal to unity; at the infinitesimal level, the parameter describing the coordinate change xμ → xμ + ξμ(x) is transverse, i.e., δμξμ = 0. Incidentally, this is the smaller symmetry one needs to propagate consistently a graviton, which is a great theoretical motivation for considering these theories. Also, the determinant of the metric, g, behaves as a "transverse scalar", so that these theories can be seen as a generalization of the better-known unimodular gravity. We present our results on the observational constraints on transverse gravity, in close relation with the claim of equivalence with general scalar-tensor theory. We also comment on the structure of the divergences of the quantum theory to the one-loop order.

On the tidal-energy tensor for two homogeneous coaxial ellipsoids

NASA Astrophysics Data System (ADS)

Caimmi, R.; Secco, L.

2001-10-01

The tidal-energy tensor for two homogeneous and coaxial ellipsoids, one lying completely within the other, is investigated in connection with the tidal action exerted by the outer ellipsoid on the inner one. Making reference to the explicit expression found in a previous paper of ours, it is shown that the generic component of the tidal-energy tensor, (i) may be expressed as the product of the corresponding component of the self-energy tensor related to the inner ellipsoid, by the density ratio, and the shape factor ratio, and (ii) equals the one due to any homogeneous, outer ellipsoid, for which the product of the density and a specified shape factor remains unchanged; in particular, the outer ellipsoid may be similar and similarly placed with respect to the inner one. In addition, an explicit expression for the Clausius-virial tensor is derived. Analogous results for the corresponding scalar quantities are also given. Further attention is paid to the particular case of spheroids.

An approach toward the numerical evaluation of multi-loop Feynman diagrams

NASA Astrophysics Data System (ADS)

Passarino, Giampiero

2001-12-01

A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model. As a first step an algorithm, proposed by F.V. Tkachov and based on the so-called generalized Bernstein functional relation, is applied to one-loop multi-leg diagrams with particular emphasis to the presence of infrared singularities, to the problem of tensorial reduction and to the classification of all singularities of a given diagram. Successively, the extension of the algorithm to two-loop diagrams is examined. The proposed solution consists in applying the functional relation to the one-loop sub-diagram which has the largest number of internal lines. In this way the integrand can be made smooth, a part from a factor which is a polynomial in xS, the vector of Feynman parameters needed for the complementary sub-diagram with the smallest number of internal lines. Since the procedure does not introduce new singularities one can distort the xS-integration hyper-contour into the complex hyper-plane, thus achieving numerical stability. The algorithm is then modified to deal with numerical evaluation around normal thresholds. Concise and practical formulas are assembled and presented, numerical results and comparisons with the available literature are shown and discussed for the so-called sunset topology.

Low rank factorization of the Coulomb integrals for periodic coupled cluster theory.

PubMed

Hummel, Felix; Tsatsoulis, Theodoros; Grüneis, Andreas

2017-03-28

We study a tensor hypercontraction decomposition of the Coulomb integrals of periodic systems where the integrals are factorized into a contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small matrices compared to the number of real space grid points. The cost of computing the matrices scales as O(N 4 ) using a regularized form of the alternating least squares algorithm. The studied factorization of the Coulomb integrals can be exploited to reduce the scaling of the computational cost of expensive tensor contractions appearing in the amplitude equations of coupled cluster methods with respect to system size. We apply the developed methodologies to calculate the adsorption energy of a single water molecule on a hexagonal boron nitride monolayer in a plane wave basis set and periodic boundary conditions.

Tensorial Minkowski functionals of triply periodic minimal surfaces

PubMed Central

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

2012-01-01

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

Combining the boundary shift integral and tensor-based morphometry for brain atrophy estimation

NASA Astrophysics Data System (ADS)

Michalkiewicz, Mateusz; Pai, Akshay; Leung, Kelvin K.; Sommer, Stefan; Darkner, Sune; Sørensen, Lauge; Sporring, Jon; Nielsen, Mads

2016-03-01

Brain atrophy from structural magnetic resonance images (MRIs) is widely used as an imaging surrogate marker for Alzheimers disease. Their utility has been limited due to the large degree of variance and subsequently high sample size estimates. The only consistent and reasonably powerful atrophy estimation methods has been the boundary shift integral (BSI). In this paper, we first propose a tensor-based morphometry (TBM) method to measure voxel-wise atrophy that we combine with BSI. The combined model decreases the sample size estimates significantly when compared to BSI and TBM alone.

On-off closed-loop control of vagus nerve stimulation for the adaptation of heart rate.

PubMed

Ugalde, Hector Romero; Le Rolle, Virginie; Bel, Alain; Bonnet, Jean-Luc; Andreu, David; Mabo, Philippe; Carrault, Guy; Hernández, Alfredo I

2014-01-01

Vagus nerve stimulation (VNS) is a potential therapeutic approach in a number of clinical applications. Although VNS is commonly delivered in an open-loop approach, it is now recognized that closed-loop approaches may be necessary to optimize the therapy and minimize side effects of neuro-stimulation devices. In this paper, we describe a prototype system for real-time control of the instantaneous heart rate, working synchronously with the heart period. As a first step, an on-off control method has been integrated. The system is evaluated on one sheep with induced heart failure, showing the interest of the proposed approach.

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

NASA Astrophysics Data System (ADS)

Hori, Takayuki; Ohya, Jun; Kurumisawa, Jun

2009-02-01

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

Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks

DOE PAGES

Park, Jong-Kyu; Logan, Nikolas C.

2017-03-01

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly formore » each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.« less

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

DOE PAGES

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

2017-03-07

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

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

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

Rai, Prashant; Sargsyan, Khachik; Najm, Habib

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

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

NASA Astrophysics Data System (ADS)

Afanasjev, Anatoli; Litvinova, Elena

2014-09-01

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

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

PubMed

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

2017-10-12

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

Axial point groups: rank 1, 2, 3 and 4 property tensor tables.

PubMed

Litvin, Daniel B

2015-05-01

The form of a physical property tensor of a quasi-one-dimensional material such as a nanotube or a polymer is determined from the material's axial point group. Tables of the form of rank 1, 2, 3 and 4 property tensors are presented for a wide variety of magnetic and non-magnetic tensor types invariant under each point group in all 31 infinite series of axial point groups. An application of these tables is given in the prediction of the net polarization and magnetic-field-induced polarization in a one-dimensional longitudinal conical magnetic structure in multiferroic hexaferrites.

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.

Running with rugby balls: bulk renormalization of codimension-2 branes

NASA Astrophysics Data System (ADS)

Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.

2013-01-01

We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

Topics in Nonsupersymmetric Scattering Amplitudes in Gauge and Gravity Theories

NASA Astrophysics Data System (ADS)

Nohle, Joshua David

In Chapters 1 and 2, we introduce and review the duality between color and kinematics in Yang-Mills theory uncovered by Bern, Carrasco and Johansson (BCJ). In Chapter 3, we provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions. In Chapter 4, we extend the four-point one-loop nonsupersymmetric pure Yang-Mills discussion of Chapter 3 to include fermions and scalars circulating in the loop with all external gluons. This gives another nontrivial loop-level example showing that the duality between color and kinematics holds in nonsupersymmetric gauge theory. The construction is valid in any spacetime dimension and written in terms of formal polarization vectors. We also convert these expressions into a four-dimensional form with explicit external helicity states. Using this, we compare our results to one-loop duality-satisfying amplitudes that are already present in literature. In Chapter 5, we switch from the topic of color-kinematics duality to discuss the recently renewed interest in the soft behavior of gravitons and gluons. Specifically, we discuss the subleading low-energy behavior. Cachazo and Strominger recently proposed an extension of the soft-graviton theorem found by Weinberg. In addition, they proved the validity of their extension at tree level. This was motivated by a Virasoro symmetry of the gravity S-matrix related to BMS symmetry. As shown long ago by Weinberg, the leading soft behavior is not corrected by loops. In contrast, we show in Chapter 6 that with the standard definition of soft limits in dimensional regularization, the subleading behavior is anomalous and modified by loop effects. We argue that there are no new types of corrections to the first subleading behavior beyond one loop and to the second subleading behavior beyond two loops. To facilitate our investigation, we introduce a new momentum-conservation prescription for defining the subleading terms of the soft limit. We discuss the loop-level subleading soft behavior of gauge-theory amplitudes before turning to gravity amplitudes. In Chapter 7, we show that at tree level, on-shell gauge invariance can be used to fully determine the first subleading soft-gluon behavior and the first two subleading soft-graviton behaviors. Our proofs of the behaviors for n-gluon and n-graviton tree amplitudes are valid in D dimensions and are similar to Low's proof of universality of the first subleading behavior of photons. In contrast to photons coupling to massive particles, in four dimensions the soft behaviors of gluons and gravitons are corrected by loop effects. We comment on how such corrections arise from this perspective. We also show that loop corrections in graviton amplitudes arising from scalar loops appear only at the second soft subleading order. This case is particularly transparent because it is not entangled with graviton infrared singularities. Our result suggests that if we set aside the issue of infrared singularities, soft-graviton Ward identities of extended BMS symmetry are not anomalous through the first subleading order. Finally, in Chapter 8, we conclude this dissertation with a discussion of the evanescent effects on nonsupersymmetric gravity at two loops. Evanescent operators such as the Gauss- Bonnet term have vanishing perturbative matrix elements in exactly D = 4 dimensions. Similarly, evanescent fields do not propagate in D = 4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this chapter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (non-evanescent) R3 counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D = 4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop conformal anomaly---the coefficient of the Gauss-Bonnet operator---changes under p-form duality transformations. We concur, and also find that the leading R3 divergence changes under duality transformations. Nevertheless, in both cases the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. Its renormalization-scale dependence is unaltered. (Abstract shortened by UMI.).

Longitudinal brain white matter alterations in minimal hepatic encephalopathy before and after liver transplantation.

PubMed

Lin, Wei-Che; Chou, Kun-Hsien; Chen, Chao-Long; Chen, Hsiu-Ling; Lu, Cheng-Hsien; Li, Shau-Hsuan; Huang, Chu-Chung; Lin, Ching-Po; Cheng, Yu-Fan

2014-01-01

Cerebral edema is the common pathogenic mechanism for cognitive impairment in minimal hepatic encephalopathy. Whether complete reversibility of brain edema, cognitive deficits, and their associated imaging can be achieved after liver transplantation remains an open question. To characterize white matter integrity before and after liver transplantation in patients with minimal hepatic encephalopathy, multiple diffusivity indices acquired via diffusion tensor imaging was applied. Twenty-eight patients and thirty age- and sex-matched healthy volunteers were included. Multiple diffusivity indices were obtained from diffusion tensor images, including mean diffusivity, fractional anisotropy, axial diffusivity and radial diffusivity. The assessment was repeated 6-12 month after transplantation. Differences in white matter integrity between groups, as well as longitudinal changes, were evaluated using tract-based spatial statistical analysis. Correlation analyses were performed to identify first scan before transplantation and interval changes among the neuropsychiatric tests, clinical laboratory tests, and diffusion tensor imaging indices. After transplantation, decreased water diffusivity without fractional anisotropy change indicating reversible cerebral edema was found in the left anterior cingulate, claustrum, postcentral gyrus, and right corpus callosum. However, a progressive decrease in fractional anisotropy and an increase in radial diffusivity suggesting demyelination were noted in temporal lobe. Improved pre-transplantation albumin levels and interval changes were associated with better recoveries of diffusion tensor imaging indices. Improvements in interval diffusion tensor imaging indices in the right postcentral gyrus were correlated with visuospatial function score correction. In conclusion, longitudinal voxel-wise analysis of multiple diffusion tensor imaging indices demonstrated different white matter changes in minimal hepatic encephalopathy patients. Transplantation improved extracellular cerebral edema and the results of associated cognition tests. However, white matter demyelination may advance in temporal lobe.

Vectorial model for guided-mode resonance gratings

NASA Astrophysics Data System (ADS)

Fehrembach, A.-L.; Gralak, B.; Sentenac, A.

2018-04-01

We propose a self-consistent vectorial method, based on a Green's function technique, to describe the resonances that appear in guided-mode resonance gratings. The model provides intuitive expressions of the reflectivity and transmittivity matrices of the structure, involving coupling integrals between the modes of a planar reference structure and radiative modes. When one mode is excited, the diffracted field for a suitable polarization can be written as the sum of a resonant and a nonresonant term, thus extending the intuitive approach used to explain the Fano shape of the resonance in scalar configurations. When two modes are excited, we derive a physical analysis in a configuration which requires a vectorial approach. We provide numerical validations of our model. From a technical point of view, we show how the Green's tensor of our planar reference structure can be expressed as two scalar Green's functions, and how to deal with the singularity of the Green's tensor.

An Integrated Loop Model of Corrective Feedback and Oral English Learning: A Case of International Students in the United States

ERIC Educational Resources Information Center

Lee, Eun Jeong

2017-01-01

The author in this study introduces an integrated corrective feedback (CF) loop to schematize the interplay between CF and independent practice in L2 oral English learning among advanced-level adult ESL students. The CF loop integrates insights from the Interaction, Output, and Noticing Hypotheses to show how CF can help or harm L2 learners'…

Variational optical flow estimation based on stick tensor voting.

PubMed

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

2013-07-01

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

Comments on "A Closed-Form Solution to Tensor Voting: Theory and Applications".

PubMed

Maggiori, Emmanuel; Lotito, Pablo; Manterola, Hugo Luis; del Fresno, Mariana

2014-12-01

We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the proposed formulation leads to unexpected results which do not satisfy the constraints for a Tensor Voting output, hence they cannot be interpreted. Given that the closed-form expression is said to be an analytic equivalent solution, unexpected outputs should not be encountered unless there are flaws in the proof. We analyzed the underlying math to find which were the causes of these unexpected results. In this commentary we show that their proposal does not in fact provide a proper analytic solution to Tensor Voting and we indicate the flaws in the proof.

Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the regularization invariant symmetric momentum-subtraction schemes

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

Almeida, Leandro G.; Physics Department, Brookhaven National Laboratory, Upton, New York 11973; Sturm, Christian

2010-09-01

Light quark masses can be determined through lattice simulations in regularization invariant momentum-subtraction (RI/MOM) schemes. Subsequently, matching factors, computed in continuum perturbation theory, are used in order to convert these quark masses from a RI/MOM scheme to the MS scheme. We calculate the two-loop corrections in QCD to these matching factors as well as the three-loop mass anomalous dimensions for the RI/SMOM and RI/SMOM{sub {gamma}{sub {mu}} }schemes. These two schemes are characterized by a symmetric subtraction point. Providing the conversion factors in the two different schemes allows for a better understanding of the systematic uncertainties. The two-loop expansion coefficients ofmore » the matching factors for both schemes turn out to be small compared to the traditional RI/MOM schemes. For n{sub f}=3 quark flavors they are about 0.6%-0.7% and 2%, respectively, of the leading order result at scales of about 2 GeV. Therefore, they will allow for a significant reduction of the systematic uncertainty of light quark mass determinations obtained through this approach. The determination of these matching factors requires the computation of amputated Green's functions with the insertions of quark bilinear operators. As a by-product of our calculation we also provide the corresponding results for the tensor operator.« less

Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes

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

Sturm, C.; Almeida, L.

2010-04-26

Light quark masses can be determined through lattice simulations in regularization invariant momentum-subtraction (RI/MOM) schemes. Subsequently, matching factors, computed in continuum perturbation theory, are used in order to convert these quark masses from a RI/MOM scheme to the {ovr MS} scheme. We calculate the two-loop corrections in QCD to these matching factors as well as the three-loop mass anomalous dimensions for the RI/SMOM and RI/SMOM{sub {gamma}{mu}} schemes. These two schemes are characterized by a symmetric subtraction point. Providing the conversion factors in the two different schemes allows for a better understanding of the systematic uncertainties. The two-loop expansion coefficients ofmore » the matching factors for both schemes turn out to be small compared to the traditional RI/MOM schemes. For n{sub f} = 3 quark flavors they are about 0.6%-0.7% and 2%, respectively, of the leading order result at scales of about 2 GeV. Therefore, they will allow for a significant reduction of the systematic uncertainty of light quark mass determinations obtained through this approach. The determination of these matching factors requires the computation of amputated Green's functions with the insertions of quark bilinear operators. As a by-product of our calculation we also provide the corresponding results for the tensor operator.« less

Double closed-loop control of integrated optical resonance gyroscope with mean-square exponential stability.

PubMed

Li, Hui; Liu, Liying; Lin, Zhili; Wang, Qiwei; Wang, Xiao; Feng, Lishuang

2018-01-22

A new double closed-loop control system with mean-square exponential stability is firstly proposed to optimize the detection accuracy and dynamic response characteristic of the integrated optical resonance gyroscope (IORG). The influence mechanism of optical nonlinear effects on system detection sensitivity is investigated to optimize the demodulation gain, the maximum sensitivity and the linear work region of a gyro system. Especially, we analyze the effect of optical parameter fluctuation on the parameter uncertainty of system, and investigate the influence principle of laser locking-frequency noise on the closed-loop detection accuracy of angular velocity. The stochastic disturbance model of double closed-loop IORG is established that takes the unfavorable factors such as optical effect nonlinearity, disturbed disturbance, optical parameter fluctuation and unavoidable system noise into consideration. A robust control algorithm is also designed to guarantee the mean-square exponential stability of system with a prescribed H ∞ performance in order to improve the detection accuracy and dynamic performance of IORG. The conducted experiment results demonstrate that the IORG has a dynamic response time less than 76us, a long-term bias stability 7.04°/h with an integration time of 10s over one-hour test, and the corresponding bias stability 1.841°/h based on Allan deviation, which validate the effectiveness and usefulness of the proposed detection scheme.

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.

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.

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

Birmingham, D.; Kantowski, R.; Milton, K.A.

