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

NASA Astrophysics Data System (ADS)

Solomon, Adam R.; Trodden, Mark

2018-02-01

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

Antisymmetric tensor generalizations of affine vector fields.

PubMed

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*

PubMed Central

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

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.

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

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Fujita, Tomohiro; Komatsu, Eiichiro

2018-06-01

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

Scalar field coupling to Einstein tensor in regular black hole spacetime

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wu, Chen

2018-02-01

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

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.

The Topology of Three-Dimensional Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

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

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

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

Tensorial Calibration. 2. Second Order Tensorial Calibration.

DTIC Science & Technology

1987-10-12

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

Possibilities of the regional gravity field recovery from first-, second- and third-order radial derivatives of the disturbing gravitational potential measured on moving platforms

NASA Astrophysics Data System (ADS)

Pitonak, Martin; Sprlak, Michal; Novak, Pavel; Tenzer, Robert

2016-04-01

Recently realized gravity-dedicated satellite missions allow for measuring values of scalar, vectorial (Gravity Recovery And Climate Experiment - GRACE) and second-order tensorial (Gravity field and steady-state Ocean Circulation Explorer - GOCE) parameters of the Earth's gravitational potential. Theoretical aspects related to using moving sensors for measuring elements of the third-order gravitational tensor are currently under investigation, e.g., the gravity field-dedicated satellite mission OPTIMA (OPTical Interferometry for global Mass change detection from space) should measure third-order derivatives of the Earth's gravitational potential. This contribution investigates regional recovery of the disturbing gravitational potential on the Earth's surface from satellite and aerial observations of the first-, second- and third-order radial derivatives of the disturbing gravitational potential. Synthetic measurements along a satellite orbit at the altitude of 250 km and along an aircraft track at the altitude of 10 km are synthetized from the global gravitational model EGM2008 and polluted by the Gaussian noise. The process of downward continuation is stabilized by the Tikhonov regularization. Estimated values of the disturbing gravitational potential are compared with the same quantity synthesized directly from EGM2008.

Order Reduction, Projectability and Constraints of Second-Order Field Theories and Higher-Order Mechanics

NASA Astrophysics Data System (ADS)

Gaset, Jordi; Román-Roy, Narciso

2016-12-01

The projectability of Poincaré-Cartan forms in a third-order jet bundle J3π onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint algorithm for the associated Euler-Lagrange equations in J3π. The results are applied to study the Hilbert Lagrangian for the Einstein equations (in vacuum) from a multisymplectic point of view. Thus we show how these equations are a consequence of the application of the constraint algorithm to the geometric field equations, meanwhile the other constraints are related with the fact that this second-order theory is equivalent to a first-order theory. Furthermore, the case of higher-order mechanics is also studied as a particular situation.

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.

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

NASA Astrophysics Data System (ADS)

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

2010-10-01

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

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

NASA Astrophysics Data System (ADS)

Wu, Qiang; Zhu, Tao; Wang, Anzhong

2018-05-01

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

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.

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

PubMed

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

2011-01-01

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

Second-order reconstruction of the inflationary potential

NASA Technical Reports Server (NTRS)

Liddle, Andrew R.; Turner, Michael S.

1994-01-01

To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, n and n(sub T), and their contributions to the variance of the quadrupole CBR temperature anisotropy, S and T. In addition, there is a 'consistency relation' between these quantities: n(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/S) + 0.15(n-1)). As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Pade approximate as a greatly improved alternative.

Second-order (2 +1 ) -dimensional anisotropic hydrodynamics

NASA Astrophysics Data System (ADS)

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

2014-11-01

We present a complete formulation of second-order (2 +1 ) -dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.

Estimating cosmic velocity fields from density fields and tidal tensors

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

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

NASA Astrophysics Data System (ADS)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

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

Skyrme interaction to second order in nuclear matter

NASA Astrophysics Data System (ADS)

Kaiser, N.

2015-09-01

Based on the phenomenological Skyrme interaction various density-dependent nuclear matter quantities are calculated up to second order in many-body perturbation theory. The spin-orbit term as well as two tensor terms contribute at second order to the energy per particle. The simultaneous calculation of the isotropic Fermi-liquid parameters provides a rigorous check through the validity of the Landau relations. It is found that published results for these second order contributions are incorrect in most cases. In particular, interference terms between s-wave and p-wave components of the interaction can contribute only to (isospin or spin) asymmetry energies. Even with nine adjustable parameters, one does not obtain a good description of the empirical nuclear matter saturation curve in the low density region 0\\lt ρ \\lt 2{ρ }0. The reason for this feature is the too strong density-dependence {ρ }8/3 of several second-order contributions. The inclusion of the density-dependent term \\frac{1}{6}{t}3{ρ }1/6 is therefore indispensable for a realistic description of nuclear matter in the Skyrme framework.

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

PubMed Central

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

2009-01-01

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

Surface‐wave Green’s tensors in the near field

USGS Publications Warehouse

Haney, Matt; Nakahara, Hisashi

2014-01-01

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

Irreducible structure, symmetry and average of Eshelby's tensor fields in isotropic elasticity

NASA Astrophysics Data System (ADS)

Zheng, Q.-S.; Zhao, Z.-H.; Du, D.-X.

2006-02-01

The strain field ɛ(x) in an infinitely large, homogenous, and isotropic elastic medium induced by a uniform eigenstrain ɛ0 in a domain ω depends linearly upon ɛ0 : ɛij(x)=Sijklω(x)ɛkl0. It has been a long-standing conjecture that the Eshelby's tensor field Sω(x) is uniform inside ω if and only if ω is ellipsoidally shaped. Because of the minor index symmetry Sijklω=Sjiklω=Sijlkω, Sω might have a maximum of 36 or nine independent components in three or two dimensions, respectively. In this paper, using the irreducible decomposition of Sω, we show that the isotropic part S of Sω vanishes outside ω and is uniform inside ω with the same value as the Eshelby's tensor S0 for 3D spherical or 2D circular domains. We further show that the anisotropic part Aω=Sω-S of Sω is characterized by a second- and a fourth-order deviatoric tensors and therefore have at maximum 14 or four independent components as characteristics of ω's geometry. Remarkably, the above irreducible structure of Sω is independent of ω's geometry (e.g., shape, orientation, connectedness, convexity, boundary smoothness, etc.). Interesting consequences have implication for a number of recently findings that, for example, both the values of Sω at the center of a 2D Cn(n⩾3,n≠4)-symmetric or 3D icosahedral ω and the average value of Sω over such a ω are equal to S0.

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

NASA Astrophysics Data System (ADS)

Dvoeglazov, V. V.

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Current density tensors

NASA Astrophysics Data System (ADS)

Lazzeretti, Paolo

2018-04-01

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

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

PubMed

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

2004-05-01

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

A Review of Tensors and Tensor Signal Processing

NASA Astrophysics Data System (ADS)

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

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

Electric field effect on the second-order nonlinear optical properties of parabolic and semiparabolic quantum wells

NASA Astrophysics Data System (ADS)

Zhang, Li; Xie, Hong-Jing

2003-12-01

By using the compact-density-matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG) susceptibility tensor is given in the electric-field-biased parabolic and semiparabolic quantum wells (QW’s). The simple analytical formula for the SHG susceptibility in the systems is also deduced. By adopting the methods of envelope wave function and displacement harmonic oscillation, the electronic states in parabolic and semi parabolic QW’s with applied electric fields are exactly solved. Numerical results on typical AlxGa1-xAl/GaAs materials show that, for the same effective widths, the SHG susceptibility in semiparabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semiparabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably. Moreover, the SHG susceptibility also sensitively depends on the relaxation rate of the systems.

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

PubMed

Papadopoulo, Théo; Ghosh, Aurobrata; Deriche, Rachid

2014-01-01

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

Effective description of higher-order scalar-tensor theories

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

Langlois, David; Mancarella, Michele; Vernizzi, Filippo

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

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

NASA Astrophysics Data System (ADS)

Wang, Bo; Zhang, Yang

2017-11-01

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

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.

Method and apparatus for second-rank tensor generation

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang (Inventor)

1991-01-01

A method and apparatus are disclosed for generation of second-rank tensors using a photorefractive crystal to perform the outer-product between two vectors via four-wave mixing, thereby taking 2n input data to a control n squared output data points. Two orthogonal amplitude modulated coherent vector beams x and y are expanded and then parallel sides of the photorefractive crystal in exact opposition. A beamsplitter is used to direct a coherent pumping beam onto the crystal at an appropriate angle so as to produce a conjugate beam that is the matrix product of the vector beam that propagates in the exact opposite direction from the pumping beam. The conjugate beam thus separated is the tensor output xy (sup T).

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

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2018-05-01

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

Extended scalar-tensor theories of gravity

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

Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo

2016-04-21

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

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Second-order closure models for supersonic turbulent flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu

1991-01-01

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

Second-order closure models for supersonic turbulent flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu

1991-01-01

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

Second-order differential equations for bosons with spin j ≥ 1 and in the bases of general tensor-spinors of rank 2j

NASA Astrophysics Data System (ADS)

Banda Guzmán, V. M.; Kirchbach, M.

2016-09-01

A boson of spin j≥ 1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second-order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly D^{(j,0)oplus (0,j)} representation specific second-order differential equation, which is derivable from a Lagrangian and whose solutions do not violate causality. The equation under discussion presents itself as the product of the Klein-Gordon operator with a momentum-independent projector on Lorentz irreducible representation spaces constructed from one of the Casimir invariants of the spin-Lorentz group. The basis used is that of general tensor-spinors of rank 2 j.

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

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

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

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

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

On improving the efficiency of tensor voting.

PubMed

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

2011-11-01

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

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

NASA Astrophysics Data System (ADS)

Lu, Biao; Luo, Zhicai; Zhong, Bo; Zhou, Hao; Flechtner, Frank; Förste, Christoph; Barthelmes, Franz; Zhou, Rui

2017-11-01

Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model's spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components V_{xy} and V_{yz} of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE's inclination of 96.7° . With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of V_{xy} and V_{yz} are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a

Second order nonlinear QED processes in ultra-strong laser fields

NASA Astrophysics Data System (ADS)

Mackenroth, Felix

2017-10-01

In the interaction of ultra-intense laser fields with matter the ever increasing peak laser intensities render nonlinear QED effects ever more important. For long, ultra-intense laser pulses scattering large systems, like a macroscopic plasma, the interaction time can be longer than the scattering time, leading to multiple scatterings. These are usually approximated as incoherent cascades of single-vertex processes. Under certain conditions, however, this common cascade approximation may be insufficient, as it disregards several effects such as coherent processes, quantum interferences or pulse shape effects. Quantifying deviations of the full amplitude of multiple scatterings from the commonly employed cascade approximations is a formidable, yet unaccomplished task. In this talk we are going to discuss how to compute second order nonlinear QED amplitudes and relate them to the conventional cascade approximation. We present examples for typical second order processes and benchmark the full result against common approximations. We demonstrate that the approximation of multiple nonlinear QED scatterings as a cascade of single interactions has certain limitations and discuss these limits in light of upcoming experimental tests.

Second-order Boltzmann equation: gauge dependence and gauge invariance

NASA Astrophysics Data System (ADS)

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

2013-08-01

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

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

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

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

Second-order Cosmological Perturbations Engendered by Point-like Masses

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

Brilenkov, Ruslan; Eingorn, Maxim, E-mail: ruslan.brilenkov@gmail.com, E-mail: maxim.eingorn@gmail.com

2017-08-20

In the ΛCDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second‐order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second‐order scalar, vector, and tensor metric corrections are suitable at arbitrary distances, including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfillment of all Einstein equations, as well as self‐consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological back-reaction manifestations by means of relativistic simulations are also outlined.

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

NASA Astrophysics Data System (ADS)

Becattini, F.; Grossi, E.

2015-08-01

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

Black holes in vector-tensor theories

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

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

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

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

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

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

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

First- and second-order processing in transient stereopsis.

PubMed

Edwards, M; Pope, D R; Schor, C M

2000-01-01

Large-field stimuli were used to investigate the interaction of first- and second-order pathways in transient-stereo processing. Stimuli consisted of sinewave modulations in either the mean luminance (first-order stimulus) or the contrast (second-order stimulus) of a dynamic-random-dot field. The main results of the present study are that: (1) Depth could be extracted with both the first-order and second-order stimuli; (2) Depth could be extracted from dichoptically mixed first- and second-order stimuli, however, the same stimuli, when presented as a motion sequence, did not result in a motion percept. Based upon these findings we conclude that the transient-stereo system processes both first- and second-order signals, and that these two signals are pooled prior to the extraction of transient depth. This finding of interaction between first- and second-order stereoscopic processing is different from the independence that has been found with the motion system.

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

{open_quotes}Quadrupoled{close_quotes} materials for second-order nonlinear optics

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

Hubbard, S.F.; Petschek, R.G.; Singer, K.D.

1997-10-01

We describe a new approach to second-order nonlinear optical materials, namely quadrupoling. This approach is valid in the regime of Kleinman (full permutation) symmetry breaking, and thus requires a two- or three dimensional microscopic nonlinearity at wavelengths away from material resonances. This {open_quotes}quadrupolar{close_quotes} nonlinearity arises from the second rank pseudotensor of the rotationally invariant representation of the second-order nonlinear optical tensor. We have experimentally investigated candidate molecules comprised of chiral camphorquinone derivatives by measuring the scalar invariant associated with the rank two pseudotensor using hyper-Rayleigh scattering. We have found sizable scalar figures of merit for several compounds using light formore » which the second harmonic wavelengths are greater than 100 nm longer than the absorption peak location. At these wavelengths, the quadrupolar scalar is as large as the polar (EFISH) scalar of p-nitroaniline. Prospects for applications are discussed.« less

Second rank direction cosine spherical tensor operators and the nuclear electric quadrupole hyperfine structure Hamiltonian of rotating molecules

NASA Astrophysics Data System (ADS)

di Lauro, C.

2018-03-01

Transformations of vector or tensor properties from a space-fixed to a molecule-fixed axis system are often required in the study of rotating molecules. Spherical components λμ,ν of a first rank irreducible tensor can be obtained from the direction cosines between the two axis systems, and a second rank tensor with spherical components λμ,ν(2) can be built from the direct product λ × λ. It is shown that the treatment of the interaction between molecular rotation and the electric quadrupole of a nucleus is greatly simplified, if the coefficients in the axis-system transformation of the gradient of the electric field of the outer charges at the coupled nucleus are arranged as spherical components λμ,ν(2). Then the reduced matrix elements of the field gradient operators in a symmetric top eigenfunction basis, including their dependence on the molecule-fixed z-angular momentum component k, can be determined from the knowledge of those of λ(2) . The hyperfine structure Hamiltonian Hq is expressed as the sum of terms characterized each by a value of the molecule-fixed index ν, whose matrix elements obey the rule Δk = ν. Some of these terms may vanish because of molecular symmetry, and the specific cases of linear and symmetric top molecules, orthorhombic molecules, and molecules with symmetry lower than orthorhombic are considered. Each ν-term consists of a contraction of the rotational tensor λ(2) and the nuclear quadrupole tensor in the space-fixed frame, and its matrix elements in the rotation-nuclear spin coupled representation can be determined by the standard spherical tensor methods.

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

Reisert, Marco; Burkhardt, Hans

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

A preliminary compressible second-order closure model for high speed flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu

1989-01-01

A preliminary version of a compressible second-order closure model that was developed in connection with the National Aero-Space Plane Project is presented. The model requires the solution of transport equations for the Favre-averaged Reynolds stress tensor and dissipation rate. Gradient transport hypotheses are used for the Reynolds heat flux, mass flux, and turbulent diffusion terms. Some brief remarks are made about the direction of future research to generalize the model.

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

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

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

2012-10-15

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

Erratum to Surface‐wave green’s tensors in the near field

USGS Publications Warehouse

Haney, Matthew M.; Hisashi Nakahara,

2016-01-01

Haney and Nakahara (2014) derived expressions for surface‐wave Green’s tensors that included near‐field behavior. Building on the result for a force source, Haney and Nakahara (2014) further derived expressions for a general point moment tensor source using the exact Green’s tensors. However, it has come to our attention that, although the Green’s tensors were correct, the resulting expressions for a general point moment tensor source were missing some terms. In this erratum, we provide updated expressions with these missing terms. The inclusion of the missing terms changes the example given in Haney and Nakahara (2014).

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

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

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

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

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

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

Interacting Non-Abelian Anti-Symmetric Tensor Field Theories

NASA Astrophysics Data System (ADS)

Ekambaram, K.; Vytheeswaran, A. S.

2018-04-01

Non-Abelian Anti-symmetric Tensor fields interacting with vector fields have a complicated constraint structure. We enlarge the gauge invariance in this system. Relevant gauge invariant quantities including the Hamiltonian are obtained. We also make introductory remarks on a different but more complicated gauge theory.

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

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

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu; Han, Daozhi, E-mail: djhan@iu.edu

2017-02-01

In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less

Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields

NASA Astrophysics Data System (ADS)

Zhu, Xiaoyu

2018-05-01

A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We investigate a time-reversal-invariant topological superconductor in two dimensions and demonstrate that an in-plane magnetic field could transform it into a second-order topological superconductor. A detailed analysis reveals that the magnetic field gives rise to mass terms which take distinct values among the edges, and Majorana corner states naturally emerge at the intersection of two adjacent edges with opposite masses. With the rotation of the magnetic field, Majorana corner states localized around the boundary may hop from one corner to a neighboring one and eventually make a full circle around the system when the field rotates by 2 π . In the end, we briefly discuss physical realizations of this system.

Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

PubMed

Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

2016-07-12

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

The energy-momentum tensor(s) in classical gauge theories

DOE PAGES

Blaschke, Daniel N.; Gieres, François; Reboud, Méril; ...

2016-07-12

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. In conclusion, the relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.

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.

Crossing Fibers Detection with an Analytical High Order Tensor Decomposition

PubMed Central

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

2014-01-01

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

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

NASA Astrophysics Data System (ADS)

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

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

Tensor Minkowski Functionals for random fields on the sphere

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

A solver for General Unilateral Polynomial Matrix Equation with Second-Order Matrices Over Prime Finite Fields

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-03-01

The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.

