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

NASA Astrophysics Data System (ADS)

Luminari, Nicola; Airiau, Christophe; Bottaro, Alessandro

2017-11-01

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

Self-adaptive tensor network states with multi-site correlators

NASA Astrophysics Data System (ADS)

Kovyrshin, Arseny; Reiher, Markus

2017-12-01

We introduce the concept of self-adaptive tensor network states (SATNSs) based on multi-site correlators. The SATNS ansatz gradually extends its variational space incorporating the most important next-order correlators into the ansatz for the wave function. The selection of these correlators is guided by entanglement-entropy measures from quantum information theory. By sequentially introducing variational parameters and adjusting them to the system under study, the SATNS ansatz achieves keeping their number significantly smaller than the total number of full-configuration interaction parameters. The SATNS ansatz is studied for manganocene in its lowest-energy sextet and doublet states; the latter of which is known to be difficult to describe. It is shown that the SATNS parametrization solves the convergence issues found for previous correlator-based tensor network states.

15N CSA tensors and 15N-1H dipolar couplings of protein hydrophobic core residues investigated by static solid-state NMR

NASA Astrophysics Data System (ADS)

Vugmeyster, Liliya; Ostrovsky, Dmitry; Fu, Riqiang

2015-10-01

In this work, we assess the usefulness of static 15N NMR techniques for the determination of the 15N chemical shift anisotropy (CSA) tensor parameters and 15N-1H dipolar splittings in powder protein samples. By using five single labeled samples of the villin headpiece subdomain protein in a hydrated lyophilized powder state, we determine the backbone 15N CSA tensors at two temperatures, 22 and -35 °C, in order to get a snapshot of the variability across the residues and as a function of temperature. All sites probed belonged to the hydrophobic core and most of them were part of α-helical regions. The values of the anisotropy (which include the effect of the dynamics) varied between 130 and 156 ppm at 22 °C, while the values of the asymmetry were in the 0.32-0.082 range. The Leu-75 and Leu-61 backbone sites exhibited high mobility based on the values of their temperature-dependent anisotropy parameters. Under the assumption that most differences stem from dynamics, we obtained the values of the motional order parameters for the 15N backbone sites. While a simple one-dimensional line shape experiment was used for the determination of the 15N CSA parameters, a more advanced approach based on the ;magic sandwich; SAMMY pulse sequence (Nevzorov and Opella, 2003) was employed for the determination of the 15N-1H dipolar patterns, which yielded estimates of the dipolar couplings. Accordingly, the motional order parameters for the dipolar interaction were obtained. It was found that the order parameters from the CSA and dipolar measurements are highly correlated, validating that the variability between the residues is governed by the differences in dynamics. The values of the parameters obtained in this work can serve as reference values for developing more advanced magic-angle spinning recoupling techniques for multiple labeled samples.

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

PubMed

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

2017-05-26

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

Constraining modified theories of gravity with the galaxy bispectrum

NASA Astrophysics Data System (ADS)

Yamauchi, Daisuke; Yokoyama, Shuichiro; Tashiro, Hiroyuki

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Basak, Anup; Levitas, Valery I.

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-01-01

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

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.

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

PubMed

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

2009-07-01

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

Tensor-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

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.

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige

2017-10-01

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

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.

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

PubMed

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

2015-04-21

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

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

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

Mukherjee, Suvodip; Das, Santanu; Souradeep, Tarun

2015-01-01

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

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

PubMed

Freistühler, Heinrich; Temple, Blake

2014-06-08

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

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

PubMed Central

Freistühler, Heinrich; Temple, Blake

2014-01-01

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

The Bargmann-Wigner equations in spherical space

NASA Astrophysics Data System (ADS)

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

2006-01-01

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

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.

Inversion of calcite twin data for paleostress (1) : improved Etchecopar technique tested on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Daniel, Jean-Marc; Schueller, Sylvie

2015-04-01

Inversion of calcite twin data are known to be a powerful tool to reconstruct the past-state of stress in carbonate rocks of the crust, especially in fold-and-thrust belts and sedimentary basins. This is of key importance to constrain results of geomechanical modelling. Without proposing a new inversion scheme, this contribution reports some recent improvements of the most efficient stress inversion technique to date (Etchecopar, 1984) that allows to reconstruct the 5 parameters of the deviatoric paleostress tensors (principal stress orientations and differential stress magnitudes) from monophase and polyphase twin data sets. The improvements consist in the search of the possible tensors that account for the twin data (twinned and untwinned planes) and the aid to the user to define the best stress tensor solution, among others. We perform a systematic exploration of an hypersphere in 4 dimensions by varying different parameters, Euler's angles and the stress ratio. We first record all tensors with a minimum penalization function accounting for 20% of the twinned planes. We then define clusters of tensors following a dissimilarity criterion based on the stress distance between the 4 parameters of the reduced stress tensors and a degree of disjunction of the related sets of twinned planes. The percentage of twinned data to be explained by each tensor is then progressively increased and tested using the standard Etchecopar procedure until the best solution that explains the maximum number of twinned planes and the whole set of untwinned planes is reached. This new inversion procedure is tested on monophase and polyphase numerically-generated as well as natural calcite twin data in order to more accurately define the ability of the technique to separate more or less similar deviatoric stress tensors applied in sequence on the samples, to test the impact of strain hardening through the change of the critical resolved shear stress for twinning as well as to evaluate the possible bias due to measurement uncertainties or clustering of grain optical axes in the samples.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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.

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

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

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

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.

Multiple sclerosis: changes in microarchitecture of white matter tracts after training with a video game balance board.

PubMed

Prosperini, Luca; Fanelli, Fulvia; Petsas, Nikolaos; Sbardella, Emilia; Tona, Francesca; Raz, Eytan; Fortuna, Deborah; De Angelis, Floriana; Pozzilli, Carlo; Pantano, Patrizia

2014-11-01

To determine if high-intensity, task-oriented, visual feedback training with a video game balance board (Nintendo Wii) induces significant changes in diffusion-tensor imaging ( DTI diffusion-tensor imaging ) parameters of cerebellar connections and other supratentorial associative bundles and if these changes are related to clinical improvement in patients with multiple sclerosis. The protocol was approved by local ethical committee; each participant provided written informed consent. In this 24-week, randomized, two-period crossover pilot study, 27 patients underwent static posturography and brain magnetic resonance (MR) imaging at study entry, after the first 12-week period, and at study termination. Thirteen patients started a 12-week training program followed by a 12-week period without any intervention, while 14 patients received the intervention in reverse order. Fifteen healthy subjects also underwent MR imaging once and underwent static posturography. Virtual dissection of white matter tracts was performed with streamline tractography; values of DTI diffusion-tensor imaging parameters were then obtained for each dissected tract. Repeated measures analyses of variance were performed to evaluate whether DTI diffusion-tensor imaging parameters significantly changed after intervention, with false discovery rate correction for multiple hypothesis testing. There were relevant differences between patients and healthy control subjects in postural sway and DTI diffusion-tensor imaging parameters (P < .05). Significant main effects of time by group interaction for fractional anisotropy and radial diffusivity of the left and right superior cerebellar peduncles were found (F2,23 range, 5.555-3.450; P = .036-.088 after false discovery rate correction). These changes correlated with objective measures of balance improvement detected at static posturography (r = -0.381 to 0.401, P < .05). However, both clinical and DTI diffusion-tensor imaging changes did not persist beyond 12 weeks after training. Despite the low statistical power (35%) due to the small sample size, the results showed that training with the balance board system modified the microstructure of superior cerebellar peduncles. The clinical improvement observed after training might be mediated by enhanced myelination-related processes, suggesting that high-intensity, task-oriented exercises could induce favorable microstructural changes in the brains of patients with multiple sclerosis.

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.

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

Stress as an order parameter for the glass transition

NASA Astrophysics Data System (ADS)

Visscher, P. B.; Logan, W. T.

1990-09-01

The stress tensor has been considered as a possible order parameter for the liquid-glass transition, and its autocorrelation matrix (elements of which are the integrands in the Green-Kubo formulas for bulk and shear viscosity) have been measured in simulations. However, only the k=0 spatial Fourier component has apparently been previously measured. We have measured four Fourier components of all matrix elements of the stress-stress correlation function, and we find that some of those with nonzero wave vector are significantly more persistent (slower decaying) than the k=0 component.

Killing-Yano tensors of order n - 1

NASA Astrophysics Data System (ADS)

Batista, Carlos

2014-08-01

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

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

NASA Astrophysics Data System (ADS)

Böbel, A.; Knapek, C. A.; Räth, C.

2018-05-01

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

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.

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

NASA Astrophysics Data System (ADS)

Mucci, Domenico; Nicolodi, Lorenzo

2017-12-01

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

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; this projection operation effectively corrects the mainshock data for path-related amplitude anomalies in a way similar to, but more flexible than, empirical Green function (EGF) techniques.

Visualizing second order tensor fields with hyperstreamlines

NASA Technical Reports Server (NTRS)

Delmarcelle, Thierry; Hesselink, Lambertus

1993-01-01

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

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*

PubMed Central

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

2012-01-01

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

Decomposition of a symmetric second-order tensor

NASA Astrophysics Data System (ADS)

Heras, José A.

2018-05-01

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

Viable inflationary evolution from Einstein frame loop quantum cosmology

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

An Exploration into Diffusion Tensor Imaging in the Bovine Ocular Lens

PubMed Central

Vaghefi, Ehsan; Donaldson, Paul J.

2013-01-01

We describe our development of the diffusion tensor imaging modality for the bovine ocular lens. Diffusion gradients were added to a spin-echo pulse sequence and the relevant parameters of the sequence were refined to achieve good diffusion weighting in the lens tissue, which demonstrated heterogeneous regions of diffusive signal attenuation. Decay curves for b-value (loosely summarizes the strength of diffusion weighting) and TE (determines the amount of magnetic resonance imaging-obtained signal) were used to estimate apparent diffusion coefficients (ADC) and T2 in different lens regions. The ADCs varied by over an order of magnitude and revealed diffusive anisotropy in the lens. Up to 30 diffusion gradient directions, and 8 signal acquisition averages, were applied to lenses in culture in order to improve maps of diffusion tensor eigenvalues, equivalent to ADC, across the lens. From these maps, fractional anisotropy maps were calculated and compared to known spatial distributions of anisotropic molecular fluxes in the lens. This comparison suggested new hypotheses and experiments to quantitatively assess models of circulation in the avascular lens. PMID:23459990

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.

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

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.

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

NASA Astrophysics Data System (ADS)

Ciattoni, Alessandro; Rizza, Carlo

2015-05-01

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

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

PubMed

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

2007-04-01

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

Probabilistic-driven oriented Speckle reducing anisotropic diffusion with application to cardiac ultrasonic images.

PubMed

Vegas-Sanchez-Ferrero, G; Aja-Fernandez, S; Martin-Fernandez, M; Frangi, A F; Palencia, C

2010-01-01

A novel anisotropic diffusion filter is proposed in this work with application to cardiac ultrasonic images. It includes probabilistic models which describe the probability density function (PDF) of tissues and adapts the diffusion tensor to the image iteratively. For this purpose, a preliminary study is performed in order to select the probability models that best fit the stastitical behavior of each tissue class in cardiac ultrasonic images. Then, the parameters of the diffusion tensor are defined taking into account the statistical properties of the image at each voxel. When the structure tensor of the probability of belonging to each tissue is included in the diffusion tensor definition, a better boundaries estimates can be obtained instead of calculating directly the boundaries from the image. This is the main contribution of this work. Additionally, the proposed method follows the statistical properties of the image in each iteration. This is considered as a second contribution since state-of-the-art methods suppose that noise or statistical properties of the image do not change during the filter process.

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

PubMed

Li, Sazi; Li, Wei; Chen, Ziyu

2015-06-01

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

Order-parameter tensor description of HPr in a medium of oriented bicelles.

PubMed

van Lune, Franciska; Manning, Linda; Dijkstra, Klaas; Berendsen, Herman J C; Scheek, Ruud M

2002-07-01

Residual dipolar couplings between 15N and 1H nuclear spins in HPr were used to determine the protein's orientation in a medium of bicelles, oriented by a magnetic field. In the case of wild-type HPr the protein's non-spherical shape can explain its orientation in this medium. In the case of the F48W mutant it was found that at least one other mechanism contributes to the observed orientation of the protein, to a degree that depends on the concentration of phosphate ions in the medium. We propose that the F48W mutant has a weak affinity towards the bicelle-surfaces that decreases with increasing phosphate concentrations. We used an order-parameter description to analyse this situation and to determine the axis of main order and the sign of the order parameter pertaining to this additional orientation mechanism.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

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

Generalized Higher Order Orthogonal Iteration for Tensor Learning and Decomposition.

PubMed

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

2016-12-01

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

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.

Vainshtein mechanism after GW170817

NASA Astrophysics Data System (ADS)

Crisostomi, Marco; Koyama, Kazuya

2018-01-01

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

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1983-01-01

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

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

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

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

Assessing the Uncertainties on Seismic Source Parameters: Towards Realistic Estimates of Moment Tensor Determinations

NASA Astrophysics Data System (ADS)

Magnoni, F.; Scognamiglio, L.; Tinti, E.; Casarotti, E.

2014-12-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Moment tensor catalogues are ordinarily used by geoscientists, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their own analysis. The 2012 May 20 Emilia mainshock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. An uncertainty of ~0.5 units in magnitude leads to a controversial knowledge of the real size of the event. The possible uncertainty associated to this estimate could be critical for the inference of other seismological parameters, suggesting caution for seismic hazard assessment, coulomb stress transfer determination and other analyses where self-consistency is important. In this work, we focus on the variability of the moment tensor solution, highlighting the effect of four different velocity models, different types and ranges of filtering, and two different methodologies. Using a larger dataset, to better quantify the source parameter uncertainty, we also analyze the variability of the moment tensor solutions depending on the number, the epicentral distance and the azimuth of used stations. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, cannot be considered an absolute value and requires to come out with the related uncertainties and in a reproducible framework characterized by disclosed assumptions and explicit processing workflows.

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

Asymmetric rotor-like probes to polarized fluorescence study of the macroscopically oriented uniaxial media: Model parameters recognition

NASA Astrophysics Data System (ADS)

Buczkowski, M.; Fisz, J. J.

2008-07-01

In this paper the possibility of the numerical data modelling in the case of angle- and time-resolved fluorescence spectroscopy is investigated. The asymmetric fluorescence probes are assumed to undergo the restricted rotational diffusion in a hosting medium. This process is described quantitatively by the diffusion tensor and the aligning potential. The evolution of the system is expressed in terms of the Smoluchowski equation with an appropriate time-developing operator. A matrix representation of this operator is calculated, then symmetrized and diagonalized. The resulting propagator is used to generate the synthetic noisy data set that imitates results of experimental measurements. The data set serves as a groundwork to the χ2 optimization, performed by the genetic algorithm followed by the gradient search, in order to recover model parameters, which are diagonal elements of the diffusion tensor, aligning potential expansion coefficients and directions of the electronic dipole moments. This whole procedure properly identifies model parameters, showing that the outlined formalism should be taken in the account in the case of analysing real experimental data.

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Baritzhack, Itzhack Y.; Markley, F. Landis

1988-01-01

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

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

NASA Astrophysics Data System (ADS)

Jaques, Luís; Pascal, Christophe

2017-09-01

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

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

PubMed

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

2009-12-21

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

Limits on tensor coupling from neutron β decay

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

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

PubMed

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

2016-05-08

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

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)

The Landau-de Gennes approach revisited: A minimal self-consistent microscopic theory for spatially inhomogeneous nematic liquid crystals

NASA Astrophysics Data System (ADS)

Gârlea, Ioana C.; Mulder, Bela M.

2017-12-01

We design a novel microscopic mean-field theory of inhomogeneous nematic liquid crystals formulated entirely in terms of the tensor order parameter field. It combines the virtues of the Landau-de Gennes approach in allowing both the direction and magnitude of the local order to vary, with a self-consistent treatment of the local free-energy valid beyond the small order parameter limit. As a proof of principle, we apply this theory to the well-studied problem of a colloid dispersed in a nematic liquid crystal by including a tunable wall coupling term. For the two-dimensional case, we investigate the organization of the liquid crystal and the position of the point defects as a function of the strength of the coupling constant.

A closed-form solution to tensor voting: theory and applications.

PubMed

Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard

2012-08-01

We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

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).

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

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

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

Cosmology in generalized Proca theories

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

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

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

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

Structural modeling of carbonaceous mesophase amphotropic mixtures under uniaxial extensional flow.

PubMed

Golmohammadi, Mojdeh; Rey, Alejandro D

2010-07-21

The extended Maier-Saupe model for binary mixtures of model carbonaceous mesophases (uniaxial discotic nematogens) under externally imposed flow, formulated in previous studies [M. Golmohammadi and A. D. Rey, Liquid Crystals 36, 75 (2009); M. Golmohammadi and A. D. Rey, Entropy 10, 183 (2008)], is used to characterize the effect of uniaxial extensional flow and concentration on phase behavior and structure of these mesogenic blends. The generic thermorheological phase diagram of the single-phase binary mixture, given in terms of temperature (T) and Deborah (De) number, shows the existence of four T-De transition lines that define regions that correspond to the following quadrupolar tensor order parameter structures: (i) oblate (perpendicular, parallel), (ii) prolate (perpendicular, parallel), (iii) scalene O(perpendicular, parallel), and (iv) scalene P(perpendicular, parallel), where the symbols (perpendicular, parallel) indicate alignment of the tensor order ellipsoid with respect to the extension axis. It is found that with increasing T the dominant component of the mixture exhibits weak deviations from the well-known pure species response to uniaxial extensional flow (uniaxial perpendicular nematic-->biaxial nematic-->uniaxial parallel paranematic). In contrast, the slaved component shows a strong deviation from the pure species response. This deviation is dictated by the asymmetric viscoelastic coupling effects emanating from the dominant component. Changes in conformation (oblate <==> prolate) and orientation (perpendicular <==> parallel) are effected through changes in pairs of eigenvalues of the quadrupolar tensor order parameter. The complexity of the structural sensitivity to temperature and extensional flow is a reflection of the dual lyotropic/thermotropic nature (amphotropic nature) of the mixture and their cooperation/competition. The analysis demonstrates that the simple structures (biaxial nematic and uniaxial paranematic) observed in pure discotic mesogens under uniaxial extensional flow are significantly enriched by the interaction of the lyotropic/thermotropic competition with the binary molecular architectures and with the quadrupolar nature of the flow.