We use two methods of computing the unique logarithmically divergent part of the Casimir energy for massive scalar and spinor fields defined on even-dimensional Kaluza-Klein spaces of the form M/sup 4/ x S/sup N//sup 1/ x S/sup N//sup 2/ x xxx. Both methods (heat kernel and direct) give identical results. The first evaluates the required internal zeta function by identifying it in the asymptotic expansion of the trace of the heat kernel, and the second evaluates the zeta function directly using the Euler-Maclaurin sum formula. In Appendix C we tabulate these energies for all spaces of total internal dimension lessmore » than or equal to6. These methods are easily applied to vector and tensor fields needed in computing one-loop vacuum gravitational energies on these spaces. Stable solutions are given for internal structure S/sup 2/ x S/sup 2/.« less

On the Weyl anomaly of 4D conformal higher spins: a holographic approach

NASA Astrophysics Data System (ADS)

Acevedo, S.; Aros, R.; Bugini, F.; Diaz, D. E.

2017-11-01

We present a first attempt to derive the full (type-A and type-B) Weyl anomaly of four dimensional conformal higher spin (CHS) fields in a holographic way. We obtain the type-A and type-B Weyl anomaly coefficients for the whole family of 4D CHS fields from the one-loop effective action for massless higher spin (MHS) Fronsdal fields evaluated on a 5D bulk Poincaré-Einstein metric with an Einstein metric on its conformal boundary. To gain access to the type-B anomaly coefficient we assume, for practical reasons, a Lichnerowicz-type coupling of the bulk Fronsdal fields with the bulk background Weyl tensor. Remarkably enough, our holographic findings under this simplifying assumption are certainly not unknown: they match the results previously found on the boundary counterpart under the assumption of factorization of the CHS higher-derivative kinetic operator into Laplacians of "partially massless" higher spins on Einstein backgrounds.

The value of neurosurgical and intraoperative magnetic resonance imaging and diffusion tensor imaging tractography in clinically integrated neuroanatomy modules: a cross-sectional study.

PubMed

Familiari, Giuseppe; Relucenti, Michela; Heyn, Rosemarie; Baldini, Rossella; D'Andrea, Giancarlo; Familiari, Pietro; Bozzao, Alessandro; Raco, Antonino

2013-01-01

Neuroanatomy is considered to be one of the most difficult anatomical subjects for students. To provide motivation and improve learning outcomes in this area, clinical cases and neurosurgical images from diffusion tensor imaging (DTI) tractographies produced using an intraoperative magnetic resonance imaging apparatus (MRI/DTI) were presented and discussed during integrated second-year neuroanatomy, neuroradiology, and neurosurgery lectures over the 2008-2011 period. Anonymous questionnaires, evaluated according to the Likert scale, demonstrated that students appreciated this teaching procedure. Academic performance (examination grades for neuroanatomy) of the students who attended all integrated lectures of neuroanatomy, was slightly though significantly higher compared to that of students who attended these lectures only occasionally or not at all (P=0.04). Significantly better results were obtained during the national progress test (focusing on morphology) by students who attended the MRI/DTI-assisted lectures, compared to those who did so only in part or not at all, compared to the average student participating in the national test. These results were obtained by students attending the second, third and, in particular, the fourth year (P≤0.0001) courses during the three academic years mentioned earlier. This integrated neuroanatomy model can positively direct students in the direction of their future professional careers without any extra expense to the university. In conclusion, interactive learning tools, such as lectures integrated with intraoperative MRI/DTI images, motivate students to study and enhance their neuroanatomy education. Copyright © 2013 American Association of Anatomists.

WGM Temperature Tracker

NASA Technical Reports Server (NTRS)

Strekalov, Dmitry V.

2012-01-01

This software implements digital control of a WGM (whispering-gallerymode) resonator temperature based on the dual-mode approach. It comprises one acquisition (dual-channel) and three control modules. The interaction of the proportional-integral loops is designed in the original way, preventing the loops from fighting. The data processing is organized in parallel with the acquisition, which allows the computational overhead time to be suppressed or often completely avoided. WGM resonators potentially provide excellent optical references for metrology, clocks, spectroscopy, and other applications. However, extremely accurate (below micro-Kelvin) temperature stabilization is required. This software allows one specifically advantageous method of such stabilization to be implemented, which is immune to a variety of effects that mask the temperature variation. WGM Temperature Tracker 2.3 (see figure) is a LabVIEW code developed for dual-mode temperature stabilization of WGM resonators. It has allowed for the temperature stabilization at the level of 200 nK with one-second integration time, and 6 nK with 10,000-second integration time, with the above room-temperature set point. This software, in conjunction with the appropriate hardware, can be used as a noncryogenic temperature sensor/ controller with sub-micro-Kelvin sensitivity, which at the time of this reporting considerably outperforms the state of the art.

An Optimized Integrator Windup Protection Technique Applied to a Turbofan Engine Control

NASA Technical Reports Server (NTRS)

Watts, Stephen R.; Garg, Sanjay

1995-01-01

This paper introduces a new technique for providing memoryless integrator windup protection which utilizes readily available optimization software tools. This integrator windup protection synthesis provides a concise methodology for creating integrator windup protection for each actuation system loop independently while assuring both controller and closed loop system stability. The individual actuation system loops' integrator windup protection can then be combined to provide integrator windup protection for the entire system. This technique is applied to an H(exp infinity) based multivariable control designed for a linear model of an advanced afterburning turbofan engine. The resulting transient characteristics are examined for the integrated system while encountering single and multiple actuation limits.

Seamless Warping of Diffusion Tensor Fields

PubMed Central

Hao, Xuejun; Bansal, Ravi; Plessen, Kerstin J.; Peterson, Bradley S.

2008-01-01

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create “seams” or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT datasets seamlessly from one imaging space to another. Once the bijection has been achieved and tensors have been correctly relocated to the template space, we can appropriately reorient tensors in the template space using a warping method based on Procrustean estimation. PMID:18334425

Virtual Electrochemical Strain Microscopy of Polycrystalline LiCoO2 Films

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

Chung, Ding-wen; Balke, Nina; Kalinin, Sergei V

2011-01-01

A recently developed technique, electrochemical strain microscopy (ESM), utilizes the strong coupling between ionic current and anisotropic volumetric chemical expansion of lithium-ion electrode materials to dynamically probe the sub-one-hundred? nm inter-facial kinetic intercalation properties. A numerical technique based on the finite element method was developed to analyze the underlying physics that govern the ESM signal generation and establish relations to battery performance. The performed analysis demonstrates that the diffusion path within a thin film is tortuous and the extent of lithium diffusion into the electrode is dependent on the SPM-tip-imposed overpotential frequency. The detected surface actuation gives rise to themore » development of an electromechanical hysteresis loop whose shape is dependent on grain size and overpotential frequency. Shape and tilting angle of the loop are classified into low and high frequency regimes, separated by a transition frequency which is also a function of lithium diffusivity and grain size, f{sub T} = D//{sup 2}. Research shows that the crystallographic orientation of the surface actuated grain has a significant impact on the shape of the loop. The polycrystalline crystallographic orientation of the grains induces a diffusion path network in the electrode which impacts on the mechanical reliability of the battery. Simulations demonstrate that continuous battery cycling results in a cumulative capacity loss as a result of the hysteric non-reversible lithium intercalation. Furthermore, results suggest that ESM has the capability to infer the local out-of-plane lithium diffusivity and the out-of-plane contribution to Vegard tensor.« less

Virtual Electrochemical Strain Microscopy of Polycrystalline LiCoO2 Films

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

Chung, Ding-Wen; Balke, Nina; Kalinin, Sergei V.

2011-08-03

A recently developed technique, electrochemical strain microscopy (ESM), utilizes the strong coupling between ionic current and anisotropic volumetric chemical expansion of lithium-ion electrode materials to dynamically probe the sub-one-hundred? nm inter-facial kinetic intercalation properties. A numerical technique based on the finite element method was developed to analyze the underlying physics that govern the ESM signal generation and establish relations to battery performance. The performed analysis demonstrates that the diffusion path within a thin film is tortuous and the extent of lithium diffusion into the electrode is dependent on the SPM-tip-imposed overpotential frequency. The detected surface actuation gives rise to themore » development of an electromechanical hysteresis loop whose shape is dependent on grain size and overpotential frequency. Shape and tilting angle of the loop are classified into low and high frequency regimes, separated by a transition frequency which is also a function of lithium diffusivity and grain size, f T = D/l₂. Research shows that the crystallographic orientation of the surface actuated grain has a significant impact on the shape of the loop. The polycrystalline crystallographic orientation of the grains induces a diffusion path network in the electrode which impacts on the mechanical reliability of the battery. Simulations demonstrate that continuous battery cycling results in a cumulative capacity loss as a result of the hysteric non-reversible lithium intercalation. Furthermore, results suggest that ESM has the capability to infer the local out-of-plane lithium diffusivity and the out-of-plane contribution to Vegard tensor.« less

On space of integrable quantum field theories

DOE PAGES

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

2016-12-21

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

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.

Killing spinors and related symmetries in six dimensions

NASA Astrophysics Data System (ADS)

Batista, Carlos

2016-03-01

Benefiting from the index spinorial formalism, the Killing spinor equation is integrated in six-dimensional spacetimes. The integrability conditions for the existence of a Killing spinor are worked out and the Killing spinors are classified into two algebraic types; in the first type the scalar curvature of the spacetime must be negative, while in the second type the spacetime must be an Einstein manifold. In addition, the equations that define Killing-Yano (KY) and closed conformal Killing-Yano (CCKY) tensors are expressed in the index notation and, as consequence, all nonvanishing KY and CCKY tensors that can be generated from a Killing spinor are made explicit.

Dictionary-Based Tensor Canonical Polyadic Decomposition

NASA Astrophysics Data System (ADS)

Cohen, Jeremy Emile; Gillis, Nicolas

2018-04-01

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.

The excitation of long period seismic waves by a source spanning a structural discontinuity

NASA Astrophysics Data System (ADS)

Woodhouse, J. H.

Simple theoretical results are obtained for the excitation of seismic waves by an indigenous seismic source in the case that the source volume is intersected by a structural discontinuity. In the long wavelength approximation the seismic radiation is identical to that of a point source placed on one side of the discontinuity or of a different point source placed on the other side. The moment tensors of these two equivalent sources are related by a specific linear transformation and may differ appreciably both in magnitude and geometry. Either of these sources could be obtained by linear inversion of seismic data but the physical interpretation is more complicated than in the usual case. A source which involved no volume change would, for example, yield an isotropic component if, during inversion, it were assumed to lie on the wrong side of the discontinuity. The problem of determining the true moment tensor of the source is indeterminate unless further assumptions are made about the stress glut distribution; one way to resolve this indeterminancy is to assume proportionality between the integrated stress glut on each side of the discontinuity.

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

NASA Astrophysics Data System (ADS)

Nakatani, Naoki; Chan, Garnet Kin-Lic

2013-04-01

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

Results from Carbon Dioxide Washout Testing Using a Suited Manikin Test Apparatus with a Space Suit Ventilation Test Loop

NASA Technical Reports Server (NTRS)

Chullen, Cinda; Conger, Bruce; McMillin, Summer; Vonau, Walt; Kanne, Bryan; Korona, Adam; Swickrath, Mike

2016-01-01

NASA is developing an advanced portable life support system (PLSS) to meet the needs of a new NASA advanced space suit. The PLSS is one of the most critical aspects of the space suit providing the necessary oxygen, ventilation, and thermal protection for an astronaut performing a spacewalk. The ventilation subsystem in the PLSS must provide sufficient carbon dioxide (CO2) removal and ensure that the CO2 is washed away from the oronasal region of the astronaut. CO2 washout is a term used to describe the mechanism by which CO2 levels are controlled within the helmet to limit the concentration of CO2 inhaled by the astronaut. Accumulation of CO2 in the helmet or throughout the ventilation loop could cause the suited astronaut to experience hypercapnia (excessive carbon dioxide in the blood). A suited manikin test apparatus (SMTA) integrated with a space suit ventilation test loop was designed, developed, and assembled at NASA in order to experimentally validate adequate CO2 removal throughout the PLSS ventilation subsystem and to quantify CO2 washout performance under various conditions. The test results from this integrated system will be used to validate analytical models and augment human testing. This paper presents the system integration of the PLSS ventilation test loop with the SMTA including the newly developed regenerative Rapid Cycle Amine component used for CO2 removal and tidal breathing capability to emulate the human. The testing and analytical results of the integrated system are presented along with future work.

Integrated Vehicle Thermal Management - Combining Fluid Loops in Electric Drive Vehicles (Presentation)

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

Rugh, J. P.

2013-07-01

Plug-in hybrid electric vehicles and electric vehicles have increased vehicle thermal management complexity, using separate coolant loop for advanced power electronics and electric motors. Additional thermal components result in higher costs. Multiple cooling loops lead to reduced range due to increased weight. Energy is required to meet thermal requirements. This presentation for the 2013 Annual Merit Review discusses integrated vehicle thermal management by combining fluid loops in electric drive vehicles.

Steady-state probability density function of the phase error for a DPLL with an integrate-and-dump device

NASA Technical Reports Server (NTRS)

Simon, M.; Mileant, A.

1986-01-01

The steady-state behavior of a particular type of digital phase-locked loop (DPLL) with an integrate-and-dump circuit following the phase detector is characterized in terms of the probability density function (pdf) of the phase error in the loop. Although the loop is entirely digital from an implementation standpoint, it operates at two extremely different sampling rates. In particular, the combination of a phase detector and an integrate-and-dump circuit operates at a very high rate whereas the loop update rate is very slow by comparison. Because of this dichotomy, the loop can be analyzed by hybrid analog/digital (s/z domain) techniques. The loop is modeled in such a general fashion that previous analyses of the Real-Time Combiner (RTC), Subcarrier Demodulator Assembly (SDA), and Symbol Synchronization Assembly (SSA) fall out as special cases.

Integrated design of cryogenic refrigerator and liquid-nitrogen circulation loop for HTS cable

NASA Astrophysics Data System (ADS)

Chang, Ho-Myung; Ryu, Ki Nam; Yang, Hyung Suk

2016-12-01

A new concept of cryogenic cooling system is proposed and investigated for application to long-length HTS cables. One of major obstacles to the cable length of 1 km or longer is the difficulty in circulating liquid nitrogen (LN) along the cables, since the temperature rise and pressure drop of LN flow could be excessively large. This study attempts a breakthrough by integrating the refrigerator with the LN circulation loop in order to eliminate the cryogenic LN pumps, and generate a large LN flow with the power of compressors at ambient temperature. A variety of thermodynamic structures are investigated on standard and modified Claude cycles, where nitrogen is used as refrigerant and the LN circulation loop is included as part of the closed cycle. Four proposed cycles are fully analyzed and optimized with a process simulator (Aspen HYSYS) to evaluate the FOM (figure of merit) and examine the feasibility. The modified dual-pressure cycle cooled with expander stream is recommended for long HTS cables.

Mean-Lagrangian formalism and covariance of fluid turbulence.

PubMed

Ariki, Taketo

2017-05-01

Mean-field-based Lagrangian framework is developed for the fluid turbulence theory, which enables physically objective discussions, especially, of the history effect. Mean flow serves as a purely geometrical object of Lie group theory, providing useful operations to measure the objective rate and history integration of the general tensor field. The proposed framework is applied, on the one hand, to one-point closure model, yielding an objective expression of the turbulence viscoelastic effect. Application to two-point closure, on the other hand, is also discussed, where natural extension of known Lagrangian correlation is discovered on the basis of an extended covariance group.

Inflationary spectra with inverse-volume corrections in loop quantum cosmology and their observational constraints from Planck 2015 data

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

Zhu, Tao; Wang, Anzhong; Wu, Qiang

We first derive the primordial power spectra, spectral indices and runnings of both scalar and tensor perturbations of a flat inflationary universe to the second-order approximations of the slow-roll parameters, in the framework of loop quantum cosmology with the inverse-volume quantum corrections. This represents an extension of our previous work in which the parameter σ was assumed to be an integer, where σ characterizes the quantum corrections and in general can take any of values from the range σ  element of  (0, 6]. Restricting to the first-order approximations of the slow-roll parameters, we find corrections to the results obtained previously inmore » the literature, and point out the causes for such errors. To our best knowledge, these represent the most accurate calculations of scalar and tensor perturbations given so far in the literature. Then, fitting the perturbations to the recently released data by Planck (2015), we obtain the most severe constraints for various values of σ. Using these constraints as our referring point, we discuss whether these quantum gravitational corrections can lead to measurable signatures in the future cosmological observations. We show that, depending on the value of σ, the scale-dependent contributions to the relativistic inflationary spectra due to the inverse-volume corrections could be well within the range of the detectability of the forthcoming generations of experiments, such as the Stage IV experiments.« less

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

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

NASA Astrophysics Data System (ADS)

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

2005-08-01

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

MULTISCALE TENSOR ANISOTROPIC FILTERING OF FLUORESCENCE MICROSCOPY FOR DENOISING MICROVASCULATURE.

PubMed

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

2015-04-01

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

Differential equations for loop integrals in Baikov representation

NASA Astrophysics Data System (ADS)

Bosma, Jorrit; Larsen, Kasper J.; Zhang, Yang

2018-05-01

We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.