Second-order singular pertubative theory for gravitational lenses

NASA Astrophysics Data System (ADS)

Alard, C.

2018-03-01

The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second-order expansion is considered as a small correction to the first-order expansion. Using this approach, it is demonstrated that in practice the second-order expansion is reducible to a first order expansion via a re-definition of the first-order pertubative fields. Even if in usual applications the second-order correction is small the reducibility of the second-order expansion to the first-order expansion indicates a potential degeneracy issue. In general, this degeneracy is hard to break. A useful and simple second-order approximation is the thin source approximation, which offers a direct estimation of the correction. The practical application of the corrections derived in this paper is illustrated by using an elliptical NFW lens model. The second-order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude, it is clear that for accurate modelization of gravitational lenses using the perturbative method the second-order perturbative expansion should be considered. In particular, an evaluation of the degeneracy due to the second-order term should be performed, for which the thin source approximation is particularly useful.

Navier-Stokes computation of compressible turbulent flows with a second order closure

NASA Technical Reports Server (NTRS)

Dingus, C.; Kollmann, W.

1991-01-01

The objective was the development of a complete second order closure for wall bounded flows, including all components of the dissipation rate tensor and a numerical solution procedure for the resulting system of equations. The main topics discussed are the closure of the pressure correlations and the viscous destruction terms in the dissipation rate equations and the numerical solution scheme based on a block-tridiagonal solver for the nine equations required for the prediction of plane or axisymmetric flows.

Tensor tomography on Cartan–Hadamard manifolds

NASA Astrophysics Data System (ADS)

Lehtonen, Jere; Railo, Jesse; Salo, Mikko

2018-04-01

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

Hamiltonian approach to second order gauge invariant cosmological perturbations

NASA Astrophysics Data System (ADS)

Domènech, Guillem; Sasaki, Misao

2018-01-01

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

Diffusion tensor analysis with invariant gradients and rotation tangents.

PubMed

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

2007-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Integrability conditions for Killing-Yano tensors and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Batista, Carlos

2015-01-01

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano tensor of order p to generate a Killing-Yano tensor of order (p -1 ) . Finally, it is proved that in maximally symmetric spaces the covariant derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor and that every conformal Killing-Yano tensor is uniquely decomposed as the sum of a Killing-Yano tensor and a closed conformal Killing-Yano tensor.

Spin polarized phases in strongly interacting matter: Interplay between axial-vector and tensor mean fields

NASA Astrophysics Data System (ADS)

Maruyama, Tomoyuki; Nakano, Eiji; Yanase, Kota; Yoshinaga, Naotaka

2018-06-01

The spontaneous spin polarization of strongly interacting matter due to axial-vector- and tensor-type interactions is studied at zero temperature and high baryon-number densities. We start with the mean-field Lagrangian for the axial-vector and tensor interaction channels and find in the chiral limit that the spin polarization due to the tensor mean field (U ) takes place first as the density increases for sufficiently strong coupling constants, and then the spin polarization due to the axial-vector mean field (A ) emerges in the region of the finite tensor mean field. This can be understood as making the axial-vector mean-field finite requires a broken chiral symmetry somehow, which is achieved by the finite tensor mean field in the present case. It is also found from the symmetry argument that there appear the type I (II) Nambu-Goldstone modes with a linear (quadratic) dispersion in the spin polarized phase with U ≠0 and A =0 (U ≠0 and A ≠0 ), although these two phases exhibit the same symmetry breaking pattern.

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

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

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

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

Calculating Second-Order Effects in MOSFET's

NASA Technical Reports Server (NTRS)

Benumof, Reuben; Zoutendyk, John A.; Coss, James R.

1990-01-01

Collection of mathematical models includes second-order effects in n-channel, enhancement-mode, metal-oxide-semiconductor field-effect transistors (MOSFET's). When dimensions of circuit elements relatively large, effects neglected safely. However, as very-large-scale integration of microelectronic circuits leads to MOSFET's shorter or narrower than 2 micrometer, effects become significant in design and operation. Such computer programs as widely-used "Simulation Program With Integrated Circuit Emphasis, Version 2" (SPICE 2) include many of these effects. In second-order models of n-channel, enhancement-mode MOSFET, first-order gate-depletion region diminished by triangular-cross-section deletions on end and augmented by circular-wedge-cross-section bulges on sides.

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

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

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

Retrodictive determinism. [covariant and transformational behavior of tensor fields in hydrodynamics and thermodynamics

NASA Technical Reports Server (NTRS)

Kiehn, R. M.

1976-01-01

With respect to irreversible, non-homeomorphic maps, contravariant and covariant tensor fields have distinctly natural covariance and transformational behavior. For thermodynamic processes which are non-adiabatic, the fact that the process cannot be represented by a homeomorphic map emphasizes the logical arrow of time, an idea which encompasses a principle of retrodictive determinism for covariant tensor fields.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

Regional Recovery of the Disturbing Gravitational Potential from Satellite Observations of First-, Second- and Third-order Radial Derivatives of the Disturbing Gravitational Potential

NASA Astrophysics Data System (ADS)

Novak, P.; Pitonak, M.; Sprlak, M.

2015-12-01

Recently realized gravity-dedicated satellite missions allow for measuring values of scalar, vectorial (Gravity Recovery And Climate Experiment - GRACE) and second-order tensorial (Gravity field and steady-state Ocean Circulation Explorer - GOCE) parameters of the Earth's gravitational potential. Theoretical aspects related to using moving sensors for measuring elements of a third-order gravitational tensor are currently under investigation, e.g. the gravity-dedicated satellite mission OPTIMA (OPTical Interferometry for global Mass change detection from space) should measure third-order derivatives of the Earth's gravitational potential. This contribution investigates regional recovery of the disturbing gravitational potential on the Earth's surface from satellite observations of first-, second- and third-order radial derivatives of the disturbing gravitational potential. Synthetic measurements along a satellite orbit at the altitude of 250 km are synthetized from the global gravitational model EGM2008 and polluted by the Gaussian noise. The process of downward continuation is stabilized by the Tikhonov regularization. Estimated values of the disturbing gravitational potential are compared with the same quantity synthesized directly from EGM2008. Finally, this contribution also discusses merging a regional solution into a global field as a patchwork.

On scalar and vector fields coupled to the energy-momentum tensor

NASA Astrophysics Data System (ADS)

Jiménez, Jose Beltrán; Cembranos, Jose A. R.; Sánchez Velázquez, Jose M.

2018-05-01

We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we build the action by means of an iterative process that leads to an infinite series, which can be resumed as the solution of a set of differential equations. We show that, in some particular cases, the equations become algebraic and that is also possible to find solutions in the form of polynomials. We briefly review the case of the scalar field that has already been studied in the literature and extend the analysis to the case of derivative (disformal) couplings. We then explore theories with vector fields, distinguishing between gauge-and non-gauge-invariant couplings. Interactions with matter are also considered, taking a scalar field as a proxy for the matter sector. We also discuss the ambiguity introduced by superpotential (boundary) terms in the definition of the energy-momentum tensor and use them to show that it is also possible to generate Galileon-like interactions with this procedure. We finally use collider and astrophysical observations to set constraints on the dimensionful coupling which characterises the phenomenology of these models.

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.

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

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

Pitoňák, Martin; Šprlák, Michal; Tenzer, Robert

2017-05-01

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

Enhancement of the second plateau in solid high-order harmonic spectra by the two-color fields.

PubMed

Li, Jin-Bin; Zhang, Xiao; Yue, Sheng-Jun; Wu, Hong-Mei; Hu, Bi-Tao; Du, Hong-Chuan

2017-08-07

We theoretically investigate high-order harmonic generation (HHG) from solids in two-color fields. It is found that under the premise of maintaining the same amplitude, the intensity of the second plateau can be enhanced by two to three orders in a proper two-color field compared with the result in the monochromatic field with the same frequency as the driving pulse of the two-color field. This can be attributed to the fact that most excited electrons can be driven to the top of the first conduction band due to the larger vector potential of the two-color fields, which leads to the higher electron population of upper conduction bands. Moreover, we also find that isolated attosecond pulses can be generated from solids by choosing a proper two-color field that allows the electrons to reach the top of the first conduction band only once. This work provides a promising method for extending the range of solid HHG spectra in experiments.

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

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

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

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

Beam-plasma instability in inhomogeneous magnetic field and second order cyclotron resonance effects

NASA Astrophysics Data System (ADS)

Trakhtengerts, V. Y.; Hobara, Y.; Demekhov, A. G.; Hayakawa, M.

1999-03-01

A new analytical approach to cyclotron instability of electron beams with sharp gradients in velocity space (step-like distribution function) is developed taking into account magnetic field inhomogeneity and nonstationary behavior of the electron beam velocity. Under these conditions, the conventional hydrodynamic instability of such beams is drastically modified and second order resonance effects become important. It is shown that the optimal conditions for the instability occur for nonstationary quasimonochromatic wavelets whose frequency changes in time. The theory developed permits one to estimate the wave amplification and spatio-temporal characteristics of these wavelets.

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

Algorithms for computing solvents of unilateral second-order matrix polynomials over prime finite fields using lambda-matrices

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-01-01

The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.

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

NASA Astrophysics Data System (ADS)

Anderson, David; Yunes, Nicolás

2017-09-01

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

Expressions for optical scalars and deflection angle at second order in terms of curvature scalars

NASA Astrophysics Data System (ADS)

Crisnejo, Gabriel; Gallo, Emanuel

2018-04-01

We present formal expressions for the optical scalars in terms of the curvature scalars in the weak gravitational lensing regime at second order in perturbations of a flat background without mentioning the extension of the lens or their shape. Also, by considering the thin lens approximation for static and axially symmetric configurations we obtain an expression for the second-order deflection angle which generalizes our previous result presented by Gallo and Moreschi [Phys. Rev. D 83, 083007 (2011)., 10.1103/PhysRevD.83.083007]. As applications of these formulas we compute the optical scalars for some known family of metrics, and we recover expressions for the deflection angle. In contrast to other works in the subject, our formalism allows a straightforward identification of how the different components of the curvature tensor contribute to the optical scalars and deflection angle. We also discuss in what sense the Schwarzschild solution can be thought as a true thin lens at second order.

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

NASA Astrophysics Data System (ADS)

Karam, Alexandros; Pappas, Thomas; Tamvakis, Kyriakos

2017-09-01

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

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.

Superconducting tensor gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

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

A critical comparison of second order closures with direct numerical simulation of homogeneous turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Lumley, John L.

1991-01-01

Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

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

Models of second-order effects in metal-oxide-semiconductor field-effect transistors for computer applications

NASA Technical Reports Server (NTRS)

Benumof, Reuben; Zoutendyk, John; Coss, James

1988-01-01

Second-order effects in metal-oxide-semiconductor field-effect transistors (MOSFETs) are important for devices with dimensions of 2 microns or less. The short and narrow channel effects and drain-induced barrier lowering primarily affect threshold voltage, but formulas for drain current must also take these effects into account. In addition, the drain current is sensitive to channel length modulation due to pinch-off or velocity saturation and is diminished by electron mobility degradation due to normal and lateral electric fields in the channel. A model of a MOSFET including these considerations and emphasizing charge conservation is discussed.

Pavlovian second-order conditioned analgesia.

PubMed

Ross, R T

1986-01-01

Three experiments with rat subjects assessed conditioned analgesia in a Pavlovian second-order conditioning procedure by using inhibition of responding to thermal stimulation as an index of pain sensitivity. In Experiment 1, rats receiving second-order conditioning showed longer response latencies during a test of pain sensitivity in the presence of the second-order conditioned stimulus (CS) than rats receiving appropriate control procedures. Experiment 2 found that extinction of the first-order CS had no effect on established second-order conditioned analgesia. Experiment 3 evaluated the effects of post second-order conditioning pairings of morphine and the shock unconditioned stimulus (US). Rats receiving paired morphine-shock presentations showed significantly shorter response latencies during a hot-plate test of pain sensitivity in the presence of the second-order CS than did groups of rats receiving various control procedures; second-order analgesia was attenuated. These data extend the associative account of conditioned analgesia to second-order conditioning situations and are discussed in terms of the mediation of both first- and second-order analgesia by an association between the CS and a representation or expectancy of the US, which may directly activate endogenous pain inhibition systems.

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

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

Fermionic topological quantum states as tensor networks

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Second-order dissipative hydrodynamics for plasma with chiral asymmetry and vorticity

NASA Astrophysics Data System (ADS)

Gorbar, E. V.; Rybalka, D. O.; Shovkovy, I. A.

2017-05-01

By making use of the chiral kinetic theory in the relaxation-time approximation, we derive an Israel-Stewart type formulation of the hydrodynamic equations for a chiral relativistic plasma made of neutral particles (e.g., neutrinos). The effects of chiral asymmetry are captured by including an additional continuity equation for the axial charge, as well as the leading-order quantum corrections due to the spin of particles. In a formulation of the chiral kinetic theory used, we introduce a symmetric form of the energy-momentum tensor that is suitable for the description of a weakly nonuniform chiral plasma. By construction, the energy and momentum are conserved to the same leading order in the Planck constant as the kinetic equation itself. By making use of such a chiral kinetic theory and the Chapman-Enskog approach, we obtain a set of second-order dissipative hydrodynamic equations. The effects of the fluid vorticity and velocity fluctuations on the dispersion relations of chiral vortical waves are analyzed.

Studies of Second Order Optical Nonlinearities of 4-Aminobenzophenone (ABP) Single Crystal Films

NASA Astrophysics Data System (ADS)

Bhowmik, Achintya; Thakur, Mrinal

1998-03-01

Specific organic materials exhibit very high second order optical susceptibilities. Growth of single crystal films of these materials and characterization of nonlinear optical properties are necessary for implementation of device applications. We have grown large-area films ( 1 cm^2 area, 4 μm thick) of ABP by a modification of the shear method. Single crystal nature of the films was confirmed by polarized optical microscopy. X-ray diffraction analysis showed a [100] surface orientation. The absorption spectra revealed transparency from 390 nm to 1940 nm. Significant elements of the second order optical susceptibility tensor were measured by detailed SHG experiments using a Nd:YAG laser (1064 nm, 100 ps, 82 MHz). Second-harmonic power was measured using lock-in detection with carefully selected polarization conditions while the film was rotated about the propagation direction. Using LiNbØas the reference, d-coefficients of ABP were found to be d_23=7.2 pm/V and d_22=0.7 pm/V. Type-I and type-II phase-matching directions were identified on the film by analyzing the optical indicatrix surfaces at fundamental and second-harmonic frequencies.

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

NASA Astrophysics Data System (ADS)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

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

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

NASA Astrophysics Data System (ADS)

Feng, Jinglang; Hou, Xiyun

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

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).

Stability of Horndeski vector-tensor interactions

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

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

2013-10-01

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

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

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

Feng, Jinglang; Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circularmore » restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.« less

Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory

NASA Astrophysics Data System (ADS)

Matsubara, Takahiko

2003-02-01

We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.

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

Energy-momentum tensors in linearized Einstein's theory and massive gravity: The question of uniqueness

NASA Astrophysics Data System (ADS)

Bičák, Jiří; Schmidt, Josef

2016-01-01

The question of the uniqueness of energy-momentum tensors in the linearized general relativity and in the linear massive gravity is analyzed without using variational techniques. We start from a natural ansatz for the form of the tensor (for example, that it is a linear combination of the terms quadratic in the first derivatives), and require it to be conserved as a consequence of field equations. In the case of the linear gravity in a general gauge we find a four-parametric system of conserved second-rank tensors which contains a unique symmetric tensor. This turns out to be the linearized Landau-Lifshitz pseudotensor employed often in full general relativity. We elucidate the relation of the four-parametric system to the expression proposed recently by Butcher et al. "on physical grounds" in harmonic gauge, and we show that the results coincide in the case of high-frequency waves in vacuum after a suitable averaging. In the massive gravity we show how one can arrive at the expression which coincides with the "generalized linear symmetric Landau-Lifshitz" tensor. However, there exists another uniquely given simpler symmetric tensor which can be obtained by adding the divergence of a suitable superpotential to the canonical energy-momentum tensor following from the Fierz-Pauli action. In contrast to the symmetric tensor derived by the Belinfante procedure which involves the second derivatives of the field variables, this expression contains only the field and its first derivatives. It is simpler than the generalized Landau-Lifshitz tensor but both yield the same total quantities since they differ by the divergence of a superpotential. We also discuss the role of the gauge conditions in the proofs of the uniqueness. In the Appendix, the symbolic tensor manipulation software cadabra is briefly described. It is very effective in obtaining various results which would otherwise require lengthy calculations.

Piezoelectric Field Enhanced Second-Order Nonlinear Optical Susceptibilities in Wurtzite GaN/AlGaN Quantum Wells

NASA Technical Reports Server (NTRS)

Liu, Ansheng; Chuang, S.-L.; Ning, C. Z.; Woo, Alex (Technical Monitor)

1999-01-01

Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.

Using the full tensor of GOCE gravity gradients for regional gravity field modelling

NASA Astrophysics Data System (ADS)

Lieb, Verena; Bouman, Johannes; Dettmering, Denise; Fuchs, Martin; Schmidt, Michael

2013-04-01

With its 3-axis gradiometer GOCE delivers 3-dimensional (3D) information of the Earth's gravity field. This essential advantage - e.g. compared with the 1D gravity field information from GRACE - can be used for research on the Earth's interior and for geophysical exploration. To benefit from this multidimensional measurement system, the combination of all 6 GOCE gradients and additionally the consistent combination with other gravity observations mean an innovative challenge for regional gravity field modelling. As the individual gravity gradients reflect the gravity field depending on different spatial directions, observation equations are formulated separately for each of these components. In our approach we use spherical localizing base functions to display the gravity field for specified regions. Therefore the series expansions based on Legendre polynomials have to be adopted to obtain mathematical expressions for the second derivatives of the gravitational potential which are observed by GOCE in the Cartesian Gradiometer Reference Frame (GRF). We (1) have to transform the equations from the spherical terrestrial into a Cartesian Local North-Oriented Reference Frame (LNOF), (2) to set up a 3x3 tensor of observation equations and (3) finally to rotate the tensor defined in the terrestrial LNOF into the GRF. Thus we ensure the use of the original non-rotated and unaffected GOCE measurements within the analysis procedure. As output from the synthesis procedure we then obtain the second derivatives of the gravitational potential for all combinations of the xyz Cartesian coordinates in the LNOF. Further the implementation of variance component estimation provides a flexible tool to diversify the influence of the input gradiometer observations. On the one hand the less accurate xy and yz measurements are nearly excluded by estimating large variance components. On the other hand the yy measurements, which show systematic errors increasing at high latitudes, could be

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.