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.

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

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

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

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

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

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

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

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

Gyrya, V.; Lipnikov, K.

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

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

PubMed

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

2011-04-21

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

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

PubMed Central

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-01-01

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org. PMID:26063822

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks.

PubMed

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-07-06

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

Spacetime encodings. III. Second order Killing tensors

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

Brink, Jeandrew

2010-01-15

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

Neutrino mass implications for muon decay parameters

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

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

2007-02-01

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

Leading-order calculation of hadronic contributions to the Muon g-2 using the Dyson-Schwinger approach

NASA Astrophysics Data System (ADS)

Goecke, Tobias; Fischer, Christian S.; Williams, Richard

2011-10-01

We present a calculation of the hadronic vacuum polarisation (HVP) tensor within the framework of Dyson-Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, aμ. We find aμHVP = 6760 ×10-11 which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of aμHVP and find good agreement within our approach. We also discuss the implications of our result for a corresponding calculation of the hadronic light-by-light scattering contribution to aμ.

Quantum phase transitions in a two-dimensional quantum XYX model: ground-state fidelity and entanglement.

PubMed

Li, Bo; Li, Sheng-Hao; Zhou, Huan-Qiang

2009-06-01

A systematic analysis is performed for quantum phase transitions in a two-dimensional anisotropic spin-1/2 antiferromagnetic XYX model in an external magnetic field. With the help of an innovative tensor network algorithm, we compute the fidelity per lattice site to demonstrate that the field-induced quantum phase transition is unambiguously characterized by a pinch point on the fidelity surface, marking a continuous phase transition. We also compute an entanglement estimator, defined as a ratio between the one-tangle and the sum of squared concurrences, to identify both the factorizing field and the critical point, resulting in a quantitative agreement with quantum Monte Carlo simulation. In addition, the local order parameter is "derived" from the tensor network representation of the system's ground-state wave functions.

Dictionary-Based Tensor Canonical Polyadic Decomposition

NASA Astrophysics Data System (ADS)

Cohen, Jeremy Emile; Gillis, Nicolas

2018-04-01

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

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

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

Zhu, Tao; Wang, Anzhong; Wu, Qiang

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

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.…

Einstein Revisited - Gravity in Curved Spacetime Without Event Horizons

NASA Astrophysics Data System (ADS)

Leiter, Darryl

2000-04-01

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

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.

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.

Visualising elastic anisotropy: theoretical background and computational implementation

NASA Astrophysics Data System (ADS)

Nordmann, J.; Aßmus, M.; Altenbach, H.

2018-02-01

In this article, we present the technical realisation for visualisations of characteristic parameters of the fourth-order elasticity tensor, which is classified by three-dimensional symmetry groups. Hereby, expressions for spatial representations of uc(Young)'s modulus and bulk modulus as well as plane representations of shear modulus and uc(Poisson)'s ratio are derived and transferred into a comprehensible form to computer algebra systems. Additionally, we present approaches for spatial representations of both latter parameters. These three- and two-dimensional representations are implemented into the software MATrix LABoratory. Exemplary representations of characteristic materials complete the present treatise.

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

PubMed

Wang, Wei; Takeda, Mitsuo

2006-09-01

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

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

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

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

1982-04-01

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

Preliminary AMS Study in Cretaceous Igneous Rocks of Valle Chico Complex, Uruguay: Statistical Determination of Magnetic Susceptibility

NASA Astrophysics Data System (ADS)

Barcelona, H.; Mena, M.; Sanchez-Bettucci, L.

2009-05-01

The Valle Chico Complex, at southeast Uruguay, is related Paraná-Etendeka Province. The study involved basaltic lavas, quarz-syenites, and rhyolitic and trachytic dikes. Samples were taken from 18 sites and the AMS of 250 specimens was analyzed. The AMS is modeled by a second order tensor K and it graphical representation is a symmetric ellipsoid. The axes relations determine parameters which describe different properties like shape, lineation, and foliation, degree of anisotropy and bulk magnetic susceptibility. Under this perspective, one lava, dike, or igneous body can be considered a mosaic of magnetic susceptibility domains (MSD). The DSM is an area with specific degree of homogeneity in the distribution of parameters values and cinematic conditions. An average tensor would weigh only one MSD, but if the site is a mosaic, subsets of specimens with similar parameters can be created. Hypothesis tests can be used to establish parameter similarities. It would be suitable considered as a MSD the subsets with statistically significant differences in at least one of its means parameters, and therefore, be treated independently. Once defined the MSDs the tensor analysis continues. The basalt-andesitic lavas present MSD with an NNW magnetic foliation, dipping 10. The K1 are sub-horizontal, oriented E-W and reprsent the magmatic flow direction. The quartz-syenites show a variable magnetic fabric or prolate ellipsoids mayor axes dispose parallel to the flow direction (10 to the SSE). Deformed syenites show N300/11 magnetic foliation, consistent with the trend of fractures. The K1 is subvertical. The MSD defined in rhyolitic dikes have magnetic foliations consistent with the structural trend. The trachytic dikes show an important indetermination in the magnetic response. However, a 62/N90 magnetic lineation was defined. The MSDs obtained are consistent with the geological structures and contribute to the knowledge of the tectonic, magmatic and kinematic events.

Light-cone distribution amplitudes of light JPC = 2- tensor mesons in QCD

NASA Astrophysics Data System (ADS)

Aliev, T. M.; Bilmis, S.; Yang, Kwei-Chou

2018-06-01

We present a study for two-quark light-cone distribution amplitudes for the 13D2 light tensor meson states with quantum number JPC =2-. Because of the G-parity, the chiral-even two-quark light-cone distribution amplitudes of this tensor meson are antisymmetric under the interchange of momentum fractions of the quark and antiquark in the SU(3) limit, while the chiral-odd ones are symmetric. The asymptotic leading-twist LCDAs with the strange quark mass correction are shown. We estimate the relevant parameters, the decay constants fT and fT⊥, and first Gegenbauer moment a1⊥ , by using the QCD sum rule method. These parameters play a central role in the investigation of B meson decaying into the 2- tensor mesons.

A distinguishing gravitational property for gravitational equation in higher dimensions

NASA Astrophysics Data System (ADS)

Dadhich, Naresh

2016-03-01

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

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.

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

Sarlis, N. V., E-mail: nsarlis@phys.uoa.gr; Christopoulos, S.-R. G.; Skordas, E. S.

It has been recently shown [N. V. Sarlis, Phys. Rev. E 84, 022101 (2011) and N. V. Sarlis and S.-R. G. Christopoulos, Chaos 22, 023123 (2012)] that earthquakes of magnitude M greater or equal to 7 are globally correlated. Such correlations were identified by studying the variance κ{sub 1} of natural time which has been proposed as an order parameter for seismicity. Here, we study the fluctuations of this order parameter using the Global Centroid Moment Tensor catalog for a magnitude threshold M{sub thres} = 5.0 and focus on its behavior before major earthquakes. Natural time analysis reveals that distinct minima ofmore » the fluctuations of the order parameter of seismicity appear within almost five and a half months on average before all major earthquakes of magnitude larger than 8.4. This phenomenon corroborates the recent finding [N. V. Sarlis et al., Proc. Natl. Acad. Sci. U.S.A. 110, 13734 (2013)] that similar minima of the seismicity order parameter fluctuations had preceded all major shallow earthquakes in Japan. Moreover, on the basis of these minima a statistically significant binary prediction method for earthquakes of magnitude larger than 8.4 with hit rate 100% and false alarm rate 6.67% is suggested.« less

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Fracture characterization by hybrid enumerative search and Gauss-Newton least-squares inversion methods

NASA Astrophysics Data System (ADS)

Alkharji, Mohammed N.

Most fracture characterization methods provide a general description of the fracture parameters as part of the reservoirs parameters; the fracture interaction and geometry within the reservoir is given less attention. T-Matrix and Linear Slip effective medium fracture models are implemented to invert the elastic tensor for the parameters and geometries of the fractures within the reservoir. The fracture inverse problem has an ill-posed, overdetermined, underconstrained rank-deficit system of equations. Least-squares inverse methods are used to solve the problem. A good starting initial model for the parameters is a key factor in the reliability of the inversion. Most methods assume that the starting parameters are close to the solution to avoid inaccurate local minimum solutions. The prior knowledge of the fracture parameters and their geometry is not available. We develop a hybrid, enumerative and Gauss-Newton, method that estimates the fracture parameters and geometry from the elastic tensor with no prior knowledge of the initial parameter values. The fracture parameters are separated into two groups. The first group contains the fracture parameters with no prior information, and the second group contains the parameters with known prior information. Different models are generated from the first group parameters by sampling the solution space over a predefined range of possible solutions for each parameter. Each model generated by the first group is fixed and used as a starting model to invert for the second group of parameters using the Gauss-Newton method. The least-squares residual between the observed elastic tensor and the estimated elastic tensor is calculated for each model. The model parameters that yield the least-squares residual corresponds to the correct fracture reservoir parameters and geometry. Two synthetic examples of fractured reservoirs with oil and gas saturations were inverted with no prior information about the fracture properties. The results showed that the hybrid algorithm successfully predicted the fracture parametrization, geometry, and the fluid content within the modeled reservoir. The method was also applied on an elastic tensor extracted from the Weyburn field in Saskatchewan, Canada. The solution suggested no presence of fractures but only a VTI system caused by the shale layering in the targeted reservoir, this interpretation is supported by other Weyburn field data.

Fermionic topological quantum states as tensor networks

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Variational optical flow estimation based on stick tensor voting.

PubMed

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

2013-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Einsteinian cubic gravity

NASA Astrophysics Data System (ADS)

Bueno, Pablo; Cano, Pablo A.

2016-11-01

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

Which Mechanical Invariants Are Associated With the Perception of Length and Heaviness of a Nonvisible Handheld Rod? Testing the Inertia Tensor Hypothesis

ERIC Educational Resources Information Center

Kingma, Idsart; van de Langenberg, Rolf; Beek, Peter J.

2004-01-01

It has been suggested that the inertia tensor governs many instances of haptic perception. However, the evidence is inconclusive because other candidate mechanical parameters (i.e., invariants) were not or were insufficiently controlled for in pertinent experiments. By independently varying all candidate mechanical parameters, the authors were…

Color superfluidity of neutral ultracold fermions in the presence of color-flip and color-orbit fields

NASA Astrophysics Data System (ADS)

Kurkcuoglu, Doga Murat; Sá de Melo, C. A. R.

2018-02-01

We describe how color superfluidity is modified in the presence of color-flip and color-orbit fields in the context of ultracold atoms and discuss connections between this problem and that of color superconductivity in quantum chromodynamics. We study the case of s -wave contact interactions between different colors and we identify several superfluid phases, with five being nodal and one being fully gapped. When our system is described in a mixed-color basis, the superfluid order parameter tensor is characterized by six independent components with explicit momentum dependence induced by color-orbit coupling. The nodal superfluid phases are topological in nature and the low-temperature phase diagram of the color-flip field versus the interaction parameter exhibits a pentacritical point, where all five nodal color superfluid phases converge. These results are in sharp contrast to the case of zero color-flip and color-orbit fields, where the system has perfect U(3) symmetry and possesses a superfluid phase that is characterized by fully gapped quasiparticle excitations with a single complex order parameter with no momentum dependence and by inert unpaired fermions representing a nonsuperfluid component. In the latter case, just a crossover between a Bardeen-Cooper-Schrieffer and a Bose-Einstein-condensation superfluid occurs. Furthermore, we analyze the order parameter tensor in a total pseudospin basis, investigate its momentum dependence in the singlet, triplet, and quintet sectors, and compare the results with the simpler case of spin-1/2 fermions in the presence of spin-flip and spin-orbit fields, where only singlet and triplet channels arise. Finally, we analyze in detail spectroscopic properties of color superfluids in the presence of color-flip and color-orbit fields, such as the quasiparticle excitation spectrum, momentum distribution, and density of states to help characterize all the encountered topological quantum phases, which can be realized in fermionic isotopes of lithium, potassium, and ytterbium atoms with three internal states trapped.

Light scattering from liquid crystal director fluctuations in steady magnetic fields up to 25 tesla.

PubMed

Challa, Pavan K; Curtiss, O; Williams, J C; Twieg, R; Toth, J; McGill, S; Jákli, A; Gleeson, J T; Sprunt, S N

2012-07-01

We report on homodyne dynamic light scattering measurements of orientational fluctuation modes in both calamitic and bent-core nematic liquid crystals, carried out in the new split-helix resistive magnet at the National High Magnetic Field Laboratory. The relaxation rate and inverse scattered intensity of director fluctuations exhibit a linear dependence on field-squared up to 25 tesla, which is consistent with strictly lowest order coupling of the tensor order parameter Q to field (Q(αβ)B(α)B(β)) in the nematic free energy. However, we also observe evidence of field dependence of certain nematic material parameters, an effect which may be expected from the mean field scaling of these quantities with the magnitude of Q and the predicted variation of Q with field.

Resolution of a Rank-Deficient Adjustment Model Via an Isomorphic Geometrical Setup with Tensor Structure.

DTIC Science & Technology

1987-03-01

would be transcribed as L =AX - V where L, X, and V are the vectors of constant terms, parametric corrections , and b_o bresiduals, respectively. The...tensor. a Just as du’ represents the parametric corrections in tensor notations, the necessary associated metric tensor a’ corresponds to the variance...observations, n residuals, and 0 n- parametric corrections to X (an initial set of parameters), respectively. b 0 b The vctor L is formed as 1. L where

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.

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

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

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

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

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

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

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

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

1997-01-01

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

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

PubMed Central

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

2009-01-01

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

Slowly-rotating neutron stars in massive bigravity

NASA Astrophysics Data System (ADS)

Sullivan, A.; Yunes, N.

2018-02-01

We study slowly-rotating neutron stars in ghost-free massive bigravity. This theory modifies general relativity by introducing a second, auxiliary but dynamical tensor field that couples to matter through the physical metric tensor through non-linear interactions. We expand the field equations to linear order in slow rotation and numerically construct solutions in the interior and exterior of the star with a set of realistic equations of state. We calculate the physical mass function with respect to observer radius and find that, unlike in general relativity, this function does not remain constant outside the star; rather, it asymptotes to a constant a distance away from the surface, whose magnitude is controlled by the ratio of gravitational constants. The Vainshtein-like radius at which the physical and auxiliary mass functions asymptote to a constant is controlled by the graviton mass scaling parameter, and outside this radius, bigravity modifications are suppressed. We also calculate the frame-dragging metric function and find that bigravity modifications are typically small in the entire range of coupling parameters explored. We finally calculate both the mass-radius and the moment of inertia-mass relations for a wide range of coupling parameters and find that both the graviton mass scaling parameter and the ratio of the gravitational constants introduce large modifications to both. These results could be used to place future constraints on bigravity with electromagnetic and gravitational-wave observations of isolated and binary neutron stars.

Covariant density functional theory: predictive power and first attempts of a microscopic derivation

NASA Astrophysics Data System (ADS)

Ring, Peter

2018-05-01

We discuss systematic global investigations with modern covariant density functionals. The number of their phenomenological parameters can be reduced considerable by using microscopic input from ab-initio calculations in nuclear matter. The size of the tensor force is still an open problem. Therefore we use the first full relativistic Brueckner-Hartree-Fock calculations in finite nuclear systems in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

The reconstruction of f(ϕ)R and mimetic gravity from viable slow-roll inflation

NASA Astrophysics Data System (ADS)

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

2018-04-01

In this work, we extend the bottom-up reconstruction framework of F (R) gravity to other modified gravities, and in particular for f (ϕ) R and mimetic F (R) gravities. We investigate which are the important conditions in order for the method to work, and we study several viable cosmological evolutions, focusing on the inflationary era. Particularly, for the f (ϕ) R theory case, we specify the functional form of the Hubble rate and of the scalar-to-tensor ratio as a function of the e-foldings number and accordingly, the rest of the physical quantities and also the slow-roll and the corresponding observational indices can be calculated. The same method is applied in the mimetic F (R) gravity case, and in both cases we thoroughly analyze the resulting free parameter space, in order to show that the viability of the models presented is guaranteed and secondly that there is a wide range of values of the free parameters for which the viability of the models occurs. In addition, the reconstruction method is also studied in the context of mimetic F (R) = R gravity. As we demonstrate, the resulting theory is viable, and also in this case, only the scalar-to-tensor ratio needs to be specified, since the rest follow from this condition. Finally, we discuss in brief how the reconstruction method could function for other modified gravities.

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

Cosmology in generalized Proca theories

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

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

2016-06-01

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

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

PubMed

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

2008-07-01

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

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

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

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo

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

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

NASA Astrophysics Data System (ADS)

Baker, Ben; Stachnik, Joshua; Rozhkov, Mikhail

2017-04-01

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

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.

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

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.

Sum-Frequency Generation from a Thin Cylindrical Layer

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

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

PubMed

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

2017-01-01

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

Anisotropic rotational diffusion studied by passage saturation transfer electron paramagnetic resonance

NASA Astrophysics Data System (ADS)

Robinson, Bruce H.; Dalton, Larry R.