Energy Systems Integration News | Energy Systems Integration Facility |

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-the-loop" (HIL) to connect physical devices to software models, EdgePower is drawing on NREL's are putting their controller into a synthetic environment that is called 'controller in-the-loop controller-in-the-loop platform allows us to observe the dynamics of these buildings as they implement the

Energy Systems Integration News | Energy Systems Integration Facility |

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simulation and testing platforms from each organization. Power-hardware-in-the-loop technology at the power-hardware-in-the-loop and modeling capabilities together with real data from Duke Energy and GE's , communities, and microgrids. Hardware-in-the-loop testing for power systems will be used to verify the

Energy Systems Integration News | Energy Systems Integration Facility |

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distribution feeder models for use in hardware-in-the-loop (HIL) experiments. Using this method, a full feeder ; proposes an additional control loop to improve frequency support while ensuring stable operation. The and Frequency Deviation," also proposes an additional control loop, this time to smooth the wind

Cosmic strings and the microwave sky. I - Anisotropy from moving strings

NASA Technical Reports Server (NTRS)

Stebbins, Albert

1988-01-01

A method is developed for calculating the component of the microwave anisotropy around cosmic string loops due to their rapidly changing gravitational fields. The method is only valid for impact parameters from the string much smaller than the horizon size at the time the photon passes the string. The method makes it possible to calculate the temperature pattern around arbitrary string configurations numerically in terms of one-dimensional integrals. This method is applied to temperature jump across a string, confirming and extending previous work. It is also applied to cusps and kinks on strings, and to determining the temperature pattern far from a strong loop. The temperature pattern around a few loop configurations is explicitly calculated. Comparisons with the work of Brandenberger et al. (1986) indicates that they have overestimated the MBR anisotropy from gravitational radiation emitted from loops.

Hunting Sea Mines with UUV-Based Magnetic and Electro-Optic Sensors

DTIC Science & Technology

2010-06-01

assembly of four 3-axis fluxgate magnetometers and (c) magnetometer package for underwater deployment in flooded body section. data are automatically...features the Real-time Tracking Gradiometer (RTG), which is a multi-channel tensor gradiometer using conventional fluxgate technology. Also in this...integrated together into a Bluefin12 AUV [5]. A. RTG Sensor Technology The RTG is a multi-channel tensor gradiometer using conventional fluxgate

Interaction of non-Abelian tensor gauge fields

NASA Astrophysics Data System (ADS)

Savvidy, George

2018-01-01

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

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

Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Carbon-free hydrogen production from low rank coal

NASA Astrophysics Data System (ADS)

Aziz, Muhammad; Oda, Takuya; Kashiwagi, Takao

2018-02-01

Novel carbon-free integrated system of hydrogen production and storage from low rank coal is proposed and evaluated. To measure the optimum energy efficiency, two different systems employing different chemical looping technologies are modeled. The first integrated system consists of coal drying, gasification, syngas chemical looping, and hydrogenation. On the other hand, the second system combines coal drying, coal direct chemical looping, and hydrogenation. In addition, in order to cover the consumed electricity and recover the energy, combined cycle is adopted as addition module for power generation. The objective of the study is to find the best system having the highest performance in terms of total energy efficiency, including hydrogen production efficiency and power generation efficiency. To achieve a thorough energy/heat circulation throughout each module and the whole integrated system, enhanced process integration technology is employed. It basically incorporates two core basic technologies: exergy recovery and process integration. Several operating parameters including target moisture content in drying module, operating pressure in chemical looping module, are observed in terms of their influence to energy efficiency. From process modeling and calculation, two integrated systems can realize high total energy efficiency, higher than 60%. However, the system employing coal direct chemical looping represents higher energy efficiency, including hydrogen production and power generation, which is about 83%. In addition, optimum target moisture content in drying and operating pressure in chemical looping also have been defined.

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.

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.

A resolvable subfilter-scale model specific to large-eddy simulation of under-resolved turbulence

NASA Astrophysics Data System (ADS)

Zhou, Yong; Brasseur, James G.; Juneja, Anurag

2001-09-01

Large-eddy simulation (LES) of boundary-layer flows has serious deficiencies near the surface when a viscous sublayer either does not exist (rough walls) or is not practical to resolve (high Reynolds numbers). In previous work, we have shown that the near-surface errors arise from the poor performance of algebraic subfilter-scale (SFS) models at the first several grid levels, where integral scales are necessarily under-resolved and the turbulence is highly anisotropic. In under-resolved turbulence, eddy viscosity and similarity SFS models create a spurious feedback loop between predicted resolved-scale (RS) velocity and modeled SFS acceleration, and are unable to simultaneously capture SFS acceleration and RS-SFS energy flux. To break the spurious coupling in a dynamically meaningful manner, we introduce a new modeling strategy in which the grid-resolved subfilter velocity is estimated from a separate dynamical equation containing the essential inertial interactions between SFS and RS velocity. This resolved SFS (RSFS) velocity is then used as a surrogate for the complete SFS velocity in the SFS stress tensor. We test the RSFS model by comparing LES of highly under-resolved anisotropic buoyancy-generated homogeneous turbulence with a corresponding direct numerical simulation (DNS). The new model successfully suppresses the spurious feedback loop between RS velocity and SFS acceleration, and greatly improves model predictions of the anisotropic structure of SFS acceleration and resolved velocity fields. Unlike algebraic models, the RSFS model accurately captures SFS acceleration intensity and RS-SFS energy flux, even during the nonequilibrium transient, and properly partitions SFS acceleration between SFS stress divergence and SFS pressure force.

Patient-specific models of cardiac biomechanics

NASA Astrophysics Data System (ADS)

Krishnamurthy, Adarsh; Villongco, Christopher T.; Chuang, Joyce; Frank, Lawrence R.; Nigam, Vishal; Belezzuoli, Ernest; Stark, Paul; Krummen, David E.; Narayan, Sanjiv; Omens, Jeffrey H.; McCulloch, Andrew D.; Kerckhoffs, Roy C. P.

2013-07-01

Patient-specific models of cardiac function have the potential to improve diagnosis and management of heart disease by integrating medical images with heterogeneous clinical measurements subject to constraints imposed by physical first principles and prior experimental knowledge. We describe new methods for creating three-dimensional patient-specific models of ventricular biomechanics in the failing heart. Three-dimensional bi-ventricular geometry is segmented from cardiac CT images at end-diastole from patients with heart failure. Human myofiber and sheet architecture is modeled using eigenvectors computed from diffusion tensor MR images from an isolated, fixed human organ-donor heart and transformed to the patient-specific geometric model using large deformation diffeomorphic mapping. Semi-automated methods were developed for optimizing the passive material properties while simultaneously computing the unloaded reference geometry of the ventricles for stress analysis. Material properties of active cardiac muscle contraction were optimized to match ventricular pressures measured by cardiac catheterization, and parameters of a lumped-parameter closed-loop model of the circulation were estimated with a circulatory adaptation algorithm making use of information derived from echocardiography. These components were then integrated to create a multi-scale model of the patient-specific heart. These methods were tested in five heart failure patients from the San Diego Veteran's Affairs Medical Center who gave informed consent. The simulation results showed good agreement with measured echocardiographic and global functional parameters such as ejection fraction and peak cavity pressures.

Energy Systems Integration News | Energy Systems Integration Facility |

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photovoltaic (PV) energy for its power. PV inverter hardware-in the loop testing was conducted at NREL's Energy -scale power-hardware-in-the-loop testing at the ESIF, which allows researchers and manufacturers to test field. In addition, the CGI provides hardware-in-the-loop capability combined with NWTC dynamometers

One-loop corrections from higher dimensional tree amplitudes

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

Cachazo, Freddy; He, Song; Yuan, Ellis Ye

We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n + 2 particles in five dimensions, one assumes that two of them cannot be “detected” and therefore an integration over their LIPS is carried out. The resulting object, function of the remaining n particles, is taken to be four-dimensional by restricting the corresponding momenta. We perform this procedure in the context of the tree-level CHY formulation of amplitudes. The scattering equations obtained in the procedure coincide with thosemore » derived by Geyer et al. from ambitwistor constructions and recently studied by two of the authors for bi-adjoint scalars. They have two sectors of solutions: regular and singular. We prove that the contribution from regular solutions generically gives rise to unphysical poles. However, using a BCFW argument we prove that the unphysical contributions are always homogeneous functions of the loop momentum and can be discarded. We also show that the contribution from singular solutions turns out to be homogeneous as well.« less

One-loop corrections from higher dimensional tree amplitudes

DOE PAGES

Cachazo, Freddy; He, Song; Yuan, Ellis Ye

2016-08-01

We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n + 2 particles in five dimensions, one assumes that two of them cannot be “detected” and therefore an integration over their LIPS is carried out. The resulting object, function of the remaining n particles, is taken to be four-dimensional by restricting the corresponding momenta. We perform this procedure in the context of the tree-level CHY formulation of amplitudes. The scattering equations obtained in the procedure coincide with thosemore » derived by Geyer et al. from ambitwistor constructions and recently studied by two of the authors for bi-adjoint scalars. They have two sectors of solutions: regular and singular. We prove that the contribution from regular solutions generically gives rise to unphysical poles. However, using a BCFW argument we prove that the unphysical contributions are always homogeneous functions of the loop momentum and can be discarded. We also show that the contribution from singular solutions turns out to be homogeneous as well.« less

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

PubMed

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

2015-05-01

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

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.

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

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

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

2015-05-15

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

Application of an integrated flight/propulsion control design methodology to a STOVL aircraft

NASA Technical Reports Server (NTRS)

Garg, Sanjay; Mattern, Duane L.

1991-01-01

Results are presented from the application of an emerging Integrated Flight/Propulsion Control (IFPC) design methodology to a Short Take Off and Vertical Landing (STOVL) aircraft in transition flight. The steps in the methodology consist of designing command shaping prefilters to provide the overall desired response to pilot command inputs. A previously designed centralized controller is first validated for the integrated airframe/engine plant used. This integrated plant is derived from a different model of the engine subsystem than the one used for the centralized controller design. The centralized controller is then partitioned in a decentralized, hierarchical structure comprising of airframe lateral and longitudinal subcontrollers and an engine subcontroller. Command shaping prefilters from the pilot control effector inputs are then designed and time histories of the closed loop IFPC system response to simulated pilot commands are compared to desired responses based on handling qualities requirements. Finally, the propulsion system safety and nonlinear limited protection logic is wrapped around the engine subcontroller and the response of the closed loop integrated system is evaluated for transients that encounter the propulsion surge margin limit.

Optimization of the open-loop liquid crystal adaptive optics retinal imaging system

NASA Astrophysics Data System (ADS)

Kong, Ningning; Li, Chao; Xia, Mingliang; Li, Dayu; Qi, Yue; Xuan, Li

2012-02-01

An open-loop adaptive optics (AO) system for retinal imaging was constructed using a liquid crystal spatial light modulator (LC-SLM) as the wavefront compensator. Due to the dispersion of the LC-SLM, there was only one illumination source for both aberration detection and retinal imaging in this system. To increase the field of view (FOV) for retinal imaging, a modified mechanical shutter was integrated into the illumination channel to control the size of the illumination spot on the fundus. The AO loop was operated in a pulsing mode, and the fundus was illuminated twice by two laser impulses in a single AO correction loop. As a result, the FOV for retinal imaging was increased to 1.7-deg without compromising the aberration detection accuracy. The correction precision of the open-loop AO system was evaluated in a closed-loop configuration; the residual error is approximately 0.0909λ (root-mean-square, RMS), and the Strehl ratio ranges to 0.7217. Two subjects with differing rates of myopia (-3D and -5D) were tested. High-resolution images of capillaries and photoreceptors were obtained.

Noncoherent Symbol Synchronization Techniques

NASA Technical Reports Server (NTRS)

Simon, Marvin

2005-01-01

Traditional methods for establishing symbol synchronization (sync) in digital communication receivers assume that carrier sync has already been established, i.e., the problem is addressed at the baseband level assuming that a 'perfect' estimate of carrier phase is available. We refer to this approach as coherent symbol sync. Since, for NRZ signaling, a suppressed carrier sync loop such as an I-Q Costas loop includes integrate-and-dump (I and D) filters in its in-phase (1) and quadrature (Q) arms, the traditional approach is to first track the carrier in the absence of symbol sync information, then feed back the symbol sync estimate to these filters, and then iterate between the two to a desirable operating level In this paper, we revisit the symbol sync problem by examining methods for obtaining such sync in the absence of carrier phase information, i.e., so-called noncoherent symbol sync loops. We compare the performance of these loops with that of a well-known coherent symbol sync loop and examine the conditions under which one is preferable over the other.

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.

A brief note on Weyl frames and canonical transformations in geometrical scalar–tensor theories of gravity

NASA Astrophysics Data System (ADS)

Barreto, A. B.; Pucheu, M. L.; Romero, C.

2018-02-01

We consider scalar–tensor theories of gravity defined in Weyl integrable space-time and show that for time-lapse extended Robertson–Walker metrics in the ADM formalism a class of Weyl transformations corresponding to change of frames induce canonical transformations between different representations of the phase space. In this context, we discuss the physical equivalence of two distinct Weyl frames at the classical level.

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

DOE PAGES

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

2015-11-01

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

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

NASA Astrophysics Data System (ADS)

Eden, Burkhard; Smirnov, Vladimir A.

2016-10-01

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

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.

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.

Decomposition of a symmetric second-order tensor

NASA Astrophysics Data System (ADS)

Heras, José A.

2018-05-01

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

A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the subtraction terms I

NASA Astrophysics Data System (ADS)

Somogyi, Gábor; Trócsányi, Zoltán

2008-08-01

In previous articles we outlined a subtraction scheme for regularizing doubly-real emission and real-virtual emission in next-to-next-to-leading order (NNLO) calculations of jet cross sections in electron-positron annihilation. In order to find the NNLO correction these subtraction terms have to be integrated over the factorized unresolved phase space and combined with the two-loop corrections. In this paper we perform the integration of all one-parton unresolved subtraction terms.

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.

Integration of Hardware-in-the-loop Facilities Over the Internet

DTIC Science & Technology

2009-04-15

This briefing discusses a hardware in loop vehicle simulator in Warren, Michigan that provides the driver with realistic power response from the Power and Energy Systems Integration Lab over the internet.

Optical microresonator for application to an opto-electronic oscillator

NASA Astrophysics Data System (ADS)

Wu, Yu-Mei; Vivien, Laurent; Cassan, Eric; Luong, Vu Hai Nam; Nguyen, Lam Duy; Journet, Bernard

2010-02-01

Optoelectronic oscillators are classically based on a feedback fiber loop acting as a delay line for high spectral purity. One of the problems due to long fiber loops is the size and the requirement of temperature control. Going toward integrated solutions requires the introduction of optical resonators with a very high quality factor. A structure based on silicon on insulator material has been designed for application to an oscillator working at 8 GHz. The micro-resonator has a stadium shape with a ridge of 30 nm height, 1 μm width, a millimetric radius and a gap of some microns in agreement with the required free spectral range. A quality factor of 500000 can be achieved leading to an equivalent fiber loop of 2 km.

Water soluble contrast enema examination of the integrity of the rectal anastomosis prior to loop ileostomy reversal may be superfluous.

PubMed

Larsson, Anna; Lindmark, Gudrun; Syk, Ingvar; Buchwald, Pamela

2015-03-01

Defunctioning loop ileostomy in low anterior resection (LAR) is routinely used to reduce consequences of anastomotic leakage. The purpose of this study was to analyze which examination technique is optimal for evaluating the integrity of the anastomosis prior to loop ileostomy reversal. Retrospective analysis of 95 patients who had been subjected to LAR at Helsingborg Hospital and Skåne University Hospital, Sweden, was undertaken between January 2007 and June 2009. The examination techniques of the rectal anastomosis prior to reversal and the clinical outcome after reversal were studied. Radiologic anastomosis control using water soluble contrast enema, digital rectal examination (DRE), and rectoscopy were performed in 53 % (50/95), 98 % (93/95), and 69 % (66/95), respectively. In two patients, no control of the anastomosis was performed before reversal. Fifty-two percent (49/95) of the patients were examined using all techniques. Six patients demonstrated leakage detected before reversal of which two were only radiological leakages. These two patients underwent loop ileostomy reversal after delay without complications. They were the only ones where the three examination techniques did not prove coherence. Four patients had symptomatic leakage; these were detected with rectoscopy and DRE and verified with enema. Three patients developed anastomotic leakage after loop ileostomy reversal despite normal preoperative examinations. Two of these patients had rectovaginal fistulas (AVFs). This retrospective study indicates that contrast enema does not provide additional information if rectoscopy and DRE are normal. Despite negative examinations, three of nine leakages were diagnosed after loop ileostomy reversal. Especially, AVFs seem difficult to diagnose.

White matter deficits assessed by diffusion tensor imaging and cognitive dysfunction in psychostimulant users with comorbid human immunodeficiency virus infection.

PubMed

Tang, Victor M; Lang, Donna J; Giesbrecht, Chantelle J; Panenka, William J; Willi, Taylor; Procyshyn, Ric M; Vila-Rodriguez, Fidel; Jenkins, Willough; Lecomte, Tania; Boyda, Heidi N; Aleksic, Ana; MacEwan, G William; Honer, William G; Barr, Alasdair M

2015-09-30

Psychostimulant drug use is commonly associated with drug-related infection, including the human immunodeficiency virus (HIV). Both psychostimulant use and HIV infection are known to damage brain white matter and impair cognition. To date, no study has examined white matter integrity using magnetic resonance imaging (MRI) diffusion tensor imaging (DTI) in chronic psychostimulant users with comorbid HIV infection, and determined the relationship of white matter integrity to cognitive function. Twenty-one subjects (mean age 37.5 ± 9.0 years) with a history of heavy psychostimulant use and HIV infection (8.7 ± 4.3 years) and 22 matched controls were scanned on a 3T MRI. Fractional anisotropy (FA) values were calculated with DTI software. Four regions of interest were manually segmented, including the genu of the corpus callosum, left and right anterior limbs of the internal capsule, and the anterior commissure. Subjects also completed a neurocognitive battery and questionnaires about physical and mental health. The psychostimulant using, HIV positive group displayed decreased white matter integrity, with significantly lower FA values for all white matter tracts (p < 0.05). This group also exhibited decreased cognitive performance on tasks that assessed cognitive set-shifting, fine motor speed and verbal memory. FA values for the white matter tracts correlated with cognitive performance on many of the neurocognitive tests. White matter integrity was thus impaired in subjects with psychostimulant use and comorbid HIV infection, which predicted worsened cognitive performance on a range of tests. Further study on this medical comorbidity is required.

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.