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

PubMed Central

2017-01-01

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

Binocular Combination of Second-Order Stimuli

PubMed Central

Zhou, Jiawei; Liu, Rong; Zhou, Yifeng; Hess, Robert F.

2014-01-01

Phase information is a fundamental aspect of visual stimuli. However, the nature of the binocular combination of stimuli defined by modulations in contrast, so-called second-order stimuli, is presently not clear. To address this issue, we measured binocular combination for first- (luminance modulated) and second-order (contrast modulated) stimuli using a binocular phase combination paradigm in seven normal adults. We found that the binocular perceived phase of second-order gratings depends on the interocular signal ratio as has been previously shown for their first order counterparts; the interocular signal ratios when the two eyes were balanced was close to 1 in both first- and second-order phase combinations. However, second-order combination is more linear than previously found for first-order combination. Furthermore, binocular combination of second-order stimuli was similar regardless of whether the carriers in the two eyes were correlated, anti-correlated, or uncorrelated. This suggests that, in normal adults, the binocular phase combination of second-order stimuli occurs after the monocular extracting of the second-order modulations. The sensory balance associated with this second-order combination can be obtained from binocular phase combination measurements. PMID:24404180

Second order tensor finite element

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.

1990-01-01

The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

A unified tensor level set for image segmentation.

PubMed

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

2010-06-01

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

Collective Modes in a Trapped Gas from Second-Order Hydrodynamics

NASA Astrophysics Data System (ADS)

Lewis, William; Romatschke, Paul

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

The second-order theory of electromagnetic hot ion beam instabilities. [in interplanetary magnetic field

NASA Technical Reports Server (NTRS)

Gary, S. P.; Tokar, R. L.

1985-01-01

The present investigation is concerned with the application of a second-order theory for electromagnetic instabilities in a collisionless plasma to two modes which resonate with hot ion beams. The application of the theory is strictly limited to the linear growth phase. However, the application of the theory may be extended to obtain a description of the beam at postsaturation if the wave-beam resonance is sufficiently broad in velocity space. Under the considered limitations, it is shown that, as in the cold beam case, the fluctuating fields do not gain appreciable momentum and that the primary exchange of momentum is between the beam and main component.

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.

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.

Complete Moment Tensor Determination of Induced Seismicity in Unconventional and Conventional Oil/Gas Fields

NASA Astrophysics Data System (ADS)

Gu, C.; Li, J.; Toksoz, M. N.

2013-12-01

Induced seismicity occurs both in conventional oil/gas fields due to production and water injection and in unconventional oil/gas fields due to hydraulic fracturing. Source mechanisms of these induced earthquakes are of great importance for understanding their causes and the physics of the seismic processes in reservoirs. Previous research on the analysis of induced seismic events in conventional oil/gas fields assumed a double couple (DC) source mechanism. However, recent studies have shown a non-negligible percentage of a non-double-couple (non-DC) component of source moment tensor in hydraulic fracturing events (Šílený et al., 2009; Warpinski and Du, 2010; Song and Toksöz, 2011). In this study, we determine the full moment tensor of the induced seismicity data in a conventional oil/gas field and for hydrofrac events in an unconventional oil/gas field. Song and Toksöz (2011) developed a full waveform based complete moment tensor inversion method to investigate a non-DC source mechanism. We apply this approach to the induced seismicity data from a conventional gas field in Oman. In addition, this approach is also applied to hydrofrac microseismicity data monitored by downhole geophones in four wells in US. We compare the source mechanisms of induced seismicity in the two different types of gas fields and explain the differences in terms of physical processes.

A second-order orientation-contrast stimulus for population-receptive-field-based retinotopic mapping.

PubMed

Yildirim, Funda; Carvalho, Joana; Cornelissen, Frans W

2018-01-01

Visual field or retinotopic mapping is one of the most frequently used paradigms in fMRI. It uses activity evoked by position-varying high luminance contrast visual patterns presented throughout the visual field for determining the spatial organization of cortical visual areas. While the advantage of using high luminance contrast is that it tends to drive a wide range of neural populations - thus resulting in high signal-to-noise BOLD responses - this may also be a limitation, especially for approaches that attempt to squeeze more information out of the BOLD response, such as population receptive field (pRF) mapping. In that case, more selective stimulation of a subset of neurons - despite reduced signals - could result in better characterization of pRF properties. Here, we used a second-order stimulus based on local differences in orientation texture - to which we refer as orientation contrast - to perform retinotopic mapping. Participants in our experiment viewed arrays of Gabor patches composed of a foreground (a bar) and a background. These could only be distinguished on the basis of a difference in patch orientation. In our analyses, we compare the pRF properties obtained using this new orientation contrast-based retinotopy (OCR) to those obtained using classic luminance contrast-based retinotopy (LCR). Specifically, in higher order cortical visual areas such as LO, our novel approach resulted in non-trivial reductions in estimated population receptive field size of around 30%. A set of control experiments confirms that the most plausible cause for this reduction is that OCR mainly drives neurons sensitive to orientation contrast. We discuss how OCR - by limiting receptive field scatter and reducing BOLD displacement - may result in more accurate pRF localization as well. Estimation of neuronal properties is crucial for interpreting cortical function. Therefore, we conclude that using our approach, it is possible to selectively target particular neuronal

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Microscopic cascading of second-order molecular nonlinearity: New design principles for enhancing third-order nonlinearity.

PubMed

Baev, Alexander; Autschbach, Jochen; Boyd, Robert W; Prasad, Paras N

2010-04-12

Herein, we develop a phenomenological model for microscopic cascading and substantiate it with ab initio calculations. It is shown that the concept of local microscopic cascading of a second-order nonlinearity can lead to a third-order nonlinearity, without introducing any new loss mechanisms that could limit the usefulness of our approach. This approach provides a new molecular design protocol, in which the current great successes achieved in producing molecules with extremely large second-order nonlinearity can be used in a supra molecular organization in a preferred orientation to generate very large third-order response magnitudes. The results of density functional calculations for a well-known second-order molecule, (para)nitroaniline, show that a head-to-tail dimer configuration exhibits enhanced third-order nonlinearity, in agreement with the phenomenological model which suggests that such an arrangement will produce cascading due to local field effects.

Second-order nonlinearity induced transparency.

PubMed

Zhou, Y H; Zhang, S S; Shen, H Z; Yi, X X

2017-04-01

In analogy to electromagnetically induced transparency, optomechanically induced transparency was proposed recently in [Science330, 1520 (2010)SCIEAS0036-807510.1126/science.1195596]. In this Letter, we demonstrate another form of induced transparency enabled by second-order nonlinearity. A practical application of the second-order nonlinearity induced transparency is to measure the second-order nonlinear coefficient. Our scheme might find applications in quantum optics and quantum information processing.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

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

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

1993-01-01

Solid-state NMR spectroscopy is well established as a method for describing molecular structure with resolution on the atomic scale. Many of the NMR observables result from anisotropic interactions between the nuclear spin and its environment. These observables can be described by second-rank tensors. For example, the eigenvalues of the traceless symmetric part of the hydrogen chemical shift (CS) tensor provide information about the strength of inter- or intramolecular hydrogen bonding. On the other hand, the eigenvectors of the deuterium electric field gradient (EFG) tensor give deuteron/proton bond directions with an accuracy rivalled only by neutron diffraction. In this paper themore » authors report structural information of this type for the amide and carboxyl hydrogen sites in a single crystal of the model peptide N-acetyl-D,L-valine (NAV). They use deuterium NMR to infer both the EFG and CS tensors at the amide and carboxyl hydrogen sites in NAV. Advantages of this technique over multiple-pulse proton NMR are that it works in the presence of {sup 14}N spins which are very hard to decouple from protons and that additional information in form of the EFG tensors can be derived. The change in the CS and EFG tensors upon exchange of a deuteron for a proton (the isotope effect) is anticipated to be very small; the effect on the CS tensors is certainly smaller than the experimental errors. NAV has served as a model peptide before in a variety of NMR studies, including those concerned with developing solid-state NMR spectroscopy as a method for determining the structure of proteins. NMR experiments on peptide or protein samples which are oriented in at least one dimension can provide important information about the three-dimensional structure of the peptide or the protein. In order to interpret the NMR data in terms of the structure of the polypeptide, the relationship of the CS and EFG tensors to the local symmetry elements of an amino acide, e.g., the peptide

Second order closure modeling of turbulent buoyant wall plumes

NASA Technical Reports Server (NTRS)

Zhu, Gang; Lai, Ming-Chia; Shih, Tsan-Hsing

1992-01-01

Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.

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

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

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

The total energy-momentum tensor for electromagnetic fields in a dielectric

NASA Astrophysics Data System (ADS)

Crenshaw, Michael E.

2017-08-01

Radiation pressure is an observable consequence of optically induced forces on materials. On cosmic scales, radiation pressure is responsible for the bending of the tails of comets as they pass near the sun. At a much smaller scale, optically induced forces are being investigated as part of a toolkit for micromanipulation and nanofabrication technology [1]. A number of practical applications of the mechanical effects of light-matter interaction are discussed by Qiu, et al. [2]. The promise of the nascent nanophotonic technology for manufacturing small, low-power, high-sensitivity sensors and other devices has likely motivated the substantial current interest in optical manipulation of materials at the nanoscale, see, for example, Ref. [2] and the references therein. While substantial progress toward optical micromanipulation has been achieved, e.g. optical tweezers [1], in this report we limit our consideration to the particular issue of optically induced forces on a transparent dielectric material. As a matter of electromagnetic theory, these forces remain indeterminate and controversial. Due to the potential applications in nanotechnology, the century-old debate regarding these forces, and the associated momentums, has ramped up considerably in the physics community. The energy-momentum tensor is the centerpiece of conservation laws for the unimpeded, inviscid, incompressible flow of non-interacting particles in the continuum limit in an otherwise empty volume. The foundations of the energy-momentum tensor and the associated tensor conservation theory come to electrodynamics from classical continuum dynamics by applying the divergence theorem to a Taylor series expansion of a property density field of a continuous flow in an otherwise empty volume. The dust tensor is a particularly simple example of an energy-momentum tensor that deals with particles of matter in the continuum limit in terms of the mass density ρm, energy density ρmc 2 , and momentum density �

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.

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

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

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

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.

Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization.

PubMed

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

2016-03-01

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

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

PubMed

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

2011-06-01

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

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

NASA Astrophysics Data System (ADS)

Cao, Wei-Guang; Xie, Yi

2018-03-01

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

Practical considerations for a second-order directional hearing aid microphone system

NASA Astrophysics Data System (ADS)

Thompson, Stephen C.

2003-04-01

First-order directional microphone systems for hearing aids have been available for several years. Such a system uses two microphones and has a theoretical maximum free-field directivity index (DI) of 6.0 dB. A second-order microphone system using three microphones could provide a theoretical increase in free-field DI to 9.5 dB. These theoretical maximum DI values assume that the microphones have exactly matched sensitivities at all frequencies of interest. In practice, the individual microphones in the hearing aid always have slightly different sensitivities. For the small microphone separation necessary to fit in a hearing aid, these sensitivity matching errors degrade the directivity from the theoretical values, especially at low frequencies. This paper shows that, for first-order systems the directivity degradation due to sensitivity errors is relatively small. However, for second-order systems with practical microphone sensitivity matching specifications, the directivity degradation below 1 kHz is not tolerable. A hybrid order directive system is proposed that uses first-order processing at low frequencies and second-order directive processing at higher frequencies. This hybrid system is suggested as an alternative that could provide improved directivity index in the frequency regions that are important to speech intelligibility.

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

NASA Astrophysics Data System (ADS)

Gürses, Metin

2010-10-01

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

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.

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

PubMed

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

2017-08-02

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

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

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

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

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

Turbulent fluid motion 2: Scalars, vectors, and tensors

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

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

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

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

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

A new formulation of the dispersion tensor in homogeneous porous media

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-05-01

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

Selfishness as second-order altruism

PubMed Central

Eldakar, Omar Tonsi; Wilson, David Sloan

2008-01-01

Selfishness is seldom considered a group-beneficial strategy. In the typical evolutionary formulation, altruism benefits the group, selfishness undermines altruism, and the purpose of the model is to identify mechanisms, such as kinship or reciprocity, that enable altruism to evolve. Recent models have explored punishment as an important mechanism favoring the evolution of altruism, but punishment can be costly to the punisher, making it a form of second-order altruism. This model identifies a strategy called “selfish punisher” that involves behaving selfishly in first-order interactions and altruistically in second-order interactions by punishing other selfish individuals. Selfish punishers cause selfishness to be a self-limiting strategy, enabling altruists to coexist in a stable equilibrium. This polymorphism can be regarded as a division of labor, or mutualism, in which the benefits obtained by first-order selfishness help to “pay” for second-order altruism. PMID:18448681

Full Moment Tensor Analysis Using First Motion Data at The Geysers Geothermal Field

NASA Astrophysics Data System (ADS)

Boyd, O.; Dreger, D. S.; Lai, V. H.; Gritto, R.

2012-12-01

Seismicity associated with geothermal energy production at The Geysers Geothermal Field in northern California has been increasing during the last forty years. We investigate source models of over fifty earthquakes with magnitudes ranging from Mw 3.5 up to Mw 4.5. We invert three-component, complete waveform data from broadband stations of the Berkeley Digital Seismic Network, the Northern California Seismic Network and the USA Array deployment (2005-2007) for the complete, six-element moment tensor. Some solutions are double-couple while others have substantial non-double-couple components. To assess the stability and significance of non-double-couple components, we use a suite of diagnostic tools including the F-test, Jackknife test, bootstrap and network sensitivity solution (NSS). The full moment tensor solutions of the studied events tend to plot in the upper half of the Hudson source type diagram where the fundamental source types include +CLVD, +LVD, tensile-crack, DC and explosion. Using the F-test to compare the goodness-of-fit values between the full and deviatoric moment tensor solutions, most of the full moment tensor solutions do not show a statistically significant improvement in fit over the deviatoric solutions. Because a small isotropic component may not significantly improve the fit, we include first motion polarity data to better constrain the full moment tensor solutions.

The tensor distribution function.

PubMed

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

2009-01-01

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

Covariant conserved currents for scalar-tensor Horndeski theory

NASA Astrophysics Data System (ADS)

Schmidt, J.; Bičák, J.

2018-04-01

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

A Second Look at Second-Order Belief Attribution in Autism.

ERIC Educational Resources Information Center

Tager-Flusberg, Helen; Sullivan, Kate

1994-01-01

Twelve students with autism and 12 with mental retardation, who had passed a first-order test of false belief, were given a second-order reasoning task. No intergroup performance differences were seen. Findings suggest that the difficulty for both groups with the second-order task lies in information processing demands rather than conceptual…

Minutia Tensor Matrix: A New Strategy for Fingerprint Matching

PubMed Central

Fu, Xiang; Feng, Jufu

2015-01-01

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

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

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

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

2012-02-01

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

Phase-field-crystal model for ordered crystals

NASA Astrophysics Data System (ADS)

Alster, Eli; Elder, K. R.; Hoyt, Jeffrey J.; Voorhees, Peter W.

2017-02-01

We describe a general method to model multicomponent ordered crystals using the phase-field-crystal (PFC) formalism. As a test case, a generic B2 compound is investigated. We are able to produce a line of either first-order or second-order order-disorder phase transitions, features that have not been incorporated in existing PFC approaches. Further, it is found that the only elastic constant for B2 that depends on ordering is C11. This B2 model is then used to study antiphase boundaries (APBs). The APBs are shown to reproduce classical mean-field results. Dynamical simulations of ordering across small-angle grain boundaries predict that dislocation cores pin the evolution of APBs.

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

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-09-01

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

Radiation-reaction force on a small charged body to second order

NASA Astrophysics Data System (ADS)

Moxon, Jordan; Flanagan, Éanna

2018-05-01

In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self-force. We extend to higher order in the total charge a previous rigorous derivation of the electromagnetic self-force in flat spacetime by Gralla, Harte, and Wald. The method introduced by Gralla, Harte, and Wald computes the self-force from the Maxwell field equations and conservation of stress-energy in a limit where the charge, size, and mass of the body go to zero, and it does not require regularization of a singular self-field. For our higher-order computation, an adjustment of the definition of the mass of the body is necessary to avoid including self-energy from the electromagnetic field sourced by the body in the distant past. We derive the evolution equations for the mass, spin, and center-of-mass position of the body through second order. We derive, for the first time, the second-order acceleration dependence of the evolution of the spin (self-torque), as well as a mixing between the extended body effects and the acceleration-dependent effects on the overall body motion.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Large optical second-order nonlinearity of poled WO3-TeO2 glass.

PubMed

Tanaka, K; Narazaki, A; Hirao, K

2000-02-15

Second-harmonic generation, one of the second-order nonlinear optical properties of thermally and electrically poled WO>(3)-TeO>(2) glasses, has been examined. We poled glass samples with two thicknesses (0.60 and 0.86 mm) at various temperatures to explore the effects of external electric field strength and poling temperature on second-order nonlinearity. The dependence of second-harmonic intensity on the poling temperature is maximum at a specific poling temperature. A second-order nonlinear susceptibility of 2.1 pm/V was attained for the 0.60-mm-thick glass poled at 250 degrees C. This value is fairly large compared with those for poled silica and tellurite glasses reported thus far. We speculate that the large third-order nonlinear susceptibility of WO>(3)- TeO>(2) glasses gives rise to the large second-order nonlinearity by means of a X((2)) = 3X((3)) E(dc) process.