1980-01-01

The stochastic Liouville equation for the spin density matrix is modified to consider the effects of Brownian anisotropic rotational diffusion upon electron paramagnetic resonance (EPR) and saturation transfer electron paramagnetic resonance (ST-EPR) spectra. Spectral shapes and the ST-EPR parameters L″/L, C'/C, and H″/H defined by Thomas, Dalton, and Hyde at X-band microwave frequencies [J. Chem. Phys. 65, 3006 (1976)] are examined and discussed in terms of the rotational times τ∥ and τ⊥ and in terms of other defined correlation times for systems characterized by magnetic tensors of axial symmetry and for systems characterized by nonaxially symmetric magnetic tensors. For nearly axially symmetric magnetic tensors, such as nitroxide spin labels studied employing 1-3 GHz microwaves, ST-EPR spectra for systems undergoing anisotropic rotational diffusion are virtually indistinguishable from spectra for systems characterized by isotropic diffusion. For nonaxially symmetric magnetic tensors, such as nitroxide spin labels studied employing 8-35 GHz microwaves, the high field region of the ST-EPR spectra, and hence the H″/H parameter, will be virtually indistinguishable from spectra, and parameter values, obtained for isotropic diffusion. On the other hand, the central spectral region at x-band microwave frequencies, and hence the C'/C parameter, is sensitive to the anisotropic diffusion model provided that a unique and static relationship exists between the magnetic and diffusion tensors. Random labeling or motion of the spin label relative to the biomolecule whose hydrodynamic properties are to be investigated will destroy spectral sensitivity to anisotropic motion. The sensitivity to anisotropic motion is enhanced in proceeding to 35 GHz with the increased sensitivity evident in the low field half of the EPR and ST-EPR spectra. The L″/L parameter is thus a meaningful indicator of anisotropic motion when compared with H″/H parameter analysis. However, consideration of spectral shapes suggests that the C'/C parameter definition is not meaningfully extended from 9.5 to 35 GHz. Alternative definitions of the L″/L and C'/C parameters are proposed for those microwave frequencies for which the electron Zeeman anisotropy is comparable to or greater than the electron-nitrogen nuclear hyperfine anisotropy.

On butterfly effect in higher derivative gravities

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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

NASA Astrophysics Data System (ADS)

Batista, Carlos

2015-04-01

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

On Adapting the Tensor Voting Framework to Robust Color Image Denoising

NASA Astrophysics Data System (ADS)

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

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

Tensor Galileons and gravity

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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.

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.

Geomanetically Induced Currents (GIC) calculation, impact assessment on transmission system and validation using 3-D earth conductivity tensors and GIC measurements.

NASA Astrophysics Data System (ADS)

Sharma, R.; McCalley, J. D.

2016-12-01

Geomagnetic disturbance (GMD) causes the flow of geomagnetically induced currents (GIC) in the power transmission system that may cause large scale power outages and power system equipment damage. In order to plan for defense against GMD, it is necessary to accurately estimate the flow of GICs in the power transmission system. The current calculation as per NERC standards uses the 1-D earth conductivity models that don't reflect the coupling between the geoelectric and geomagnetic field components in the same direction. For accurate estimation of GICs, it is important to have spatially granular 3-D earth conductivity tensors, accurate DC network model of the transmission system and precisely estimated or measured input in the form of geomagnetic or geoelectric field data. Using these models and data the pre event, post event and online planning and assessment can be performed. The pre, post and online planning can be done by calculating GIC, analyzing voltage stability margin, identifying protection system vulnerabilities and estimating heating in transmission equipment. In order to perform the above mentioned tasks, an established GIC calculation and analysis procedure is needed that uses improved geophysical and DC network models obtained by model parameter tuning. The issue is addressed by performing the following tasks; 1) Geomagnetic field data and improved 3-D earth conductivity tensors are used to plot the geoelectric field map of a given area. The obtained geoelectric field map then serves as an input to the PSS/E platform, where through DC circuit analysis the GIC flows are calculated. 2) The computed GIC is evaluated against GIC measurements in order to fine tune the geophysical and DC network model parameters for any mismatch in the calculated and measured GIC. 3) The GIC calculation procedure is then adapted for a one in 100 year storm, in order to assess the impact of the worst case GMD on the power system. 4) Using the transformer models, the voltage stability margin would be analyzed for various real and synthetic geomagnetic or geoelectric field inputs, by calculating the reactive power absorbed by the transformers during an event. All four steps will help the electric utilities and planners to make use of better and accurate estimation techniques for GIC calculation, and impact assessment for future GMD events.

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.

On the use of water phantom images to calibrate and correct eddy current induced artefacts in MR diffusion tensor imaging.

PubMed

Bastin, M E; Armitage, P A

2000-07-01

The accurate determination of absolute measures of diffusion anisotropy in vivo using single-shot, echo-planar imaging techniques requires the acquisition of a set of high signal-to-noise ratio, diffusion-weighted images that are free from eddy current induced image distortions. Such geometric distortions can be characterized and corrected in brain imaging data using magnification (M), translation (T), and shear (S) distortion parameters derived from separate water phantom calibration experiments. Here we examine the practicalities of using separate phantom calibration data to correct high b-value diffusion tensor imaging data by investigating the stability of these distortion parameters, and hence the eddy currents, with time. It is found that M, T, and S vary only slowly with time (i.e., on the order of weeks), so that calibration scans need not be performed after every patient examination. This not only minimises the scan time required to collect the calibration data, but also the computational time needed to characterize these eddy current induced distortions. Examples of how measurements of diffusion anisotropy are improved using this post-processing scheme are also presented.

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.

Comparison of the Cut-and-Paste and Full Moment Tensor Methods for Estimating Earthquake Source Parameters

NASA Astrophysics Data System (ADS)

Templeton, D.; Rodgers, A.; Helmberger, D.; Dreger, D.

2008-12-01

Earthquake source parameters (seismic moment, focal mechanism and depth) are now routinely reported by various institutions and network operators. These parameters are important for seismotectonic and earthquake ground motion studies as well as calibration of moment magnitude scales and model-based earthquake-explosion discrimination. Source parameters are often estimated from long-period three- component waveforms at regional distances using waveform modeling techniques with Green's functions computed for an average plane-layered models. One widely used method is waveform inversion for the full moment tensor (Dreger and Helmberger, 1993). This method (TDMT) solves for the moment tensor elements by performing a linearized inversion in the time-domain that minimizes the difference between the observed and synthetic waveforms. Errors in the seismic velocity structure inevitably arise due to either differences in the true average plane-layered structure or laterally varying structure. The TDMT method can account for errors in the velocity model by applying a single time shift at each station to the observed waveforms to best match the synthetics. Another method for estimating source parameters is the Cut-and-Paste (CAP) method. This method breaks the three-component regional waveforms into five windows: vertical and radial component Pnl; vertical and radial component Rayleigh wave; and transverse component Love waves. The CAP method performs a grid search over double-couple mechanisms and allows the synthetic waveforms for each phase (Pnl, Rayleigh and Love) to shift in time to account for errors in the Green's functions. Different filtering and weighting of the Pnl segment relative to surface wave segments enhances sensitivity to source parameters, however, some bias may be introduced. This study will compare the TDMT and CAP methods in two different regions in order to better understand the advantages and limitations of each method. Firstly, we will consider the northeastern China/Korean Peninsula region where average plane-layered structure is well known and relatively laterally homogenous. Secondly, we will consider the Middle East where crustal and upper mantle structure is laterally heterogeneous due to recent and ongoing tectonism. If time allows we will investigate the efficacy of each method for retrieving source parameters from synthetic data generated using a three-dimensional model of seismic structure of the Middle East, where phase delays are known to arise from path-dependent structure.

Constraints on the cosmological parameters from BICEP2, Planck, and WMAP

NASA Astrophysics Data System (ADS)

Cheng, Cheng; Huang, Qing-Guo

2014-11-01

In this paper we constrain the cosmological parameters, in particular the tilt of tensor power spectrum, by adopting Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 and Wilkinson Microwaves Anisotropy Probe 9-year Polarization data. We find that a blue tilted tensor power spectrum is preferred at more than confidence level if the data from B2 are assumed to be totally interpreted as the relic gravitational waves, but a scale-invariant tensor power spectrum is consistent with the data once the polarized dust is taken into account. The recent Planck 353 GHz HFI dust polarization data imply that the B2 data are perfectly consistent with there being no gravitational wave signal.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Rotation Dynamics Do Not Determine the Unexpected Isotropy of Methyl Radical EPR Spectra.

PubMed

Benetis, Nikolas P; Dmitriev, Yurij; Mocci, Francesca; Laaksonen, Aatto

2015-09-03

A simple first-principles electronic structure computation, further qc (quantum chemistry) computation, of the methyl radical gives three equal hf (hyperfine) couplings for the three protons with the unpaired electron. The corresponding dipolar tensors were notably rhombic and had different orientations and regular magnitude components, as they should, but what the overall A-tensor was seen by the electron spin is a different story! The final g = (2.002993, 2.002993, 2.002231) tensor and the hf coupling results obtained in vacuum, at the B3LYP/EPRIII level of theory clearly indicate that in particular the above A = (-65.19, -65.19, 62.54) MHz tensor was axial to a first approximation without considering any rotational dynamics for the CH3. This approximation was not applicable, however, for the trifluoromethyl CF3 radical, a heavier and nonplanar rotor with very anisotropic hf coupling, used here for comparison. Finally, a derivation is presented explaining why there is actually no need for the CH3 radicals to consider additional rotational dynamics in order for the electron to obtain an axially symmetric hf (hyperfine) tensor by considering the simultaneous dipolar couplings of the three protons. An additional consequence is an almost isotropic A-tensor for the electron spin of the CH3 radical. To the best of our knowledge, this point has not been discussed in the literature before. The unexpected isotropy of the EPR parameters of CH3 was solely attributed to the rotational dynamics and was not clearly separated from the overall symmetry of the species. The present theoretical results allowed a first explanation of the "forbidden" satellite lines in the CH3 EPR spectrum. The satellites are a fingerprint of the radical rotation, helping thus in distinguishing the CH3 reorientation from quantum rotation at very low temperatures.

Diffusion tensor imaging with direct cytopathological validation: characterisation of decorin treatment in experimental juvenile communicating hydrocephalus.

PubMed

Aojula, Anuriti; Botfield, Hannah; McAllister, James Patterson; Gonzalez, Ana Maria; Abdullah, Osama; Logan, Ann; Sinclair, Alexandra

2016-05-31

In an effort to develop novel treatments for communicating hydrocephalus, we have shown previously that the transforming growth factor-β antagonist, decorin, inhibits subarachnoid fibrosis mediated ventriculomegaly; however decorin's ability to prevent cerebral cytopathology in communicating hydrocephalus has not been fully examined. Furthermore, the capacity for diffusion tensor imaging to act as a proxy measure of cerebral pathology in multiple sclerosis and spinal cord injury has recently been demonstrated. However, the use of diffusion tensor imaging to investigate cytopathological changes in communicating hydrocephalus is yet to occur. Hence, this study aimed to determine whether decorin treatment influences alterations in diffusion tensor imaging parameters and cytopathology in experimental communicating hydrocephalus. Moreover, the study also explored whether diffusion tensor imaging parameters correlate with cellular pathology in communicating hydrocephalus. Accordingly, communicating hydrocephalus was induced by injecting kaolin into the basal cisterns in 3-week old rats followed immediately by 14 days of continuous intraventricular delivery of either human recombinant decorin (n = 5) or vehicle (n = 6). Four rats remained as intact controls and a further four rats served as kaolin only controls. At 14-days post-kaolin, just prior to sacrifice, routine magnetic resonance imaging and magnetic resonance diffusion tensor imaging was conducted and the mean diffusivity, fractional anisotropy, radial and axial diffusivity of seven cerebral regions were assessed by voxel-based analysis in the corpus callosum, periventricular white matter, caudal internal capsule, CA1 hippocampus, and outer and inner parietal cortex. Myelin integrity, gliosis and aquaporin-4 levels were evaluated by post-mortem immunohistochemistry in the CA3 hippocampus and in the caudal brain of the same cerebral structures analysed by diffusion tensor imaging. Decorin significantly decreased myelin damage in the caudal internal capsule and prevented caudal periventricular white matter oedema and astrogliosis. Furthermore, decorin treatment prevented the increase in caudal periventricular white matter mean diffusivity (p = 0.032) as well as caudal corpus callosum axial diffusivity (p = 0.004) and radial diffusivity (p = 0.034). Furthermore, diffusion tensor imaging parameters correlated primarily with periventricular white matter astrocyte and aquaporin-4 levels. Overall, these findings suggest that decorin has the therapeutic potential to reduce white matter cytopathology in hydrocephalus. Moreover, diffusion tensor imaging is a useful tool to provide surrogate measures of periventricular white matter pathology in communicating hydrocephalus.

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.

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.

Grid-search Moment Tensor Estimation: Implementation and CTBT-related Application

NASA Astrophysics Data System (ADS)

Stachnik, J. C.; Baker, B. I.; Rozhkov, M.; Friberg, P. A.; Leifer, J. M.

2017-12-01

This abstract presents a review work related to moment tensor estimation for Expert Technical Analysis at the Comprehensive Test Ban Treaty Organization. In this context of event characterization, estimation of key source parameters provide important insights into the nature of failure in the earth. For example, if the recovered source parameters are indicative of a shallow source with large isotropic component then one conclusion is that it is a human-triggered explosive event. However, an important follow-up question in this application is - does an alternative hypothesis like a deeper source with a large double couple component explain the data approximately as well as the best solution? Here we address the issue of both finding a most likely source and assessing its uncertainty. Using the uniform moment tensor discretization of Tape and Tape (2015) we exhaustively interrogate and tabulate the source eigenvalue distribution (i.e., the source characterization), tensor orientation, magnitude, and source depth. The benefit of the grid-search is that we can quantitatively assess the extent to which model parameters are resolved. This provides a valuable opportunity during the assessment phase to focus interpretation on source parameters that are well-resolved. Another benefit of the grid-search is that it proves to be a flexible framework where different pieces of information can be easily incorporated. To this end, this work is particularly interested in fitting teleseismic body waves and regional surface waves as well as incorporating teleseismic first motions when available. Being that the moment tensor search methodology is well-established we primarily focus on the implementation and application. We present a highly scalable strategy for systematically inspecting the entire model parameter space. We then focus on application to regional and teleseismic data recorded during a handful of natural and anthropogenic events, report on the grid-search optimum, and discuss the resolution of interesting and/or important recovered source properties.

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Zhong, Yiyuan; Chen, Chaojian; Tang, Jingtian; Kalscheuer, Thomas; Maurer, Hansruedi; Li, Yang

2018-03-01

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

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

NASA Astrophysics Data System (ADS)

Dima, Alexandru; Vernizzi, Filippo

2018-05-01

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

The conformal limit of inflation in the era of CMB polarimetry

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

Pajer, Enrico; Wijck, Jaap V.S. van; Pimentel, Guilherme L., E-mail: enrico.pajer@gmail.com, E-mail: g.leitepimentel@uva.nl, E-mail: j.v.s.vanwijck@uu.nl

2017-06-01

We argue that the non-detection of primordial tensor modes has taught us a great deal about the primordial universe. In single-field slow-roll inflation, the current upper bound on the tensor-to-scalar ratio, r <0.07 (95% CL), implies that the Hubble slow-roll parameters obey ε||η , and therefore establishes the existence of a new hierarchy. We dub this regime the conformal limit of (slow-roll) inflation, and show that it includes Starobinsky-like inflation as well as all viable single-field models with a sub-Planckian field excursion. In this limit, all primordial correlators are constrained by the full conformal group to leading non-trivial order inmore » slow-roll. This fixes the power spectrum and the full bispectrum, and leads to the ''conformal'' shape of non-Gaussianity. The size of non-Gaussianity is related to the running of the spectral index by a consistency condition, and therefore it is expected to be small. In passing, we clarify the role of boundary terms in the ζ action, the order to which constraint equations need to be solved, and re-derive our results using the Wheeler-deWitt formalism.« less

Uniform function constants of motion and their first-order perturbation

NASA Astrophysics Data System (ADS)

Prato, Domingo; Hamity, Victor H.

2005-05-01

The main purpose of this work is to present some uniform function constants of motion rather than the well-known quantities arising from spacetime symmetries. These constants are usually associated with the intrinsic characteristics of the trajectories of a particle in a central potential field. We treat two cases. The first is the Lenz vector which sometimes is found in the literature [1, 2]; the other is associated with the isotropic harmonic oscillator, of relative importance in some simple models of the classical molecular interaction. The first example is applied to describe the perturbation of the trajectories in the Rutherford scattering and the precession of the Keplerian orbit of a planet. In the other case the conserved quantity is a symmetric tensor. We find the eigenvectors and eigenvalues of that tensor while at the same time we obtain the solution to the problem of calculating the rotation rate of the orbits in first order of a perturbation parameter in the potential energy, by performing a simple coordinate transformation in the Cartesian plane. We think that the present work addresses many aspects of mechanics with a didactical interest in other physics or mathematics courses.

Spin-Mechanical Inertia in Antiferromagnet

NASA Astrophysics Data System (ADS)

Cheng, Ran; Wu, Xiaochuan; Xiao, Di

Interplay between spin dynamics and mechanical motions is responsible for numerous striking phenomena, which has shaped a rapidly expanding field known as spin-mechanics. The guiding principle of this field has been the conservation of angular momentum that involves both quantum spins and classical mechanical rotations. However, in an antiferromagnet, the macroscopic magnetization vanishes while the order parameter (Néel order) does not carry an angular momentum. It is therefore not clear whether the order parameter dynamics has any mechanical consequence as its ferromagnetic counterparts. Here we demonstrate that the Néel order dynamics affects the mechanical motion of a rigid body by modifying its inertia tensor in the presence of strong magnetocrystalline anisotropy. This effect depends on temperature when magnon excitations are considered. Such a spin-mechanical inertia can produce measurable consequences at nanometer scales. Our discovery establishes spin-mechanical inertia as an essential ingredient to properly describe spin-mechanical effects in AFs, which supplements the known governing physics from angular momentum conservation. This work was supported by the DOE, Basic Energy Sciences, Grant No. DE-SC0012509. D.X. also acknowledges support from a Research Corporation for Science Advancement Cottrell Scholar Award.