Curvature tensors unified field equations on SEXn

NASA Astrophysics Data System (ADS)

Chung, Kyung Tae; Lee, Il Young

1988-09-01

We study the curvature tensors and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U λ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.

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.

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

Two integrator loop quadrature oscillators: A review.

PubMed

Soliman, Ahmed M

2013-01-01

A review of the two integrator loop oscillator circuits providing two quadrature sinusoidal output voltages is given. All the circuits considered employ the minimum number of capacitors namely two except one circuit which uses three capacitors. The circuits considered are classified to four different classes. The first class includes floating capacitors and floating resistors and the active building blocks realizing these circuits are the Op Amp or the OTRA. The second class employs grounded capacitors and includes floating resistors and the active building blocks realizing these circuits are the DCVC or the unity gain cells or the CFOA. The third class employs grounded capacitors and grounded resistors and the active building blocks realizing these circuits are the CCII. The fourth class employs grounded capacitors and no resistors and the active building blocks realizing these circuits are the TA. Transformation methods showing the generation of different classes from each other is given in details and this is one of the main objectives of this paper.

Open-loop digital frequency multiplier

NASA Technical Reports Server (NTRS)

Moore, R. C.

1977-01-01

Monostable multivibrator is implemented by using digital integrated circuits where multiplier constant is too large for conventional phase-locked-loop integrated circuit. A 400 Hz clock is generated by divide-by-N counter from 1 Hz timing reference.

NLO cross sections in 4 dimensions without DREG

NASA Astrophysics Data System (ADS)

Hernández-Pinto, R. J.; Driencourt-Mangin, F.; Rodrigo, G.; Sborlini, G. F. R.

2016-10-01

In this review, we present a new method for computing physical cross sections at NLO accuracy in QCD without using the standard Dimensional Regularisation. The algorithm is based on the Loop-Tree Duality theorem, which allow us to obtain loop integrals as a sum of phase-space integrals; in this way, transforming loop integrals into phase-space integrals, we propose a method to merge virtual and real contributions in order to find observables at NLO in d = 4 space-time dimensions. In addition, the strategy described is used for computing the γ* → qq̅(g) process. A more detailed discussion related on this topic can be found in Ref [1].

Path integrals and the WKB approximation in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam

2010-12-01

We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.

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.

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).

EEG Classification for Hybrid Brain-Computer Interface Using a Tensor Based Multiclass Multimodal Analysis Scheme

PubMed Central

Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang

2016-01-01

Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI. PMID:26880873

EEG Classification for Hybrid Brain-Computer Interface Using a Tensor Based Multiclass Multimodal Analysis Scheme.

PubMed

Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang

2016-01-01

Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI.

Spontaneous emission in the presence of a realistically sized cylindrical waveguide

NASA Astrophysics Data System (ADS)

Dung, Ho Trung

2016-02-01

Various quantities characterizing the spontaneous emission process of a dipole emitter including the emission rate and the emission pattern can be expressed in terms of the Green tensor of the surrounding environment. By expanding the Green tensor around some analytically known background one as a Born series, and truncating it under appropriate conditions, complicated boundaries can be tackled with ease. However, when the emitter is embedded in the medium, even the calculation of the first-order term in the Born series is problematic because of the presence of a singularity. We show how to eliminate this singularity for a medium of arbitrary size and shape by expanding around the bulk medium rather than vacuum. In the highly symmetric configuration of an emitter located on the axis of a realistically sized cylinder, it is shown that the singularity can be removed by changing the integral variables and then the order of integration. Using both methods, we investigate the spontaneous emission rate of an initially excited two-level dipole emitter, embedded in a realistically sized cylinder, which can be a common optical fiber in the long-length limit and a disk in the short-length limit. The spatial distribution of the emitted light is calculated using the Born-expansion approach, and local-field corrections to the spontaneous emission rate are briefly discussed.

The Full Ward-Takahashi Identity for Colored Tensor Models

NASA Astrophysics Data System (ADS)

Pérez-Sánchez, Carlos I.

2018-03-01

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

Elastic fields, dipole tensors, and interaction between self-interstitial atom defects in bcc transition metals

NASA Astrophysics Data System (ADS)

Dudarev, S. L.; Ma, Pui-Wai

2018-03-01

Density functional theory (DFT) calculations show that self-interstitial atom (SIA) defects in nonmagnetic body-centered-cubic (bcc) metals adopt strongly anisotropic configurations, elongated in the <111 > direction [S. Han et al., Phys. Rev. B 66, 220101 (2002), 10.1103/PhysRevB.66.220101; D. Nguyen-Manh et al., Phys. Rev. B 73, 020101 (2006), 10.1103/PhysRevB.73.020101; P. M. Derlet et al., Phys. Rev. B 76, 054107 (2007), 10.1103/PhysRevB.76.054107; S. L. Dudarev, Annu. Rev. Mater. Res. 43, 35 (2013), 10.1146/annurev-matsci-071312-121626]. Elastic distortions, associated with such anisotropic atomic structures, appear similar to distortions around small prismatic dislocation loops, although the extent of this similarity has never been quantified. We derive analytical formulas for the dipole tensors of SIA defects, which show that, in addition to the prismatic dislocation looplike character, the elastic field of a SIA defect also has a significant isotropic dilatation component. Using empirical potentials and DFT calculations, we parametrize dipole tensors of <111 > defects for all the nonmagnetic bcc transition metals. This enables a quantitative evaluation of the energy of elastic interaction between the defects, which also shows that in a periodic three-dimensional simple cubic arrangement of crowdions, long-range elastic interactions between a defect and all its images favor a <111 > orientation of the defect.

Unmanned Aircraft Systems Human-in-the-Loop Controller and Pilot Acceptability Study: Collision Avoidance, Self-Separation, and Alerting Times (CASSAT)

NASA Technical Reports Server (NTRS)

Comstock, James R., Jr.; Ghatas, Rania W.; Vincent, Michael J.; Consiglio, Maria C.; Munoz, Cesar; Chamberlain, James P.; Volk, Paul; Arthur, Keith E.

2016-01-01

The Federal Aviation Administration (FAA) has been mandated by the Congressional funding bill of 2012 to open the National Airspace System (NAS) to Unmanned Aircraft Systems (UAS). With the growing use of unmanned systems, NASA has established a multi-center "UAS Integration in the NAS" Project, in collaboration with the FAA and industry, and is guiding its research efforts to look at and examine crucial safety concerns regarding the integration of UAS into the NAS. Key research efforts are addressing requirements for detect-and-avoid (DAA), self-separation (SS), and collision avoidance (CA) technologies. In one of a series of human-in-the-loop experiments, NASA Langley Research Center set up a study known as Collision Avoidance, Self-Separation, and Alerting Times (CASSAT). The first phase assessed active air traffic controller interactions with DAA systems and the second phase examined reactions to the DAA system and displays by UAS Pilots at a simulated ground control station (GCS). Analyses of the test results from Phase I and Phase II are presented in this paper. Results from the CASSAT study and previous human-in-the-loop experiments will play a crucial role in the FAA's establishment of rules, regulations, and procedures to safely, efficiently, and effectively integrate UAS into the NAS.

Hardware-in-the-Loop Co-simulation of Distribution Grid for Demand Response

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

Rotger-Griful, Sergi; Chatzivasileiadis, Spyros; Jacobsen, Rune H.

2016-06-20

In modern power systems, co-simulation is proposed as an enabler for analyzing the interactions between disparate systems. This paper introduces the co-simulation platform Virtual Grid Integration Laboratory (VirGIL) including Hardware-in-the-Loop testing, and demonstrates its potential to assess demand response strategies. VirGIL is based on a modular architecture using the Functional Mock-up Interface industrial standard to integrate new simulators. VirGIL combines state-of-the-art simulators in power systems, communications, buildings, and control. In this work, VirGIL is extended with a Hardware-in-the-Loop component to control the ventilation system of a real 12-story building in Denmark. VirGIL capabilities are illustrated in three scenarios: load following,more » primary reserves and load following aggregation. Experimental results show that the system can track one minute changing signals and it can provide primary reserves for up-regulation. Furthermore, the potential of aggregating several ventilation systems is evaluated considering the impact at distribution grid level and the communications protocol effect.« less

Algorithms for tensor network renormalization

NASA Astrophysics Data System (ADS)

Evenbly, G.

2017-01-01

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

A framework for incorporating DTI Atlas Builder registration into Tract-Based Spatial Statistics and a simulated comparison to standard TBSS.

PubMed

Leming, Matthew; Steiner, Rachel; Styner, Martin

2016-02-27

Tract-based spatial statistics (TBSS) 6 is a software pipeline widely employed in comparative analysis of the white matter integrity from diffusion tensor imaging (DTI) datasets. In this study, we seek to evaluate the relationship between different methods of atlas registration for use with TBSS and different measurements of DTI (fractional anisotropy, FA, axial diffusivity, AD, radial diffusivity, RD, and medial diffusivity, MD). To do so, we have developed a novel tool that builds on existing diffusion atlas building software, integrating it into an adapted version of TBSS called DAB-TBSS (DTI Atlas Builder-Tract-Based Spatial Statistics) by using the advanced registration offered in DTI Atlas Builder 7 . To compare the effectiveness of these two versions of TBSS, we also propose a framework for simulating population differences for diffusion tensor imaging data, providing a more substantive means of empirically comparing DTI group analysis programs such as TBSS. In this study, we used 33 diffusion tensor imaging datasets and simulated group-wise changes in this data by increasing, in three different simulations, the principal eigenvalue (directly altering AD), the second and third eigenvalues (RD), and all three eigenvalues (MD) in the genu, the right uncinate fasciculus, and the left IFO. Additionally, we assessed the benefits of comparing the tensors directly using a functional analysis of diffusion tensor tract statistics (FADTTS 10 ). Our results indicate comparable levels of FA-based detection between DAB-TBSS and TBSS, with standard TBSS registration reporting a higher rate of false positives in other measurements of DTI. Within the simulated changes investigated here, this study suggests that the use of DTI Atlas Builder's registration enhances TBSS group-based studies.

All-loop Mondrian diagrammatics and 4-particle amplituhedron

NASA Astrophysics Data System (ADS)

An, Yang; Li, Yi; Li, Zhinan; Rao, Junjie

2018-06-01

Based on 1712.09990 which handles the 4-particle amplituhedron at 3-loop, we have found an extremely simple pattern, yet far more non-trivial than one might naturally expect: the all-loop Mondrian diagrammatics. By further simplifying and rephrasing the key relation of positivity in the amplituhedron setting, remarkably, we find a completeness relation unifying all diagrams of the Mondrian types for the 4-particle integrand of planar N = 4 SYM to all loop orders, each of which can be mapped to a simple product following a few plain rules designed for this relation. The explicit examples we investigate span from 3-loop to 7-loop order, and based on them, we classify the basic patterns of Mondrian diagrams into four types: the ladder, cross, brick-wall and spiral patterns. Interestingly, for some special combinations of ordered subspaces (a concept defined in the previous work), we find failed exceptions of the completeness relation which are called "anomalies", nevertheless, they substantially give hints on the all-loop recursive proof of this relation. These investigations are closely related to the combinatoric knowledge of separable permutations and Schröder numbers, and go even further from a diagrammatic perspective. For physical relevance, we need to further consider dual conformal invariance for two basic diagrammatic patterns to correct the numerator for a local integrand involving one or both of such patterns, while the denominator encoding its pole structure and also the sign factor, are already fixed by rules of the completeness relation. With this extra treatment to ensure the integrals are dual conformally invariant, each Mondrian diagram can be exactly translated to its corresponding physical loop integrand after being summed over all ordered subspaces that admit it.

Generalizations of polylogarithms for Feynman integrals

NASA Astrophysics Data System (ADS)

Bogner, Christian

2016-10-01

In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the computation of Feynman integrals in terms of multiple polylogarithms. Furthermore we discuss elliptic generalizations of polylogarithms which have shown to be useful in the computation of the massive two-loop sunrise integral.

Elastic constants of hcp 4He: Path-integral Monte Carlo results versus experiment

NASA Astrophysics Data System (ADS)

Ardila, Luis Aldemar Peña; Vitiello, Silvio A.; de Koning, Maurice

2011-09-01

The elastic constants of hcp 4He are computed using the path-integral Monte Carlo (PIMC) method. The stiffness coefficients are obtained by imposing different distortions to a periodic cell containing 180 atoms, followed by measurement of the elements of the corresponding stress tensor. For this purpose an appropriate path-integral expression for the stress tensor observable is derived and implemented into the pimc++ package. In addition to allowing the determination of the elastic stiffness constants, this development also opens the way to an explicit atomistic determination of the Peierls stress for dislocation motion using the PIMC technique. A comparison of the results to available experimental data shows an overall good agreement of the density dependence of the elastic constants, with the single exception of C13. Additional calculations for the bcc phase, on the other hand, show good agreement for all elastic constants.

Kinematics of velocity and vorticity correlations in turbulent flow

NASA Technical Reports Server (NTRS)

Bernard, P. S.

1983-01-01

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

On squares of representations of compact Lie algebras

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

Zeier, Robert, E-mail: robert.zeier@ch.tum.de; Zimborás, Zoltán, E-mail: zimboras@gmail.com

We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the summore » of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems.« less

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. .

Automated Coronal Loop Identification using Digital Image Processing Techniques

NASA Astrophysics Data System (ADS)

Lee, J. K.; Gary, G. A.; Newman, T. S.

2003-05-01

The results of a Master's thesis study of computer algorithms for automatic extraction and identification (i.e., collectively, "detection") of optically-thin, 3-dimensional, (solar) coronal-loop center "lines" from extreme ultraviolet and X-ray 2-dimensional images will be presented. The center lines, which can be considered to be splines, are proxies of magnetic field lines. Detecting the loops is challenging because there are no unique shapes, the loop edges are often indistinct, and because photon and detector noise heavily influence the images. Three techniques for detecting the projected magnetic field lines have been considered and will be described in the presentation. The three techniques used are (i) linear feature recognition of local patterns (related to the inertia-tensor concept), (ii) parametric space inferences via the Hough transform, and (iii) topological adaptive contours (snakes) that constrain curvature and continuity. Since coronal loop topology is dominated by the magnetic field structure, a first-order magnetic field approximation using multiple dipoles provides a priori information that has also been incorporated into the detection process. Synthesized images have been generated to benchmark the suitability of the three techniques, and the performance of the three techniques on both synthesized and solar images will be presented and numerically evaluated in the presentation. The process of automatic detection of coronal loops is important in the reconstruction of the coronal magnetic field where the derived magnetic field lines provide a boundary condition for magnetic models ( cf. , Gary (2001, Solar Phys., 203, 71) and Wiegelmann & Neukirch (2002, Solar Phys., 208, 233)). . This work was supported by NASA's Office of Space Science - Solar and Heliospheric Physics Supporting Research and Technology Program.

Engineering Encodable Lanthanide-Binding Tags (LBTs) into Loop Regions of Proteins

PubMed Central

Barthelmes, Katja; Reynolds, Anne M.; Peisach, Ezra; Jonker, Hendrik R. A.; DeNunzio, Nicholas J.; Allen, Karen N.; Imperiali, Barbara; Schwalbe, Harald

2011-01-01

Lanthanide-binding-tags (LBTs) are valuable tools for investigation of protein structure, function, and dynamics by NMR spectroscopy, X-ray crystallography and luminescence studies. We have inserted LBTs into three different loop positions (denoted L, R, and S) of the model protein interleukin-1β and varied the length of the spacer between the LBT and the protein (denoted 1-3). Luminescence studies demonstrate that all nine constructs bind Tb3+ tightly in the low nanomolar range. No significant change in the fusion protein occurs from insertion of the LBT, as shown by two X-ray crystallographic structures of the IL1β-S1 and IL1β-L3 constructs and for the remaining constructs by comparing 1H-15N-HSQC NMR spectra with wild-type IL1β. Additionally, binding of LBT-loop IL1β proteins to their native binding partner in vitro remains unaltered. X-ray crystallographic phasing was successful using only the signal from the bound lanthanide. Large residual dipolar couplings (RDCs) could be determined by NMR spectroscopy for all LBT-loop-constructs and revealed that the LBT-2 series were rigidly incorporated into the interleukin-1β structure. The paramagnetic NMR spectra of loop-LBT mutant IL1β-R2 were assigned and the Δχ tensor components were calculated based on RDCs and pseudocontact shifts (PCSs). A structural model of the IL1β-R2 construct was calculated using the paramagnetic restraints. The current data provide support that encodable LBTs serve as versatile biophysical tags when inserted into loop regions of proteins of known structure or predicted via homology modelling. PMID:21182275

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

NASA Astrophysics Data System (ADS)

Cui, S. T.

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

Conformal Yano-Killing Tensors for Space-times with Cosmological Constant

NASA Astrophysics Data System (ADS)

Czajka, P.; Jezierski, J.

We present a new method for constructing conformal Yano-Killing tensors in five-di\\-men\\-sio\\-nal Anti-de Sitter space-time. The found tensors are represented in two different coordinate systems. We also discuss, in terms of CYK tensors, global charges which are well defined for asymptotically (five-dimensional) Anti-de Sitter space-time. Additionally in Appendix we present our own derivation of conformal Killing one-forms in four-dimensional Anti-de Sitter space-time as an application of the Theorem presented in the paper.

A massive Feynman integral and some reduction relations for Appell functions

NASA Astrophysics Data System (ADS)

Shpot, M. A.

2007-12-01

New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses m12 and m22 in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with respect to the masses mi2. Equating our expressions with previously known results in terms of Gauss hypergeometric functions yields reduction relations for the involved Appell functions that are apparently new mathematical results.

Landau singularities from the amplituhedron

DOE PAGES

Dennen, T.; Prlina, I.; Spradlin, M.; ...

2017-06-28

We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N = 4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. We illustrate the algorithm applied to the one- and two-loop MHV amplitudes.