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

PubMed

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

2013-09-07

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

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

NASA Astrophysics Data System (ADS)

Shertzer, Richard H.; Adams, Edward E.

2018-03-01

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

Monitoring by forward scatter radar techniques: an improved second-order analytical model

NASA Astrophysics Data System (ADS)

Falconi, Marta Tecla; Comite, Davide; Galli, Alessandro; Marzano, Frank S.; Pastina, Debora; Lombardo, Pierfrancesco

2017-10-01

In this work, a second-order phase approximation is introduced to provide an improved analytical model of the signal received in forward scatter radar systems. A typical configuration with a rectangular metallic object illuminated while crossing the baseline, in far- or near-field conditions, is considered. An improved second-order model is compared with a simplified one already proposed by the authors and based on a paraxial approximation. A phase error analysis is carried out to investigate benefits and limitations of the second-order modeling. The results are validated by developing full-wave numerical simulations implementing the relevant scattering problem on a commercial tool.

Research on the sonic boom problem. Part 1: Second-order solutions for the flow field around slender bodies in supersonic flow for sonic boom analysis

NASA Technical Reports Server (NTRS)

Landahl, M.; Loefgren, P.

1973-01-01

A second-order theory for supersonic flow past slender bodies is presented. Through the introduction of characteristic coordinates as independent variables and the expansion procedure proposed by Lin and Oswatitsch, a uniformly valid solution is obtained for the whole flow field in the axisymmetric case and for far field in the general three-dimensional case. For distances far from the body the theory is an extension of Whitham's first-order solution and for the domain close to the body it is a modification of Van Dyke's second-order solution in the axisymmetric case. From the theory useful formulas relating flow deflections to the Whitham F-function are derived, which permits one to determine the sonic boom strength from wind tunnel measurements fairly close to the body.

An Analysis of Second-Order Autoshaping

ERIC Educational Resources Information Center

Ward-Robinson, Jasper

2004-01-01

Three mechanisms can explain second-order conditioning: (1) The second-order conditioned stimulus (CS2) could activate a representation of the first-order conditioned stimulus (CS1), thereby provoking the conditioned response (CR); The CS2 could enter into an excitatory association with either (2) the representation governing the CR, or (3) with a…

Second-order motions contribute to vection.

PubMed

Gurnsey, R; Fleet, D; Potechin, C

1998-09-01

First- and second-order motions differ in their ability to induce motion aftereffects (MAEs) and the kinetic depth effect (KDE). To test whether second-order stimuli support computations relating to motion-in-depth we examined the vection illusion (illusory self motion induced by image flow) using a vection stimulus (V, expanding concentric rings) that depicted a linear path through a circular tunnel. The set of vection stimuli contained differing amounts of first- and second-order motion energy (ME). Subjects reported the duration of the perceived MAEs and the duration of their vection percept. In Experiment 1 both MAEs and vection durations were longest when the first-order (Fourier) components of V were present in the stimulus. In Experiment 2, V was multiplicatively combined with static noise carriers having different check sizes. The amount of first-order ME associated with V increases with check size. MAEs were found to increase with check size but vection durations were unaffected. In general MAEs depend on the amount of first-order ME present in the signal. Vection, on the other hand, appears to depend on a representation of image flow that combines first- and second-order ME.

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

PubMed

Brand, H R; Pleiner, H; Svenšek, D

2014-09-01

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

Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities

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

Roppo, V.; Charles M. Bowden Research Facility, US Army RDECOM, Redstone Arsenal, Alabama 35803; Cojocaru, C.

We predict and experimentally observe the enhancement by three orders of magnitude of phase mismatched second and third harmonic generation in a GaAs cavity at 650 and 433 nm, respectively, well above the absorption edge. Phase locking between the pump and the harmonics changes the effective dispersion of the medium and inhibits absorption. Despite hostile conditions the harmonics resonate inside the cavity and become amplified leading to relatively large conversion efficiencies. Field localization thus plays a pivotal role despite the presence of absorption, and ushers in a new class of semiconductor-based devices in the visible and uv ranges.

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

NASA Astrophysics Data System (ADS)

Hohm, Olaf; Wang, Yi-Nan

2015-04-01

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

Prediction model of sinoatrial node field potential using high order partial least squares.

PubMed

Feng, Yu; Cao, Hui; Zhang, Yanbin

2015-01-01

High order partial least squares (HOPLS) is a novel data processing method. It is highly suitable for building prediction model which has tensor input and output. The objective of this study is to build a prediction model of the relationship between sinoatrial node field potential and high glucose using HOPLS. The three sub-signals of the sinoatrial node field potential made up the model's input. The concentration and the actuation duration of high glucose made up the model's output. The results showed that on the premise of predicting two dimensional variables, HOPLS had the same predictive ability and a lower dispersion degree compared with partial least squares (PLS).

Local White Matter Geometry from Diffusion Tensor Gradients

PubMed Central

Savadjiev, Peter; Kindlmann, Gordon L.; Bouix, Sylvain; Shenton, Martha E.; Westin, Carl-Fredrik

2009-01-01

We introduce a mathematical framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia. PMID:19896542

Local White Matter Geometry from Diffusion Tensor Gradients

PubMed Central

Savadjiev, Peter; Kindlmann, Gordon L.; Bouix, Sylvain; Shenton, Martha E.; Westin, Carl-Fredrik

2010-01-01

We introduce a mathematical framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia. PMID:20426006

MRI diffusion tensor reconstruction with PROPELLER data acquisition.

PubMed

Cheryauka, Arvidas B; Lee, James N; Samsonov, Alexei A; Defrise, Michel; Gullberg, Grant T

2004-02-01

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.

On the 4D generalized Proca action for an Abelian vector field

NASA Astrophysics Data System (ADS)

Allys, Erwan; Beltrán Almeida, Juan P.; Peter, Patrick; Rodríguez, Yeinzon

2016-09-01

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 05 (2014) 015 and Phys. Lett. B 757 (2016) 405 and complements those of JCAP 02 (2016) 004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field Aμ, the Faraday tensor Fμν and its Hodge dual tilde Fμν.

The Invar tensor package: Differential invariants of Riemann

NASA Astrophysics Data System (ADS)

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

2008-10-01

the distribution. To obtain the Mathematica and Maple database files click on this link. Classification:1.5, 5 Does the new version supersede the previous version?:Yes. The previous version (1.0) only handled algebraic invariants. The current version (2.0) has been extended to cover differential invariants as well. Nature of problem:Manipulation and simplification of scalar polynomial expressions formed from the Riemann tensor and its covariant derivatives. Solution method:Algorithms of computational group theory to simplify expressions with tensors that obey permutation symmetries. Tables of syzygies of the scalar invariants of the Riemann tensor. Reasons for new version:With this new version, the user can manipulate differential invariants of the Riemann tensor. Differential invariants are required in many physical problems in classical and quantum gravity. Summary of revisions:The database of syzygies has been expanded by a factor of 30. New commands were added in order to deal with the enlarged database and to manipulate the covariant derivative. Restrictions:The present version only handles scalars, and not expressions with free indices. Additional comments:The distribution file for this program is over 53 Mbytes and therefore is not delivered directly when download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. Running time:One second to fully reduce any monomial of the Riemann tensor up to degree 7 or order 10 in terms of independent invariants. The Mathematica notebook included in the distribution takes approximately 5 minutes to run.

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

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

NASA Astrophysics Data System (ADS)

Kugo, T.; Ohashi, K.

2002-12-01

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

Susceptibility Tensor Imaging (STI) of the Brain

PubMed Central

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

2016-01-01

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

The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry.

PubMed

Yang, Yi; Tang, Xiangyang

2012-12-01

The x-ray differential phase contrast imaging implemented with the Talbot interferometry has recently been reported to be capable of providing tomographic images corresponding to attenuation-contrast, phase-contrast, and dark-field contrast, simultaneously, from a single set of projection data. The authors believe that, along with small-angle x-ray scattering, the second-order phase derivative Φ(") (s)(x) plays a role in the generation of dark-field contrast. In this paper, the authors derive the analytic formulae to characterize the contribution made by the second-order phase derivative to the dark-field contrast (namely, second-order differential phase contrast) and validate them via computer simulation study. By proposing a practical retrieval method, the authors investigate the potential of second-order differential phase contrast imaging for extensive applications. The theoretical derivation starts at assuming that the refractive index decrement of an object can be decomposed into δ = δ(s) + δ(f), where δ(f) corresponds to the object's fine structures and manifests itself in the dark-field contrast via small-angle scattering. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the contribution made by δ(s), which corresponds to the object's smooth structures, to the dark-field contrast are derived. Through computer simulation with specially designed numerical phantoms, an x-ray differential phase contrast imaging system implemented with the Talbot interferometry is utilized to evaluate and validate the derived formulae. The same imaging system is also utilized to evaluate and verify the capability of the proposed method to retrieve the second-order differential phase contrast for imaging, as well as its robustness over the dimension of detector cell and the number of steps in grating shifting. Both analytic formulae and computer simulations show that, in addition to small-angle scattering, the contrast generated by the

Automatic deformable diffusion tensor registration for fiber population analysis.

PubMed

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

2008-01-01

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

Minkowski Tensors in Two Dimensions: Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields

NASA Astrophysics Data System (ADS)

Appleby, Stephen; Chingangbam, Pravabati; Park, Changbom; Hong, Sungwook E.; Kim, Juhan; Ganesan, Vidhya

2018-05-01

We apply the Minkowski tensor statistics to two-dimensional slices of the three-dimensional matter density field. The Minkowski tensors are a set of functions that are sensitive to directionally dependent signals in the data and, furthermore, can be used to quantify the mean shape of density fields. We begin by reviewing the definition of Minkowski tensors and introducing a method of calculating them from a discretely sampled field. Focusing on the statistic {W}21,1—a 2 × 2 matrix—we calculate its value for both the entire excursion set and individual connected regions and holes within the set. To study the morphology of structures within the excursion set, we calculate the eigenvalues λ 1, λ 2 for the matrix {W}21,1 of each distinct connected region and hole and measure their mean shape using the ratio β \\equiv < {λ }2/{λ }1> . We compare both {W}21,1 and β for a Gaussian field and a smoothed density field generated from the latest Horizon Run 4 cosmological simulation to study the effect of gravitational collapse on these functions. The global statistic {W}21,1 is essentially independent of gravitational collapse, as the process maintains statistical isotropy. However, β is modified significantly, with overdensities becoming relatively more circular compared to underdensities at low redshifts. When applying the statistics to a redshift-space distorted density field, the matrix {W}21,1 is no longer proportional to the identity matrix, and measurements of its diagonal elements can be used to probe the large-scale velocity field.

Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles

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

Sabitov, I Kh

We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class C{sup 1} both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface. Bibliography: 15 entries.

Second order gradiometer and dc SQUID integrated on a planar substrate

NASA Astrophysics Data System (ADS)

van Nieuwenhuyzen, G. J.; de Waal, V. J.

1985-02-01

An integrated system of a thin-film niobium dc superconducting quantum interference device (SQUID) and a second order gradiometer on a planar substrate is described. The system consists of a dc SQUID with eight loops in parallel, each sensitive to the second derivative ∂2Bz/∂x2 of the magnetic field. The calculated SQUID inductance is 1.3 nH. With an overall size of 16×16.5 mm2 a sensitivity of 1.5×10-9 Tm-2 Hz-1/2 is obtained. The measured transfer function for uniform fields perpendicular to the plane of the gradiometer is 2.1×10-7 T Φ-10.

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.

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

NASA Astrophysics Data System (ADS)

Kobayashi, Tsutomu; Hiramatsu, Takashi

2018-05-01

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

Anisotropic tensor power spectrum at interferometer scales induced by tensor squeezed non-Gaussianity

NASA Astrophysics Data System (ADS)

Ricciardone, Angelo; Tasinato, Gianmassimo

2018-02-01

We develop a scenario of inflation with spontaneously broken time and space diffeomorphisms, with distinctive features for the primordial tensor modes. Inflationary tensor fluctuations are not conserved outside the horizon, and can acquire a mass during the inflationary epoch. They can evade the Higuchi bound around de Sitter space, thanks to interactions with the fields driving expansion. Correspondingly, the primordial stochastic gravitational wave background (SGWB) is characterised by a tuneable scale dependence, and can be detectable at interferometer scales. In this set-up, tensor non-Gaussianity can be parametrically enhanced in the squeezed limit. This induces a coupling between long and short tensor modes, leading to a specific quadrupolar anisotropy in the primordial SGWB spectrum, which can be used to build estimators for tensor non-Gaussianity. We analyse how our inflationary system can be tested with interferometers, also discussing how an interferometer can be sensitive to a primordial anisotropic SGWB.

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.

A novel unsplit perfectly matched layer for the second-order acoustic wave equation.

PubMed

Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan

2014-08-01

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach. Copyright © 2014 Elsevier B.V. All rights reserved.

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

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.

Generalized Israel junction conditions for a fourth-order brane world

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

Balcerzak, Adam; Dabrowski, Mariusz P.

2008-01-15

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

On the energy-momentum tensor in Moyal space

DOE PAGES

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

2015-06-26

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

Magnetic Compensation for Second-Order Doppler Shift in LITS

NASA Technical Reports Server (NTRS)

Burt, Eric; Tjoelker, Robert

2008-01-01

The uncertainty in the frequency of a linear-ion-trap frequency standard (LITS) can be reduced substantially by use of a very small magnetic inhomogeneity tailored to compensate for the residual second-order Doppler shift. An effect associated with the relativistic time dilatation, one cause of the second-order Doppler shift, is ion motion that is attributable to the trapping radio-frequency (RF)electromagnetic field used to trap ions. The second-order Doppler shift is reduced by using a multi-pole trap; however it is still the largest source of systematic frequency shift in the latest generation of LITSs, which are among the most stable clocks in the world. The present compensation scheme reduces the frequency instability of the affected LITS to about a tenth of its previous value. The basic principles of prior generation LITSs were discussed in several prior NASA Tech Briefs articles. Below are recapitulated only those items of basic information necessary to place the present development in context. A LITS includes a microwave local oscillator, the frequency of which is stabilized by comparison with the frequency of the ground state hyperfine transition of 199Hg+ ions. The comparison involves a combination of optical and microwave excitation and interrogation of the ions in a linear ion trap in the presence of a nominally uniform magnetic field. In the current version of the LITS, there are two connected traps (see figure): (1) a quadrupole trap wherein the optical excitation and measurement take place and (2) a 12-pole trap (denoted the resonance trap), wherein the microwave interrogation takes place. The ions are initially loaded into the quadrupole trap and are thereafter shuttled between the two traps. Shuttling ions into the resonance trap allows sensitive microwave interrogation to take place well away from loading interference. The axial magnetic field for the resonance trap is generated by an electric current in a finely wound wire coil surrounded by

Second-order nonlinear optical properties of composite material of an azo-chromophore with a tricyanodiphenyl acceptor in a poly(styrene-co-methyl methacrylate) matrix

NASA Astrophysics Data System (ADS)

Shelkovnikov, Vladimir; Selivanova, Galina; Lyubas, Gleb; Korotaev, Sergey; Shundrina, Inna; Tretyakov, Evgeny; Zueva, Ekaterina; Plekhanov, Alexander; Mikerin, Sergey; Simanchuk, Andrey

2017-07-01

The composite material of new synthesized 4-((4-(N,N-n-dibutylamino) phenyl)diazenyl)-biphenyl-2,3,4-tricarbonitrile (GAS dye) in commercial poly(styrene-co-methyl methacrylate) (PSMMA) was prepared, poled and its nonlinear optical properties compared with DR1 dye were studied. High thermal stability of the composite material was revealed, and the maximal concentration of the chromophore was found to reach ∼20 wt%. The dipole moment, polarizability tensor, and first hyperpolarizability tensor of the investigated dyes were calculated by within the framework of the coupled perturbed density functional theory. A nanosecond second-harmonic generation Maker fringes technique was used which is capable of providing the magnitude of the second-order nonlinearity of optical materials at a wavelength of 1064 nm. For the tested GAS-PSMMA composite material, maximal coefficient d33 was found to be 50 pm/V. The nonlinear optical response, which was achieved here, shows possible usefulness of the GAS dye as a component for molecular design of nonlinear-optical materials with advanced characteristics.

Waveform-based Bayesian full moment tensor inversion and uncertainty determination for the induced seismicity in an oil/gas field

NASA Astrophysics Data System (ADS)

Gu, Chen; Marzouk, Youssef M.; Toksöz, M. Nafi

2018-03-01

Small earthquakes occur due to natural tectonic motions and are induced by oil and gas production processes. In many oil/gas fields and hydrofracking processes, induced earthquakes result from fluid extraction or injection. The locations and source mechanisms of these earthquakes provide valuable information about the reservoirs. Analysis of induced seismic events has mostly assumed a double-couple source mechanism. However, recent studies have shown a non-negligible percentage of non-double-couple components of source moment tensors in hydraulic fracturing events, assuming a full moment tensor source mechanism. Without uncertainty quantification of the moment tensor solution, it is difficult to determine the reliability of these source models. This study develops a Bayesian method to perform waveform-based full moment tensor inversion and uncertainty quantification for induced seismic events, accounting for both location and velocity model uncertainties. We conduct tests with synthetic events to validate the method, and then apply our newly developed Bayesian inversion approach to real induced seismicity in an oil/gas field in the sultanate of Oman—determining the uncertainties in the source mechanism and in the location of that event.

Second-order topological insulators and superconductors with an order-two crystalline symmetry

NASA Astrophysics Data System (ADS)

Geier, Max; Trifunovic, Luka; Hoskam, Max; Brouwer, Piet W.

2018-05-01

Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a three-dimensional crystal. A second-order topological phase can be induced by the presence of a bulk crystalline symmetry. Building on Shiozaki and Sato's complete classification of bulk crystalline phases with an order-two crystalline symmetry [Phys. Rev. B 90, 165114 (2014), 10.1103/PhysRevB.90.165114], such as mirror reflection, twofold rotation, or inversion symmetry, we classify all corresponding second-order topological insulators and superconductors. The classification also includes antiunitary symmetries and antisymmetries.