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.

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.

The structure of an integral membrane peptide: a deuterium NMR study of gramicidin.

PubMed Central

Prosser, R S; Daleman, S I; Davis, J H

1994-01-01

Solid state deuterium NMR was employed on oriented multilamellar dispersions consisting of 1,2-dilauryl-sn-glycero-3-phosphatidylcholine and deuterium (2H) exchange-labeled gramicidin D, at a lipid to protein molar ratio (L/P) of 15:1, in order to study the dynamic structure of the channel conformation of gramicidin in a liquid crystalline phase. The corresponding spectra were used to discriminate between several structural models for the channel structure of gramicidin (based on the left- and right-handed beta 6.3 LD helix) and other models based on a structure obtained from high resolution NMR. The oriented spectrum is complicated by the fact that many of the doublets, corresponding to the 20 exchangeable sites, partially overlap. Furthermore, the asymmetry parameter, eta, of the electric field gradient tensor of the amide deuterons is large (approximately 0.2) and many of the amide groups are involved in hydrogen bonding, which is known to affect the quadrupole coupling constant. In order to account for these complications in simulating the spectra in the fast motional regime, an ab initio program called Gaussian 90 was employed, which permitted us to calculate, by quantum mechanical means, the complete electric field gradient tensor for each residue in gramicidin (using two structural models). Our results indicated that the left-handed helical models were inconsistent with our observed spectra, whereas a model based on the high-resolution structure derived by Arseniev and coworkers, but relaxed by a simple energy minimization procedure, was consistent with our observed spectra. The molecular order parameter was then estimated from the motional narrowing assuming the relaxed (right-handed) Arseniev structure. Our resultant order parameter of SZZ = 0.91 translates into an rms angle of 14 degrees, formed by the helix axis and the local bilayer normal. The strong resemblance between our spectra (and also those reported for gramicidin in 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC) multilayers) and the spectra of the same peptide incorporated in a lyotropic nematic phase, suggests that the lyotropic nematic phase simulates the local environment of the lipid bilayer. PMID:7520293

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

NASA Astrophysics Data System (ADS)

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

2010-06-01

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

Validation of buoyancy driven spectral tensor model using HATS data

NASA Astrophysics Data System (ADS)

Chougule, A.; Mann, J.; Kelly, M.; Larsen, G. C.

2016-09-01

We present a homogeneous spectral tensor model for wind velocity and temperature fluctuations, driven by mean vertical shear and mean temperature gradient. Results from the model, including one-dimensional velocity and temperature spectra and the associated co-spectra, are shown in this paper. The model also reproduces two-point statistics, such as coherence and phases, via cross-spectra between two points separated in space. Model results are compared with observations from the Horizontal Array Turbulence Study (HATS) field program (Horst et al. 2004). The spectral velocity tensor in the model is described via five parameters: the dissipation rate (ɛ), length scale of energy-containing eddies (L), a turbulence anisotropy parameter (Γ), gradient Richardson number (Ri) representing the atmospheric stability and the rate of destruction of temperature variance (ηθ).

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.

In flight estimations of Cassini spacecraft inertia tensor and thruster magnitude

NASA Technical Reports Server (NTRS)

Feldman, Antonette; Lee, Allan Y.

2006-01-01

This paper describes two methods used by the Cassini Attitude Control team to determine these key parameters and how flight telemetry was used to estimate them. The method for estimating the spacecraft inertia tensor exploits the conservation of angular momentum during spacecraft slews under reaction wheel control.

Comparison of aquifer characteristics derived from local and regional aquifer tests.

USGS Publications Warehouse

Randolph, R.B.; Krause, R.E.; Maslia, M.L.

1985-01-01

A comparison of the aquifer parameter values obtained through the analysis of a local and a regional aquifer test involving the same area in southeast Georgia is made in order to evaluate the validity of extrapolating local aquifer-test results for use in large-scale flow simulations. Time-drawdown and time-recovery data were analyzed by using both graphical and least-squares fitting of the data to the Theis curve. Additionally, directional transmissivity, transmissivity tensor, and angle of anisotropy were computed for both tests. -from Authors Georgia drawdown transmissivity regional aquifer tests

Constraining modified gravitational theories by weak lensing with Euclid

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

Martinelli, Matteo; Calabrese, Erminia; De Bernardis, Francesco

2011-01-15

Future proposed satellite missions such as Euclid can offer the opportunity to test general relativity on cosmic scales through mapping of the galaxy weak-lensing signal. In this paper we forecast the ability of these experiments to constrain modified gravity scenarios such as those predicted by scalar-tensor and f(R) theories. We find that Euclid will improve constraints expected from the Planck satellite on these modified theories of gravity by 2 orders of magnitude. We discuss parameter degeneracies and the possible biases introduced by modifications to gravity.

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

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2018-03-01

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

Strain, magnetic anisotropy, and anisotropic magnetoresistance in (Ga,Mn)As on high-index substrates: Application to (113)A -oriented layers

NASA Astrophysics Data System (ADS)

Dreher, L.; Donhauser, D.; Daeubler, J.; Glunk, M.; Rapp, C.; Schoch, W.; Sauer, R.; Limmer, W.

2010-06-01

Based on a detailed theoretical examination of the lattice distortion in high-index epilayers in terms of continuum mechanics, expressions are deduced that allow the calculation and experimental determination of the strain tensor for (hhl) -oriented (Ga,Mn)As layers. Analytical expressions are derived for the strain-dependent free-energy density and for the resistivity tensor for monoclinic and orthorhombic crystal symmetries, phenomenologically describing the magnetic anisotropy and anisotropic magnetoresistance by appropriate anisotropy and resistivity parameters, respectively. Applying the results to (113)A orientation with monoclinic crystal symmetry, the expressions are used to determine the strain tensor and the shear angle of a series of (113)A -oriented (Ga,Mn)As layers by high-resolution x-ray diffraction and to probe the magnetic anisotropy and anisotropic magnetoresistance at 4.2 K by means of angle-dependent magnetotransport. Whereas the transverse-resistivity parameters are nearly unaffected by the magnetic field, the parameters describing the longitudinal resistivity are strongly field dependent.

FADTTSter: accelerating hypothesis testing with functional analysis of diffusion tensor tract statistics

NASA Astrophysics Data System (ADS)

Noel, Jean; Prieto, Juan C.; Styner, Martin

2017-03-01

Functional Analysis of Diffusion Tensor Tract Statistics (FADTTS) is a toolbox for analysis of white matter (WM) fiber tracts. It allows associating diffusion properties along major WM bundles with a set of covariates of interest, such as age, diagnostic status and gender, and the structure of the variability of these WM tract properties. However, to use this toolbox, a user must have an intermediate knowledge in scripting languages (MATLAB). FADTTSter was created to overcome this issue and make the statistical analysis accessible to any non-technical researcher. FADTTSter is actively being used by researchers at the University of North Carolina. FADTTSter guides non-technical users through a series of steps including quality control of subjects and fibers in order to setup the necessary parameters to run FADTTS. Additionally, FADTTSter implements interactive charts for FADTTS' outputs. This interactive chart enhances the researcher experience and facilitates the analysis of the results. FADTTSter's motivation is to improve usability and provide a new analysis tool to the community that complements FADTTS. Ultimately, by enabling FADTTS to a broader audience, FADTTSter seeks to accelerate hypothesis testing in neuroimaging studies involving heterogeneous clinical data and diffusion tensor imaging. This work is submitted to the Biomedical Applications in Molecular, Structural, and Functional Imaging conference. The source code of this application is available in NITRC.

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

NASA Astrophysics Data System (ADS)

Lello, Louis; Boyanovsky, Daniel

2014-05-01

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

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.

Entanglement branching operator

NASA Astrophysics Data System (ADS)

Harada, Kenji

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-10-01

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

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

PubMed

Hanrath, Michael; Engels-Putzka, Anna

2010-08-14

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

Theoretical study of diaquamalonatozinc(II) single crystal for applications in non-linear optical devices

NASA Astrophysics Data System (ADS)

Chakraborty, Mitesh; Rai, Vineet Kumar

2017-12-01

The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM) with the microscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. g-tensor and D-tensor, has been determined by using the ORCA program package developed by F Neese et al. The unrestricted Kohn-Sham orbitals-based Pederson-Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin-orbit tensor (D^{SO}) of the axial ZFS parameter D. The effects of spin-spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin-spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson-Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn-Sham-based natural orbital with Pederson-Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of Mn^{2+} ion in the host matrix.

Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

PubMed Central

Li, Zhining; Zhang, Yingtang; Yin, Gang

2018-01-01

The measurement error of the differencing (i.e., using two homogenous field sensors at a known baseline distance) magnetic gradient tensor system includes the biases, scale factors, nonorthogonality of the single magnetic sensor, and the misalignment error between the sensor arrays, all of which can severely affect the measurement accuracy. In this paper, we propose a low-cost artificial vector calibration method for the tensor system. Firstly, the error parameter linear equations are constructed based on the single-sensor’s system error model to obtain the artificial ideal vector output of the platform, with the total magnetic intensity (TMI) scalar as a reference by two nonlinear conversions, without any mathematical simplification. Secondly, the Levenberg–Marquardt algorithm is used to compute the integrated model of the 12 error parameters by nonlinear least-squares fitting method with the artificial vector output as a reference, and a total of 48 parameters of the system is estimated simultaneously. The calibrated system outputs along the reference platform-orthogonal coordinate system. The analysis results show that the artificial vector calibrated output can track the orientation fluctuations of TMI accurately, effectively avoiding the “overcalibration” problem. The accuracy of the error parameters’ estimation in the simulation is close to 100%. The experimental root-mean-square error (RMSE) of the TMI and tensor components is less than 3 nT and 20 nT/m, respectively, and the estimation of the parameters is highly robust. PMID:29373544

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

A 3D generic inverse dynamic method using wrench notation and quaternion algebra.

PubMed

Dumas, R; Aissaoui, R; de Guise, J A

2004-06-01

In the literature, conventional 3D inverse dynamic models are limited in three aspects related to inverse dynamic notation, body segment parameters and kinematic formalism. First, conventional notation yields separate computations of the forces and moments with successive coordinate system transformations. Secondly, the way conventional body segment parameters are defined is based on the assumption that the inertia tensor is principal and the centre of mass is located between the proximal and distal ends. Thirdly, the conventional kinematic formalism uses Euler or Cardanic angles that are sequence-dependent and suffer from singularities. In order to overcome these limitations, this paper presents a new generic method for inverse dynamics. This generic method is based on wrench notation for inverse dynamics, a general definition of body segment parameters and quaternion algebra for the kinematic formalism.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

High-order regularization in lattice-Boltzmann equations

NASA Astrophysics Data System (ADS)

Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

2017-04-01

A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

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

NASA Astrophysics Data System (ADS)

Karl, S.; Neuberg, J.

2011-12-01

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

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

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

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

2016-12-15

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

Large number limit of multifield inflation

NASA Astrophysics Data System (ADS)

Guo, Zhong-Kai

2017-12-01

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

On the running of the spectral index to all orders: a new model-dependent approach to constrain inflationary models

NASA Astrophysics Data System (ADS)

Zarei, Moslem

2016-06-01

In conventional model-independent approaches, the power spectrum of primordial perturbations is characterized by such free parameters as the spectral index, its running, the running of running, and the tensor-to-scalar ratio. In this work we show that, at least for simple inflationary potentials, one can find the primordial scalar and tensor power spectra exactly by resumming over all the running terms. In this model-dependent method, we expand the power spectra about the pivot scale to find the series terms as functions of the e-folding number for some single field models of inflation. Interestingly, for the viable models studied here, one can sum over all the terms and evaluate the exact form of the power spectra. This in turn gives more accurate parametrization of the specific models studied in this work. We finally compare our results with recent cosmic microwave background data to find that our new power spectra are in good agreement with the data.

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

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

PubMed

Carmichael, Owen; Sakhanenko, Lyudmila

2015-05-15

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

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

PubMed Central

Carmichael, Owen; Sakhanenko, Lyudmila

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-02-01

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

Anisotropic mesoscale eddy transport in ocean general circulation models

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

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

PubMed

Bahn, M M

1999-07-01

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

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

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.

Octupolar tensors for liquid crystals

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed Central

Loui, Psyche; Schlaug, Gottfried

2009-01-01

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

Scalar field coupling to Einstein tensor in regular black hole spacetime

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wu, Chen

2018-02-01

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

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

PubMed

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

2016-11-01

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

Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

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

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity frommore » general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.« less

Neutron Star Models in Alternative Theories of Gravity

NASA Astrophysics Data System (ADS)

Manolidis, Dimitrios

We study the structure of neutron stars in a broad class of alternative theories of gravity. In particular, we focus on Scalar-Tensor theories and f(R) theories of gravity. We construct static and slowly rotating numerical star models for a set of equations of state, including a polytropic model and more realistic equations of state motivated by nuclear physics. Observable quantities such as masses, radii, etc are calculated for a set of parameters of the theories. Specifically for Scalar-Tensor theories, we also calculate the sensitivities of the mass and moment of inertia of the models to variations in the asymptotic value of the scalar field at infinity. These quantities enter post-Newtonian equations of motion and gravitational waveforms of two body systems that are used for gravitational-wave parameter estimation, in order to test these theories against observations. The construction of numerical models of neutron stars in f(R) theories of gravity has been difficult in the past. Using a new formalism by Jaime, Patino and Salgado we were able to construct models with high interior pressure, namely pc > rho c/3, both for constant density models and models with a polytropic equation of state. Thus, we have shown that earlier objections to f(R) theories on the basis of the inability to construct viable neutron star models are unfounded.

Effective gravitational couplings for cosmological perturbations in generalized Proca theories

NASA Astrophysics Data System (ADS)

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

2016-08-01

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

Unified Stress Tensor of the Hydration Water Layer

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Unified stress tensor of the hydration water layer.

PubMed

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

2013-12-13

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

Consistent scalar and tensor perturbation power spectra in single fluid matter bounce with dark energy era

NASA Astrophysics Data System (ADS)

Bacalhau, Anna Paula; Pinto-Neto, Nelson; Vitenti, Sandro Dias Pinto

2018-04-01

We investigate cosmological scenarios containing one canonical scalar field with an exponential potential in the context of bouncing models, in which the bounce happens due to quantum cosmological effects. The only possible bouncing solutions in this scenario (discarding an infinitely fine-tuned exception) must have one and only one dark energy phase, occurring either in the contracting era or in the expanding era. Hence, these bounce solutions are necessarily asymmetric. Naturally, the more convenient solution is the one in which the dark energy phase happens in the expanding era, in order to be a possible explanation for the current accelerated expansion indicated by cosmological observations. In this case, one has the picture of a Universe undergoing a classical dust contraction from very large scales, the initial repeller of the model, moving to a classical stiff-matter contraction near the singularity, which is avoided due to the quantum bounce. The Universe is then launched to a dark energy era, after passing through radiation- and dust-dominated phases, finally returning to the dust expanding phase, the final attractor of the model. We calculate the spectral indices and amplitudes of scalar and tensor perturbations numerically, considering the whole history of the model, including the bounce phase itself, without making any approximation nor using any matching condition on the perturbations. As the background model is necessarily dust dominated in the far past, the usual adiabatic vacuum initial conditions can be easily imposed in this era. Hence, this is a cosmological model in which the presence of dark energy behavior in the Universe does not turn the usual vacuum initial conditions prescription for cosmological perturbation in bouncing models problematic. Scalar and tensor perturbations end up being almost scale invariant, as expected. The background parameters can be adjusted, without fine-tunings, to yield the observed amplitude for scalar perturbations and also for the ratio between tensor and scalar amplitudes, r =T /S ≲0.1 . The amplification of scalar perturbations over tensor perturbations takes place only around the bounce, due to quantum effects, and it would not occur if General Relativity has remained valid throughout this phase. Hence, this is a bouncing model in which a single field induces not only an expanding background dark energy phase but also produces all observed features of cosmological perturbations of quantum mechanical origin at linear order.

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

NASA Astrophysics Data System (ADS)

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

2012-07-01

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

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

DTIC Science & Technology

1993-10-31

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

White matter correlates of cognitive domains in normal aging with diffusion tensor imaging.

PubMed

Sasson, Efrat; Doniger, Glen M; Pasternak, Ofer; Tarrasch, Ricardo; Assaf, Yaniv

2013-01-01

The ability to perform complex as well as simple cognitive tasks engages a network of brain regions that is mediated by the white matter fiber bundles connecting them. Different cognitive tasks employ distinctive white matter fiber bundles. The temporal lobe and its projections subserve a variety of key functions known to deteriorate during aging. In a cohort of 52 healthy subjects (ages 25-82 years), we performed voxel-wise regression analysis correlating performance in higher-order cognitive domains (executive function, information processing speed, and memory) with white matter integrity, as measured by diffusion tensor imaging (DTI) fiber tracking in the temporal lobe projections [uncinate fasciculus (UF), fornix, cingulum, inferior longitudinal fasciculus (ILF), and superior longitudinal fasciculus (SLF)]. The fiber tracts were spatially registered and statistical parametric maps were produced to spatially localize the significant correlations. Results showed that performance in the executive function domain is correlated with DTI parameters in the left SLF and right UF; performance in the information processing speed domain is correlated with fractional anisotropy (FA) in the left cingulum, left fornix, right and left ILF and SLF; and the memory domain shows significant correlations with DTI parameters in the right fornix, right cingulum, left ILF, left SLF and right UF. These findings suggest that DTI tractography enables anatomical definition of region of interest (ROI) for correlation of behavioral parameters with diffusion indices, and functionality can be correlated with white matter integrity.