Integrated Collision Avoidance System for Air Vehicle

NASA Technical Reports Server (NTRS)

Lin, Ching-Fang (Inventor)

2013-01-01

Collision with ground/water/terrain and midair obstacles is one of the common causes of severe aircraft accidents. The various data from the coremicro AHRS/INS/GPS Integration Unit, terrain data base, and object detection sensors are processed to produce collision warning audio/visual messages and collision detection and avoidance of terrain and obstacles through generation of guidance commands in a closed-loop system. The vision sensors provide more information for the Integrated System, such as, terrain recognition and ranging of terrain and obstacles, which plays an important role to the improvement of the Integrated Collision Avoidance System.

The Twist Tensor Nuclear Norm for Video Completion.

PubMed

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

2017-12-01

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

Highly integrated optical heterodyne phase-locked loop with phase/frequency detection.

PubMed

Lu, Mingzhi; Park, Hyunchul; Bloch, Eli; Sivananthan, Abirami; Bhardwaj, Ashish; Griffith, Zach; Johansson, Leif A; Rodwell, Mark J; Coldren, Larry A

2012-04-23

A highly-integrated optical phase-locked loop with a phase/frequency detector and a single-sideband mixer (SSBM) has been proposed and demonstrated for the first time. A photonic integrated circuit (PIC) has been designed, fabricated and tested, together with an electronic IC (EIC). The PIC integrates a widely-tunable sampled-grating distributed-Bragg-reflector laser, an optical 90 degree hybrid and four high-speed photodetectors on the InGaAsP/InP platform. The EIC adds a single-sideband mixer, and a digital phase/frequency detector, to provide single-sideband heterodyne locking from -9 GHz to 7.5 GHz. The loop bandwith is 400 MHz. © 2012 Optical Society of America

Tensor sufficient dimension reduction

PubMed Central

Zhong, Wenxuan; Xing, Xin; Suslick, Kenneth

2015-01-01

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

Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

NASA Astrophysics Data System (ADS)

Babadjian, Jean-François; Mora, Maria Giovanna

2018-04-01

This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic - perfectly plastic materials obeying a Drucker-Prager or Mohr-Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.

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

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

NASA Astrophysics Data System (ADS)

Caldwell, T. Grant; Bibby, Hugh M.

1998-12-01

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

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.

Fully Integrated Biopotential Acquisition Analog Front-End IC

PubMed Central

Song, Haryong; Park, Yunjong; Kim, Hyungseup; Ko, Hyoungho

2015-01-01

A biopotential acquisition analog front-end (AFE) integrated circuit (IC) is presented. The biopotential AFE includes a capacitively coupled chopper instrumentation amplifier (CCIA) to achieve low input referred noise (IRN) and to block unwanted DC potential signals. A DC servo loop (DSL) is designed to minimize the offset voltage in the chopper amplifier and low frequency respiration artifacts. An AC coupled ripple rejection loop (RRL) is employed to reduce ripple due to chopper stabilization. A capacitive impedance boosting loop (CIBL) is designed to enhance the input impedance and common mode rejection ratio (CMRR) without additional power consumption, even under an external electrode mismatch. The AFE IC consists of two-stage CCIA that include three compensation loops (DSL, RRL, and CIBL) at each CCIA stage. The biopotential AFE is fabricated using a 0.18 µm one polysilicon and six metal layers (1P6M) complementary metal oxide semiconductor (CMOS) process. The core chip size of the AFE without input/output (I/O) pads is 10.5 mm2. A fourth-order band-pass filter (BPF) with a pass-band in the band-width from 1 Hz to 100 Hz was integrated to attenuate unwanted signal and noise. The overall gain and band-width are reconfigurable by using programmable capacitors. The IRN is measured to be 0.94 µVRMS in the pass band. The maximum amplifying gain of the pass-band was measured as 71.9 dB. The CIBL enhances the CMRR from 57.9 dB to 67 dB at 60 Hz under electrode mismatch conditions. PMID:26437404

Integrated Electronic Warfare Systems Aboard the United States Navy 21st Century Warship

DTIC Science & Technology

2009-12-01

automated operation using a Human-In-the-Loop that could be integrated into existing and future combat systems. A model was developed that demonstrates...complete range of automated operation using a Human-In-the-Loop that could be integrated into existing and future combat systems. A model was developed...44 1. Base Case Model

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.

A proposal of a local modified QCD

NASA Astrophysics Data System (ADS)

Cabo Montes de Oca, A.

2012-06-01

A local and renormalizable version of a modified PQCD introduced in previous works is presented. The construction indicates that it could be equivalent to massless QCD. The case in which only quark condensate effects are retained is discussed in more detail. Then, the appearing auxiliary fermion fields can be integrated, leading to a theory with the action of massless QCD, to which one local and gauge invariant Lagrangian term for each quark flavour is added. Those action terms are defined by two gluon and two quark fields, in a form curiously not harming power counting renormalizability. The gluon self-energy is evaluated in second order in the gauge coupling and all orders in the new quark couplings, and the result became transversal as required by the gauge invariance. The vacuum energy was also calculated in the two-loop approximation and became gauge parameter independent. The possibilities that higher-loop contributions to the vacuum energy allow the generation of a quark mass hierarchy as a flavour symmetry-breaking effect are commented. The decision on this issue needs a further evaluation of more than two-loop contributions, in which more than one type of quark loops start appearing, possibly leading to interference effects in the vacuum energy.

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.

QED contributions to electron g-2

NASA Astrophysics Data System (ADS)

Laporta, Stefano

2018-05-01

In this paper I briefly describe the results of the numerical evaluation of the mass-independent 4-loop contribution to the electron g-2 in QED with 1100 digits of precision. In particular I also show the semi-analytical fit to the numerical value, which contains harmonic polylogarithms of eiπ/3, e2iπ/3 and eiπ/2 one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. I give also some information about the methods and the program used.

An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

NASA Astrophysics Data System (ADS)

Ananthanarayan, B.; Bijnens, Johan; Ghosh, Shayan; Hebbar, Aditya

2016-12-01

We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files in the Electronic Supplementary Material to this paper, which may serve as pedagogical supplements to the methods described in this paper.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0

NASA Astrophysics Data System (ADS)

Borowka, Sophia; Carter, Jonathon; Heinrich, Gudrun

2013-02-01

We present the program SecDec 2.0, which contains various new features. First, it allows the numerical evaluation of multi-loop integrals with no restriction on the kinematics. Dimensionally regulated ultraviolet and infrared singularities are isolated via sector decomposition, while threshold singularities are handled by a deformation of the integration contour in the complex plane. As an application, we present numerical results for various massive two-loop four-point diagrams. SecDec 2.0 also contains new useful features for the calculation of more general parameter integrals, related for example to phase space integrals. Program summaryProgram title: SecDec 2.0 Catalogue identifier: AEIR_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 156829 No. of bytes in distributed program, including test data, etc.: 2137907 Distribution format: tar.gz Programming language: Wolfram Mathematica, Perl, Fortran/C++. Computer: From a single PC to a cluster, depending on the problem. Operating system: Unix, Linux. RAM: Depending on the complexity of the problem Classification: 4.4, 5, 11.1. Catalogue identifier of previous version: AEIR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1566 Does the new version supersede the previous version?: Yes Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories. Numerical integration in the presence of integrable singularities (e.g., kinematic thresholds). Solution method: Algebraic extraction of singularities in dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter ɛ, where the coefficients are finite integrals over the unit hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way. Reasons for new version: In the previous version the calculation of multi-scale integrals was restricted to the Euclidean region. Now multi-loop integrals with arbitrary physical kinematics can be evaluated. Another major improvement is the possibility of full parallelization. Summary of revisions: No restriction on the kinematics for multi-loop integrals. The integrand can be constructed from the topological cuts of the diagram. Possibility of full parallelization. Numerical integration of multi-loop integrals written in C++ rather than Fortran. Possibility to loop over ranges of parameters. Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. The restriction that multi-scale integrals could only be evaluated at Euclidean points is superseded in version 2.0. Running time: Between a few minutes and several days, depending on the complexity of the problem. Test runs provided take only seconds.

White Matter Integrity and Pictorial Reasoning in High-Functioning Children with Autism

ERIC Educational Resources Information Center

Sahyoun, Cherif P.; Belliveau, John W.; Mody, Maria

2010-01-01

The current study investigated the neurobiological role of white matter in visuospatial versus linguistic processing abilities in autism using diffusion tensor imaging. We examined differences in white matter integrity between high-functioning children with autism (HFA) and typically developing controls (CTRL), in relation to the groups' response…

Dark energy and modified gravity in the Effective Field Theory of Large-Scale Structure

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper [1], focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.

The effective hyper-Kähler potential in the N = 2 supersymmetric QCD

NASA Astrophysics Data System (ADS)

Ketov, Sergei V.

1997-02-01

The effective low-energy hyper-Kähler potential for a massive N = 2 matter in N = 2 super-QCD is investigated. TheN = 2 extended supersymmetry severely restricts the N = 2 matter self-couplings so that their exact form can be fixed by a few parameters, which is apparent in the N = 2 harmonic superspace. In the N = 2 QED with a single matter hypermultiplet, the one-loop perturbative calculations lead to the Taub-NUT hyper-Kähler metric in the massive case, and a free metric in the massless case. It is remarkable that the naive non-renormalization `theorem' does not apply. There exists a manifestly N = 2 supersymmetric duality transformation converting the low-energy effective action for the N = 2 QED hypermultiplet into a sum of the quadratic and the improved (non-polynomial) actions for an N = 2 tensor multiplet. The duality transformation also gives a simple connection between the low-energy effective action in the N = 2 harmonic superspace and the component results.

On non-primitively divergent vertices of Yang-Mills theory

NASA Astrophysics Data System (ADS)

Huber, Markus Q.

2017-11-01

Two correlation functions of Yang-Mills beyond the primitively divergent ones, the two-ghost-two-gluon and the four-ghost vertices, are calculated and their influence on lower vertices is examined. Their full (transverse) tensor structure is taken into account. As input, a solution of the full two-point equations - including two-loop terms - is used that respects the resummed perturbative ultraviolet behavior. A clear hierarchy is found with regard to the color structure that reduces the number of relevant dressing functions. The impact of the two-ghost-two-gluon vertex on the three-gluon vertex is negligible, which is explained by the fact that all non-small dressing functions drop out due to their color factors. Only in the ghost-gluon vertex a small net effect below 2% is seen. The four-ghost vertex is found to be extremely small in general. Since these two four-point functions do not enter into the propagator equations, these findings establish their small overall effect on lower correlation functions.

Constructive tensorial group field theory I: The {U(1)} -{T^4_3} model

NASA Astrophysics Data System (ADS)

Lahoche, Vincent

2018-05-01

The loop vertex expansion (LVE) is a constructive technique using canonical combinatorial tools. It works well for quantum field theories without renormalization, which is the case of the field theory studied in this paper. Tensorial group field theories (TGFTs) are a new class of field theories proposed to quantize gravity. This paper is devoted to a very simple TGFT for rank three tensors with U(1) group and quartic interactions, hence nicknamed -. It has no ultraviolet divergence, and we show, with the LVE, that it is Borel summable in its coupling constant.

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.

LiDAR point classification based on sparse representation

NASA Astrophysics Data System (ADS)

Li, Nan; Pfeifer, Norbert; Liu, Chun

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

Khoromskaia, Venera; Khoromskij, Boris N.

2014-12-01

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

TNSPackage: A Fortran2003 library designed for tensor network state methods

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

A platform for dynamic simulation and control of movement based on OpenSim and MATLAB.

PubMed

Mansouri, Misagh; Reinbolt, Jeffrey A

2012-05-11

Numerical simulations play an important role in solving complex engineering problems and have the potential to revolutionize medical decision making and treatment strategies. In this paper, we combine the rapid model-based design, control systems and powerful numerical method strengths of MATLAB/Simulink with the simulation and human movement dynamics strengths of OpenSim by developing a new interface between the two software tools. OpenSim is integrated with Simulink using the MATLAB S-function mechanism, and the interface is demonstrated using both open-loop and closed-loop control systems. While the open-loop system uses MATLAB/Simulink to separately reproduce the OpenSim Forward Dynamics Tool, the closed-loop system adds the unique feature of feedback control to OpenSim, which is necessary for most human movement simulations. An arm model example was successfully used in both open-loop and closed-loop cases. For the open-loop case, the simulation reproduced results from the OpenSim Forward Dynamics Tool with root mean square (RMS) differences of 0.03° for the shoulder elevation angle and 0.06° for the elbow flexion angle. MATLAB's variable step-size integrator reduced the time required to generate the forward dynamic simulation from 7.1s (OpenSim) to 2.9s (MATLAB). For the closed-loop case, a proportional-integral-derivative controller was used to successfully balance a pole on model's hand despite random force disturbances on the pole. The new interface presented here not only integrates the OpenSim and MATLAB/Simulink software tools, but also will allow neuroscientists, physiologists, biomechanists, and physical therapists to adapt and generate new solutions as treatments for musculoskeletal conditions. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

The spectral expansion of the elasticity random field

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

Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

2014-12-10

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

Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2011-04-01

We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of Stäckel-Killing and Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Quantum symmetry operators for the Klein-Gordon and Dirac equations are constructed from Killing tensors. The transfer of the classical conserved quantities to the quantum mechanical level is analyzed in connection with quantum anomalies.

UV-IR mixing in nonassociative Snyder ϕ4 theory

NASA Astrophysics Data System (ADS)

Meljanac, Stjepan; Mignemi, Salvatore; Trampetic, Josip; You, Jiangyang

2018-03-01

Using a quantization of the nonassociative and noncommutative Snyder ϕ4 scalar field theory in a Hermitian realization, we present in this article analytical formulas for the momentum-conserving part of the one-loop two-point function of this theory in D -, 4-, and 3-dimensional Euclidean spaces, which are exact with respect to the noncommutative deformation parameter β . We prove that these integrals are regularized by the Snyder deformation. These results indicate that the Snyder deformation does partially regularize the UV divergences of the undeformed theory, as it was proposed decades ago. Furthermore, it is observed that different nonassociative ϕ4 products can generate different momentum-conserving integrals. Finally, most importantly, a logarithmic infrared divergence emerges in one of these interaction terms. We then analyze sample momentum nonconserving integral qualitatively and show that it could exhibit IR divergence too. Therefore, infrared divergences should exist, in general, in the Snyder ϕ4 theory. We consider infrared divergences at the limit p →0 as UV/IR mixings induced by nonassociativity, since they are associated to the matching UV divergence in the zero-momentum limit and appear in specific types of nonassociative ϕ4 products. We also discuss the extrapolation of the Snyder deformation parameter β to negative values as well as certain general properties of one-loop quantum corrections in Snyder ϕ4 theory at the zero-momentum limit.

Neuronavigation Based on Track Density Image Extracted from Deterministic High-Definition Fiber Tractography.

PubMed

Wei, Peng-Hu; Cong, Fei; Chen, Ge; Li, Ming-Chu; Yu, Xin-Guang; Bao, Yu-Hai

2017-02-01

Diffusion tensor imaging-based navigation is unable to resolve crossing fibers or to determine with accuracy the fanning, origin, and termination of fibers. It is important to improve the accuracy of localizing white matter fibers for improved surgical approaches. We propose a solution to this problem using navigation based on track density imaging extracted from high-definition fiber tractography (HDFT). A 28-year-old asymptomatic female patient with a left-lateral ventricle meningioma was enrolled in the present study. Language and visual tests, magnetic resonance imaging findings, both preoperative and postoperative HDFT, and the intraoperative navigation and surgery process are presented. Track density images were extracted from tracts derived using full q-space (514 directions) diffusion spectrum imaging (DSI) and integrated into a neuronavigation system. Navigation accuracy was verified via intraoperative records and postoperative DSI tractography, as well as a functional examination. DSI successfully represented the shape and range of the Meyer loop and arcuate fasciculus. Extracted track density images from the DSI were successfully integrated into the navigation system. The relationship between the operation channel and surrounding tracts was consistent with the postoperative findings, and the patient was functionally intact after the surgery. DSI-based TDI navigation allows for the visualization of anatomic features such as fanning and angling and helps to identify the range of a given tract. Moreover, our results show that our HDFT navigation method is a promising technique that preserves neural function. Copyright © 2016 Elsevier Inc. All rights reserved.

An integrand reconstruction method for three-loop amplitudes

NASA Astrophysics Data System (ADS)

Badger, Simon; Frellesvig, Hjalte; Zhang, Yang

2012-08-01

We consider the maximal cut of a three-loop four point function with massless kinematics. By applying Gröbner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.

Two-Loop Gell-Mann Function for General Renormalizable N = 1 Supersymmetric Theory, Regularized by Higher Derivatives

NASA Astrophysics Data System (ADS)

Shevtsova, Ekaterina

2011-10-01

For the general renormalizable N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives, a two-loop β-function is calculated. It is shown that all integrals, needed for its obtaining are integrals of total derivatives.

Empirical Performance Model-Driven Data Layout Optimization and Library Call Selection for Tensor Contraction Expressions

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

Lu, Qingda; Gao, Xiaoyang; Krishnamoorthy, Sriram

Empirical optimizers like ATLAS have been very effective in optimizing computational kernels in libraries. The best choice of parameters such as tile size and degree of loop unrolling is determined by executing different versions of the computation. In contrast, optimizing compilers use a model-driven approach to program transformation. While the model-driven approach of optimizing compilers is generally orders of magnitude faster than ATLAS-like library generators, its effectiveness can be limited by the accuracy of the performance models used. In this paper, we describe an approach where a class of computations is modeled in terms of constituent operations that are empiricallymore » measured, thereby allowing modeling of the overall execution time. The performance model with empirically determined cost components is used to perform data layout optimization together with the selection of library calls and layout transformations in the context of the Tensor Contraction Engine, a compiler for a high-level domain-specific language for expressing computational models in quantum chemistry. The effectiveness of the approach is demonstrated through experimental measurements on representative computations from quantum chemistry.« less

Quantum heating as an alternative of reheating

NASA Astrophysics Data System (ADS)

Akhmedov, Emil T.; Bascone, Francesco

2018-02-01

To model a realistic situation for the beginning we consider massive real scalar ϕ4 theory in a (1 +1 )-dimensional asymptotically static Minkowski spacetime with an intermediate stage of expansion. To have an analytic headway we assume that scalars have a big mass. At past and future infinities of the background we have flat Minkowski regions which are joint by the inflationary expansion region. We use the tree-level Keldysh propagator in the theory in question to calculate the expectation value of the stress-energy tensor which is, thus, due to the excitations of the zero-point fluctuations. Then we show that even for large mass, if the de Sitter expansion stage is long enough, the quantum loop corrections to the expectation value of the stress-energy tensor are not negligible in comparison with the tree-level contribution. That is revealed itself via the excitation of the higher-point fluctuations of the exact modes: during the expansion stage a nonzero particle number density for the exact modes is generated. This density is not Planckian and serves as a quench which leads to a thermalization in the out Minkowski stage.