Second order Pseudo-gaussian shaper

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

Beche, Jean-Francois

2002-11-22

The purpose of this document is to provide a calculus spreadsheet for the design of second-order pseudo-gaussian shapers. A very interesting reference is given by C.H. Mosher ''Pseudo-Gaussian Transfer Functions with Superlative Recovery'', IEEE TNS Volume 23, p. 226-228 (1976). Fred Goulding and Don Landis have studied the structure of those filters and their implementation and this document will outline the calculation leading to the relation between the coefficients of the filter. The general equation of the second order pseudo-gaussian filter is: f(t) = P{sub 0} {center_dot} e{sup -3kt} {center_dot} sin{sup 2}(kt). The parameter k is a normalization factor.

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

PubMed

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

2014-07-01

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

More on the scalar-tensor BF theory

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

Singh, Harvendra

2009-09-15

This work is based on an earlier proposal [H. Singh, Phys. Lett. B 673, 68 (2009)] that the membrane BF theory consists of matter fields along with Chern-Simons fields as well as the auxiliary pairs of scalar and tensor fields. In particular, we discuss the supersymmetry aspects of such a membrane theory. It is concluded that the theory possesses maximal supersymmetry, and it is related to the L-BLG theory via a field map. We obtain fuzzy-sphere solution, and corresponding tensor field configuration is given.

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.

Effect of second-order exchange in electron-hydrogen scattering

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

Madison, D.H.; Bray, I.; McCarthy, I.

1990-05-07

The electron-hydrogen scattering problem has been a nemesis to theoretical atomic physicists due to the fact that even the most sophisticated of theoretical calculations, both perturbative and nonperturbative, do not agree with experiment. The current opinion is that the perturbative approach cannot be used for this problem since recent second-order calculations are not in agreement with the experimental data and higher-order calculations are deemed impractical. However, these second-order calculations neglected second-order exchange. We have now added exchange to the second-order calculation and have found that the primary source of disagreement between experiment and theory for intermediate energies is attributable notmore » to higher-order terms but to second-order exchange.« less

Killing(-Yano) tensors in string theory

NASA Astrophysics Data System (ADS)

Chervonyi, Yuri; Lunin, Oleg

2015-09-01

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

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.

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

PubMed

Jia, Chengcheng; Fu, Yun

2016-07-09

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

f(R)-gravity from Killing tensors

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos

2016-04-01

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

Effets non-lineaires de second ordre dans les verres de silice

NASA Astrophysics Data System (ADS)

Godbout, Nicolas

Materials possessing inversion symmetry can not have a non-zero second-order susceptibility tensor. Since silica glasses are amorphous and isotropic, they possess this symmetry and therefore do not exhibit second-order nonlinear optical effects. However, the symmetry can be broken by several processes. The central question of this thesis is the determination of the mechanisms responsible for the second-order susceptibility in silica glasses after thermal poling. The presence of this nonlinearity arises through one of these mechanisms: the orientation of dipolar moieties possessing a second-order hyperpolarisability, or the build-up of a permanent electric field by charge motion which creates an apparent χ(2) through the already present χ (3). The dipole orientation model has a bigger potential of generating high optical nonlinearities than the built-in field model. This conclusion is based on a study of the crystalline structures of silica. The measurement of Maker fringes is the most informative technique for characterization of the optical properties of bulk poled samples. Measurements on Infrasil™ and Suprasil™ samples show an optically active layer of approximately 9 and 23 microns, with χ(2) susceptibilities of approximately 0.07 pm/V and 0.02 pm/V respectively. The analysis of Maker fringes in a similar sample suggests that the sign of the surface and bulk χ (2)-s is different, supporting the built-in field model as the origin of χ(2). Based on the results analyzed in this thesis, the second- order susceptibility of silica glasses after thermal poling results from the creation of a permanent built-in electric field caused by the movement of cations coupled to the pre-existing third-order nonlinearity. This claim is based on: the observed pump polarization dependence of Maker fringes, predictions of a steady-state ion migration model about the resulting optical properties and their confirmation by optical measurements; the presence of a bulk

Einstein-aether theory with a Maxwell field: General formalism

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

Balakin, Alexander B., E-mail: Alexander.Balakin@kpfu.ru; Lemos, José P.S., E-mail: joselemos@ist.utl.pt

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shearmore » and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.« less

Investigation of the linear and second-order nonlinear optical properties of molecular crystals within the local field theory.

PubMed

Seidler, Tomasz; Stadnicka, Katarzyna; Champagne, Benoît

2013-09-21

In this paper it is shown that modest calculations combining first principles evaluations of the molecular properties with electrostatic interaction schemes to account for the crystal environment effects are reliable for predicting and interpreting the experimentally measured electric linear and second-order nonlinear optical susceptibilities of molecular crystals within the experimental error bars. This is illustrated by considering two molecular crystals, namely: 2-methyl-4-nitroaniline and 4-(N,N-dimethylamino)-3-acetamidonitrobenzene. Three types of surrounding effects should be accounted for (i) the polarization due to the surrounding molecules, described here by static electric fields originating from their electric dipoles or charge distributions, (ii) the intermolecular interactions, which affect the geometry and particularly the molecular conformation, and (iii) the screening of the external electric field by the constitutive molecules. This study further highlights the role of electron correlation on the linear and nonlinear responses of molecular crystals and the challenge of describing frequency dispersion.

Detection, localization and classification of multiple dipole-like magnetic sources using magnetic gradient tensor data

NASA Astrophysics Data System (ADS)

Gang, Yin; Yingtang, Zhang; Hongbo, Fan; Zhining, Li; Guoquan, Ren

2016-05-01

We have developed a method for automatic detection, localization and classification (DLC) of multiple dipole sources using magnetic gradient tensor data. First, we define modified tilt angles to estimate the approximate horizontal locations of the multiple dipole-like magnetic sources simultaneously and detect the number of magnetic sources using a fixed threshold. Secondly, based on the isotropy of the normalized source strength (NSS) response of a dipole, we obtain accurate horizontal locations of the dipoles. Then the vertical locations are calculated using magnitude magnetic transforms of magnetic gradient tensor data. Finally, we invert for the magnetic moments of the sources using the measured magnetic gradient tensor data and forward model. Synthetic and field data sets demonstrate effectiveness and practicality of the proposed method.

Experimental determination of the carboxylate oxygen electric-field-gradient and chemical shielding tensors in L-alanine and L-phenylalanine

NASA Astrophysics Data System (ADS)

Yamada, Kazuhiko; Asanuma, Miwako; Honda, Hisashi; Nemoto, Takahiro; Yamazaki, Toshio; Hirota, Hiroshi

2007-10-01

We report a solid-state 17O NMR study of the 17O electric-field-gradient (EFG) and chemical shielding (CS) tensors for each carboxylate group in polycrystalline L-alanine and L-phenylalanine. The magic angle spinning (MAS) and stationary 17O NMR spectra of these compounds were obtained at 9.4, 14.1, and 16.4 T. Analyzes of these 17O NMR spectra yielded reliable experimental NMR parameters including 17O CS tensor components, 17O quadrupole coupling parameters, and the relative orientations between the 17O CS and EFG tensors. The extensive quantum chemical calculations at both the restricted Hartree-Fock and density-functional theories were carried out with various basis sets to evaluate the quality of quantum chemical calculations for the 17O NMR tensors in L-alanine. For 17O CS tensors, the calculations at the B3LYP/D95 ∗∗ level could reasonably reproduce 17O CS tensors, but they still showed some discrepancies in the δ11 components by approximately 36 ppm. For 17O EFG calculations, it was advantageous to use calibrated Q value to give acceptable CQ values. The calculated results also demonstrated that not only complete intermolecular hydrogen-bonding networks to target oxygen in L-alanine, but also intermolecular interactions around the NH3+ group were significant to reproduce the 17O NMR tensors.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

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.

Investigating local network interactions underlying first- and second-order processing.

PubMed

Ellemberg, Dave; Allen, Harriet A; Hess, Robert F

2004-01-01

We compared the spatial lateral interactions for first-order cues to those for second-order cues, and investigated spatial interactions between these two types of cues. We measured the apparent modulation depth of a target Gabor at fixation, in the presence and the absence of horizontally flanking Gabors. The Gabors' gratings were either added to (first-order) or multiplied with (second-order) binary 2-D noise. Apparent "contrast" or modulation depth (i.e., the perceived difference between the high and low luminance regions for the first-order stimulus, or between the high and low contrast regions for the second-order stimulus) was measured with a modulation depth-matching paradigm. For each observer, the first- and second-order Gabors were equated for apparent modulation depth without the flankers. Our results indicate that at the smallest inter-element spacing, the perceived reduction in modulation depth is significantly smaller for the second-order than for the first-order stimuli. Further, lateral interactions operate over shorter distances and the spatial frequency and orientation tuning of the suppression effect are broader for second- than first-order stimuli. Finally, first- and second-order information interact in an asymmetrical fashion; second-order flankers do not reduce the apparent modulation depth of the first-order target, whilst first-order flankers reduce the apparent modulation depth of the second-order target.

Nonequilibrium Second-Order Phase Transition in a Cooper-Pair Insulator.

PubMed

Doron, A; Tamir, I; Mitra, S; Zeltzer, G; Ovadia, M; Shahar, D

2016-02-05

In certain disordered superconductors, upon increasing the magnetic field, superconductivity terminates with a direct transition into an insulating phase. This phase is comprised of localized Cooper pairs and is termed a Cooper-pair insulator. The current-voltage characteristics measured in this insulating phase are highly nonlinear and, at low temperatures, exhibit abrupt current jumps. Increasing the temperature diminishes the jumps until the current-voltage characteristics become continuous. We show that a direct correspondence exists between our system and systems that undergo an equilibrium, second-order, phase transition. We illustrate this correspondence by comparing our results to the van der Waals equation of state for the liquid-gas mixture. We use the similarities to identify a critical point where an out of equilibrium second-order-like phase transition occurs in our system. Approaching the critical point, we find a power-law behavior with critical exponents that characterizes the transition.

Multireference second order perturbation theory with a simplified treatment of dynamical correlation.

PubMed

Xu, Enhua; Zhao, Dongbo; Li, Shuhua

2015-10-13

A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.

Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings

NASA Astrophysics Data System (ADS)

Ganor, Ori J.

2018-02-01

"Curvepole (2,0)-theory" is a deformation of the (2,0)-theory with nonlocal interactions. A curvepole is defined as a two-dimensional generalization of a dipole. It is an object of fixed two-dimensional shape of which the boundary is a charged curve that interacts with a 2-form gauge field. Curvepole theory was previously only defined indirectly via M-theory. Here, we propose a supersymmetric Lagrangian, constructed explicitly up to quartic terms, for an "Abelian" curvepole theory, which is an interacting deformation of the free (2,0) tensor multiplet. This theory contains fields of which the quanta are curvepoles (i.e., fixed-shape strings). Supersymmetry is preserved (at least up to quartic terms) if the shape of the curvepoles is (two-dimensional) planar. This nonlocal six-dimensional quantum field theory may also serve as a UV completion for certain (local) five-dimensional gauge theories.

A time correlation function theory describing static field enhanced third order optical effects at interfaces.

PubMed

Neipert, Christine; Space, Brian

2006-12-14

Sum vibrational frequency spectroscopy, a second order optical process, is interface specific in the dipole approximation. At charged interfaces, there exists a static field, and as a direct consequence, the experimentally detected signal is a combination of enhanced second and static field induced third order contributions. There is significant evidence in the literature of the importance/relative magnitude of this third order contribution, but no previous molecularly detailed approach existed to separately calculate the second and third order contributions. Thus, for the first time, a molecularly detailed time correlation function theory is derived here that allows for the second and third order contributions to sum frequency vibrational spectra to be individually determined. Further, a practical, molecular dynamics based, implementation procedure for the derived correlation functions that describe the third order phenomenon is also presented. This approach includes a novel generalization of point atomic polarizability models to calculate the hyperpolarizability of a molecular system. The full system hyperpolarizability appears in the time correlation functions responsible for third order contributions in the presence of a static field.

Magnetic field induced evolution of intertwined orders in the Kitaev magnet β -Li2IrO3

NASA Astrophysics Data System (ADS)

Rousochatzakis, Ioannis; Perkins, Natalia B.

2018-05-01

Recent scattering experiments in the 3D Kitaev magnet β -Li2IrO3 have shown that a relatively weak magnetic field along the crystallographic b axis drives the system from its incommensurate counter-rotating order to a correlated magnet, with a significant uniform `zigzag' component superimposing the magnetization along the field. Here it is shown that the zigzag order is not emerging from its linear coupling to the field (via a staggered, off-diagonal element of the g tensor) but from its intertwining with the incommensurate order and the longitudinal magnetization. The emerging picture explains all qualitative experimental findings at zero and finite fields, including the rapid decline of the incommensurate order with field and the so-called intensity sum rule. The latter are shown to be independent signatures of the smallness of the Heisenberg exchange J , compared to the Kitaev coupling K and the off-diagonal anisotropy Γ . Remarkably, in the regime of interest, the field H* at which the incommensurate component vanishes, depends essentially only on J , which allows us to extract an estimate of J ≃4 K from reported measurements of H*. We also comment on recent experiments in pressurized β -Li2IrO3 and conclude that J decreases with pressure.

Investigation of second-order hyperpolarizability of some organic compounds

NASA Astrophysics Data System (ADS)

Tajalli, H.; Zirak, P.; Ahmadi, S.

2003-04-01

In this work, we have measured the second order hyperpolarizability of some organic materials with (EFISH) method and also calculated the second order hyperpolarizability of 13 organic compound with Mopac6 software and investigated the different factors that affect the amount of second order hyperpolarizability and ways to increase it.

First and second order derivatives for optimizing parallel RF excitation waveforms

NASA Astrophysics Data System (ADS)

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

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

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

Wu, Bofeng; Huang, Chao-Guang

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

Iwamoto, Mitsumasa; Zhong-can, Ou-Yang

2012-11-01

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

Nanosecond electric modification of order parameters

NASA Astrophysics Data System (ADS)

Borshch, Volodymyr

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

Superquantile/CVaR Risk Measures: Second-Order Theory

DTIC Science & Technology

2015-07-31

order superquantile risk minimization as well as superquantile regression , a proposed second-order version of quantile regression . Keywords...minimization as well as superquantile regression , a proposed second-order version of quantile regression . 15. SUBJECT TERMS 16. SECURITY...superquantilies, because it is deeply tied to generalized regression . The joint formula (3) is central to quantile regression , a well known alternative

On Lovelock analogs of the Riemann tensor

NASA Astrophysics Data System (ADS)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

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

On the Tensorial Nature of Fluxes in Continuous Media.

ERIC Educational Resources Information Center

Stokes, Vijay Kumar; Ramkrishna, Doraiswami

1982-01-01

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

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

PubMed Central

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

2017-01-01

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

Surfing gravitational waves: can bigravity survive growing tensor modes?

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

Amendola, Luca; Könnig, Frank; Martinelli, Matteo

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

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

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

Second-order processing of four-stroke apparent motion.

PubMed

Mather, G; Murdoch, L

1999-05-01

In four-stroke apparent motion displays, pattern elements oscillate between two adjacent positions and synchronously reverse in contrast, but appear to move unidirectionally. For example, if rightward shifts preserve contrast but leftward shifts reverse contrast, consistent rightward motion is seen. In conventional first-order displays, elements reverse in luminance contrast (e.g. light elements become dark, and vice-versa). The resulting perception can be explained by responses in elementary motion detectors turned to spatio-temporal orientation. Second-order motion displays contain texture-defined elements, and there is some evidence that they excite second-order motion detectors that extract spatio-temporal orientation following the application of a non-linear 'texture-grabbing' transform by the visual system. We generated a variety of second-order four-stroke displays, containing texture-contrast reversals instead of luminance contrast reversals, and used their effectiveness as a diagnostic test for the presence of various forms of non-linear transform in the second-order motion system. Displays containing only forward or only reversed phi motion sequences were also tested. Displays defined by variation in luminance, contrast, orientation, and size were effective. Displays defined by variation in motion, dynamism, and stereo were partially or wholly ineffective. Results obtained with contrast-reversing and four-stroke displays indicate that only relatively simple non-linear transforms (involving spatial filtering and rectification) are available during second-order energy-based motion analysis.

Second-order variational equations for N-body simulations

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2016-07-01

First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.

A second-order 3D electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a Yee mesh

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

Bauer, Carl A., E-mail: bauerca@colorado.ed; Werner, Gregory R.; Cary, John R.

A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell's equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardsonmore » extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.« less

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

PubMed

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

2008-07-23

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

Photo-induced second-order nonlinearity in stoichiometric silicon nitride waveguides

NASA Astrophysics Data System (ADS)

Porcel, Marco A. G.; Mak, Jesse; Taballione, Caterina; Schermerhorn, Victoria K.; Epping, Jörn P.; van der Slot, Peter J. M.; Boller, Klaus-J.

2017-12-01

We report the observation of second-harmonic generation in stoichiometric silicon nitride waveguides grown via low-pressure chemical vapour deposition. Quasi-rectangular waveguides with a large cross section were used, with a height of 1 {\\mu}m and various different widths, from 0.6 to 1.2 {\\mu}m, and with various lengths from 22 to 74 mm. Using a mode-locked laser delivering 6-ps pulses at 1064 nm wavelength with a repetition rate of 20 MHz, 15% of the incoming power was coupled through the waveguide, making maximum average powers of up to 15 mW available in the waveguide. Second-harmonic output was observed with a delay of minutes to several hours after the initial turn-on of pump radiation, showing a fast growth rate between 10$^{-4}$ to 10$^{-2}$ s$^{-1}$, with the shortest delay and highest growth rate at the highest input power. After this first, initial build-up, the second-harmonic became generated instantly with each new turn-on of the pump laser power. Phase matching was found to be present independent of the used waveguide width, although the latter changes the fundamental and second-harmonic phase velocities. We address the presence of a second-order nonlinearity and phase matching, involving an initial, power-dependent build-up, to the coherent photogalvanic effect. The effect, via the third-order nonlinearity and multiphoton absorption leads to a spatially patterned charge separation, which generates a spatially periodic, semi-permanent, DC-field-induced second-order susceptibility with a period that is appropriate for quasi-phase matching. The maximum measured second-harmonic conversion efficiency amounts to 0.4% in a waveguide with 0.9 x 1 {\\mu}m$^2$ cross section and 36 mm length, corresponding to 53 {\\mu}W at 532 nm with 13 mW of IR input coupled into the waveguide. The according $\\chi^{(2)}$ amounts to 3.7 pm/V, as retrieved from the measured conversion efficiency.