New solutions of exotic charged black holes and their stability

NASA Astrophysics Data System (ADS)

Farhangkhah, N.

2016-01-01

We find a class of charged black hole solutions in third-order Lovelock Gravity. To obtain this class of solutions, we are not confined to the usual assumption of maximal symmetry on the horizon and will consider the solution whose boundary is Einstein space with supplementary conditions on its Weyl tensor. The Weyl tensor of such exotic horizons exposes two chargelike parameter to the solution. These parameters in addition with the electric charge, cause different features in comparison with the charged solution with constant-curvature horizon. For this class of asymptotically (A)dS solutions, the electric charge dominates the behavior of the metric as r goes to zero, and thus the central singularity is always timelike. We also compute the thermodynamic quantities for these solutions and will show that the first law of thermodynamics is satisfied. We also show that the extreme black holes with nonconstant-curvature horizons whose Ricci scalar are zero or a positive constant could exist depending on the value of the electric charge and chargelike parameters. Finally, we investigate the stability of the black holes by analyzing the behavior of free energy and heat capacity specially in the limits of small and large horizon radius. We will show that in contrast with charged solution with constant-curvature horizon, a phase transition occurs between very small and small black holes from a stable phase to an unstable one, while the large black holes show stability to both perturbative and nonperturbative fluctuations.

Application of multigrid methods to the solution of liquid crystal equations on a SIMD computer

NASA Technical Reports Server (NTRS)

Farrell, Paul A.; Ruttan, Arden; Zeller, Reinhardt R.

1993-01-01

We will describe a finite difference code for computing the equilibrium configurations of the order-parameter tensor field for nematic liquid crystals in rectangular regions by minimization of the Landau-de Gennes Free Energy functional. The implementation of the free energy functional described here includes magnetic fields, quadratic gradient terms, and scalar bulk terms through the fourth order. Boundary conditions include the effects of strong surface anchoring. The target architectures for our implementation are SIMD machines, with interconnection networks which can be configured as 2 or 3 dimensional grids, such as the Wavetracer DTC. We also discuss the relative efficiency of a number of iterative methods for the solution of the linear systems arising from this discretization on such architectures.

Atomistic determination of flexoelectric properties of crystalline dielectrics

NASA Astrophysics Data System (ADS)

Maranganti, R.; Sharma, P.

2009-08-01

Upon application of a uniform strain, internal sublattice shifts within the unit cell of a noncentrosymmetric dielectric crystal result in the appearance of a net dipole moment: a phenomenon well known as piezoelectricity. A macroscopic strain gradient on the other hand can induce polarization in dielectrics of any crystal structure, even those which possess a centrosymmetric lattice. This phenomenon, called flexoelectricity, has both bulk and surface contributions: the strength of the bulk contribution can be characterized by means of a material property tensor called the bulk flexoelectric tensor. Several recent studies suggest that strain-gradient induced polarization may be responsible for a variety of interesting and anomalous electromechanical phenomena in materials including electromechanical coupling effects in nonuniformly strained nanostructures, “dead layer” effects in nanocapacitor systems, and “giant” piezoelectricity in perovskite nanostructures among others. In this work, adopting a lattice dynamics based microscopic approach we provide estimates of the flexoelectric tensor for certain cubic crystalline ionic salts, perovskite dielectrics, III-V and II-VI semiconductors. We compare our estimates with experimental/theoretical values wherever available and also revisit the validity of an existing empirical scaling relationship for the magnitude of flexoelectric coefficients in terms of material parameters. It is interesting to note that two independent groups report values of flexoelectric properties for perovskite dielectrics that are orders of magnitude apart: Cross and co-workers from Penn State have carried out experimental studies on a variety of materials including barium titanate while Catalan and co-workers from Cambridge used theoretical ab initio techniques as well as experimental techniques to study paraelectric strontium titanate as well as ferroelectric barium titanate and lead titanate. We find that, in the case of perovskite dielectrics, our estimates agree to an order of magnitude with the experimental and theoretical estimates for strontium titanate. For barium titanate however, while our estimates agree to an order of magnitude with existing ab initio calculations, there exists a large discrepancy with experimental estimates. The possible reasons for the observed deviations are discussed.

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

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2015-04-01

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

An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs

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

Kolda, Tamara G.; Mayo, Jackson R.

2014-12-11

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

The Twist Tensor Nuclear Norm for Video Completion.

PubMed

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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.

Electronic structures and magnetic/optical properties of metal phthalocyanine complexes

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

Baba, Shintaro; Suzuki, Atsushi, E-mail: suzuki@mat.usp.ac.jp; Oku, Takeo

2016-02-01

Electronic structures and magnetic / optical properties of metal phthalocyanine complexes were studied by quantum calculations using density functional theory. Effects of central metal and expansion of π orbital on aromatic ring as conjugation system on the electronic structures, magnetic, optical properties and vibration modes of infrared and Raman spectra of metal phthalocyanines were investigated. Electron and charge density distribution and energy levels near frontier orbital and excited states were influenced by the deformed structures varied with central metal and charge. The magnetic parameters of chemical shifts in {sup 13}C-nuclear magnetic resonance ({sup 13}C-NMR), principle g-tensor, A-tensor, V-tensor of electricmore » field gradient and asymmetry parameters derived from the deformed structures with magnetic interaction of nuclear quadruple interaction based on electron and charge density distribution with a bias of charge near ligand under crystal field.« less

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

NASA Astrophysics Data System (ADS)

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

2012-11-01

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

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

PubMed Central

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

2013-01-01

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

Primordial perturbations from dilaton-induced gauge fields

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

Choi, Kiwoon; Choi, Ki-Young; Kim, Hyungjin

2015-10-01

We study the primordial scalar and tensor perturbations in inflation scenario involving a spectator dilaton field. In our setup, the rolling spectator dilaton causes a tachyonic instability of gauge fields, leading to a copious production of gauge fields in the superhorizon regime, which generates additional scalar and tensor perturbations through gravitational interactions. Our prime concern is the possibility to enhance the tensor-to-scalar ratio r relative to the standard result, while satisfying the observational constraints. To this end, we allow the dilaton field to be stabilized before the end of inflation, but after the CMB scales exit the horizon. We showmore » that for the inflaton slow roll parameter ε ∼> 10{sup −3}, the tensor-to-scalar ratio in our setup can be enhanced only by a factor of O(1) compared to the standard result. On the other hand, for smaller ε corresponding to a lower inflation energy scale, a much bigger enhancement can be achieved, so that our setup can give rise to an observably large r∼> 10{sup −2} even when ε|| 10{sup −3}. The tensor perturbation sourced by the spectator dilaton can have a strong scale dependence, and is generically red-tilted. We also discuss a specific model to realize our scenario, and identify the parameter region giving an observably large r for relatively low inflation energy scales.« less

R 2 inflation to probe non-perturbative quantum gravity

NASA Astrophysics Data System (ADS)

Koshelev, Alexey S.; Sravan Kumar, K.; Starobinsky, Alexei A.

2018-03-01

It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, R + R 2, or shortly R 2, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R 2 model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index ( n s ), a tensor-to-scalar ratio ( r) and a tensor tilt ( n t ). It appears that n s remains the same as in the local R 2 inflation in the leading slow-roll approximation, while r and n t get modified due to modification of the tensor power spectrum. This class of models allows for any value of r < 0.07 with a modified consistency relation which can be fixed by future observations of primordial B-modes of the CMB polarization. This makes the UV complete R 2 gravity a natural target for future CMB probes.

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

NASA Astrophysics Data System (ADS)

Stepanova, L. V.

2017-12-01

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

LiDAR point classification based on sparse representation

NASA Astrophysics Data System (ADS)

Li, Nan; Pfeifer, Norbert; Liu, Chun

2017-04-01

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

13C and (15)N chemical shift tensors in adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine.

PubMed

Stueber, Dirk; Grant, David M

2002-09-04

The (13)C and (15)N chemical shift tensor principal values for adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine are measured on natural abundance samples. Additionally, the (13)C and (15)N chemical shielding tensor principal values in these four nucleosides are calculated utilizing various theoretical approaches. Embedded ion method (EIM) calculations improve significantly the precision with which the experimental principal values are reproduced over calculations on the corresponding isolated molecules with proton-optimized geometries. The (13)C and (15)N chemical shift tensor orientations are reliably assigned in the molecular frames of the nucleosides based upon chemical shielding tensor calculations employing the EIM. The differences between principal values obtained in EIM calculations and in calculations on isolated molecules with proton positions optimized inside a point charge array are used to estimate the contributions to chemical shielding arising from intermolecular interactions. Moreover, the (13)C and (15)N chemical shift tensor orientations and principal values correlate with the molecular structure and the crystallographic environment for the nucleosides and agree with data obtained previously for related compounds. The effects of variations in certain EIM parameters on the accuracy of the shielding tensor calculations are investigated.

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.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Cosmological constraints on Brans-Dicke theory.

PubMed

Avilez, A; Skordis, C

2014-07-04

We report strong cosmological constraints on the Brans-Dicke (BD) theory of gravity using cosmic microwave background data from Planck. We consider two types of models. First, the initial condition of the scalar field is fixed to give the same effective gravitational strength Geff today as the one measured on Earth, GN. In this case, the BD parameter ω is constrained to ω>692 at the 99% confidence level, an order of magnitude improvement over previous constraints. In the second type, the initial condition for the scalar is a free parameter leading to a somewhat stronger constraint of ω>890, while Geff is constrained to 0.981

Parameter Estimation in Atmospheric Data Sets

NASA Technical Reports Server (NTRS)

Wenig, Mark; Colarco, Peter

2004-01-01

In this study the structure tensor technique is used to estimate dynamical parameters in atmospheric data sets. The structure tensor is a common tool for estimating motion in image sequences. This technique can be extended to estimate other dynamical parameters such as diffusion constants or exponential decay rates. A general mathematical framework was developed for the direct estimation of the physical parameters that govern the underlying processes from image sequences. This estimation technique can be adapted to the specific physical problem under investigation, so it can be used in a variety of applications in trace gas, aerosol, and cloud remote sensing. As a test scenario this technique will be applied to modeled dust data. In this case vertically integrated dust concentrations were used to derive wind information. Those results can be compared to the wind vector fields which served as input to the model. Based on this analysis, a method to compute atmospheric data parameter fields will be presented. .

Advanced Computational Techniques in Regional Wave Studies

DTIC Science & Technology

1990-01-03

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

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

NASA Technical Reports Server (NTRS)

Lee, Moon Joo

1990-01-01

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

Advanced Signal Processing & Classification: UXO Standardized Test Site Data

DTIC Science & Technology

2012-04-01

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

New Views on Dark Matter from Emergent Gravity

NASA Astrophysics Data System (ADS)

Sun, Sichun; Zhang, Yun-Long

2018-01-01

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

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.

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

Cosmology in beyond-generalized Proca theories

NASA Astrophysics Data System (ADS)

Nakamura, Shintaro; Kase, Ryotaro; Tsujikawa, Shinji

2017-05-01

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

Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: Implication for the 5 d transition metal oxides A OsO4 (A =K ,Rb, and Cs)

NASA Astrophysics Data System (ADS)

Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi

2018-01-01

We report our theoretical predictions on the linear magnetoelectric (ME) effects originating from odd-parity multipoles associated with spontaneous spin and orbital ordering on a diamond structure. We derive a two-orbital model for d electrons in eg orbitals by including the effective spin-orbit coupling which arises from the mixing between eg and t2 g orbitals. We show that the model acquires a net antisymmetric spin-orbit coupling once staggered spin and orbital orders occur spontaneously. The staggered orders are accompanied by odd-parity multipoles: magnetic monopole, quadrupoles, and toroidal dipoles. We classify the types of the odd-parity multipoles according to the symmetry of the spin and orbital orders. Furthermore, by computing the ME tensor using the linear response theory, we show that the staggered orders induce a variety of the linear ME responses. We elaborate all possible ME responses for each staggered order, which are useful to identify the order parameter and to detect the odd-parity multipoles by measuring the ME effects. We also elucidate the effect of lowering symmetry by a tetragonal distortion, which leads to richer ME responses. The implications of our results are discussed for the 5 d transition metal oxides, A OsO4 (A =K,Rb, and Cs) , in which the order parameters are not fully identified.

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

Sasakura, Naoki

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

Superconducting tensor gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

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

Brane f(R) gravity cosmologies

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

Balcerzak, Adam; DaPbrowski, Mariusz P.

2010-06-15

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

Gaugeon formalism for the second-rank antisymmetric tensor gauge fields

NASA Astrophysics Data System (ADS)

Aochi, Masataka; Endo, Ryusuke; Miura, Hikaru

2018-02-01

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

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1981-01-01

Research centered on basic topics in the modeling and feedback control of nonlinear dynamical systems is reported. Of special interest were the following topics: (1) the role of series descriptions, especially insofar as they relate to questions of scheduling, in the control of gas turbine engines; (2) the use of algebraic tensor theory as a technique for parameterizing such descriptions; (3) the relationship between tensor methodology and other parts of the nonlinear literature; (4) the improvement of interactive methods for parameter selection within a tensor viewpoint; and (5) study of feedback gain representation as a counterpart to these modeling and parameterization ideas.

Beyond generalized Proca theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

PubMed

Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J

2017-01-01

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D , observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄ . When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model.

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments*

PubMed Central

Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J.

2017-01-01

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model. PMID:28989561

Symmetric Topological Phases and Tensor Network States

NASA Astrophysics Data System (ADS)

Jiang, Shenghan

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

Nuclear magnetic and nuclear quadrupole resonance parameters of β-carboline derivatives calculated using density functional theory

NASA Astrophysics Data System (ADS)

Ahmadinejad, Neda; Tari, Mostafa Talebi

2017-04-01

A density functional theory (DFT) calculations using B3LYP/6-311++G( d,p) method were carried out to investigate the relative stability of the molecules of β-carboline derivatives such as harmaline, harmine, harmalol, harmane and norharmane. Calculated nuclear quadrupole resonance (NQR) parameters were used to determine the 14N nuclear quadrupole coupling constant χ, asymmetry parameter η and EFG tensor ( q zz ). For better understanding of the electronic structure of β-carboline derivatives, natural bond orbital (NBO) analysis, isotropic and anisotropic NMR chemical shieldings were calculated for 14N nuclei using GIAO method for the optimized structures. The NBO analysis shows that pyrrole ring nitrogen (N9) atom has greater tendency than pyridine ring nitrogen (N2) atom to participate in resonance interactions and aromaticity development in the all of these structures. The NMR and NQR parameters were studied in order to find the correlations between electronic structure and the structural stability of the studied molecules.

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

NASA Technical Reports Server (NTRS)

Peterson, D.

1979-01-01

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

Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions

NASA Astrophysics Data System (ADS)

Reinken, Henning; Klapp, Sabine H. L.; Bär, Markus; Heidenreich, Sebastian

2018-02-01

In this paper, we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic model (pushers or pullers), which include hydrodynamic interactions on both small length scales (polar alignment of neighboring swimmers) and large length scales, where the solvent flow interacts with the order parameter field. The flow field is determined via the Stokes equation supplemented by an ansatz for the stress tensor. In addition to hydrodynamic interactions, we allow for nematic pair interactions stemming from excluded-volume effects. The results here substantially extend and generalize earlier findings [S. Heidenreich et al., Phys. Rev. E 94, 020601 (2016), 10.1103/PhysRevE.94.020601], in which we derived a two-dimensional hydrodynamic theory. From the corresponding mean-field Fokker-Planck equation combined with a self-consistent closure scheme, we derive nonlinear field equations for the polar and the nematic order parameter, involving gradient terms of up to fourth order. We find that the effective microswimmer dynamics depends on the coupling between solvent flow and orientational order. For very weak coupling corresponding to a high viscosity of the suspension, the dynamics of mesoscale turbulence can be described by a simplified model containing only an effective microswimmer velocity.

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.

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

DOE PAGES

Lyakh, Dmitry I.

2015-01-05

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

Anisotropic Mesoscale Eddy Transport in Ocean General Circulation Models

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Evolution of axis ratios from phase space dynamics of triaxial collapse

NASA Astrophysics Data System (ADS)

Nadkarni-Ghosh, Sharvari; Arya, Bhaskar

2018-04-01

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

Near real-time estimation of the seismic source parameters in a compressed domain

NASA Astrophysics Data System (ADS)

Rodriguez, Ismael A. Vera

Seismic events can be characterized by its origin time, location and moment tensor. Fast estimations of these source parameters are important in areas of geophysics like earthquake seismology, and the monitoring of seismic activity produced by volcanoes, mining operations and hydraulic injections in geothermal and oil and gas reservoirs. Most available monitoring systems estimate the source parameters in a sequential procedure: first determining origin time and location (e.g., epicentre, hypocentre or centroid of the stress glut density), and then using this information to initialize the evaluation of the moment tensor. A more efficient estimation of the source parameters requires a concurrent evaluation of the three variables. The main objective of the present thesis is to address the simultaneous estimation of origin time, location and moment tensor of seismic events. The proposed method displays the benefits of being: 1) automatic, 2) continuous and, depending on the scale of application, 3) of providing results in real-time or near real-time. The inversion algorithm is based on theoretical results from sparse representation theory and compressive sensing. The feasibility of implementation is determined through the analysis of synthetic and real data examples. The numerical experiments focus on the microseismic monitoring of hydraulic fractures in oil and gas wells, however, an example using real earthquake data is also presented for validation. The thesis is complemented with a resolvability analysis of the moment tensor. The analysis targets common monitoring geometries employed in hydraulic fracturing in oil wells. Additionally, it is presented an application of sparse representation theory for the denoising of one-component and three-component microseismicity records, and an algorithm for improved automatic time-picking using non-linear inversion constraints.