Topology in colored tensor models via crystallization theory

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

An optimization approach for fitting canonical tensor decompositions.

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

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

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

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

Mnemonic discrimination relates to perforant path integrity: An ultra-high resolution diffusion tensor imaging study.

PubMed

Bennett, Ilana J; Stark, Craig E L

2016-03-01

Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network. Copyright © 2015 Elsevier Inc. All rights reserved.

Postural control model interpretation of stabilogram diffusion analysis

NASA Technical Reports Server (NTRS)

Peterka, R. J.

2000-01-01

Collins and De Luca [Collins JJ. De Luca CJ (1993) Exp Brain Res 95: 308-318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior.

Analyses of Disruption of Cerebral White Matter Integrity in Schizophrenia with MR Diffusion Tensor Fiber Tracking Method

NASA Astrophysics Data System (ADS)

Yamamoto, Utako; Kobayashi, Tetsuo; Kito, Shinsuke; Koga, Yoshihiko

We have analyzed cerebral white matter using magnetic resonance diffusion tensor imaging (MR-DTI) to measure the diffusion anisotropy of water molecules. The goal of this study is the quantitative evaluation of schizophrenia. Diffusion tensor images are acquired for patients with schizophrenia and healthy comparison subjects, group-matched for age, sex, and handedness. Fiber tracking is performed on the superior longitudinal fasciculus for the comparison between the patient and comparison groups. We have analysed and compared the cross-sectional area on the starting coronal plane and the mean and standard deviation of the fractional anisotropy and the apparent diffusion coefficient along fibers in the right and left hemispheres. In the right hemisphere, the cross-sectional areas in patient group are significantly smaller than those in the comparison group. Furthermore, in the comparison group, the cross-sectional areas in the right hemisphere are significantly larger than those in the left hemisphere, whereas there is no significant difference in the patient group. These results suggest that we may evaluate the disruption in white matter integrity in schizophrenic patients quantitatively by comparing the cross-sectional area of the superior longitudinal fasciculus in the right and left hemispheres.

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.

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

Gravitational waves and large field inflation

NASA Astrophysics Data System (ADS)

Linde, Andrei

2017-02-01

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

White matter integrity in Asperger syndrome: a preliminary diffusion tensor magnetic resonance imaging study in adults.

PubMed

Bloemen, Oswald J N; Deeley, Quinton; Sundram, Fred; Daly, Eileen M; Barker, Gareth J; Jones, Derek K; van Amelsvoort, Therese A M J; Schmitz, Nicole; Robertson, Dene; Murphy, Kieran C; Murphy, Declan G M

2010-10-01

Autistic Spectrum Disorder (ASD), including Asperger syndrome and autism, is a highly genetic neurodevelopmental disorder. There is a consensus that ASD has a biological basis, and it has been proposed that it is a "connectivity" disorder. Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) allows measurement of the microstructural integrity of white matter (a proxy measure of "connectivity"). However, nobody has investigated the microstructural integrity of whole brain white matter in people with Asperger syndrome. We measured the fractional anisotropy (FA), mean diffusivity (MD) and radial diffusivity (RD) of white matter, using DT-MRI, in 13 adults with Asperger syndrome and 13 controls. The groups did not differ significantly in overall intelligence and age. FA, MD and RD were assessed using whole brain voxel-based techniques. Adults with Asperger syndrome had a significantly lower FA than controls in 13 clusters. These were largely bilateral and included white matter in the internal capsule, frontal, temporal, parietal and occipital lobes, cingulum and corpus callosum. Adults with Asperger syndrome have widespread significant differences from controls in white matter microstructural integrity.

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.

Power Hardware-in-the-Loop Evaluation of PV Inverter Grid Support on Hawaiian Electric Feeders: Preprint

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

Nelson, Austin; Prabakar, Kumaraguru; Nagarajan, Adarsh

As more grid-connected photovoltaic (PV) inverters become compliant with evolving interconnections requirements, there is increased interest from utilities in understanding how to best deploy advanced grid-support functions (GSF) in the field. One efficient and cost-effective method to examine such deployment options is to leverage power hardware-in-the-loop (PHIL) testing methods. Two Hawaiian Electric feeder models were converted to real-time models in the OPAL-RT real-time digital testing platform, and integrated with models of GSF capable PV inverters that were modeled from characterization test data. The integrated model was subsequently used in PHIL testing to evaluate the effects of different fixed power factormore » and volt-watt control settings on voltage regulation of the selected feeders. The results of this study were provided as inputs for field deployment and technical interconnection requirements for grid-connected PV inverters on the Hawaiian Islands.« less

Integrated tools for control-system analysis

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Proffitt, Melissa S.; Clark, David R.

1989-01-01

The basic functions embedded within a user friendly software package (MATRIXx) are used to provide a high level systems approach to the analysis of linear control systems. Various control system analysis configurations are assembled automatically to minimize the amount of work by the user. Interactive decision making is incorporated via menu options and at selected points, such as in the plotting section, by inputting data. There are five evaluations such as the singular value robustness test, singular value loop transfer frequency response, Bode frequency response, steady-state covariance analysis, and closed-loop eigenvalues. Another section describes time response simulations. A time response for random white noise disturbance is available. The configurations and key equations used for each type of analysis, the restrictions that apply, the type of data required, and an example problem are described. One approach for integrating the design and analysis tools is also presented.

Close-loop performance of a high precision deflectometry controlled deformable mirror (DCDM) unit for wavefront correction in adaptive optics system

NASA Astrophysics Data System (ADS)

Huang, Lei; Zhou, Chenlu; Zhao, Wenchuan; Choi, Heejoo; Graves, Logan; Kim, Daewook

2017-06-01

We present a high precision deflectometry system (DS) controlled deformable mirror (DM) solution for optical system. Different from wavefront and non-wavefront system, the DS and the DM are set to be an individual integrated DCDM unit and can be installed in one base plate. In the DCDM unit, the DS can directly provide the influence functions and surface shape of the DM to the industrial computer in any adaptive optics system. As an integrated adaptive unit, the DCDM unit could be put into various optical systems to realize aberration compensation. In this paper, the configuration and principle of the DCDM unit is introduced first. Theoretical simulation on the close-loop performance of the DCDM unit is carried out. Finally, a verification experiment is proposed to verify the compensation capability of the DCDM unit.

TRAC-PF1 code verification with data from the OTIS test facility. [Once-Through Intergral System

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

Childerson, M.T.; Fujita, R.K.

1985-01-01

A computer code (TRAC-PF1/MOD1) developed for predicting transient thermal and hydraulic integral nuclear steam supply system (NSSS) response was benchmarked. Post-small break loss-of-coolant accident (LOCA) data from a scaled, experimental facility, designated the One-Through Integral System (OTIS), were obtained for the Babcock and Wilcox NSSS and compared to TRAC predictions. The OTIS tests provided a challenging small break LOCA data set for TRAC verification. The major phases of a small break LOCA observed in the OTIS tests included pressurizer draining and loop saturation, intermittent reactor coolant system circulation, boiler-condenser mode, and the initial stages of refill. The TRAC code wasmore » successful in predicting OTIS loop conditions (system pressures and temperatures) after modification of the steam generator model. In particular, the code predicted both pool and auxiliary-feedwater initiated boiler-condenser mode heat transfer.« less

Scattering amplitudes from multivariate polynomial division

NASA Astrophysics Data System (ADS)

Mastrolia, Pierpaolo; Mirabella, Edoardo; Ossola, Giovanni; Peraro, Tiziano

2012-11-01

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Gröbner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.

Using Perturbation Theory to Reduce Noise in Diffusion Tensor Fields

PubMed Central

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

2009-01-01

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

Effective field theory of integrating out sfermions in the MSSM: Complete one-loop analysis

NASA Astrophysics Data System (ADS)

Huo, Ran

2018-04-01

We apply the covariant derivative expansion of the Coleman-Weinberg potential to the sfermion sector in the minimal supersymmetric standard model, matching it to the relevant dimension-6 operators in the standard model effective field theory at one-loop level. Emphasis is paid to nondegenerate large soft supersymmetry breaking mass squares, and the most general analytical Wilson coefficients are obtained for all pure bosonic dimension-6 operators. In addition to the non-logarithmic contributions, they generally have another logarithmic contributions. Various numerical results are shown, in particular the constraints in the large Xt branch reproducing the 125 GeV Higgs mass can be pushed to high values to almost completely probe the low stop mass region at the future FCC-ee experiment, even given the Higgs mass calculation uncertainty.

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

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

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

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

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

DOE PAGES

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

2018-05-17

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

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

Peng, Cheng

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.

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.

Parallel language constructs for tensor product computations on loosely coupled architectures

NASA Technical Reports Server (NTRS)

Mehrotra, Piyush; Van Rosendale, John

1989-01-01

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

Integrand Reduction Reloaded: Algebraic Geometry and Finite Fields

NASA Astrophysics Data System (ADS)

Sameshima, Ray D.; Ferroglia, Andrea; Ossola, Giovanni

2017-01-01

The evaluation of scattering amplitudes in quantum field theory allows us to compare the phenomenological prediction of particle theory with the measurement at collider experiments. The study of scattering amplitudes, in terms of their symmetries and analytic properties, provides a theoretical framework to develop techniques and efficient algorithms for the evaluation of physical cross sections and differential distributions. Tree-level calculations have been known for a long time. Loop amplitudes, which are needed to reduce the theoretical uncertainty, are more challenging since they involve a large number of Feynman diagrams, expressed as integrals of rational functions. At one-loop, the problem has been solved thanks to the combined effect of integrand reduction, such as the OPP method, and unitarity. However, plenty of work is still needed at higher orders, starting with the two-loop case. Recently, integrand reduction has been revisited using algebraic geometry. In this presentation, we review the salient features of integrand reduction for dimensionally regulated Feynman integrals, and describe an interesting technique for their reduction based on multivariate polynomial division. We also show a novel approach to improve its efficiency by introducing finite fields. Supported in part by the National Science Foundation under Grant PHY-1417354.

? PID output-feedback control under event-triggered protocol

NASA Astrophysics Data System (ADS)

Zhao, Di; Wang, Zidong; Ding, Derui; Wei, Guoliang; Alsaadi, Fuad E.

2018-07-01

This paper is concerned with the ? proportional-integral-derivative (PID) output-feedback control problem for a class of linear discrete-time systems under event-triggered protocols. The controller and the actuators are connected through a communication network of limited bandwidth, and an event-triggered communication mechanism is adopted to decide when a certain control signal should be transmitted to the respective actuator. Furthermore, a novel PID output-feedback controller is designed where the accumulative sum-loop (the counterpart to the integral-loop in the continues-time setting) operates on a limited time-window with hope to mitigate the effect from the past measurement data. The main objective of the problem under consideration is to design a desired PID controller such that the closed-loop system is exponentially stable and the prescribed ? disturbance rejection attenuation level is guaranteed under event-triggered protocols. By means of the Lyapunov stability theory combined with the orthogonal decomposition, sufficient conditions are established under which the addressed PID controller design problem is recast into a linear convex optimization one that can be easily solved via available software packages. Finally, a simulation example is exploited to illustrate the usefulness and effectiveness of the established control scheme.

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

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

PubMed

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

2014-02-01

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

Tensor models, Kronecker coefficients and permutation centralizer algebras

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

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

Chromatin looping defines expression of TAL1, its flanking genes, and regulation in T-ALL.

PubMed

Zhou, Yan; Kurukuti, Sreenivasulu; Saffrey, Peter; Vukovic, Milica; Michie, Alison M; Strogantsev, Ruslan; West, Adam G; Vetrie, David

2013-12-19

TAL1 is an important regulator of hematopoiesis and its expression is tightly controlled despite complexities in its genomic organization. It is frequently misregulated in T-cell acute lymphoblastic leukemia (T-ALL), often due to deletions between TAL1 and the neighboring STIL gene. To better understand the events that lead to TAL1 expression in hematopoiesis and in T-ALL, we studied looping interactions at the TAL1 locus. In TAL1-expressing erythroid cells, the locus adopts a looping "hub" which brings into close physical proximity all known TAL1 cis-regulatory elements including CTCF-bound insulators. Loss of GATA1 results in disassembly of the hub and loss of CTCF/RAD21 from one of its insulators. Genes flanking TAL1 are partly dependent on hub integrity for their transcriptional regulation. We identified looping patterns unique to TAL1-expressing T-ALL cells, and, intriguingly, loops occurring between the TAL1 and STIL genes at the common TAL1/STIL breakpoints found in T-ALL. These findings redefine how TAL1 and neighboring genes communicate within the nucleus, and indicate that looping facilitates both normal and aberrant TAL1 expression and may predispose to structural rearrangements in T-ALL. We also propose that GATA1-dependent looping mechanisms may facilitate the conservation of TAL1 regulation despite cis-regulatory remodeling during vertebrate evolution.

A Maple package for computing Gröbner bases for linear recurrence relations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Robertz, Daniel

2006-04-01

A Maple package for computing Gröbner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for example, for automatic generation of difference schemes for linear partial differential equations and for reduction of multiloop Feynman integrals. These two possible applications are illustrated by simple examples of the Laplace equation and a one-loop scalar integral of propagator type.

Viability of the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology for general potentials

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

Haro, Jaume; Amorós, Jaume, E-mail: jaime.haro@upc.edu, E-mail: jaume.amoros@upc.edu

2014-12-01

We consider the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology (LQC) for phenomenological potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding or contracting phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these potentials, numerically solving the dynamical perturbation equations we have seen that, for the particular F(T) model that we will name teleparallel versionmore » of LQC, and whose modified Friedmann equation coincides with the corresponding one in holonomy corrected LQC when one deals with the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, the corresponding equations obtained from the well-know perturbed equations in F(T) gravity lead to theoretical results that fit well with current observational data. More precisely, in this teleparallel version of LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Planck's experimental data. On the other hand, in the standard holonomy corrected LQC, using the perturbed equations obtained replacing the Ashtekar connection by a suitable sinus function and inserting some counter-terms in order to preserve the algebra of constrains, the theoretical value of the tensor/scalar ratio is smaller than in the teleparallel version, which means that there is always a set of solutions that matches with Planck's data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.« less

Two AFC Loops For Low CNR And High Dynamics

NASA Technical Reports Server (NTRS)

Hinedi, Sami M.; Aguirre, Sergio

1992-01-01

Two alternative digital automatic-frequency-control (AFC) loops proposed to acquire (or reacquire) and track frequency of received carrier radio signal. Intended for use where carrier-to-noise ratios (CNR's) low and carrier frequency characterized by high Doppler shift and Doppler rate because of high relative speed and acceleration, respectively, between transmitter and receiver. Either AFC loops used in place of phase-locked loop. New loop concepts integrate ideas from classical spectrum-estimation, digital-phase-locked-loop, and Kalman-Filter theories.

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.

Disrupted white matter integrity in heroin dependence: a controlled study utilizing diffusion tensor imaging.

PubMed

Liu, Haihong; Li, Lin; Hao, Yihui; Cao, Dong; Xu, Lin; Rohrbaugh, Robert; Xue, Zhimin; Hao, Wei; Shan, Baoci; Liu, Zhening

2008-01-01

Fractional anisotropy (FA) via diffusion tensor imaging (DTI) can quantify the white matter integrity. Exposure to addictive drugs, such as alcohol, cocaine, methamphetamine, marijuana, and nicotine has been shown to alter FA. White matter abnormalities have been shown, but it remains unclear whether the white matter FA is altered in heroin dependence. Utilizing DTI, we investigated the FA difference between heroin-dependent and control subjects by a voxel-based strategy. The FA values of the identified regions were calculated from the FA image of each subject and were correlated with clinical features including months of heroin use, age, education, and dose of methadone. Reduced FA among 16 heroin dependent subjects was located in the bilateral frontal sub-gyral regions, right precentral and left cingulate gyrus. FA in the right frontal sub-gyral was negatively correlated with duration of heroin use. The disrupted white matter integrity in right frontal white matter may occur in continuous heroin abuse.