Motion of small bodies in classical field theory

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.

2010-04-01

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

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.

On the 4D generalized Proca action for an Abelian vector field

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

Allys, Erwan; Almeida, Juan P. Beltrán; Peter, Patrick

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of http://dx.doi.org/10.1088/1475-7516/2014/05/015 and http://dx.doi.org/10.1016/j.physletb.2016.04.017 and complements those of http://dx.doi.org/10.1088/1475-7516/2016/02/004.more » We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field A{sub μ}, the Faraday tensor F{sub μν} and its Hodge dual F-tilde{sub μν}.« less

Finite Moment Tensors of Southern California Earthquakes

NASA Astrophysics Data System (ADS)

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

2003-12-01

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

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

NASA Astrophysics Data System (ADS)

Chatterjee, Arindam; Mazumdar, Anupam

2018-03-01

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

Superquantile/CVaR Risk Measures: Second-Order Theory

DTIC Science & Technology

2014-07-17

order version of quantile regression . Keywords: superquantiles, conditional value-at-risk, second-order superquantiles, mixed superquan- tiles... quantile regression . 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as Report (SAR) 18. NUMBER OF PAGES 26 19a...second-order superquantiles is in the domain of generalized regression . We laid out in [16] a parallel methodology to that of quantile regression

Tensor Network Wavefunctions for Topological Phases

NASA Astrophysics Data System (ADS)

Ware, Brayden Alexander

The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for

Mean template for tensor-based morphometry using deformation tensors.

PubMed

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

2007-01-01

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

Efficiency enhancement of slow-wave electron-cyclotron maser by a second-order shaping of the magnetic field in the low-gain limit

NASA Astrophysics Data System (ADS)

Liu, Si-Jia; Zhang, Yu-Fei; Wang, Kang; Li, Yong-Ming; Jing, Jian

2017-03-01

Based on the anomalous Doppler effect, we put forward a proposal to enhance the conversion efficiency of the slow-wave electron cyclotron masers (ECM) under the resonance condition. Compared with previous studies, we add a second-order shaping term in the guild magnetic field. Theoretical analyses and numerical calculations show that it can enhance the conversion efficiency in the low-gain limit. The case of the initial velocity spread of electrons satisfying the Gaussian distribution is also analysed numerically.

Efficiency enhancement of slow-wave electron-cyclotron maser by a second-order shaping of the magnetic field in the low-gain limit

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

Liu, Si-Jia; Zhang, Yu-Fei; Wang, Kang

Based on the anomalous Doppler effect, we put forward a proposal to enhance the conversion efficiency of the slow-wave electron cyclotron masers (ECM) under the resonance condition. Compared with previous studies, we add a second-order shaping term in the guild magnetic field. Theoretical analyses and numerical calculations show that it can enhance the conversion efficiency in the low-gain limit. The case of the initial velocity spread of electrons satisfying the Gaussian distribution is also analysed numerically.

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

PubMed

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

2011-04-21

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

A Communication-Optimal Framework for Contracting Distributed Tensors

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

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

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

Second-Order Fermi Acceleration and Emission in Blazar Jets

NASA Astrophysics Data System (ADS)

Asano, Katsuaki; Takahara, Fumio; Toma, Kenji; Kusunose, Masaaki; Kakuwa, Jun

The second-order Fermi acceleration (Fermi-II) driven by turbulence may be responsible for the electron acceleration in blazar jets. We test this model with time-dependent simulations, adopt it for 1ES 1101-232, and Mrk 421. The Fermi-II model with radial evolution of the electron injection rate and/or diffusion coefficient can reproduce the spectra from the radio to the gamma-ray regime. For Mrk 421, an external radio photon field with a luminosity of 4.9 begin{math} {times} 10 (38) erg s (-1) is required to agree with the observed GeV flux. The temporal variability of the diffusion coefficient or injection rate causes flare emission. The observed synchronicity of X-ray and TeV flares implies a decrease of the magnetic field in the flaring source region.

First-Order or Second-Order Kinetics? A Monte Carlo Answer

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2005-01-01

Monte Carlo computational experiments reveal that the ability to discriminate between first- and second-order kinetics from least-squares analysis of time-dependent concentration data is better than implied in earlier discussions of the problem. The problem is rendered as simple as possible by assuming that the order must be either 1 or 2 and that…

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

PubMed

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

2004-09-22

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

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

NASA Astrophysics Data System (ADS)

Chen, Y.; Huang, L.

2017-12-01

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

Controlling flexible structures with second order actuator dynamics

NASA Technical Reports Server (NTRS)

Inman, Daniel J.; Umland, Jeffrey W.; Bellos, John

1989-01-01

The control of flexible structures for those systems with actuators that are modeled by second order dynamics is examined. Two modeling approaches are investigated. First a stability and performance analysis is performed using a low order finite dimensional model of the structure. Secondly, a continuum model of the flexible structure to be controlled, coupled with lumped parameter second order dynamic models of the actuators performing the control is used. This model is appropriate in the modeling of the control of a flexible panel by proof-mass actuators as well as other beam, plate and shell like structural numbers. The model is verified with experimental measurements.

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

PubMed Central

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

2010-01-01

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

'Second' Ehrenfest equation for second order phase transition under hydrostatic pressure

NASA Astrophysics Data System (ADS)

Moin, Ph. B.

2018-02-01

It is shown that the fundamental conditions for the second-order phase transitions ? and ?, from which the two Ehrenfest equations follow (the 'usual' and the 'second' ones), are realised only at zero hydrostatic pressure (?). At ? the volume jump ΔV at the transition is proportional to the pressure and to the jump of the compressibility ΔζV, whereas the entropy jump ΔS is proportional to the pressure and to the jump of the thermal expansion coefficient ΔαV. This means that at non-zero hydrostatic pressure the phase transition is of the first order and is described by the Clausius-Clapeyron equation. At small pressure this equation coincides with the 'second' Ehrenfest equation ?. At high P, the Clausius-Clapeyron equation describes qualitatively the caused by the crystal compression positive curvature of the ? dependence.

Second-Order Conditioning in "Drosophila"

ERIC Educational Resources Information Center

Tabone, Christopher J.; de Belle, J. Steven

2011-01-01

Associative conditioning in "Drosophila melanogaster" has been well documented for several decades. However, most studies report only simple associations of conditioned stimuli (CS, e.g., odor) with unconditioned stimuli (US, e.g., electric shock) to measure learning or establish memory. Here we describe a straightforward second-order conditioning…

First and second order derivatives for optimizing parallel RF excitation waveforms.

PubMed

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. Copyright © 2015 Elsevier Inc. All rights reserved.

Second-order sliding mode control with experimental application.

PubMed

Eker, Ilyas

2010-07-01

In this article, a second-order sliding mode control (2-SMC) is proposed for second-order uncertain plants using equivalent control approach to improve the performance of control systems. A Proportional + Integral + Derivative (PID) sliding surface is used for the sliding mode. The sliding mode control law is derived using direct Lyapunov stability approach and asymptotic stability is proved theoretically. The performance of the closed-loop system is analysed through an experimental application to an electromechanical plant to show the feasibility and effectiveness of the proposed second-order sliding mode control and factors involved in the design. The second-order plant parameters are experimentally determined using input-output measured data. The results of the experimental application are presented to make a quantitative comparison with the traditional (first-order) sliding mode control (SMC) and PID control. It is demonstrated that the proposed 2-SMC system improves the performance of the closed-loop system with better tracking specifications in the case of external disturbances, better behavior of the output and faster convergence of the sliding surface while maintaining the stability. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Conformal killing tensors and covariant Hamiltonian dynamics

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

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

2014-12-15

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

A novel method for calculating and measuring the second-order buoyancy experienced by a magnet immersed in magnetic fluid

NASA Astrophysics Data System (ADS)

Yu, Jun; Hao, Du; Li, Decai

2018-01-01

The phenomenon whereby an object whose density is greater than magnetic fluid can be suspended stably in magnetic fluid under the magnetic field is one of the peculiar properties of magnetic fluids. Examples of applications based on the peculiar properties of magnetic fluid are sensors and actuators, dampers, positioning systems and so on. Therefore, the calculation and measurement of magnetic levitation force of magnetic fluid is of vital importance. This paper concerns the peculiar second-order buoyancy experienced by a magnet immersed in magnetic fluid. The expression for calculating the second-order buoyancy was derived, and a novel method for calculating and measuring the second-order buoyancy was proposed based on the expression. The second-order buoyancy was calculated by ANSYS and measured experimentally using the novel method. To verify the novel method, the second-order buoyancy was measured experimentally with a nonmagnetic rod stuck on the top surface of the magnet. The results of calculations and experiments show that the novel method for calculating the second-order buoyancy is correct with high accuracy. In addition, the main causes of error were studied in this paper, including magnetic shielding of magnetic fluid and the movement of magnetic fluid in a nonuniform magnetic field.

Improving sensitivity to magnetic fields and electric dipole moments by using measurements of individual magnetic sublevels

NASA Astrophysics Data System (ADS)

Tang, Cheng; Zhang, Teng; Weiss, David S.

2018-03-01

We explore ways to use the ability to measure the populations of individual magnetic sublevels to improve the sensitivity of magnetic field measurements and measurements of atomic electric dipole moments (EDMs). When atoms are initialized in the m =0 magnetic sublevel, the shot-noise-limited uncertainty of these measurements is 1 /√{2 F (F +1 ) } smaller than that of a Larmor precession measurement. When the populations in the even (or odd) magnetic sublevels are combined, we show that these measurements are independent of the tensor Stark shift and the second order Zeeman shift. We discuss the complicating effect of a transverse magnetic field and show that when the ratio of the tensor Stark shift to the transverse magnetic field is sufficiently large, an EDM measurement with atoms initialized in the superposition of the stretched states can reach the optimal sensitivity.

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.

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

PubMed

Kurashige, Yuki; Yanai, Takeshi

2011-09-07

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

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

PubMed

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

2016-05-01

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

On holographic entanglement entropy with second order excitations

NASA Astrophysics Data System (ADS)

He, Song; Sun, Jia-Rui; Zhang, Hai-Qing

2018-03-01

We study the low-energy corrections to the holographic entanglement entropy (HEE) in the boundary CFT by perturbing the bulk geometry up to second order excitations. Focusing on the case that the boundary subsystem is a strip, we show that the area of the bulk minimal surface can be expanded in terms of the conserved charges, such as mass, angular momentum and electric charge of the AdS black brane. We also calculate the variation of the energy in the subsystem and verify the validity of the first law-like relation of thermodynamics at second order. Moreover, the HEE is naturally bounded at second order perturbations if the cosmic censorship conjecture for the dual black hole still holds.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

A strategy for optical properties investigation in ABe2BO3F2 (A=K, Rb, Cs) using finite field methods

NASA Astrophysics Data System (ADS)

Mushahali, Hahaer; Mu, Baoxia; Wang, Qian; Mamat, Mamatrishat; Cao, Haibin; Yang, Guang; Jing, Qun

2018-07-01

The finite-field methods can be used to intuitively learn about the optical response and find out the atomic contributions to the birefringence and SHG tensors. In this paper, the linear and second-order nonlinear optical properties of ABe2BO3F2 family (A = K, Rb, Cs) compounds are investigated using the finite-field methods within different exchange-correlation functionals. The results show that the obtained birefringence and SHG tensors are in good agreement with the experimental values. The atomic contribution to the total birefringence was further investigated using the variation of the atomic charges, and the Born effective charges. The results show that the boron-oxygen groups give main contribution to the anisotropic birefringence.

Abelian tensor hierarchy in 4D N = 1 conformal supergravity

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Second-order hydrodynamics and universality in non-conformal holographic fluids

NASA Astrophysics Data System (ADS)

Kleinert, Philipp; Probst, Jonas

2016-12-01

We study second-order hydrodynamic transport in strongly coupled non-conformal field theories with holographic gravity duals in asymptotically anti-de Sitter space. We first derive new Kubo formulae for five second-order transport coefficients in non-conformal fluids in (3 + 1) dimensions. We then apply them to holographic RG flows induced by scalar operators of dimension Δ = 3. For general background solutions of the dual bulk geometry, we find explicit expressions for the five transport coefficients at infinite coupling and show that a specific combination, tilde{H}=2η {τ}_{π }-2(κ -{κ}^{ast})-{λ}_2 , always vanishes. We prove analytically that the Haack-Yarom identity H = 2 ητ π - 4λ1 - λ2 = 0, which is known to be true for conformal holographic fluids at infinite coupling, also holds when taking into account leading non-conformal corrections. The numerical results we obtain for two specific families of RG flows suggest that H vanishes regardless of conformal symmetry. Our work provides further evidence that the Haack-Yarom identity H = 0 may be universally satisfied by strongly coupled fluids.

Second-harmonic generation from a thin spherical layer and No-generation conditions

NASA Astrophysics Data System (ADS)

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

2017-09-01

In the Rayleigh-Gans-Debye approximation, we solve the problem of second-harmonic generation by an elliptically polarized electromagnetic wave incident on the surface of a spherical particle that is coated by an optically nonlinear layer and is placed in a dielectric. The formulas obtained characterize the spatial distribution of the electric field of the second harmonic in the far-field zone. The most general form of the second-order dielectric susceptibility tensor is considered, which contains four independent components, with three of them being nonchiral and one, chiral. Consistency and inconsistencies between the obtained solution and formulas from works of other authors are found. We analyze the directivity patterns that characterize the spatial distribution of the generated radiation for the nonchiral layer and their dependences on the anisotropy and ellipticity coefficients of the incident wave. It is found that, with increasing radius of the nonlinear layer, the generated radiation becomes more directional. Combinations of parameters for which no radiation is generated are revealed. Based on this, we propose methods for experimental determination of the anisotropy coefficients.

Human action recognition based on point context tensor shape descriptor

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Embedded Systems and TensorFlow Frameworks as Assistive Technology Solutions.

PubMed

Mulfari, Davide; Palla, Alessandro; Fanucci, Luca

2017-01-01

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

Strong second harmonic generation in two-dimensional ferroelectric IV-monochalcogenides

NASA Astrophysics Data System (ADS)

Panday, Suman Raj; Fregoso, Benjamin M.

2017-11-01

The two-dimensional ferroelectrics GeS, GeSe, SnS and SnSe are expected to have large spontaneous in-plane electric polarization and enhanced shift-current response. Using density functional methods, we show that these materials also exhibit the largest effective second harmonic generation reported so far. It can reach magnitudes up to 10~nm~V-1 which is about an order of magnitude larger than that of prototypical GaAs. To rationalize this result we model the optical response with a simple one-dimensional two-band model along the spontaneous polarization direction. Within this model the second-harmonic generation tensor is proportional to the shift-current response tensor. The large shift current and second harmonic responses of GeS, GeSe, SnS and SnSe make them promising non-linear materials for optoelectronic applications.

The known unknowns: neural representation of second-order uncertainty, and ambiguity

PubMed Central

Bach, Dominik R.; Hulme, Oliver; Penny, William D.; Dolan, Raymond J.

2011-01-01

Predictions provided by action-outcome probabilities entail a degree of (first-order) uncertainty. However, these probabilities themselves can be imprecise and embody second-order uncertainty. Tracking second-order uncertainty is important for optimal decision making and reinforcement learning. Previous functional magnetic resonance imaging investigations of second-order uncertainty in humans have drawn on an economic concept of ambiguity, where action-outcome associations in a gamble are either known (unambiguous) or completely unknown (ambiguous). Here, we relaxed the constraints associated with a purely categorical concept of ambiguity and varied the second-order uncertainty of gambles continuously, quantified as entropy over second-order probabilities. We show that second-order uncertainty influences decisions in a pessimistic way by biasing second-order probabilities, and that second-order uncertainty is negatively correlated with posterior cingulate cortex activity. The category of ambiguous (compared to non-ambiguous) gambles also biased choice in a similar direction, but was associated with distinct activation of a posterior parietal cortical area; an activation that we show reflects a different computational mechanism. Our findings indicate that behavioural and neural responses to second-order uncertainty are distinct from those associated with ambiguity and may call for a reappraisal of previous data. PMID:21451019

Tensor modes on the string theory landscape

NASA Astrophysics Data System (ADS)

Westphal, Alexander

2013-04-01

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

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

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Tsujikawa, Shinji

2018-05-01

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

Tensor distribution function

NASA Astrophysics Data System (ADS)

Leow, Alex D.; Zhu, Siwei

2008-03-01

Diffusion weighted MR imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitizing gradients along a minimum of 6 directions, second-order tensors (represetnted by 3-by-3 positive definiite matrices) can be computed to model dominant diffusion processes. However, it has been shown that conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g. crossing fiber tracts. More recently, High Angular Resolution Diffusion Imaging (HARDI) seeks to address this issue by employing more than 6 gradient directions. To account for fiber crossing when analyzing HARDI data, several methodologies have been introduced. For example, q-ball imaging was proposed to approximate Orientation Diffusion Function (ODF). Similarly, the PAS method seeks to reslove the angular structure of displacement probability functions using the maximum entropy principle. Alternatively, deconvolution methods extract multiple fiber tracts by computing fiber orientations using a pre-specified single fiber response function. In this study, we introduce Tensor Distribution Function (TDF), a probability function defined on the space of symmetric and positive definite matrices. Using calculus of variations, we solve for the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, ODF can easily be computed by analytical integration of the resulting displacement probability function. Moreover, principle fiber directions can also be directly derived from the TDF.