Gravitational waves from quasinormal modes of a class of Lorentzian wormholes

NASA Astrophysics Data System (ADS)

Aneesh, S.; Bose, Sukanta; Kar, Sayan

2018-06-01

Quasinormal modes of a two-parameter family of Lorentzian wormhole spacetimes, which arise as solutions in a specific scalar-tensor theory associated with braneworld gravity, are obtained using standard numerical methods. Being solutions in a scalar-tensor theory, these wormholes can exist with matter satisfying the weak energy condition. If one posits that the end-state of stellar-mass binary black hole mergers, of the type observed in GW150914, can be these wormholes, then we show how their properties can be measured from their distinct signatures in the gravitational waves emitted by them as they settle down in the postmerger phase from an initially perturbed state. We propose that their scalar quasinormal modes correspond to the so-called breathing modes, which normally arise in gravitational wave solutions in scalar-tensor theories. We show how the frequency and damping time of these modes depend on the wormhole parameters, including its mass. We derive the mode solutions and use them to determine how one can measure those parameters when these wormholes are the endstate of binary black hole mergers. Specifically, we find that if a breathing mode is observed in LIGO-like detectors with design sensitivity, and has a maximum amplitude equal to that of the tensor mode that was observed of GW150914, then for a range of values of the wormhole parameters, we will be able to discern it from a black hole. If in future observations we are able to confirm the existence of such wormholes, we would, at one go, have some indirect evidence of a modified theory of gravity as well as extra spatial dimensions.

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.

Combining Diffusion Tensor Metrics and DSC Perfusion Imaging: Can It Improve the Diagnostic Accuracy in Differentiating Tumefactive Demyelination from High-Grade Glioma?

PubMed

Hiremath, S B; Muraleedharan, A; Kumar, S; Nagesh, C; Kesavadas, C; Abraham, M; Kapilamoorthy, T R; Thomas, B

2017-04-01

Tumefactive demyelinating lesions with atypical features can mimic high-grade gliomas on conventional imaging sequences. The aim of this study was to assess the role of conventional imaging, DTI metrics ( p:q tensor decomposition), and DSC perfusion in differentiating tumefactive demyelinating lesions and high-grade gliomas. Fourteen patients with tumefactive demyelinating lesions and 21 patients with high-grade gliomas underwent brain MR imaging with conventional, DTI, and DSC perfusion imaging. Imaging sequences were assessed for differentiation of the lesions. DTI metrics in the enhancing areas and perilesional hyperintensity were obtained by ROI analysis, and the relative CBV values in enhancing areas were calculated on DSC perfusion imaging. Conventional imaging sequences had a sensitivity of 80.9% and specificity of 57.1% in differentiating high-grade gliomas ( P = .049) from tumefactive demyelinating lesions. DTI metrics ( p : q tensor decomposition) and DSC perfusion demonstrated a statistically significant difference in the mean values of ADC, the isotropic component of the diffusion tensor, the anisotropic component of the diffusion tensor, the total magnitude of the diffusion tensor, and rCBV among enhancing portions in tumefactive demyelinating lesions and high-grade gliomas ( P ≤ .02), with the highest specificity for ADC, the anisotropic component of the diffusion tensor, and relative CBV (92.9%). Mean fractional anisotropy values showed no significant statistical difference between tumefactive demyelinating lesions and high-grade gliomas. The combination of DTI and DSC parameters improved the diagnostic accuracy (area under the curve = 0.901). Addition of a heterogeneous enhancement pattern to DTI and DSC parameters improved it further (area under the curve = 0.966). The sensitivity increased from 71.4% to 85.7% after the addition of the enhancement pattern. DTI and DSC perfusion add profoundly to conventional imaging in differentiating tumefactive demyelinating lesions and high-grade gliomas. The combination of DTI metrics and DSC perfusion markedly improved diagnostic accuracy. © 2017 by American Journal of Neuroradiology.

Moment tensor inversions using strong motion waveforms of Taiwan TSMIP data, 1993–2009

USGS Publications Warehouse

Chang, Kaiwen; Chi, Wu-Cheng; Gung, Yuancheng; Dreger, Douglas; Lee, William H K.; Chiu, Hung-Chie

2011-01-01

Earthquake source parameters are important for earthquake studies and seismic hazard assessment. Moment tensors are among the most important earthquake source parameters, and are now routinely derived using modern broadband seismic networks around the world. Similar waveform inversion techniques can also apply to other available data, including strong-motion seismograms. Strong-motion waveforms are also broadband, and recorded in many regions since the 1980s. Thus, strong-motion data can be used to augment moment tensor catalogs with a much larger dataset than that available from the high-gain, broadband seismic networks. However, a systematic comparison between the moment tensors derived from strong motion waveforms and high-gain broadband waveforms has not been available. In this study, we inverted the source mechanisms of Taiwan earthquakes between 1993 and 2009 by using the regional moment tensor inversion method using digital data from several hundred stations in the Taiwan Strong Motion Instrumentation Program (TSMIP). By testing different velocity models and filter passbands, we were able to successfully derive moment tensor solutions for 107 earthquakes of Mw >= 4.8. The solutions for large events agree well with other available moment tensor catalogs derived from local and global broadband networks. However, for Mw = 5.0 or smaller events, we consistently over estimated the moment magnitudes by 0.5 to 1.0. We have tested accelerograms, and velocity waveforms integrated from accelerograms for the inversions, and found the results are similar. In addition, we used part of the catalogs to study important seismogenic structures in the area near Meishan Taiwan which was the site of a very damaging earthquake a century ago, and found that the structures were dominated by events with complex right-lateral strike-slip faulting during the recent decade. The procedures developed from this study may be applied to other strong-motion datasets to compliment or fill gaps in catalogs from regional broadband networks and teleseismic networks.

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

Uncertainty estimations for moment tensor inversions: the issue of the 2012 May 20 Emilia earthquake

NASA Astrophysics Data System (ADS)

Scognamiglio, Laura; Magnoni, Federica; Tinti, Elisa; Casarotti, Emanuele

2016-08-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Geoscientists ordinarily use moment tensor catalogues, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their analysis. The 2012 May 20 Emilia main shock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. A variability of ˜0.5 units in magnitude leads to a controversial knowledge of the real size of the event and reveals how the solutions could be poorly constrained. In this work, we investigate the stability of the moment tensor solution for this earthquake, studying the effect of five different 1-D velocity models, the number and the distribution of the stations used in the inversion procedure. We also introduce a 3-D velocity model to account for structural heterogeneity. We finally estimate the uncertainties associated to the computed focal planes and the obtained Mw. We conclude that our reliable source solutions provide a moment magnitude that ranges from 5.87, 1-D model, to 5.96, 3-D model, reducing the variability of the literature to ˜0.1. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, requires coming out with disclosed assumptions and explicit processing workflows. Finally and, probably more important, when moment tensor solution is used for secondary analyses it has to be combined with the same main boundary conditions (e.g. wave-velocity propagation model) to avoid conflicting results.

Differentiating G-inflation from string gas cosmology using the effective field theory approach

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

He, Minxi; Liu, Junyu; Lu, Shiyun

A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two modelsmore » produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes n {sub s} and that of tensor ones n {sub t} , which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.« less

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

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

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

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

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

DOE PAGES

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

2018-05-17

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

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

Lyakh, Dmitry I.

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

Visualization of 3-D tensor fields

NASA Technical Reports Server (NTRS)

Hesselink, L.

1996-01-01

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

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

PubMed

Balbus, Steven A

2016-10-18

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

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.

Algebra of constraints for a string in curved background

NASA Astrophysics Data System (ADS)

Wess, Julius

1990-06-01

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

TWave: High-Order Analysis of Functional MRI

PubMed Central

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

2011-01-01

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

b matrix errors in echo planar diffusion tensor imaging

PubMed Central

Boujraf, Saïd; Luypaert, Robert; Osteaux, Michel

2001-01-01

Diffusion‐weighted magnetic resonance imaging (DW‐MRI) is a recognized tool for early detection of infarction of the human brain. DW‐MRI uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive parameters that reflect the translational mobility of the water molecules in tissues. If diffusion‐weighted images with different values of b matrix are acquired during one individual investigation, it is possible to calculate apparent diffusion coefficient maps that are the elements of the diffusion tensor. The diffusion tensor elements represent the apparent diffusion coefficient of protons of water molecules in each pixel in the corresponding sample. The relation between signal intensity in the diffusion‐weighted images, diffusion tensor, and b matrix is derived from the Bloch equations. Our goal is to establish the magnitude of the error made in the calculation of the elements of the diffusion tensor when the imaging gradients are ignored. PACS number(s): 87.57. –s, 87.61.–c PMID:11602015

Unified tensor model for space-frequency spreading-multiplexing (SFSM) MIMO communication systems

NASA Astrophysics Data System (ADS)

de Almeida, André LF; Favier, Gérard

2013-12-01

This paper presents a unified tensor model for space-frequency spreading-multiplexing (SFSM) multiple-input multiple-output (MIMO) wireless communication systems that combine space- and frequency-domain spreadings, followed by a space-frequency multiplexing. Spreading across space (transmit antennas) and frequency (subcarriers) adds resilience against deep channel fades and provides space and frequency diversities, while orthogonal space-frequency multiplexing enables multi-stream transmission. We adopt a tensor-based formulation for the proposed SFSM MIMO system that incorporates space, frequency, time, and code dimensions by means of the parallel factor model. The developed SFSM tensor model unifies the tensorial formulation of some existing multiple-access/multicarrier MIMO signaling schemes as special cases, while revealing interesting tradeoffs due to combined space, frequency, and time diversities which are of practical relevance for joint symbol-channel-code estimation. The performance of the proposed SFSM MIMO system using either a zero forcing receiver or a semi-blind tensor-based receiver is illustrated by means of computer simulation results under realistic channel and system parameters.

Steps to reconcile inflationary tensor and scalar spectra

NASA Astrophysics Data System (ADS)

Miranda, Vinícius; Hu, Wayne; Adshead, Peter

2014-05-01

The recent BICEP2 B-mode polarization determination of an inflationary tensor-scalar ratio r=0.2-0.05+0.07 is in tension with simple scale-free models of inflation due to a lack of a corresponding low multipole excess in the temperature power spectrum which places a limit of r0.002<0.11 (95% C.L.) on such models. Single-field inflationary models that reconcile these two observations, even those where the tilt runs substantially, introduce a scale into the scalar power spectrum. To cancel the tensor excess, and simultaneously remove the excess already present without tensors, ideally the model should introduce this scale as a relatively sharp transition in the tensor-scalar ratio around the horizon at recombination. We consider models which generate such a step in this quantity and find that they can improve the joint fit to the temperature and polarization data by up to 2ΔlnL≈-14 without changing cosmological parameters. Precision E-mode polarization measurements should be able to test this explanation.

Chemical (knight) shift distortions of quadrupole-split deuteron powder spectra in solids

NASA Astrophysics Data System (ADS)

Torgeson, D. R.; Schoenberger, R. J.; Barnes, R. G.

In strong magnetic fields (e.g., 8 Tesla) anisotropy of the shift tensor (chemical or Knight shift) can alter the spacings of the features of quadrupole-split deuteron spectra of polycrystalline samples. Analysis of powder spectra yields both correct quadrupole coupling and symmetry parameters and all the components of the shift tensor. Synthetic and experimental examples are given to illustrate such behavior.

Reducing tensor magnetic gradiometer data for unexploded ordnance detection

USGS Publications Warehouse

Bracken, Robert E.; Brown, Philip J.

2005-01-01

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

Anisoft - Advanced Treatment of Magnetic Anisotropy Data

NASA Astrophysics Data System (ADS)

Chadima, M.

2017-12-01

Since its first release, Anisoft (Anisotropy Data Browser) has gained a wide popularity in magnetic fabric community mainly due to its simple and user-friendly interface enabling very fast visualization of magnetic anisotropy tensors. Here, a major Anisoft update is presented transforming a rather simple data viewer into a platform offering an advanced treatment of magnetic anisotropy data. The updated software introduces new enlarged binary data format which stores both in-phase and out-of-phase (if measured) susceptibility tensors (AMS) or tensors of anisotropy of magnetic remanence (AMR) together with their respective confidence ellipses and values of F-tests for anisotropy. In addition to the tensor data, a whole array of specimen orientation angles, orientation of mesoscopic foliation(s) and lineation(s) is stored for each record enabling later editing or corrections. The input data may be directly acquired by AGICO Kappabridges (AMS) or Spinner Magnetometers (AMR); imported from various data formats, including the long-time standard binary ran-format; or manually created. Multiple anisotropy files can be combined together or split into several files by manual data selection or data filtering according to their values. Anisotropy tensors are conventionally visualized as principal directions (eigenvectors) in equal-area projection (stereoplot) together with a wide array of quantitative anisotropy parameters presented in histograms or in color-coded scatter plots showing mutual relationship of up to three quantitative parameters. When dealing with AMS in variable low fields, field-independent and field-dependent components of anisotropy can be determined (Hrouda 2009). For a group of specimens, individual principal directions can be contoured, or a mean tensor and respective confidence ellipses of its principal directions can be calculated using either the Hext-Jelinek (Jelinek 1978) statistics or the Bootstrap method (Constable & Tauxe 1990). Each graphical output can be exported into several vector or raster graphical formats or, via clipboard, pasted directly into a presentation or publication manuscript. Calculated principal directions or anisotropy parameters can be exported into various types of text files ready to be visualized or processed by any software of user's choice.

Primordial fluctuations from inflation in dRGT bimetric theory of gravity

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

Sakakihara, Yuki; Research Center for the Early Universe; Tanaka, Takahiro

2016-09-19

We investigate primordial gravitational waves and curvature perturbations in de Rham-Gabadadze-Tolley (dRGT) bimetric gravity. We evaluate the power-spectra in the leading order in slow roll. Taking into account the decay of massive graviton, we find that the action up to the second order reduces to the Einstein theory with a non-minimally coupled scalar field, which is simplified to a minimally coupled model by conformal transformation. We also find that the tensor to scalar ratio for large field inflation with power law potential is larger than the general relativity counterpart for any choice of parameters in dRGT bimetric gravity. In addition,more » we confirm that the usual consistency relation holds and we have a steeper spectrum for gravitational waves.« less

Search for a nematic phase in the quasi-two-dimensional antiferromagnet CuCrO2 by NMR in an electric field

NASA Astrophysics Data System (ADS)

Sakhratov, Yu. A.; Kweon, J. J.; Choi, E. S.; Zhou, H. D.; Svistov, L. E.; Reyes, A. P.

2018-03-01

The magnetic phase diagram of CuCrO2 was studied with an alternative method of simultaneous Cu NMR and electric polarization techniques with the primary goal of demonstrating that, regardless of cooling history of the sample, the magnetic phase with specific helmet-shaped NMR spectra associated with interplanar disorder possesses electric polarization. Our result unequivocally confirms the assumption of Sakhratov et al. [Phys. Rev. B 94, 094410 (2016), 10.1103/PhysRevB.94.094410] that the high-field low-temperature phase is in fact a three-dimensional (3D) polar phase characterized by a 3D magnetic order with tensor order parameter. In comparison with the results obtained in pulsed fields, a modified phase diagram is introduced defining the upper boundary of the first-order transition from the 3D spiral to the 3D polar phase.

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

DOE PAGES

Peng, Bo; Kowalski, Karol

2017-01-25

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

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

NASA Astrophysics Data System (ADS)

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

2012-05-01

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

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

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

Peng, Bo; Kowalski, Karol

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

Parameterized post-Newtonian cosmology

NASA Astrophysics Data System (ADS)

Sanghai, Viraj A. A.; Clifton, Timothy

2017-03-01

Einstein’s theory of gravity has been extensively tested on solar system scales, and for isolated astrophysical systems, using the perturbative framework known as the parameterized post-Newtonian (PPN) formalism. This framework is designed for use in the weak-field and slow-motion limit of gravity, and can be used to constrain a large class of metric theories of gravity with data collected from the aforementioned systems. Given the potential of future surveys to probe cosmological scales to high precision, it is a topic of much contemporary interest to construct a similar framework to link Einstein’s theory of gravity and its alternatives to observations on cosmological scales. Our approach to this problem is to adapt and extend the existing PPN formalism for use in cosmology. We derive a set of equations that use the same parameters to consistently model both weak fields and cosmology. This allows us to parameterize a large class of modified theories of gravity and dark energy models on cosmological scales, using just four functions of time. These four functions can be directly linked to the background expansion of the universe, first-order cosmological perturbations, and the weak-field limit of the theory. They also reduce to the standard PPN parameters on solar system scales. We illustrate how dark energy models and scalar-tensor and vector-tensor theories of gravity fit into this framework, which we refer to as ‘parameterized post-Newtonian cosmology’ (PPNC).