Simplifying operations with an uplink/downlink integration toolkit

NASA Technical Reports Server (NTRS)

Murphy, Susan C.; Miller, Kevin J.; Guerrero, Ana Maria; Joe, Chester; Louie, John J.; Aguilera, Christine

1994-01-01

The Operations Engineering Lab (OEL) at JPL has developed a simple, generic toolkit to integrate the uplink/downlink processes, (often called closing the loop), in JPL's Multimission Ground Data System. This toolkit provides capabilities for integrating telemetry verification points with predicted spacecraft commands and ground events in the Mission Sequence Of Events (SOE) document. In the JPL ground data system, the uplink processing functions and the downlink processing functions are separate subsystems that are not well integrated because of the nature of planetary missions with large one-way light times for spacecraft-to-ground communication. Our new closed-loop monitoring tool allows an analyst or mission controller to view and save uplink commands and ground events with their corresponding downlinked telemetry values regardless of the delay in downlink telemetry and without requiring real-time intervention by the user. An SOE document is a time-ordered list of all the planned ground and spacecraft events, including all commands, sequence loads, ground events, significant mission activities, spacecraft status, and resource allocations. The SOE document is generated by expansion and integration of spacecraft sequence files, ground station allocations, navigation files, and other ground event files. This SOE generation process has been automated within the OEL and includes a graphical, object-oriented SOE editor and real-time viewing tool running under X/Motif. The SOE toolkit was used as the framework for the integrated implementation. The SOE is used by flight engineers to coordinate their operations tasks, serving as a predict data set in ground operations and mission control. The closed-loop SOE toolkit allows simple, automated integration of predicted uplink events with correlated telemetry points in a single SOE document for on-screen viewing and archiving. It automatically interfaces with existing real-time or non real-time sources of information, to display actual values from the telemetry data stream. This toolkit was designed to greatly simplify the user's ability to access and view telemetry data, and also provide a means to view this data in the context of the commands and ground events that are used to interpret it. A closed-loop system can prove especially useful in small missions with limited resources requiring automated monitoring tools. This paper will discuss the toolkit implementation, including design trade-offs and future plans for enhancing the automated capabilities.

Simplifying operations with an uplink/downlink integration toolkit

NASA Astrophysics Data System (ADS)

Murphy, Susan C.; Miller, Kevin J.; Guerrero, Ana Maria; Joe, Chester; Louie, John J.; Aguilera, Christine

1994-11-01

The Operations Engineering Lab (OEL) at JPL has developed a simple, generic toolkit to integrate the uplink/downlink processes, (often called closing the loop), in JPL's Multimission Ground Data System. This toolkit provides capabilities for integrating telemetry verification points with predicted spacecraft commands and ground events in the Mission Sequence Of Events (SOE) document. In the JPL ground data system, the uplink processing functions and the downlink processing functions are separate subsystems that are not well integrated because of the nature of planetary missions with large one-way light times for spacecraft-to-ground communication. Our new closed-loop monitoring tool allows an analyst or mission controller to view and save uplink commands and ground events with their corresponding downlinked telemetry values regardless of the delay in downlink telemetry and without requiring real-time intervention by the user. An SOE document is a time-ordered list of all the planned ground and spacecraft events, including all commands, sequence loads, ground events, significant mission activities, spacecraft status, and resource allocations. The SOE document is generated by expansion and integration of spacecraft sequence files, ground station allocations, navigation files, and other ground event files. This SOE generation process has been automated within the OEL and includes a graphical, object-oriented SOE editor and real-time viewing tool running under X/Motif. The SOE toolkit was used as the framework for the integrated implementation. The SOE is used by flight engineers to coordinate their operations tasks, serving as a predict data set in ground operations and mission control. The closed-loop SOE toolkit allows simple, automated integration of predicted uplink events with correlated telemetry points in a single SOE document for on-screen viewing and archiving. It automatically interfaces with existing real-time or non real-time sources of information, to display actual values from the telemetry data stream. This toolkit was designed to greatly simplify the user's ability to access and view telemetry data, and also provide a means to view this data in the context of the commands and ground events that are used to interpret it. A closed-loop system can prove especially useful in small missions with limited resources requiring automated monitoring tools. This paper will discuss the toolkit implementation, including design trade-offs and future plans for enhancing the automated capabilities.

PyR@TE. Renormalization group equations for general gauge theories

NASA Astrophysics Data System (ADS)

Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

2014-03-01

Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_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.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)

Multi-view non-negative tensor factorization as relation learning in healthcare data.

PubMed

Hang Wu; Wang, May D

2016-08-01

Discovering patterns in co-occurrences data between objects and groups of concepts is a useful task in many domains, such as healthcare data analysis, information retrieval, and recommender systems. These relational representations come from objects' behaviors in different views, posing a challenging task of integrating information from these views to uncover the shared latent structures. The problem is further complicated by the high dimension of data and the large ratio of missing data. We propose a new paradigm of learning semantic relations using tensor factorization, by jointly factorizing multi-view tensors and searching for a consistent underlying semantic space across each views. We formulate the idea as an optimization problem and propose efficient optimization algorithms, with a special treatment of missing data as well as high-dimensional data. Experiments results show the potential and effectiveness of our algorithms.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2016-05-01

We present a tensor hypercontracted (THC) scaled opposite spin second order Møller-Plesset perturbation theory (SOS-MP2) method. By using THC, we reduce the formal scaling of SOS-MP2 with respect to molecular size from quartic to cubic. We achieve further efficiency by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs) to accelerate integral construction and matrix multiplication. The practical scaling of GPU-accelerated atomic orbital-based THC-SOS-MP2 calculations is found to be N2.6 for reference data sets of water clusters and alanine polypeptides containing up to 1600 basis functions. The errors in correlation energy with respect to density-fitting-SOS-MP2 are less than 0.5 kcal/mol for all systems tested (up to 162 atoms).

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity.

PubMed

Song, Chenchen; Martínez, Todd J

2016-05-07

We present a tensor hypercontracted (THC) scaled opposite spin second order Møller-Plesset perturbation theory (SOS-MP2) method. By using THC, we reduce the formal scaling of SOS-MP2 with respect to molecular size from quartic to cubic. We achieve further efficiency by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs) to accelerate integral construction and matrix multiplication. The practical scaling of GPU-accelerated atomic orbital-based THC-SOS-MP2 calculations is found to be N(2.6) for reference data sets of water clusters and alanine polypeptides containing up to 1600 basis functions. The errors in correlation energy with respect to density-fitting-SOS-MP2 are less than 0.5 kcal/mol for all systems tested (up to 162 atoms).

Solving differential equations for Feynman integrals by expansions near singular points

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Integrated Research/Education University Aircraft Design Program Development

DTIC Science & Technology

2017-04-06

iterations and loop shaping compared to MIMO control methods. Despite the drawbacks, loop closure and classical methods are the design methods most commonly...AFRL-AFOSR-VA-TR-2017-0077 Integrated Research/Education University Aircraft Design Program Development Eli Livne UNIVERSITY OF WASHINGTON 4333...SUBTITLE Integrated Research/Education University Aircraft Design Program Development 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA9550-14-1-0027 5c.  PROGRAM

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

DOE PAGES

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

2015-10-15

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

O(d,d)-duality in string theory

NASA Astrophysics Data System (ADS)

Rennecke, Felix

2014-10-01

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

Newton to Einstein — dust to dust

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

Kopp, Michael; Uhlemann, Cora; Haugg, Thomas, E-mail: michael.kopp@physik.lmu.de, E-mail: cora.uhlemann@physik.lmu.de, E-mail: thomas.haugg@physik.lmu.de

We investigate the relation between the standard Newtonian equations for a pressureless fluid (dust) and the Einstein equations in a double expansion in small scales and small metric perturbations. We find that parts of the Einstein equations can be rewritten as a closed system of two coupled differential equations for the scalar and transverse vector metric perturbations in Poisson gauge. It is then shown that this system is equivalent to the Newtonian system of continuity and Euler equations. Brustein and Riotto (2011) conjectured the equivalence of these systems in the special case where vector perturbations were neglected. We show thatmore » this approach does not lead to the Euler equation but to a physically different one with large deviations already in the 1-loop power spectrum. We show that it is also possible to consistently set to zero the vector perturbations which strongly constrains the allowed initial conditions, in particular excluding Gaussian ones such that inclusion of vector perturbations is inevitable in the cosmological context. In addition we derive nonlinear equations for the gravitational slip and tensor perturbations, thereby extending Newtonian gravity of a dust fluid to account for nonlinear light propagation effects and dust-induced gravitational waves.« less

Advanced Hybrid Spacesuit Concept Featuring Integrated Open Loop and Closed Loop Ventilation Systems

NASA Technical Reports Server (NTRS)

Daniel, Brian A.; Fitzpatrick, Garret R.; Gohmert, Dustin M.; Ybarra, Rick M.; Dub, Mark O.

2013-01-01

A document discusses the design and prototype of an advanced spacesuit concept that integrates the capability to function seamlessly with multiple ventilation system approaches. Traditionally, spacesuits are designed to operate both dependently and independently of a host vehicle environment control and life support system (ECLSS). Spacesuits that operate independent of vehicle-provided ECLSS services must do so with equipment selfcontained within or on the spacesuit. Suits that are dependent on vehicle-provided consumables must remain physically connected to and integrated with the vehicle to operate properly. This innovation is the design and prototype of a hybrid spacesuit approach that configures the spacesuit to seamlessly interface and integrate with either type of vehicular systems, while still maintaining the ability to function completely independent of the vehicle. An existing Advanced Crew Escape Suit (ACES) was utilized as the platform from which to develop the innovation. The ACES was retrofitted with selected components and one-off items to achieve the objective. The ventilation system concept was developed and prototyped/retrofitted to an existing ACES. Components were selected to provide suit connectors, hoses/umbilicals, internal breathing system ducting/ conduits, etc. The concept utilizes a lowpressure- drop, high-flow ventilation system that serves as a conduit from the vehicle supply into the suit, up through a neck seal, into the breathing helmet cavity, back down through the neck seal, out of the suit, and returned to the vehicle. The concept also utilizes a modified demand-based breathing system configured to function seamlessly with the low-pressure-drop closed-loop ventilation system.

Automated event generation for loop-induced processes

DOE PAGES

Hirschi, Valentin; Mattelaer, Olivier

2015-10-22

We present the first fully automated implementation of cross-section computation and event generation for loop-induced processes. This work is integrated in the MadGraph5_aMC@NLO framework. We describe the optimisations implemented at the level of the matrix element evaluation, phase space integration and event generation allowing for the simulation of large multiplicity loop-induced processes. Along with some selected differential observables, we illustrate our results with a table showing inclusive cross-sections for all loop-induced hadronic scattering processes with up to three final states in the SM as well as for some relevant 2 → 4 processes. Furthermore, many of these are computed heremore » for the first time.« less

Ten-year outcome of early childhood traumatic brain injury: Diffusion tensor imaging of the ventral striatum in relation to executive functioning.

PubMed

Faber, J; Wilde, E A; Hanten, G; Ewing-Cobbs, L; Aitken, M E; Yallampalli, R; MacLeod, M C; Mullins, S H; Chu, Z D; Li, X; Hunter, J V; Noble-Haeusslein, L; Levin, H S

2016-01-01

The long-term effects of TBI on verbal fluency and related structures, as well as the relation between cognition and structural integrity, were evaluated. It was hypothesized that the group with TBI would evidence poorer performance on cognitive measures and a decrease in structural integrity. Between a paediatric group with TBI and a group of typically-developing children, the long-term effects of traumatic brain injury were investigated in relation to both structural integrity and cognition. Common metrics for diffusion tensor imaging (DTI) were used as indicators of white matter integrity. Using DTI, this study examined ventral striatum (VS) integrity in 21 patients aged 10-18 years sustaining moderate-to-severe traumatic brain injury (TBI) 5-15 years earlier and 16 demographically comparable subjects. All participants completed Delis-Kaplan Executive Functioning System (D-KEFS) sub-tests. The group with TBI exhibited lower fractional anisotropy (FA) and executive functioning performance and higher apparent diffusion coefficient (ADC). DTI metrics correlated with D-KEFS performance (right VS FA with Inhibition errors, right VS ADC with Letter Fluency, left VS FA and ADC with Category Switching). TBI affects VS integrity, even in a chronic phase, and may contribute to executive functioning deficits.

Testing of the Geoscience Laser Altimeter System (GLAS) Prototype Loop Heat Pipe

NASA Technical Reports Server (NTRS)

Douglas, Donya; Ku, Jentung; Kaya, Tarik

1998-01-01

This paper describes the testing of the prototype loop heat pipe (LHP) for the Geoscience Laser Altimeter System (GLAS). The primary objective of the test program was to verify the loop's heat transport and temperature control capabilities under conditions pertinent to GLAS applications. Specifically, the LHP had to demonstrate a heat transport capability of 100 W, with the operating temperature maintained within +/-2K while the condenser sink was subjected to a temperature change between 273K and 283K. Test results showed that this loop heat pipe was more than capable of transporting the required heat load and that the operating temperature could be maintained within +/-2K. However, this particular integrated evaporator-compensation chamber design resulted in an exchange of energy between the two that affected the overall operation of the system. One effect was the high temperature the LHP was required to reach before nucleation would begin due to inability to control liquid distribution during ground testing. Another effect was that the loop had a low power start-up limitation of approximately 25 W. These Issues may be a concern for other applications, although it is not expected that they will cause problems for GLAS under micro-gravity conditions.

Using the ALEGRA Code for Analysis of Quasi-Static Magnetization of Metals

DTIC Science & Technology

2015-09-01

covariant Levi - Civita skew-symmetric tensor. Using tensorial notation per- mits one to present all the equations in the universal covariant (i.e., coordinate...tensors numerically coincide with the corresponding values of the Kronnekker symbol δij, δij, δij. The Levi - Civita tensor z ijk has the main com...simulations: body -fitted (left) and regular (right). 6.1 Spatial Discretization Two mesh configurations were used: (1) a body -fitted irregular mesh

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Effect of spatially and temporally variable recharge on subsurface reactive transport of contaminants at Oak Ridge Integrated Field Research Challenge site

NASA Astrophysics Data System (ADS)

Kumar, J.; Lichtner, P. C.; Mills, R. T.; Hammond, G. E.; Svyatskiy, D.; Tang, G.; Brooks, S. C.; Watson, D. B.; Parker, J.

2011-12-01

Recharge is one of the most fundamental components of groundwater systems which drives both flow and transport in the subsurface and plays an important role in the migration of contaminants at the Oak Ridge Integrated Field Research Challenge (ORIFRC) site. The area receives an average of 137 cm of precipitation per year, most of it during winter. About 50% of the precipitation is lost to evapotranspiration, 40% runs off directly to surface water, and less than 10% recharges to ground water. The migration of the reactive contaminant plume at the site is modeled using the massively parallel flow and reactive transport model PFLOTRAN. The geology at the site consists of dipping beds of limestone, shale and sandstone with strike N 55° E and dip 45° SE, over which is superimposed a highly porous, horizontally oriented, saprolite weathering profile. To model this system in 3-D a grid was constructed with x-axis aligned with the strike of the geologic formation and z-axis vertical. This formulation requires a full permeability tensor with off-diagonal components obtained by rotation of the principal axes tensor through the formation dip angle. A full tensor capability was implemented in PFLOTRAN using the mimetic finite difference (MFD) method, a mass conserving, second-order accurate scheme with auxiliary pressure degrees of freedom at grid cell faces. A complex geochemical fluid with 17 primary reactive species and a number of minerals was implemented to model the contaminant discharged from the S-3 ponds at the ORIFRC site. A 50-year history of observed rainfall at the site was used as input to the model to estimate transient recharge conditions and to study the effect of spatially and temporally varied recharge. Results from the investigations of impact of spatio-temporal variation in recharge on the migration of contaminant plume will be presented.

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.

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

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

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

Li, Yi; Chen, Wei; Xu, Hongyi

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

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

PubMed

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

2017-08-01

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

Renormalizing a viscous fluid model for large scale structure formation

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

Führer, Florian; Rigopoulos, Gerasimos, E-mail: fuhrer@thphys.uni-heidelberg.de, E-mail: gerasimos.rigopoulos@ncl.ac.uk

2016-02-01

Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry with the full system of continuity+Euler equations and includes a viscosity term and a stochastic noise term, similar to the effective theories recently put forward to model CDM clustering. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, they are necessarily non-local in time. To ensure Galilean Invariance higher ordermore » vertices related to the viscosity and the noise must then be added and we explicitly show at one-loop that these terms act as counter terms for vertex diagrams. The Ward Identities ensure that the non-local-in-time theory can be renormalized consistently. Another possibility is to include the viscosity in the linear propagator, resulting in exponential damping at high wavenumber. The resulting local-in-time theory is then renormalizable to one loop, requiring less free parameters for its renormalization.« less

Scattering of glue by glue on the light-cone worldsheet: Helicity nonconserving amplitudes

NASA Astrophysics Data System (ADS)

Chakrabarti, D.; Qiu, J.; Thorn, C. B.

2005-09-01

We give the light-cone gauge calculation of the one-loop on-shell scattering amplitudes for gluon-gluon scattering which violate helicity conservation. We regulate infrared divergences by discretizing the p+ integrations, omitting the terms with p+=0. Collinear divergences are absent diagram by diagram for the helicity nonconserving amplitudes. We also employ a novel ultraviolet regulator that is natural for the light-cone worldsheet description of planar Feynman diagrams. We show that these regulators give the known answers for the helicity nonconserving one-loop amplitudes, which do not suffer from the usual infrared vagaries of massless particle scattering. For the maximal helicity violating process we elucidate the physics of the remarkable fact that the loop momentum integrand for the on-shell Green function associated with this process, with a suitable momentum routing of the different contributing topologies, is identically zero. We enumerate the counterterms that must be included to give Lorentz covariant results to this order, and we show that they can be described locally in the light-cone worldsheet formulation of the sum of planar diagrams.

AN MHD AVALANCHE IN A MULTI-THREADED CORONAL LOOP

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

Hood, A. W.; Cargill, P. J.; Tam, K. V.

For the first time, we demonstrate how an MHD avalanche might occur in a multithreaded coronal loop. Considering 23 non-potential magnetic threads within a loop, we use 3D MHD simulations to show that only one thread needs to be unstable in order to start an avalanche even when the others are below marginal stability. This has significant implications for coronal heating in that it provides for energy dissipation with a trigger mechanism. The instability of the unstable thread follows the evolution determined in many earlier investigations. However, once one stable thread is disrupted, it coalesces with a neighboring thread andmore » this process disrupts other nearby threads. Coalescence with these disrupted threads then occurs leading to the disruption of yet more threads as the avalanche develops. Magnetic energy is released in discrete bursts as the surrounding stable threads are disrupted. The volume integrated heating, as a function of time, shows short spikes suggesting that the temporal form of the heating is more like that of nanoflares than of constant heating.« less

Integrable open spin chains from flavored ABJM theory

NASA Astrophysics Data System (ADS)

Bai, Nan; Chen, Hui-Huang; He, Song; Wu, Jun-Bao; Yang, Wen-Li; Zhu, Meng-Qi

2017-08-01

We compute the two-loop anomalous dimension matrix in the scalar sector of planar N=3 flavored ABJM theory. Using coordinate Bethe ansatz, we obtain the reflection matrices and confirm that the boundary Yang-Baxter equations are satisfied. This establishes the integrability of this theory in the scalar sector at the two-loop order.