Symmetry breaking in tensor models

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2015-11-01

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

The simplicial Ricci tensor

NASA Astrophysics Data System (ADS)

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

2011-08-01

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

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

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Sämann, Christian; Wolf, Martin

2016-08-01

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

Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements: Calculation and application

NASA Astrophysics Data System (ADS)

Luo, Yao; Wu, Mei-Ping; Wang, Ping; Duan, Shu-Ling; Liu, Hao-Jun; Wang, Jin-Long; An, Zhan-Feng

2015-09-01

The full magnetic gradient tensor (MGT) refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

Second-order small disturbance theory for hypersonic flow over power-law bodies. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1974-01-01

A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.

Robust stability of second-order systems

NASA Technical Reports Server (NTRS)

Chuang, C.-H.

1995-01-01

It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper.

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

NASA Astrophysics Data System (ADS)

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

2004-03-01

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

Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

NASA Astrophysics Data System (ADS)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-06-01

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis-Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et al. (2013) [21] for these Berry phases, which is resolved to yield agreement with our results.

Ryu-Takayanagi formula for symmetric random tensor networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.

A General Sparse Tensor Framework for Electronic Structure Theory

DOE PAGES

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

2017-01-24

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

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

NASA Astrophysics Data System (ADS)

Miao, Xijiang; Mukhopadhyay, Rishi; Valafar, Homayoun

2008-10-01

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

Generalization of Einstein's gravitational field equations

NASA Astrophysics Data System (ADS)

Moulin, Frédéric

2017-12-01

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

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

NASA Astrophysics Data System (ADS)

Abdoli-Arani, A.; Ramezani-Arani, R.

2012-11-01

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.

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.

Extended vector-tensor theories

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

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

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

Tensor-based dynamic reconstruction method for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Second order perturbations of a macroscopic string: Covariant approach

NASA Astrophysics Data System (ADS)

Larsen, A. L.; Nicolaidis, A.

2001-06-01

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessary for a consistent computation of the energy. We also quantize the perturbations and derive the mass formula up to second order in perturbations for an observer using world-sheet time τ. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be nondiagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind.

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

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

NASA Technical Reports Server (NTRS)

Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

1992-01-01

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

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

NASA Astrophysics Data System (ADS)

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

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

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

PubMed

Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

Flavour fields in steady state: stress tensor and free energy

NASA Astrophysics Data System (ADS)

Banerjee, Avik; Kundu, Arnab; Kundu, Sandipan

2016-02-01

The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the stress tensor of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane is embedded in AdS d+1-background, for d = 2, 4, and is related to conformal anomaly. For the special case of d = 2, the universal factor has a striking resemblance to the well-known heat current formula in (1 + 1)-dimensional conformal field theory in steady-state, which endows a plausible physical interpretation to it. Interestingly, we observe a vanishing conformal anomaly in d = 6.

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

PubMed Central

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

2009-01-01

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

Birth Order and Field Dependence-Independence: A Failure to Replicate

ERIC Educational Resources Information Center

Finley, Gordon E.; Solla, Joseph

1975-01-01

The Children's Embedded Figures Test was individually administered to 116 Caucasian, middle class, second grade children. Results suggest that a child's early experience in a particular birth order position may not be related to the development of field dependence-independence in any unambiguous and simple fashion. (Author/ED)

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

ERIC Educational Resources Information Center

Barmpoutis, Angelos

2009-01-01

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

Euclidean supersymmetric solutions with the self-dual Weyl tensor

NASA Astrophysics Data System (ADS)

Nozawa, Masato

2017-07-01

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

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients

PubMed Central

Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M.

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach. PMID:23564972

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

PubMed

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

2018-05-17

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

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

Stress Fields Along Okinawa Trough and Ryukyu Arc Inferred From Regional Broadband Moment Tensors

NASA Astrophysics Data System (ADS)

Kubo, A.; Fukuyama, E.

2001-12-01

Most shallow earthquakes along Okinawa trough and Ryukyu arc are relatively small (M<5.5). Focal mechanism estimations for such events were difficult due to insufficient dataset. However, this situation is improved by regional broadband network (FREESIA). Lower limit of magnitude of the earthquakes determined becomes 1.5 smaller in M{}w than that of Harvard moment tensors. As a result, we could examine the stress field in more detail than Fournier et al.(2001, JGR, 106, 13751-) did based on surface geology and teleseismic moment tensors. In the NE Okinawa trough, extension axes are oblique to the trough strike, while in SW Okinawa trough, they are perpendicular to the trough. Fault type in SW is normal fault and gradually changes to mixture of normal and strike slip toward NE. In the Ryukyu arc, extension axes are parallel to the arc. Although this feature is not clear in the NW Ryukyu arc, arc parallel extension may be a major property of entire arc. Dominant fault type is normal fault and several strike slips with the same extensional component are included. The volcanic train is located at the edge of arc parallel extension field faced A simple explanation of the arc parallel extension is the response to the opening motion of the Okinawa trough. Another possible mechanism is forearc movement due to oblique subduction which is enhanced in SW. We consider that the Okinawa trough and the Ryukyu arc are independent stress provinces.

Second-order schedules: discrimination of components1

PubMed Central

Squires, Nancy; Norborg, James; Fantino, Edmund

1975-01-01

Pigeons were exposed to a series of second-order schedules in which the completion of a fixed number of fixed-interval components produced food. In Experiment 1, brief (2 sec) stimulus presentations occurred as each fixed-interval component was completed. During the brief-stimulus presentation terminating the last fixed-interval component, a response was required on a second key, the brief-stimulus key, to produce food. Responses on the brief-stimulus key before the last brief-stimulus presentation had no scheduled consequences, but served as a measure of the extent to which the final component was discriminated from preceding components. Whether there were one, two, four, or eight fixed-interval components, responses on the brief-stimulus key occurred during virtually every brief-stimulus presentation. In Experiment 2, an attempt was made to punish unnecessary responses on the brief-stimulus key, i.e., responses on the brief-stimulus key that occurred before the last component. None of the pigeons learned to withhold these responses, even though they produced a 15-sec timeout and loss of primary reinforcement. In Experiment 3, different key colors were associated with each component of a second-order schedule (a chain schedule). In contrast to Experiment 1, brief-stimulus key responses were confined to the last component. It was concluded that pigeons do not discriminate well between components of second-order schedules unless a unique exteroceptive cue is provided for each component. The relative discriminability of the components may account for the observed differences in initial-component response rates between comparable brief-stimulus, tandem, and chain schedules. PMID:16811868

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

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2018-06-01

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

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

PubMed Central

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

2015-01-01

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

The 3 + 1 decomposition of conformal Yano-Killing tensors and ‘momentary’ charges for the spin-2 field

NASA Astrophysics Data System (ADS)

Jezierski, Jacek; Migacz, Szymon

2015-02-01

The ‘fully charged’ spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the ‘non-waving’ part of the spin-2 field theory. Basic facts and definitions of the spin-2 field and conformal Yano-Killing tensors are introduced. Application of those two objects provides a precise definition of quasi-local gravitational charge. Next, the 3 + 1 decomposition leads to the construction of the momentary gravitational charges on the initial surface, which is applicable for Schwarzschild-like spacetimes.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

Magnetic second-order topological insulators and semimetals

NASA Astrophysics Data System (ADS)

Ezawa, Motohiko

2018-04-01

We propose magnetic second-order topological insulators (SOTIs). First, we study a three-dimensional model. It is pointed out that the previously proposed topological hinge insulator has actually surface states along the [001] direction in addition to hinge states. We gap out these surface states by introducing magnetization, obtaining a SOTI only with hinge states. The bulk topological number is the Z2 index protected by the combined symmetry of the fourfold rotation and the inversion symmetry. We next study two-dimensional magnetic SOTIs, where the corner states are robust also in the presence of the magnetization. Finally, we construct a magnetic second-order topological semimetal by layering the two-dimensional magnetic SOTIs, where hinge-arc states are robust also in the presence of the magnetization.

Quantitative analysis of hypertrophic myocardium using diffusion tensor magnetic resonance imaging

PubMed Central

Tran, Nicholas; Giannakidis, Archontis; Gullberg, Grant T.; Seo, Youngho

2016-01-01

Abstract. Systemic hypertension is a causative factor in left ventricular hypertrophy (LVH). This study is motivated by the potential to reverse or manage the dysfunction associated with structural remodeling of the myocardium in this pathology. Using diffusion tensor magnetic resonance imaging, we present an analysis of myocardial fiber and laminar sheet orientation in ex vivo hypertrophic (6 SHR) and normal (5 WKY) rat hearts using the covariance of the diffusion tensor. First, an atlas of normal cardiac microstructure was formed using the WKY b0 images. Then, the SHR and WKY b0 hearts were registered to the atlas. The acquired deformation fields were applied to the SHR and WKY heart tensor fields followed by the preservation of principal direction (PPD) reorientation strategy. A mean tensor field was then formed from the registered WKY tensor images. Calculating the covariance of the registered tensor images about this mean for each heart, the hypertrophic myocardium exhibited significantly increased myocardial fiber derangement (p=0.017) with a mean dispersion of 38.7 deg, and an increased dispersion of the laminar sheet normal (p=0.030) of 54.8 deg compared with 34.8 deg and 51.8 deg, respectively, in the normal hearts. Results demonstrate significantly altered myocardial fiber and laminar sheet structure in rats with hypertensive LVH. PMID:27872872

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

NASA Astrophysics Data System (ADS)

Matyjasek, Jerzy; Sadurski, Paweł; Telecka, Małgorzata

2014-04-01

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

Influence of second-order bracket-archwire misalignments on loads generated during third-order archwire rotation in orthodontic treatment.

PubMed

Romanyk, Dan L; George, Andrew; Li, Yin; Heo, Giseon; Carey, Jason P; Major, Paul W

2016-05-01

To investigate the influence of a rotational second-order bracket-archwire misalignment on the loads generated during third-order torque procedures. Specifically, torque in the second- and third-order directions was considered. An orthodontic torque simulator (OTS) was used to simulate the third-order torque between Damon Q brackets and 0.019 × 0.025-inch stainless steel archwires. Second-order misalignments were introduced in 0.5° increments from a neutral position, 0.0°, up to 3.0° of misalignment. A sample size of 30 brackets was used for each misalignment. The archwire was then rotated in the OTS from its neutral position up to 30° in 3° increments and then unloaded in the same increments. At each position, all forces and torques were recorded. Repeated-measures analysis of variance was used to determine if the second-order misalignments significantly affected torque values in the second- and third-order directions. From statistical analysis of the experimental data, it was found that the only statistically significant differences in third-order torque between a misaligned state and the neutral position occurred for 2.5° and 3.0° of misalignment, with mean differences of 2.54 Nmm and 2.33 Nmm, respectively. In addition, in pairwise comparisons of second-order torque for each misalignment increment, statistical differences were observed in all comparisons except for 0.0° vs 0.5° and 1.5° vs 2.0°. The introduction of a second-order misalignment during third-order torque simulation resulted in statistically significant differences in both second- and third-order torque response; however, the former is arguably clinically insignificant.

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).

Digital second-order phase-locked loop

NASA Technical Reports Server (NTRS)

Holmes, J. K.; Carl, C. C.; Tagnelia, C. R.

1975-01-01

Actual tests with second-order digital phase-locked loop at simulated relative Doppler shift of 1x0.0001 produced phase lock with timing error of 6.5 deg and no appreciable Doppler bias. Loop thus appears to achieve subcarrier synchronization and to remove bias due to Doppler shift in range of interest.

Urban Principals' Second Order Change Leadership

ERIC Educational Resources Information Center

Taylor, Rosemarye T.; La Cava, Gonzalo S.

2011-01-01

Urban school leaders have challenges in continually improving student achievement and making change as quickly as needed. To address this problem 37 non-Title I principals completed an on-line survey, Principal's Actions Survey (PAS), based on the seven responsibilities for second order change identified by Marzano, Waters, and McNulty (2005).…

Calculation and Analysis of magnetic gradient tensor components of global magnetic models

NASA Astrophysics Data System (ADS)

Schiffler, Markus; Queitsch, Matthias; Schneider, Michael; Stolz, Ronny; Krech, Wolfram; Meyer, Hans-Georg; Kukowski, Nina

2014-05-01

Magnetic mapping missions like SWARM and its predecessors, e.g. the CHAMP and MAGSAT programs, offer high resolution Earth's magnetic field data. These datasets are usually combined with magnetic observatory and survey data, and subject to harmonic analysis. The derived spherical harmonic coefficients enable magnetic field modelling using a potential series expansion. Recently, new instruments like the JeSSY STAR Full Tensor Magnetic Gradiometry system equipped with very high sensitive sensors can directly measure the magnetic field gradient tensor components. The full understanding of the quality of the measured data requires the extension of magnetic field models to gradient tensor components. In this study, we focus on the extension of the derivation of the magnetic field out of the potential series magnetic field gradient tensor components and apply the new theoretical framework to the International Geomagnetic Reference Field (IGRF) and the High Definition Magnetic Model (HDGM). The gradient tensor component maps for entire Earth's surface produced for the IGRF show low values and smooth variations reflecting the core and mantle contributions whereas those for the HDGM gives a novel tool to unravel crustal structure and deep-situated ore bodies. For example, the Thor Suture and the Sorgenfrei-Thornquist Zone in Europe are delineated by a strong northward gradient. Derived from Eigenvalue decomposition of the magnetic gradient tensor, the scaled magnetic moment, normalized source strength (NSS) and the bearing of the lithospheric sources are presented. The NSS serves as a tool for estimating the lithosphere-asthenosphere boundary as well as the depth of plutons and ore bodies. Furthermore changes in magnetization direction parallel to the mid-ocean ridges can be obtained from the scaled magnetic moment and the normalized source strength discriminates the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European

Tensor modes in pure natural inflation

NASA Astrophysics Data System (ADS)

Nomura, Yasunori; Yamazaki, Masahito

2018-05-01

We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.

Volume illustration of muscle from diffusion tensor images.

PubMed

Chen, Wei; Yan, Zhicheng; Zhang, Song; Crow, John Allen; Ebert, David S; McLaughlin, Ronald M; Mullins, Katie B; Cooper, Robert; Ding, Zi'ang; Liao, Jun

2009-01-01

Medical illustration has demonstrated its effectiveness to depict salient anatomical features while hiding the irrelevant details. Current solutions are ineffective for visualizing fibrous structures such as muscle, because typical datasets (CT or MRI) do not contain directional details. In this paper, we introduce a new muscle illustration approach that leverages diffusion tensor imaging (DTI) data and example-based texture synthesis techniques. Beginning with a volumetric diffusion tensor image, we reformulate it into a scalar field and an auxiliary guidance vector field to represent the structure and orientation of a muscle bundle. A muscle mask derived from the input diffusion tensor image is used to classify the muscle structure. The guidance vector field is further refined to remove noise and clarify structure. To simulate the internal appearance of the muscle, we propose a new two-dimensional example based solid texture synthesis algorithm that builds a solid texture constrained by the guidance vector field. Illustrating the constructed scalar field and solid texture efficiently highlights the global appearance of the muscle as well as the local shape and structure of the muscle fibers in an illustrative fashion. We have applied the proposed approach to five example datasets (four pig hearts and a pig leg), demonstrating plausible illustration and expressiveness.

Symmetry rules for the indirect nuclear spin-spin coupling tensor revisited

NASA Astrophysics Data System (ADS)

Buckingham, A. D.; Pyykkö, P.; Robert, J. B.; Wiesenfeld, L.

The symmetry rules of Buckingham and Love (1970), relating the number of independent components of the indirect spin-spin coupling tensor J to the symmetry of the nuclear sites, are shown to require modification if the two nuclei are exchanged by a symmetry operation. In that case, the anti-symmetric part of J does not transform as a second-rank polar tensor under symmetry operations that interchange the coupled nuclei and may be called an anti-tensor. New rules are derived and illustrated by simple molecular models.

Second-Order Conditioning during a Compound Extinction Treatment

ERIC Educational Resources Information Center

Pineno, Oskar; Zilski, Jessica M.; Schachtman, Todd R.

2007-01-01

Two conditioned taste aversion experiments with rats were conducted to establish if a target taste that had received a prior pairing with illness could be subject to second-order conditioning during extinction treatment in compound with a flavor that also received prior conditioning. In these experiments, the occurrence of second-order…

Radiation Forces and Torques without Stress (Tensors)

ERIC Educational Resources Information Center

Bohren, Craig F.

2011-01-01

To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…

Conservative second-order gravitational self-force on circular orbits and the effective one-body formalism

NASA Astrophysics Data System (ADS)

Bini, Donato; Damour, Thibault

2016-05-01

We consider Detweiler's redshift variable z for a nonspinning mass m1 in circular motion (with orbital frequency Ω ) around a nonspinning mass m2. We show how the combination of effective-one-body (EOB) theory with the first law of binary dynamics allows one to derive a simple, exact expression for the functional dependence of z on the (gauge-invariant) EOB gravitational potential u =(m1+m2)/R . We then use the recently obtained high-post-Newtonian(PN)-order knowledge of the main EOB radial potential A (u ;ν ) [where ν =m1m2/(m1+m2)2] to decompose the second-self-force-order contribution to the function z (m2Ω ,m1/m2) into a known part (which goes beyond the 4PN level in including the 5PN logarithmic term and the 5.5PN contribution) and an unknown one [depending on the yet unknown, 5PN, 6 PN ,… , contributions to the O (ν2) contribution to the EOB radial potential A (u ;ν )]. We apply our results to the second-self-force-order contribution to the frequency shift of the last stable orbit. We indicate the expected singular behaviors, near the lightring, of the second-self-force-order contributions to both the redshift and the EOB A potential. Our results should help both in extracting information of direct dynamical significance from ongoing second-self-force-order computations and in parametrizing their global strong-field behaviors. We also advocate computing second-self-force-order conservative quantities by iterating the time-symmetric Green-function in the background spacetime.