Bound on largest r ∼< 0.1 from sub-Planckian excursions of inflaton

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

Chatterjee, Arindam; Mazumdar, Anupam, E-mail: arindam@hri.res.in, E-mail: a.mazumdar@lancaster.ac.uk

2015-01-01

In this paper we will discuss the range of large tensor to scalar ratio, r, obtainable from a sub-Planckian excursion of a single, slow roll driven inflaton field. In order to obtain a large r for such a scenario one has to depart from a monotonic evolution of the slow roll parameters in such a way that one still satisfies all the current constraints of \\texttt(Planck), such as the scalar amplitude, the tilt in the scalar power spectrum, running and running of the tilt close to the pivot scale. Since the slow roll parameters evolve non-monotonically, we will also considermore » the evolution of the power spectrum on the smallest scales, i.e. at P{sub s}(k ∼ 10{sup 16} Mpc{sup −1})∼< 10{sup −2}, to make sure that the amplitude does not become too large. All these constraints tend to keep the tensor to scalar ratio, r ∼< 0.1. We scan three different kinds of potential for supersymmetric flat directions and obtain the benchmark points which satisfy all the constraints. We also show that it is possible to go beyond r ∼> 0.1 provided we relax the upper bound on the power spectrum on the smallest scales.« less

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

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

Lu, Qingda; Gao, Xiaoyang; Krishnamoorthy, Sriram

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

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

PubMed

Memisevic, Roland; Hinton, Geoffrey E

2010-06-01

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

Value of Formalin Fixation for the Prolonged Preservation of Rodent Myocardial Microanatomical Organization: Evidence by MR Diffusion Tensor Imaging.

PubMed

Giannakidis, Archontis; Gullberg, Grant T; Pennell, Dudley J; Firmin, David N

2016-07-01

Previous ex vivo diffusion tensor imaging (DTI) studies on formalin-fixed myocardial tissue assumed that, after some initial changes in the first 48 hr since the start of fixation, DTI parameters remain stable over time. Prolonged preservation of cardiac tissue in formalin prior to imaging has been seen many times in the DTI literature as it is considered orderly. Our objective is to define the effects of the prolonged cardiac tissue exposure to formalin on tissue microanatomical organization, as this is assessed by DTI parameters. DTI experiments were conducted on eight excised rodent hearts that were fixed by immersion in formalin. The samples were randomly divided into two equinumerous groups corresponding to shorter (∼2 weeks) and more prolonged (∼6-8 weeks) durations of tissue exposure to formalin prior to imaging. We found that when the duration of cardiac tissue exposure to formalin before imaging increased, water diffusion became less restricted, helix angle (HA) histograms flattened out and exhibited heavier tails (even though the classic HA transmural variation was preserved), and a significant loss of inter-voxel primary diffusion orientation integrity was introduced. The prolonged preservation of cardiac tissue in formalin profoundly affected its microstructural organization, as this was assessed by DTI parameters. The accurate interpretation of diffusivity profiles necessitates awareness of the pitfalls of prolonged cardiac tissue exposure duration to formalin. The acquired knowledge works to the advantage of a proper experimental design of DTI studies of fixed hearts. Anat Rec, 299:878-887, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

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

PubMed

Sakstein, Jeremy

2015-11-13

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

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

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

Zhu, Tao; Wang, Anzhong; Wu, Qiang

2015-10-01

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

Crossing Fibers Detection with an Analytical High Order Tensor Decomposition

PubMed Central

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

2014-01-01

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

Tensor hypercontraction. II. Least-squares renormalization

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

Tensor hypercontraction. II. Least-squares renormalization.

PubMed

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

2012-12-14

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

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

NASA Astrophysics Data System (ADS)

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

2013-06-01

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

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

PubMed

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

2013-06-26

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

Clustering fossils in solid inflation

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

Akhshik, Mohammad, E-mail: m.akhshik@ipm.ir

In solid inflation the single field non-Gaussianity consistency condition is violated. As a result, the long tenor perturbation induces observable clustering fossils in the form of quadrupole anisotropy in large scale structure power spectrum. In this work we revisit the bispectrum analysis for the scalar-scalar-scalar and tensor-scalar-scalar bispectrum for the general parameter space of solid. We consider the parameter space of the model in which the level of non-Gaussianity generated is consistent with the Planck constraints. Specializing to this allowed range of model parameter we calculate the quadrupole anisotropy induced from the long tensor perturbations on the power spectrum ofmore » the scalar perturbations. We argue that the imprints of clustering fossil from primordial gravitational waves on large scale structures can be detected from the future galaxy surveys.« less

Generalized Liquid Crystals: Giant Fluctuations and the Vestigial Chiral Order of I , O , and T Matter

NASA Astrophysics Data System (ADS)

Liu, Ke; Nissinen, Jaakko; Slager, Robert-Jan; Wu, Kai; Zaanen, Jan

2016-10-01

The physics of nematic liquid crystals has been the subject of intensive research since the late 19th century. However, the focus of this pursuit has been centered around uniaxial and biaxial nematics associated with constituents bearing a D∞ h or D2 h symmetry, respectively. In view of general symmetries, however, these are singularly special since nematic order can in principle involve any point-group symmetry. Given the progress in tailoring nanoparticles with particular shapes and interactions, this vast family of "generalized nematics" might become accessible in the laboratory. Little is known because the order parameter theories associated with the highly symmetric point groups are remarkably complicated, involving tensor order parameters of high rank. Here, we show that the generic features of the statistical physics of such systems can be studied in a highly flexible and efficient fashion using a mathematical tool borrowed from high-energy physics: discrete non-Abelian gauge theory. Explicitly, we construct a family of lattice gauge models encapsulating nematic ordering of general three-dimensional point-group symmetries. We find that the most symmetrical generalized nematics are subjected to thermal fluctuations of unprecedented severity. As a result, novel forms of fluctuation phenomena become possible. In particular, we demonstrate that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point-group symmetry chiral building blocks, such as I , O , and T symmetric matter.

Analytical performance bounds for multi-tensor diffusion-MRI.

PubMed

Ahmed Sid, Farid; Abed-Meraim, Karim; Harba, Rachid; Oulebsir-Boumghar, Fatima

2017-02-01

To examine the effects of MR acquisition parameters on brain white matter fiber orientation estimation and parameter of clinical interest in crossing fiber areas based on the Multi-Tensor Model (MTM). We compute the Cramér-Rao Bound (CRB) for the MTM and the parameter of clinical interest such as the Fractional Anisotropy (FA) and the dominant fiber orientations, assuming that the diffusion MRI data are recorded by a multi-coil, multi-shell acquisition system. Considering the sum-of-squares method for the reconstructed magnitude image, we introduce an approximate closed-form formula for Fisher Information Matrix that has the simplicity and easy interpretation advantages. In addition, we propose to generalize the FA and the mean diffusivity to the multi-tensor model. We show the application of the CRB to reduce the scan time while preserving a good estimation precision. We provide results showing how the increase of the number of acquisition coils compensates the decrease of the number of diffusion gradient directions. We analyze the impact of the b-value and the Signal-to-Noise Ratio (SNR). The analysis shows that the estimation error variance decreases with a quadratic rate with the SNR, and that the optimum b-values are not unique but depend on the target parameter, the context, and eventually the target cost function. In this study we highlight the importance of choosing the appropriate acquisition parameters especially when dealing with crossing fiber areas. We also provide a methodology for the optimal tuning of these parameters using the CRB. Copyright © 2016 Elsevier Inc. All rights reserved.

Performance of tensor decomposition-based modal identification under nonstationary vibration

NASA Astrophysics Data System (ADS)

Friesen, P.; Sadhu, A.

2017-03-01

Health monitoring of civil engineering structures is of paramount importance when they are subjected to natural hazards or extreme climatic events like earthquake, strong wind gusts or man-made excitations. Most of the traditional modal identification methods are reliant on stationarity assumption of the vibration response and posed difficulty while analyzing nonstationary vibration (e.g. earthquake or human-induced vibration). Recently tensor decomposition based methods are emerged as powerful and yet generic blind (i.e. without requiring a knowledge of input characteristics) signal decomposition tool for structural modal identification. In this paper, a tensor decomposition based system identification method is further explored to estimate modal parameters using nonstationary vibration generated due to either earthquake or pedestrian induced excitation in a structure. The effects of lag parameters and sensor densities on tensor decomposition are studied with respect to the extent of nonstationarity of the responses characterized by the stationary duration and peak ground acceleration of the earthquake. A suite of more than 1400 earthquakes is used to investigate the performance of the proposed method under a wide variety of ground motions utilizing both complete and partial measurements of a high-rise building model. Apart from the earthquake, human-induced nonstationary vibration of a real-life pedestrian bridge is also used to verify the accuracy of the proposed method.

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array

PubMed Central

Gao, Yu-Fei; Gui, Guan; Xie, Wei; Zou, Yan-Bin; Yang, Yue; Wan, Qun

2017-01-01

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank-(L1,L2,·) BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method. PMID:28448431

Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.

NASA Astrophysics Data System (ADS)

Pascal, C.; Jaques Ribeiro, L. M.

2017-12-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal 3D exposures of mineralised quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To further constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of 300 MPa and formation depths of 10 km. As a second step, we measured 600 subhorizontal quartz veins in all the levels of the mine. The inversion of the attitudes of the veins allowed for reconstructing the orientations of the principal axes of stress, the unscaled Mohr circle and the relative pore pressure. After merging these results with the previously obtained absolute pore pressure we reconstructed the six parameters of the paleostress tensor.

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array.

PubMed

Gao, Yu-Fei; Gui, Guan; Xie, Wei; Zou, Yan-Bin; Yang, Yue; Wan, Qun

2017-04-27

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank- ( L 1 , L 2 , · ) BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method.

Tensorial analysis of Eshelby stresses in 3D supercooled liquids

NASA Astrophysics Data System (ADS)

Lemaître, Anaël

2015-10-01

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

Generalization of Einstein's gravitational field equations

NASA Astrophysics Data System (ADS)

Moulin, Frédéric

2017-12-01

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

Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization.

PubMed

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

2016-03-01

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

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

Liakh, Dmitry I

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

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

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

Peng, Bo; Kowalski, Karol

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

Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from Deuterium

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

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

1999-01-01

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

hi-class: Horndeski in the Cosmic Linear Anisotropy Solving System

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

Zumalacárregui, Miguel; Bellini, Emilio; Sawicki, Ignacy

We present the public version of hi-class (www.hiclass-code.net), an extension of the Boltzmann code CLASS to a broad ensemble of modifications to general relativity. In particular, hi-class can calculate predictions for models based on Horndeski's theory, which is the most general scalar-tensor theory described by second-order equations of motion and encompasses any perfect-fluid dark energy, quintessence, Brans-Dicke, f ( R ) and covariant Galileon models. hi-class has been thoroughly tested and can be readily used to understand the impact of alternative theories of gravity on linear structure formation as well as for cosmological parameter extraction.

Consistency relation and non-Gaussianity in a Galileon inflation

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

Asadi, Kosar; Nozari, Kourosh, E-mail: k.asadi@stu.umz.ac.ir, E-mail: knozari@umz.ac.ir

2016-12-01

We study a particular Galileon inflation in the light of Planck2015 observational data in order to constraint the model parameter space. We study the spectrum of the primordial modes of the density perturbations by expanding the action up to the second order in perturbations. Then we pursue by expanding the action up to the third order and find the three point correlation functions to find the amplitude of the non-Gaussianity of the primordial perturbations in this setup. We study the amplitude of the non-Gaussianity both in equilateral and orthogonal configurations and test the model with recent observational data. Our analysismore » shows that for some ranges of the non-minimal coupling parameter, the model is consistent with observation and it is also possible to have large non-Gaussianity which would be observable by future improvements in experiments. Moreover, we obtain the tilt of the tensor power spectrum and test the standard inflationary consistency relation ( r = −8 n {sub T} ) against the latest bounds from the Planck2015 dataset. We find a slight deviation from the standard consistency relation in this setup. Nevertheless, such a deviation seems not to be sufficiently remarkable to be detected confidently.« less

Extracting Effective Higgs Couplings in the Golden Channel

DOE PAGES

Chen, Yi; Vega-Morales, Roberto

2014-04-08

Kinematic distributions in Higgs decays to four charged leptons, the so called ‘golden channel, are a powerful probe of the tensor structure of its couplings to neutral electroweak gauge bosons. In this study we construct the first part of a comprehensive analysis framework designed to maximize the information contained in this channel in order to perform direct extraction of the various possible Higgs couplings. We first complete an earlier analytic calculation of the leading order fully differential cross sections for the golden channel signal and background to include the 4e and 4μ final states with interference between identical final states.more » We also examine the relative fractions of the different possible combinations of scalar-tensor couplings by integrating the fully differential cross section over all kinematic variables as well as show various doubly differential spectra for both the signal and background. From these analytic expressions we then construct a ‘generator level’ analysis framework based on the maximum likelihood method. Then, we demonstrate the ability of our framework to perform multi-parameter extractions of all the possible effective couplings of a spin-0 scalar to pairs of neutral electroweak gauge bosons including any correlations. Furthermore, this framework provides a powerful method for study of these couplings and can be readily adapted to include the relevant detector and systematic effects which we demonstrate in an accompanying study to follow.« less

Symmetry breaking in tensor models

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2015-11-01

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

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

PubMed

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

2018-02-28

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

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

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

2016-02-01

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

Lithospheric Stress Tensor from Gravity and Lithospheric Structure Models

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi; Tenzer, Robert

2017-07-01

In this study we investigate the lithospheric stresses computed from the gravity and lithospheric structure models. The functional relation between the lithospheric stress tensor and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of stresses inside the lithosphere, while assuming the horizontal shear stress components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the stress spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear stress tensor components globally at the Moho interface. The results reveal that most of the lithospheric stresses are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest stresses within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced stresses (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading stresses along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated stress spectrum (between the degrees from 13 to 180).

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.

Bridging scales of crustal stress patterns using the new World Stress Map

NASA Astrophysics Data System (ADS)

Heidbach, O.; Rajabi, M.; Cui, X.; Fuchs, K. W.; Mueller, B.; Reinecker, J.; Reiter, K.; Tingay, M. R. P.; Wenzel, F.; Xie, F.; Ziegler, M.; Zoback, M. D.; Zoback, M. L.

2017-12-01

Knowledge of the contemporary crustal stress field is a key parameter for the understanding of geodynamic processes such as global plate tectonics and the earthquake cycle. It is also an essential parameter for our sustainable and safe usage of Earth's resources, which is a major challenge for energy security in the 21st century. Since 1986, the World Stress Map (WSM) project has systematically compiled present-day stress information and provides a unique public domain global database. It is a long-term project based on an international network of partners from academia and industry. All data are public and available on the project website at world-stress-map.org. For the 30th anniversary of the project a new database has been compiled, containing double the amount of data records (n=42,870) including new data records from almost 4,000 deep boreholes. The new compilation focused on areas with previously sparse data coverage in order to resolve the stress pattern on different spatial scales. The significantly higher data density can now be used to resolve stress pattern heterogeneities on regional and local scales, as well as with depth in some regions. We present three results derived from the new WSM compilation: 1.) The global comparison between absolute plate motion and the mean of the orientation of maximum horizontal stress SHmax on a regular grid shows that there is still a correlation for the North and South America plate, but deviations from this general trend are now also clearly resolved. 2.) The variability of the crustal stress pattern changes when zooming in from plate-wide scale down to basin scale at 100 km. We show examples for Eastern Australia, Oklahoma and Central Europe. This regional and local variability of the stress pattern can be used as a proxy to identify and quantify regional and local stress sources by means of geomechanical-numerical models of the 3D stress tensor. 3.) Finally we present briefly the general concept of a multi-stage 3D geomechanical-numerical model workflow based on the WSM data to describe the in situ stress tensor. 3D Geomechanical-numerical modelling of the in situ stress state is essential to derive a continuous description of the stress tensor e.g. in order to estimate the distance to a critical stress state.

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

PubMed

Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

2015-09-01

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

Eigenvector of gravity gradient tensor for estimating fault dips considering fault type

NASA Astrophysics Data System (ADS)

Kusumoto, Shigekazu

2017-12-01

The dips of boundaries in faults and caldera walls play an important role in understanding their formation mechanisms. The fault dip is a particularly important parameter in numerical simulations for hazard map creation as the fault dip affects estimations of the area of disaster occurrence. In this study, I introduce a technique for estimating the fault dip using the eigenvector of the observed or calculated gravity gradient tensor on a profile and investigating its properties through numerical simulations. From numerical simulations, it was found that the maximum eigenvector of the tensor points to the high-density causative body, and the dip of the maximum eigenvector closely follows the dip of the normal fault. It was also found that the minimum eigenvector of the tensor points to the low-density causative body and that the dip of the minimum eigenvector closely follows the dip of the reverse fault. It was shown that the eigenvector of the gravity gradient tensor for estimating fault dips is determined by fault type. As an application of this technique, I estimated the dip of the Kurehayama Fault located in Toyama, Japan, and obtained a result that corresponded to conventional fault dip estimations by geology and geomorphology. Because the gravity gradient tensor is required for this analysis, I present a technique that estimates the gravity gradient tensor from the gravity anomaly on a profile.

Attractor cosmology from nonminimally coupled gravity

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

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

Hirata, So

2003-11-20

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

Nonlinear Viscoelastic Analysis of Orthotropic Beams Using a General Third-Order Theory

DTIC Science & Technology

2012-06-20

Kirchhoff stress tensor, denoted by r and reduced strain tensor E e is given by rxx rzz rxz 8><>: 9>=>;¼ Q11ð0Þ Q13ð0Þ 0 Q13ð0Þ Q33ð0Þ 0 0 0 Q55ð0Þ...0.5 1 −0.5 0 0.5 1 (a) (b) Fig. 1. Graphs of (a) equi-spaced and (b) spectral lagrange interpolation functions for polynomial order of p = 11. 3762 V

Embedded Systems and TensorFlow Frameworks as Assistive Technology Solutions.