A new method for calculating differential distributions directly in Mellin space

NASA Astrophysics Data System (ADS)

Mitov, Alexander

2006-12-01

We present a new method for the calculation of differential distributions directly in Mellin space without recourse to the usual momentum-fraction (or z-) space. The method is completely general and can be applied to any process. It is based on solving the integration-by-parts identities when one of the powers of the propagators is an abstract number. The method retains the full dependence on the Mellin variable and can be implemented in any program for solving the IBP identities based on algebraic elimination, like Laporta. General features of the method are: (1) faster reduction, (2) smaller number of master integrals compared to the usual z-space approach and (3) the master integrals satisfy difference instead of differential equations. This approach generalizes previous results related to fully inclusive observables like the recently calculated three-loop space-like anomalous dimensions and coefficient functions in inclusive DIS to more general processes requiring separate treatment of the various physical cuts. Many possible applications of this method exist, the most notable being the direct evaluation of the three-loop time-like splitting functions in QCD.

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

Ostrogradsky in theories with multiple fields

NASA Astrophysics Data System (ADS)

de Rham, Claudia; Matas, Andrew

2016-06-01

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

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

Domènech, Guillem; Hiramatsu, Takashi; Lin, Chunshan

We consider a cosmological model in which the tensor mode becomes massive during inflation, and study the Cosmic Microwave Background (CMB) temperature and polarization bispectra arising from the mixing between the scalar mode and the massive tensor mode during inflation. The model assumes the existence of a preferred spatial frame during inflation. The local Lorentz invariance is already broken in cosmology due to the existence of a preferred rest frame. The existence of a preferred spatial frame further breaks the remaining local SO(3) invariance and in particular gives rise to a mass in the tensor mode. At linear perturbation level,more » we minimize our model so that the vector mode remains non-dynamical, while the scalar mode is the same as the one in single-field slow-roll inflation. At non-linear perturbation level, this inflationary massive graviton phase leads to a sizeable scalar-scalar-tensor coupling, much greater than the scalar-scalar-scalar one, as opposed to the conventional case. This scalar-scalar-tensor interaction imprints a scale dependent feature in the CMB temperature and polarization bispectra. Very intriguingly, we find a surprizing similarity between the predicted scale dependence and the scale-dependent non-Gaussianities at low multipoles hinted in the WMAP and Planck results.« less

Systems Performance Laboratory | Energy Systems Integration Facility | NREL

Science.gov Websites

array access Small Commercial Power Hardware in the Loop The small commercial power-hardware-in-the-loop (PHIL) test bay is dedicated to small-scale power hardware-in-the-loop studies of inverters and other , natural gas supply Multi-Inverter Power Hardware in the Loop The multi-inverter test bay is dedicated to

Integrated Reconfigurable Intelligent Systems (IRIS) for Complex Naval Systems

DTIC Science & Technology

2009-12-31

written. The new implementation supports the XML dialect called dashML. The plug-in is written in Java script using a flexible extension of the...human in the loop control was improved and documented, and the script for integration was developed; further study on theoretical framework for...reference damage controller was developed and tested; the model of human in the loop control was improved and documented, and the script for integrating

Full-Authority Fault-Tolerant Electronic Engine Control Systems for Variable Cycle Engines.

DTIC Science & Technology

1981-12-01

Geometry or Fuel Flow Scheduled as a Function of Engine State, i.e. FIGV = f( N1 C2 ) Closed Loop - Geometry or Fuel Flow Modulated To Maintain an Engine...Low Pressure Turbine Inlet Area (A41) Closed Loop (Integral) N2, T22 Core Stream Exhaust Nozzle Area (AJE) Closed Loop (Integral) N1 , T2 Duct Stream...to remain at the breakpoint value while low rotor speed reference ( N1 reference) is scheduled to decrease as a function of power lever angle (PLA), to

Identifying key nodes in multilayer networks based on tensor decomposition.

PubMed

Wang, Dingjie; Wang, Haitao; Zou, Xiufen

2017-06-01

The identification of essential agents in multilayer networks characterized by different types of interactions is a crucial and challenging topic, one that is essential for understanding the topological structure and dynamic processes of multilayer networks. In this paper, we use the fourth-order tensor to represent multilayer networks and propose a novel method to identify essential nodes based on CANDECOMP/PARAFAC (CP) tensor decomposition, referred to as the EDCPTD centrality. This method is based on the perspective of multilayer networked structures, which integrate the information of edges among nodes and links between different layers to quantify the importance of nodes in multilayer networks. Three real-world multilayer biological networks are used to evaluate the performance of the EDCPTD centrality. The bar chart and ROC curves of these multilayer networks indicate that the proposed approach is a good alternative index to identify real important nodes. Meanwhile, by comparing the behavior of both the proposed method and the aggregated single-layer methods, we demonstrate that neglecting the multiple relationships between nodes may lead to incorrect identification of the most versatile nodes. Furthermore, the Gene Ontology functional annotation demonstrates that the identified top nodes based on the proposed approach play a significant role in many vital biological processes. Finally, we have implemented many centrality methods of multilayer networks (including our method and the published methods) and created a visual software based on the MATLAB GUI, called ENMNFinder, which can be used by other researchers.

Identifying key nodes in multilayer networks based on tensor decomposition

NASA Astrophysics Data System (ADS)

Wang, Dingjie; Wang, Haitao; Zou, Xiufen

2017-06-01

The identification of essential agents in multilayer networks characterized by different types of interactions is a crucial and challenging topic, one that is essential for understanding the topological structure and dynamic processes of multilayer networks. In this paper, we use the fourth-order tensor to represent multilayer networks and propose a novel method to identify essential nodes based on CANDECOMP/PARAFAC (CP) tensor decomposition, referred to as the EDCPTD centrality. This method is based on the perspective of multilayer networked structures, which integrate the information of edges among nodes and links between different layers to quantify the importance of nodes in multilayer networks. Three real-world multilayer biological networks are used to evaluate the performance of the EDCPTD centrality. The bar chart and ROC curves of these multilayer networks indicate that the proposed approach is a good alternative index to identify real important nodes. Meanwhile, by comparing the behavior of both the proposed method and the aggregated single-layer methods, we demonstrate that neglecting the multiple relationships between nodes may lead to incorrect identification of the most versatile nodes. Furthermore, the Gene Ontology functional annotation demonstrates that the identified top nodes based on the proposed approach play a significant role in many vital biological processes. Finally, we have implemented many centrality methods of multilayer networks (including our method and the published methods) and created a visual software based on the MATLAB GUI, called ENMNFinder, which can be used by other researchers.

Portable battery-free charger for radiation dosimeters

DOEpatents

Manning, Frank W.

1984-01-01

This invention is a novel portable charger for dosimeters of the electrometer type. The charger does not require batteries or piezoelectric crystals and is of rugged construction. In a preferred embodiment, the charge includes a housing which carries means for mounting a dosimeter to be charged. The housing also includes contact means for impressing a charging voltage across the mounted dosimeter. Also, the housing carries a trigger for operating a charging system mounted in the housing. The charging system includes a magnetic loop including a permanent magnet for establishing a magnetic field through the loop. A segment of the loop is coupled to the trigger for movement thereby to positions opening and closing the loop. A coil inductively coupled with the loop generates coil-generated voltage pulses when the trigger is operated to open and close the loop. The charging system includes an electrical circuit for impressing voltage pulses from the coil across a capacitor for integrating the pulses and applying the resulting integrated voltage across the above-mentioned contact means for charging the dosimeter.

Investigation, development and application of optimal output feedback theory. Volume 2: Development of an optimal, limited state feedback outer-loop digital flight control system for 3-D terminal area operation

NASA Technical Reports Server (NTRS)

Broussard, J. R.; Halyo, N.

1984-01-01

This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.

Active Noise Control of Radiated Noise from Jets Originating NASA

NASA Technical Reports Server (NTRS)

Doty, Michael J.; Fuller, Christopher R.; Schiller, Noah H.; Turner, Travis L.

2013-01-01

The reduction of jet noise using a closed-loop active noise control system with highbandwidth active chevrons was investigated. The high frequency energy introduced by piezoelectrically-driven chevrons was demonstrated to achieve a broadband reduction of jet noise, presumably due to the suppression of large-scale turbulence. For a nozzle with one active chevron, benefits of up to 0.8 dB overall sound pressure level (OASPL) were observed compared to a static chevron nozzle near the maximum noise emission angle, and benefits of up to 1.9 dB OASPL were observed compared to a baseline nozzle with no chevrons. The closed-loop actuation system was able to effectively reduce noise at select frequencies by 1-3 dB. However, integrated OASPL did not indicate further reduction beyond the open-loop benefits, most likely due to the preliminary controller design, which was focused on narrowband performance.

Direct coordinate-free derivation of the compatibility equation for finite strains

NASA Astrophysics Data System (ADS)

Ryzhak, E. I.

2014-07-01

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness.

Complex plane integration in the modelling of electromagnetic fields in layered media: part 1. Application to a very large loop

NASA Astrophysics Data System (ADS)

Silva, Valdelírio da Silva e.; Régis, Cícero; Howard, Allen Q., Jr.

2014-02-01

This paper analyses the details of a procedure for the numerical integration of Hankel transforms in the calculation of the electromagnetic fields generated by a large horizontal loop over a 1D earth. The method performs the integration by deforming the integration path into the complex plane and applying Cauchy's theorem on a modified version of the integrand. The modification is the replacement of the Bessel functions J0 and J1 by the Hankel functions H_0^{(1)} and H_1^{(1)} respectively. The integration in the complex plane takes advantage of the exponentially decaying behaviour of the Hankel functions, allowing calculation on very small segments, instead of the infinite line of the original improper integrals. A crucial point in this problem is the location of the poles. The companion paper shows two methods to estimate the pole locations. We have used this method to calculate the fields of very large loops. Our results show that this method allows the estimation of the integrals with fewer evaluations of the integrand functions than other methods.

Covariant Hamiltonian tetrad approach to numerical relativity

NASA Astrophysics Data System (ADS)

Hamilton, Andrew J. S.

2017-12-01

A Hamiltonian approach to the equations of general relativity is proposed using the powerful mathematical language of multivector-valued differential forms. In the approach, the gravitational coordinates are the 12 spatial components of the line interval (the vierbein) including their antisymmetric parts, and their 12 conjugate momenta. A feature of the proposed formalism is that it allows Lorentz gauge freedoms to be imposed on the Lorentz connections rather than on the vierbein, which may facilitate numerical integration in some challenging problems. The 40 Hamilton's equations comprise 12 +12 =24 equations of motion, ten constraint equations (first class constraints, which must be arranged on the initial hypersurface of constant time, but which are guaranteed thereafter by conservation laws), and six identities (second class constraints). The six identities define a trace-free spatial tensor that is the gravitational analog of the magnetic field of electromagnetism. If the gravitational magnetic field is promoted to an independent field satisfying its own equation of motion, then the system becomes the Wahlquist-Estabrook-Buchman-Bardeen (WEBB) system, which is known to be strongly hyperbolic. Some other approaches, including Arnowitt-Deser-Misner, Baumgarte-Shapiro-Shibata-Nakamura, WEBB, and loop quantum gravity, are translated into the language of multivector-valued forms, bringing out their underlying mathematical structure.

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

PubMed

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

2017-07-01

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

Quantitative Tractography and Volumetric MRI in Blast and Blunt Force TBI: Predictors of Neurocognitive and Behavioral Outcome

DTIC Science & Technology

2016-10-01

are related to mechanism of injury as well as white matter integrity using diffusion tensor imaging (DTI). We are also collecting and analyzing...APOE ε4] and brain-derived neurotrophic factor [BDNF]) to brain integrity , neuropsychological functioning, and neurobehavioral outcome. 15. SUBJECT...contribution of genetic factors (Apolipoprotein-E ε-4 [APOE ε4] and brain-derived neurotrophic factor [BDNF]) to brain integrity , neuropsychological

Iterative Tensor Voting for Perceptual Grouping of Ill-Defined Curvilinear Structures: Application to Adherens Junctions

PubMed Central

Loss, Leandro A.; Bebis, George; Parvin, Bahram

2012-01-01

In this paper, a novel approach is proposed for perceptual grouping and localization of ill-defined curvilinear structures. Our approach builds upon the tensor voting and the iterative voting frameworks. Its efficacy lies on iterative refinements of curvilinear structures by gradually shifting from an exploratory to an exploitative mode. Such a mode shifting is achieved by reducing the aperture of the tensor voting fields, which is shown to improve curve grouping and inference by enhancing the concentration of the votes over promising, salient structures. The proposed technique is applied to delineation of adherens junctions imaged through fluorescence microscopy. This class of membrane-bound macromolecules maintains tissue structural integrity and cell-cell interactions. Visually, it exhibits fibrous patterns that may be diffused, punctate and frequently perceptual. Besides the application to real data, the proposed method is compared to prior methods on synthetic and annotated real data, showing high precision rates. PMID:21421432

View-Dependent Streamline Deformation and Exploration

PubMed Central

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

2016-01-01

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

View-Dependent Streamline Deformation and Exploration

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

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

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

Implementation and application of a gradient enhanced crystal plasticity model

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Dimensions of Attention Associated With the Microstructure of Corona Radiata White Matter.

PubMed

Stave, Elise A; De Bellis, Michael D; Hooper, Steven R; Woolley, Donald P; Chang, Suk Ki; Chen, Steven D

2017-04-01

Mirsky proposed a model of attention that included these dimensions: focus/execute, sustain, stabilize, encode, and shift. The neural correlates of these dimensions were investigated within corona radiata subregions in healthy youth. Diffusion tensor imaging and neuropsychological assessments were conducted in 79 healthy, right-handed youth aged 4-17 years. Diffusion tensor imaging maps were analyzed using standardized parcellation methods. Partial Pearson correlations between neuropsychological standardized scores, representing these attention dimensions, and diffusion tensor imaging measures of corona radiata subregions were calculated after adjusting for gender and IQ. Significant correlations were found between the focus/execute, sustain, stabilize, and shift dimensions and imaging metrics in hypothesized corona radiata subregions. Results suggest that greater microstructural white matter integrity of the corona radiata is partly associated with attention across 4 attention dimensions. Findings suggest that white matter microstructure of the corona radiata is a neural correlate of several, but not all, attention dimensions.

Dimensions of Attention Associated with the Microstructure of Corona Radiata White Matter

PubMed Central

Stave, Elise A.; Hooper, Stephen R.; Woolley, Donald P.; Chang, Suk Ki; Chen, Steven D.

2016-01-01

Mirsky proposed a model of attention that included these dimensions: focus/execute, sustain, stabilize, encode, and shift. The neural correlates of these dimensions were investigated within corona radiate subregions in healthy youth. Diffusion tensor imaging and neuropsychological assessments were conducted in 79 healthy, right-handed youth aged 4–17 years. Diffusion tensor imaging maps were analyzed using standardized parcellation methods. Partial Pearson correlations between neuropsychological standardized scores, representing these attention dimensions, and diffusion tensor imaging measures of corona radiate subregions were calculated after adjusting for gender and IQ. Significant correlations were found between the focus/execute, sustain, stabilize and shift dimensions and imaging metrics in hypothesized corona radiate subregions. Results suggest that greater microstructural white matter integrity of the corona radiata is partly associated with attention across four attention dimensions. Findings suggest that white matter microstructure of the corona radiata is a neural correlate of several, but not all, attention dimensions. PMID:28090797

View-Dependent Streamline Deformation and Exploration.

PubMed

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

2016-07-01

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

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity

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

Song, Chenchen; Martínez, Todd J.; SLAC National Accelerator Laboratory, Menlo Park, California 94025

We present a tensor hypercontracted (THC) scaled opposite spin second order Møller-Plesset perturbation theory (SOS-MP2) method. By using THC, we reduce the formal scaling of SOS-MP2 with respect to molecular size from quartic to cubic. We achieve further efficiency by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs) to accelerate integral construction and matrix multiplication. The practical scaling of GPU-accelerated atomic orbital-based THC-SOS-MP2 calculations is found to be N{sup 2.6} for reference data sets of water clusters and alanine polypeptides containing up to 1600 basis functions. The errors in correlation energy with respect to density-fitting-SOS-MP2 aremore » less than 0.5 kcal/mol for all systems tested (up to 162 atoms).« less

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.

A tensorial description of particle perception in black-hole physics

NASA Astrophysics Data System (ADS)

Barbado, Luis C.; Barceló, Carlos; Garay, Luis J.; Jannes, G.

2016-09-01

In quantum field theory in curved backgrounds, one typically distinguishes between objective, tensorial quantities such as the renormalized stress-energy tensor (RSET) and subjective, nontensorial quantities such as Bogoliubov coefficients which encode perception effects associated with the specific trajectory of a detector. In this work, we propose a way to treat both objective and subjective notions on an equal tensorial footing. For that purpose, we define a new tensor which we will call the perception renormalized stress-energy tensor (PeRSET). The PeRSET is defined as the subtraction of the RSET corresponding to two different vacuum states. Based on this tensor, we can define perceived energy densities and fluxes. The PeRSET helps us to have a more organized and systematic understanding of various results in the literature regarding quantum field theory in black hole spacetimes. We illustrate the physics encoded in this tensor by working out various examples of special relevance.

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.

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

PubMed Central

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

2017-01-01

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

Efficient numerical evaluation of Feynman integrals

NASA Astrophysics Data System (ADS)

Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran

2016-03-01

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)