Divertor with a third-order null of the poloidal field

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

Ryutov, D. D.; Umansky, M. V.

2013-09-15

A concept and preliminary feasibility analysis of a divertor with the third-order poloidal field null is presented. The third-order null is the point where not only the field itself but also its first and second spatial derivatives are zero. In this case, the separatrix near the null-point has eight branches, and the number of strike-points increases from 2 (as in the standard divertor) to six. It is shown that this magnetic configuration can be created by a proper adjustment of the currents in a set of three divertor coils. If the currents are somewhat different from the required values, themore » configuration becomes that of three closely spaced first-order nulls. Analytic approach, suitable for a quick orientation in the problem, is used. Potential advantages and disadvantages of this configuration are briefly discussed.« less

Compactly supported linearised observables in single-field inflation

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

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

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

Real-time fringe pattern demodulation with a second-order digital phase-locked loop.

PubMed

Gdeisat, M A; Burton, D R; Lalor, M J

2000-10-10

The use of a second-order digital phase-locked loop (DPLL) to demodulate fringe patterns is presented. The second-order DPLL has better tracking ability and more noise immunity than the first-order loop. Consequently, the second-order DPLL is capable of demodulating a wider range of fringe patterns than the first-order DPLL. A basic analysis of the first- and the second-order loops is given, and a performance comparison between the first- and the second-order DPLL's in analyzing fringe patterns is presented. The implementation of the second-order loop in real time on a commercial parallel image processing system is described. Fringe patterns are grabbed and processed, and the resultant phase maps are displayed concurrently.

Differential effects of exogenous and endogenous attention on second-order texture contrast sensitivity

PubMed Central

Barbot, Antoine; Landy, Michael S.; Carrasco, Marisa

2012-01-01

The visual system can use a rich variety of contours to segment visual scenes into distinct perceptually coherent regions. However, successfully segmenting an image is a computationally expensive process. Previously we have shown that exogenous attention—the more automatic, stimulus-driven component of spatial attention—helps extract contours by enhancing contrast sensitivity for second-order, texture-defined patterns at the attended location, while reducing sensitivity at unattended locations, relative to a neutral condition. Interestingly, the effects of exogenous attention depended on the second-order spatial frequency of the stimulus. At parafoveal locations, attention enhanced second-order contrast sensitivity to relatively high, but not to low second-order spatial frequencies. In the present study we investigated whether endogenous attention—the more voluntary, conceptually-driven component of spatial attention—affects second-order contrast sensitivity, and if so, whether its effects are similar to those of exogenous attention. To that end, we compared the effects of exogenous and endogenous attention on the sensitivity to second-order, orientation-defined, texture patterns of either high or low second-order spatial frequencies. The results show that, like exogenous attention, endogenous attention enhances second-order contrast sensitivity at the attended location and reduces it at unattended locations. However, whereas the effects of exogenous attention are a function of the second-order spatial frequency content, endogenous attention affected second-order contrast sensitivity independent of the second-order spatial frequency content. This finding supports the notion that both exogenous and endogenous attention can affect second-order contrast sensitivity, but that endogenous attention is more flexible, benefitting performance under different conditions. PMID:22895879

Temporal Frequency Modulates Reaction Time Responses to First-Order and Second-Order Motion

ERIC Educational Resources Information Center

Hutchinson, Claire V.; Ledgeway, Tim

2010-01-01

This study investigated the effect of temporal frequency and modulation depth on reaction times for discriminating the direction of first-order (luminance-defined) and second-order (contrast-defined) motion, equated for visibility using equal multiples of direction-discrimination threshold. Results showed that reaction times were heavily…

Spacecraft attitude determination using a second-order nonlinear filter

NASA Technical Reports Server (NTRS)

Vathsal, S.

1987-01-01

The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.

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

DOE PAGES

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

2015-04-20

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

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-02-25

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

Field-controllable second harmonic generation at a graphene oxide heterointerface

NASA Astrophysics Data System (ADS)

Fernandes, Gustavo E.; Kim, Jin Ho; Osgood, Richard, III; Xu, Jimmy

2018-03-01

We report on the voltage-dependent SHG signal obtained in a reduced-graphene oxide (rGO)/p-type Si heterointerface. A simple qualitative model considering the interaction between the heterointerface depletion region potential and the naturally occurring surface dipole layer on the rGO is introduced to account for the characteristics of the SHG signal, specifically, a minimum point at ≈ -3 V bias on the rGO side of the interface. This feature-rich system has the potential to provide field-controllable surface-dipole moments and second-order nonlinearities, which may find applications in tunable nonlinear photonic devices for realizing second-harmonic generation and optical-rectification.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Second-order subsonic airfoil theory including edge effects

NASA Technical Reports Server (NTRS)

Van Dyke, Milton D

1956-01-01

Several recent advances in plane subsonic flow theory are combined into a unified second-order theory for airfoil sections of arbitrary shape. The solution is reached in three steps: the incompressible result is found by integration, it is converted into the corresponding subsonic compressible result by means of the second-order compressibility rule, and it is rendered uniformly valid near stagnation points by further rules. Solutions for a number of airfoils are given and are compared with the results of other theories and of experiment. A straight-forward computing scheme is outlined for calculating the surface velocities and pressures on any airfoil at any angle of attack

The Multi-Orientable Random Tensor Model, a Review

NASA Astrophysics Data System (ADS)

Tanasa, Adrian

2016-06-01

After its introduction (initially within a group field theory framework) in [Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages, arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last years into a solid alternative of the celebrated colored (and colored-like) random tensor model. In this paper we review the most important results of the study of this MO model: the implementation of the 1/N expansion and of the large N limit (N being the size of the tensor), the combinatorial analysis of the various terms of this expansion and finally, the recent implementation of a double scaling limit.

FASTSIM2: a second-order accurate frictional rolling contact algorithm

NASA Astrophysics Data System (ADS)

Vollebregt, E. A. H.; Wilders, P.

2011-01-01

In this paper we consider the frictional (tangential) steady rolling contact problem. We confine ourselves to the simplified theory, instead of using full elastostatic theory, in order to be able to compute results fast, as needed for on-line application in vehicle system dynamics simulation packages. The FASTSIM algorithm is the leading technology in this field and is employed in all dominant railway vehicle system dynamics packages (VSD) in the world. The main contribution of this paper is a new version "FASTSIM2" of the FASTSIM algorithm, which is second-order accurate. This is relevant for VSD, because with the new algorithm 16 times less grid points are required for sufficiently accurate computations of the contact forces. The approach is based on new insights in the characteristics of the rolling contact problem when using the simplified theory, and on taking precise care of the contact conditions in the numerical integration scheme employed.

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

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

Hirata, So

2003-11-20

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

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.

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

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

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

Brink, Jeandrew

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Second-order evaluations of orthogonal and symplectic Yangians

NASA Astrophysics Data System (ADS)

Karakhanyan, D. R.; Kirschner, R.

2017-08-01

Orthogonal or symplectic Yangians are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with the corresponding so( n) or sp(2 m) symmetry. We investigate the second-order solution conditions, where the expansion of L( u) in u -1 is truncated at the second power, and we derive the relations for the two nontrivial terms in L( u).

Variability and Variation in Second Language Acquisition Orders: A Dynamic Reevaluation

ERIC Educational Resources Information Center

Lowie, Wander; Verspoor, Marjolijn

2015-01-01

The traditional morpheme order studies in second language acquisition have tried to demonstrate the existence of a fixed order of acquisition of English morphemes, regardless of the second language learner's background. Such orders have been taken as evidence of the preprogrammed nature of language acquisition. This article argues for a…

Tensor network state correspondence and holography

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder

2018-01-01

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

Polarization-Modulated Second Harmonic Generation Microscopy in Collagen

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

Stoller, P C

Collagen is a key structural protein in the body; several pathological conditions lead to changes in collagen. Among imaging modalities that can be used in vivo, second harmonic generation (SHG) microscopy has a key advantage: it provides {approx}1 {micro}m resolution information about collagen structure as a function of depth. A new technique--polarization-modulated SHG--is presented: it permits simultaneous measurement of collagen orientation, of a lower bound on the magnitude of the second order nonlinear susceptibility tensor, and of the ratio of the two independent elements in this tensor. It is applied to characterizing SHG in collagen and to determining effects ofmore » biologically relevant changes in collagen structure. The magnitude of the second harmonic signal in two dimensional images varies with position even in structurally homogeneous tissue; this phenomenon is due to interference between second harmonic light generated by neighboring fibrils, which are randomly oriented parallel or anti-parallel to each other. Studies in which focal spot size was varied indicated that regions where fibrils are co-oriented are less than {approx}1.5 {micro}m in diameter. A quartz reference was used to determine the spot size as well as a lower limit (d{sub xxx} > 0.3 pm/V) for the magnitude of the second order nonlinear susceptibility. The ratio of the two independent tensor elements ranged between d{sub XYY}/d{sub XXX} = 0.60 and 0.75. SHG magnitude alone was not useful for identifying structural anomalies in collagenous tissue. Instead, changes in the polarization dependence of SHG were used to analyze biologically relevant perturbations in collagen structure. Changes in polarization dependence were observed in dehydrated samples, but not in highly crosslinked samples, despite significant alterations in packing structure. Complete thermal denaturation and collagenase digestion produced samples with no detectable SHG signal. Collagen orientation was measured in

Near- and far-field investigation of dark and bright higher order resonances in square loop elements at mid-infrared wavelengths.

PubMed

Tucker, Eric; D'Archangel, Jeffrey; Boreman, Glenn

2017-03-06

Three different size gold square loop structures were fabricated as arrays on ZnS over a ground plane and designed to have absorptive fundamental, second order, and third order resonances at a wavelength of 10.6 µm and 60° off-normal. The angular dependent far-field spectral absorptivity was investigated over the mid-infrared for each size loop array. It was found that the second order modes were dark at normal incidence, but became excited at off-normal incidence, which is consistent with previous work for similar geometry structures. Furthermore, near-field measurements and simulations at a wavelength of 10.6 µm and 60° off-normal showed that the second order mode (quadrupolar) of the medium size loop yielded a near-field response similar in magnitude to the fundamental mode (dipolar) of the small size loop, which can be important for sensing related applications where both strong near-field enhancement and more uniform or less localized field is beneficial.

Bioethics in Denmark. Moving from first- to second-order analysis?

PubMed

Nielsen, Morten Ebbe Juul; Andersen, Martin Marchman

2014-07-01

This article examines two current debates in Denmark--assisted suicide and the prioritization of health resources--and proposes that such controversial bioethical issues call for distinct philosophical analyses: first-order examinations, or an applied philosophy approach, and second-order examinations, what might be called a political philosophical approach. The authors argue that although first-order examination plays an important role in teasing out different moral points of view, in contemporary democratic societies, few, if any, bioethical questions can be resolved satisfactorily by means of first-order analyses alone, and that bioethics needs to engage more closely with second-order enquiries and the question of legitimacy in general.

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Second order upwind Lagrangian particle method for Euler equations

DOE PAGES

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

2016-06-01

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

Second order upwind Lagrangian particle method for Euler equations

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

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

Global diffusion of cosmic rays in random magnetic fields

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Efficient second harmonic generation by para-nitroaniline embedded in electro-spun polymeric nanofibres

NASA Astrophysics Data System (ADS)

Gonçalves, Hugo; Saavedra, Inês; Ferreira, Rute AS; Lopes, PE; de Matos Gomes, Etelvina; Belsley, Michael

2018-03-01

Intense well polarized second harmonic light was generated by poly(methyl methacrylate) nanofibres with embedded para-nitroaniline nanocrystals. Subwavelength diameter fibres were electro-spun using a 1:2 weight ratio of chromophore to polymer. Analysis of the generated second harmonic light indicates that the para-nitroaniline molecules, which nominally crystalize in the centrosymmetric space group, were organized into noncentrosymmetric structures leading to a second order susceptibility dominated by a single tensor element. Under the best deposition conditions, the nanofibrers display an effective nonlinear optical susceptibility approximately two orders of magnitude greater than that of potassium dihydrogen phosphate. Generalizing this approach to a broad range of organic molecules with strong individual molecular second order nonlinear responses, but which nominally form centrosymmetric organic crystals, could open a new pathway for the fabrication of efficient sub-micron sized second harmonic light generators.

Sakata-Taketani spin-0 theory with external field interactions - Lagrangian formalism and causal properties

NASA Technical Reports Server (NTRS)

Guertin, R. F.; Wilson, T. L.

1977-01-01

To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.

Plenoptic imaging with second-order correlations of light

NASA Astrophysics Data System (ADS)

Pepe, Francesco V.; Scarcelli, Giuliano; Garuccio, Augusto; D'Angelo, Milena

2016-01-01

Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable tridimensional imaging in a single shot. We demonstrate that it is possible to implement plenoptic imaging through second-order correlations of chaotic light, thus enabling to overcome the typical limitations of classical plenoptic devices.

Chameleons with field-dependent couplings

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

Brax, Philippe; Bruck, Carsten van de; Mota, David F.

2010-10-15

Certain scalar-tensor theories exhibit the so-called chameleon mechanism, whereby observational signatures of scalar fields are hidden by a combination of self-interactions and interactions with ambient matter. Not all scalar-tensor theories exhibit such a chameleon mechanism, which has been originally found in models with inverse power runaway potentials and field-independent couplings to matter. In this paper we investigate field theories with field-dependent couplings and a power-law potential for the scalar field. We show that the theory indeed is a chameleon field theory. We find the thin-shell solution for a spherical body and investigate the consequences for Eoet-Wash experiments, fifth-force searches andmore » Casimir-force experiments. Requiring that the scalar field evades gravitational tests, we find that the coupling is sensitive to a mass scale which is of order of the Hubble scale today.« less

Molecular Static Third-Order Polarizabilities of Carbon-Cage Fullerenes and their Correlation with Three Geometric Parameters: Group Order, Aromaticity, and Size

NASA Technical Reports Server (NTRS)

Moore, Craig E.; Cardelino, Beatriz H.; Frazier, Donald O.; Niles, Julian; Wang, Xian-Qiang

1997-01-01

Calculations were performed on the valence contribution to the static molecular third-order polarizabilities (gamma) of thirty carbon-cage fullerenes (C60, C70, five isomers of C78, and twenty-three isomers of C84). The molecular structures were obtained from B3LYP/STO-3G calculations. The values of the tensor elements and an associated numerical uncertainty were obtained using the finite-field approach and polynomial expansions of orders four to eighteen of polarization versus static electric field data. The latter information was obtained from semiempirical calculations using the AM1 hamiltonian.

Synchronization from Second Order Network Connectivity Statistics

PubMed Central

Zhao, Liqiong; Beverlin, Bryce; Netoff, Theoden; Nykamp, Duane Q.

2011-01-01

We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates. PMID:21779239

Optimal second order sliding mode control for nonlinear uncertain systems.

PubMed

Das, Madhulika; Mahanta, Chitralekha

2014-07-01

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Parallel Coding of First- and Second-Order Stimulus Attributes by Midbrain Electrosensory Neurons

PubMed Central

McGillivray, Patrick; Vonderschen, Katrin; Fortune, Eric S.; Chacron, Maurice J.

2015-01-01

Natural stimuli often have time-varying first-order (i.e., mean) and second-order (i.e., variance) attributes that each carry critical information for perception and can vary independently over orders of magnitude. Experiments have shown that sensory systems continuously adapt their responses based on changes in each of these attributes. This adaptation creates ambiguity in the neural code as multiple stimuli may elicit the same neural response. While parallel processing of first- and second-order attributes by separate neural pathways is sufficient to remove this ambiguity, the existence of such pathways and the neural circuits that mediate their emergence have not been uncovered to date. We recorded the responses of midbrain electrosensory neurons in the weakly electric fish Apteronotus leptorhynchus to stimuli with first- and second-order attributes that varied independently in time. We found three distinct groups of midbrain neurons: the first group responded to both first- and second-order attributes, the second group responded selectively to first-order attributes, and the last group responded selectively to second-order attributes. In contrast, all afferent hindbrain neurons responded to both first- and second-order attributes. Using computational analyses, we show how inputs from a heterogeneous population of ON- and OFF-type afferent neurons are combined to give rise to response selectivity to either first- or second-order stimulus attributes in midbrain neurons. Our study thus uncovers, for the first time, generic and widely applicable mechanisms by which parallel processing of first- and second-order stimulus attributes emerges in the brain. PMID:22514313

Effects of Second-Order Hydrodynamics on a Semisubmersible Floating Offshore Wind Turbine: Preprint

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

Bayati, I.; Jonkman, J.; Robertson, A.

2014-07-01

The objective of this paper is to assess the second-order hydrodynamic effects on a semisubmersible floating offshore wind turbine. Second-order hydrodynamics induce loads and motions at the sum- and difference-frequencies of the incident waves. These effects have often been ignored in offshore wind analysis, under the assumption that they are significantly smaller than first-order effects. The sum- and difference-frequency loads can, however, excite eigenfrequencies of the system, leading to large oscillations that strain the mooring system or vibrations that cause fatigue damage to the structure. Observations of supposed second-order responses in wave-tank tests performed by the DeepCwind consortium at themore » MARIN offshore basin suggest that these effects might be more important than originally expected. These observations inspired interest in investigating how second-order excitation affects floating offshore wind turbines and whether second-order hydrodynamics should be included in offshore wind simulation tools like FAST in the future. In this work, the effects of second-order hydrodynamics on a floating semisubmersible offshore wind turbine are investigated. Because FAST is currently unable to account for second-order effects, a method to assess these effects was applied in which linearized properties of the floating wind system derived from FAST (including the 6x6 mass and stiffness matrices) are used by WAMIT to solve the first- and second-order hydrodynamics problems in the frequency domain. The method has been applied to the OC4-DeepCwind semisubmersible platform, supporting the NREL 5-MW baseline wind turbine. The loads and response of the system due to the second-order hydrodynamics are analysed and compared to first-order hydrodynamic loads and induced motions in the frequency domain. Further, the second-order loads and induced response data are compared to the loads and motions induced by aerodynamic loading as solved by FAST.« less