PubMed

Mulfari, Davide; Palla, Alessandro; Fanucci, Luca

2017-01-01

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

Magnetism of the 35 K superconductor CsEuFe4As4

NASA Astrophysics Data System (ADS)

Albedah, Mohammed A.; Nejadsattari, Farshad; Stadnik, Zbigniew M.; Liu, Yi; Cao, Guang-Han

2018-04-01

The results of ab initio hyperfine-interaction parameters calculations, and of x-ray diffraction and 57Fe and 151Eu Mössbauer spectroscopy study of the new 35 K superconductor CsEuFe4As4 are reported. The superconductor crystallizes in the tetragonal space group P4/mmm with the lattice parameters a = 3.8956(1) Å and c = 13.6628(5) Å. It is demonstrated unequivocally that there is no magnetic order of the Fe magnetic moments down to 2.1 K and that the ferromagnetic order is associated with the Eu magnetic moments. The Curie temperature TC = 15.97(8) K determined from the temperature dependence of the hyperfine magnetic field at 151Eu nuclei is shown to be compatible with the temperature dependence of the transferred hyperfine magnetic field at 57Fe nuclei that is induced by the ferromagnetically ordered Eu sublattice. The Eu magnetic moments are shown to be perpendicular to the crystallographic c-axis. The temperature dependence of the principal component of the electric field gradient tensor, both at Fe and Eu sites, is well described by a T 3/2 power-law relation. Good agreement between the calculated and measured hyperfine-interaction parameters is observed. The Debye temperature of CsEuFe4As4 is found to be 295(3) K.

Mössbauer spectroscopy measurements on the 35.5 K superconductor Rb1 -δEuFe4As4

NASA Astrophysics Data System (ADS)

Albedah, Mohammed A.; Nejadsattari, Farshad; Stadnik, Zbigniew M.; Liu, Yi; Cao, Guang-Han

2018-04-01

The results of x-ray diffraction and 57Fe and 151Eu Mössbauer spectroscopy measurements, supplemented with ab initio hyperfine-interaction parameter calculations, on the new 35.5 K superconductor Rb1 -δEuFe4As4 are presented. The superconductor crystallizes in the tetragonal space group P 4 /m m m with the lattice parameters a =3.8849 (1 ) Å and c =13.3370 (3 ) Å. It is shown that there is no magnetic order of the Fe magnetic moments down to 2.1 K and that the ferromagnetic order is associated solely with the Eu magnetic moments. The Curie temperature TC=16.54 (8 ) K is determined from the temperature dependence of both the hyperfine magnetic field at 151Eu nuclei and the transferred hyperfine magnetic field at 57Fe nuclei that is induced by the ferromagnetically ordered Eu sublattice. The Eu magnetic moments are demonstrated to be perpendicular to the crystallographic c axis. The temperature dependence of the principal component of the electric field gradient tensor, at both Fe and Eu sites, is well described by a T3 /2 power-law relation. Good agreement between the calculated and measured hyperfine-interaction parameters is observed. The Debye temperature of Rb1 -δEuFe4As4 is found to be 391(8) K.

Scalar-tensor extension of the ΛCDM model

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

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

2016-11-01

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

Basic concepts of MR imaging, diffusion MR imaging, and diffusion tensor imaging.

PubMed

de Figueiredo, Eduardo H M S G; Borgonovi, Arthur F N G; Doring, Thomas M

2011-02-01

MR image contrast is based on intrinsic tissue properties and specific pulse sequences and parameter adjustments. A growing number of MRI imaging applications are based on diffusion properties of water. To better understand MRI diffusion-weighted imaging, a brief overview of MR physics is presented in this article followed by physics of the evolving techniques of diffusion MR imaging and diffusion tensor imaging. Copyright © 2011. Published by Elsevier Inc.

Subgraph augmented non-negative tensor factorization (SANTF) for modeling clinical narrative text

PubMed Central

Xin, Yu; Hochberg, Ephraim; Joshi, Rohit; Uzuner, Ozlem; Szolovits, Peter

2015-01-01

Objective Extracting medical knowledge from electronic medical records requires automated approaches to combat scalability limitations and selection biases. However, existing machine learning approaches are often regarded by clinicians as black boxes. Moreover, training data for these automated approaches at often sparsely annotated at best. The authors target unsupervised learning for modeling clinical narrative text, aiming at improving both accuracy and interpretability. Methods The authors introduce a novel framework named subgraph augmented non-negative tensor factorization (SANTF). In addition to relying on atomic features (e.g., words in clinical narrative text), SANTF automatically mines higher-order features (e.g., relations of lymphoid cells expressing antigens) from clinical narrative text by converting sentences into a graph representation and identifying important subgraphs. The authors compose a tensor using patients, higher-order features, and atomic features as its respective modes. We then apply non-negative tensor factorization to cluster patients, and simultaneously identify latent groups of higher-order features that link to patient clusters, as in clinical guidelines where a panel of immunophenotypic features and laboratory results are used to specify diagnostic criteria. Results and Conclusion SANTF demonstrated over 10% improvement in averaged F-measure on patient clustering compared to widely used non-negative matrix factorization (NMF) and k-means clustering methods. Multiple baselines were established by modeling patient data using patient-by-features matrices with different feature configurations and then performing NMF or k-means to cluster patients. Feature analysis identified latent groups of higher-order features that lead to medical insights. We also found that the latent groups of atomic features help to better correlate the latent groups of higher-order features. PMID:25862765

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

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

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

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

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

Constant-roll tachyon inflation and observational constraints

NASA Astrophysics Data System (ADS)

Gao, Qing; Gong, Yungui; Fei, Qin

2018-05-01

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

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

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

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

Vector and tensor contributions to the curvature perturbation at second order

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

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

2016-02-01

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

Anisotropic rheology of a polycrystalline aggregate and convection in planetary mantles

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

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

PubMed

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

2018-03-09

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

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

PubMed Central

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Brandenburg, John

2012-10-01

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

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.

Higgs-portal assisted Higgs inflation with a sizeable tensor-to-scalar ratio

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

Kim, Jinsu; Ko, Pyungwon; Park, Wan-Il, E-mail: kimjinsu@kias.re.kr, E-mail: pko@kias.re.kr, E-mail: Wanil.Park@uv.es

We show that the Higgs portal interactions involving extra dark Higgs field can save generically the original Higgs inflation of the standard model (SM) from the problem of a deep non-SM vacuum in the SM Higgs potential. Specifically, we show that such interactions disconnect the top quark pole mass from inflationary observables and allow multi-dimensional parameter space to save the Higgs inflation, thanks to the additional parameters (the dark Higgs boson mass m {sub φ}, the mixing angle α between the SM Higgs H and dark Higgs Φ, and the mixed quartic coupling) affecting RG-running of the Higgs quartic coupling.more » The effect of Higgs portal interactions may lead to a larger tensor-to-scalar ratio, 0.08 ∼< r ∼< 0.1, by adjusting relevant parameters in wide ranges of α and m {sub φ}, some region of which can be probed at future colliders. Performing a numerical analysis we find an allowed region of parameters, matching the latest Planck data.« less

Inversion of calcite twin data for paleostress orientations and magnitudes: A new technique tested and calibrated on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Schueller, Sylvie; Daniel, Jean-Marc

2018-01-01

The inversion of calcite twin data is a powerful tool to reconstruct paleostresses sustained by carbonate rocks during their geological history. Following Etchecopar's (1984) pioneering work, this study presents a new technique for the inversion of calcite twin data that reconstructs the 5 parameters of the deviatoric stress tensors from both monophase and polyphase twin datasets. The uncertainties in the parameters of the stress tensors reconstructed by this new technique are evaluated on numerically-generated datasets. The technique not only reliably defines the 5 parameters of the deviatoric stress tensor, but also reliably separates very close superimposed stress tensors (30° of difference in maximum principal stress orientation or switch between σ3 and σ2 axes). The technique is further shown to be robust to sampling bias and to slight variability in the critical resolved shear stress. Due to our still incomplete knowledge of the evolution of the critical resolved shear stress with grain size, our results show that it is recommended to analyze twin data subsets of homogeneous grain size to minimize possible errors, mainly those concerning differential stress values. The methodological uncertainty in principal stress orientations is about ± 10°; it is about ± 0.1 for the stress ratio. For differential stresses, the uncertainty is lower than ± 30%. Applying the technique to vein samples within Mesozoic limestones from the Monte Nero anticline (northern Apennines, Italy) demonstrates its ability to reliably detect and separate tectonically significant paleostress orientations and magnitudes from naturally deformed polyphase samples, hence to fingerprint the regional paleostresses of interest in tectonic studies.

Improved object optimal synthetic description, modeling, learning, and discrimination by GEOGINE computational kernel

NASA Astrophysics Data System (ADS)

Fiorini, Rodolfo A.; Dacquino, Gianfranco

2005-03-01

GEOGINE (GEOmetrical enGINE), a state-of-the-art OMG (Ontological Model Generator) based on n-D Tensor Invariants for n-Dimensional shape/texture optimal synthetic representation, description and learning, was presented in previous conferences elsewhere recently. Improved computational algorithms based on the computational invariant theory of finite groups in Euclidean space and a demo application is presented. Progressive model automatic generation is discussed. GEOGINE can be used as an efficient computational kernel for fast reliable application development and delivery in advanced biomedical engineering, biometric, intelligent computing, target recognition, content image retrieval, data mining technological areas mainly. Ontology can be regarded as a logical theory accounting for the intended meaning of a formal dictionary, i.e., its ontological commitment to a particular conceptualization of the world object. According to this approach, "n-D Tensor Calculus" can be considered a "Formal Language" to reliably compute optimized "n-Dimensional Tensor Invariants" as specific object "invariant parameter and attribute words" for automated n-Dimensional shape/texture optimal synthetic object description by incremental model generation. The class of those "invariant parameter and attribute words" can be thought as a specific "Formal Vocabulary" learned from a "Generalized Formal Dictionary" of the "Computational Tensor Invariants" language. Even object chromatic attributes can be effectively and reliably computed from object geometric parameters into robust colour shape invariant characteristics. As a matter of fact, any highly sophisticated application needing effective, robust object geometric/colour invariant attribute capture and parameterization features, for reliable automated object learning and discrimination can deeply benefit from GEOGINE progressive automated model generation computational kernel performance. Main operational advantages over previous, similar approaches are: 1) Progressive Automated Invariant Model Generation, 2) Invariant Minimal Complete Description Set for computational efficiency, 3) Arbitrary Model Precision for robust object description and identification.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

A computational NMR study on zigzag aluminum nitride nanotubes

NASA Astrophysics Data System (ADS)

Bodaghi, Ali; Mirzaei, Mahmoud; Seif, Ahmad; Giahi, Masoud

2008-12-01

A computational nuclear magnetic resonance (NMR) study is performed to investigate the electronic structure properties of the single-walled zigzag aluminum nitride nanotubes (AlNNTs). The chemical-shielding (CS) tensors are calculated at the sites of Al-27 and N-15 nuclei in three structural forms of AlNNT including H-saturated, Al-terminated, and N-terminated ones. The structural forms are firstly optimized and then the calculated CS tensors in the optimized structures are converted to chemical-shielding isotropic (CSI) and chemical-shielding anisotropic (CSA) parameters. The calculated parameters reveal that various Al-27 and N-15 nuclei are divided into some layers with equivalent electrostatic properties; furthermore, Al and N can act as Lewis base and acid, respectively. In the Al-terminated and N-terminated forms of AlNNT, in which one mouth of the nanotube is terminated by aluminum and nitrogen nuclei, respectively, just the CS tensors of the nearest nuclei to the mouth of the nanotube are significantly changed due to removal of saturating hydrogen atoms. Density functional theory (DFT) calculations are performed using GAUSSIAN 98 package of program.

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

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

Wu Shuangqing

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

Application of Bayesian model averaging to measurements of the primordial power spectrum

NASA Astrophysics Data System (ADS)

Parkinson, David; Liddle, Andrew R.

2010-11-01

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG, and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940

Generalized liquid crystals: Giant fluctuations and the vestigial chiral order of I , O , and T matter

DOE PAGES

Liu, Ke; Nissinen, Jaakko; Slager, Robert -Jan; ...

2016-10-31

Here, the physics of nematic liquid crystals has been the subject of intensive research since the late 19th century. However, the focus of this pursuit has been centered around uniaxial and biaxial nematics associated with constituents bearing a D ∞h or D 2h symmetry, respectively. In view of general symmetries, however, these are singularly special since nematic order can in principle involve any point-group symmetry. Given the progress in tailoring nanoparticles with particular shapes and interactions, this vast family of “generalized nematics” might become accessible in the laboratory. Little is known because the order parameter theories associated with the highlymore » symmetric point groups are remarkably complicated, involving tensor order parameters of high rank. Here, we show that the generic features of the statistical physics of such systems can be studied in a highly flexible and efficient fashion using a mathematical tool borrowed from high-energy physics: discrete non-Abelian gauge theory. Explicitly, we construct a family of lattice gauge models encapsulating nematic ordering of general three-dimensional point-group symmetries. We find that the most symmetrical generalized nematics are subjected to thermal fluctuations of unprecedented severity. As a result, novel forms of fluctuation phenomena become possible. In particular, we demonstrate that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point-group symmetry chiral building blocks, such as I, O, and T symmetric matter.« less

DTI and VBM reveal white matter changes without associated gray matter changes in patients with idiopathic restless legs syndrome

PubMed Central

Belke, Marcus; Heverhagen, Johannes T; Keil, Boris; Rosenow, Felix; Oertel, Wolfgang H; Stiasny-Kolster, Karin; Knake, Susanne; Menzler, Katja

2015-01-01

Background and Purpose We evaluated cerebral white and gray matter changes in patients with iRLS in order to shed light on the pathophysiology of this disease. Methods Twelve patients with iRLS were compared to 12 age- and sex-matched controls using whole-head diffusion tensor imaging (DTI) and voxel-based morphometry (VBM) techniques. Evaluation of the DTI scans included the voxelwise analysis of the fractional anisotropy (FA), radial diffusivity (RD), and axial diffusivity (AD). Results Diffusion tensor imaging revealed areas of altered FA in subcortical white matter bilaterally, mainly in temporal regions as well as in the right internal capsule, the pons, and the right cerebellum. These changes overlapped with changes in RD. Voxel-based morphometry did not reveal any gray matter alterations. Conclusions We showed altered diffusion properties in several white matter regions in patients with iRLS. White matter changes could mainly be attributed to changes in RD, a parameter thought to reflect altered myelination. Areas with altered white matter microstructure included areas in the internal capsule which include the corticospinal tract to the lower limbs, thereby supporting studies that suggest changes in sensorimotor pathways associated with RLS. PMID:26442748

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Chaplygin gas inspired scalar fields inflation via well-known potentials

NASA Astrophysics Data System (ADS)

Jawad, Abdul; Butt, Sadaf; Rani, Shamaila

2016-08-01

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

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

PubMed

Soliman, George; Yevick, David; Jessop, Paul

2014-09-01

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

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

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

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

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

Axially symmetric non-static domain walls in scalar-tensor theories of gravitation

NASA Astrophysics Data System (ADS)

Adhav, K. S.; Nimkar, A. S.; Naidu, R. L.

2007-12-01

An axially symmetric non-static space-time is considered in the presence of thick domain walls in the scalar-tensor theories formulated by Brans and Dicke (Phys. Rev. 124:925, 1961) and Saez and Ballester (Phys. Lett. A 113:467, 1985). Exact cosmological models, in both the theories, are presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983), for Hubble’s parameter. Some physical and kinematical properties of the models are discussed.

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

Casadio, Roberto; Orlandi, Alessio; Kühnel, Florian, E-mail: casadio@bo.infn.it, E-mail: florian.kuhnel@fysik.su.se, E-mail: aorlandi@bo.infn.it

Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investigate possible modifications to the Hubble parameter and following corrections to the cosmic microwave background spectrum. In this model, scalar and tensor perturbations are generated by the quantum depletion of the background inflaton and graviton condensate respectively. We show how the inflaton mass affects the power spectra and the tensor-to-scalar ratio. Masses approaching the Planck scale would lead to strong deviations, while standard spectra are recovered for an inflaton mass much smaller than the Planck mass.

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

Dreger, Douglas S.; Ford, Sean R.; Walter, William R.

Research was carried out investigating the feasibility of using a regional distance seismic waveform moment tensor inverse procedure to estimate source parameters of nuclear explosions and to use the source inversion results to develop a source-type discrimination capability. The results of the research indicate that it is possible to robustly determine the seismic moment tensor of nuclear explosions, and when compared to natural seismicity in the context of the a Hudson et al. (1989) source-type diagram they are found to separate from populations of earthquakes and underground cavity collapse seismic sources.

Multilinear Computing and Multilinear Algebraic Geometry

DTIC Science & Technology

2016-08-10

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

Green-Kubo relations for the viscosity of biaxial nematic liquid crystals

NASA Astrophysics Data System (ADS)

Sarman, Sten

1996-09-01

We derive Green-Kubo relations for the viscosities of a biaxial nematic liquid crystal. In this system there are seven shear viscosities, three twist viscosities, and three cross coupling coefficients between the antisymmetric strain rate and the symmetric traceless pressure tensor. According to the Onsager reciprocity relations these couplings are equal to the cross couplings between the symmetric traceless strain rate and the antisymmetric pressure. Our method is based on a comparison of the microscopic linear response generated by the SLLOD equations of motion for planar Couette flow (so named because of their close connection to the Doll's tensor Hamiltonian) and the macroscopic linear phenomenological relations between the pressure tensor and the strain rate. In order to obtain simple Green-Kubo relations we employ an equilibrium ensemble where the angular velocities of the directors are identically zero. This is achieved by adding constraint torques to the equations for the molecular angular accelerations. One finds that all the viscosity coefficients can be expressed as linear combinations of time correlation function integrals (TCFIs). This is much simpler compared to the expressions in the conventional canonical ensemble, where the viscosities are complicated rational functions of the TCFIs. The reason for this is, that in the constrained angular velocity ensemble, the thermodynamic forces are given external parameters whereas the thermodynamic fluxes are ensemble averages of phase functions. This is not the case in the canonical ensemble. The simplest way of obtaining numerical estimates of viscosity coefficients of a particular molecular model system is to evaluate these fluctuation relations by equilibrium molecular dynamics simulations.

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

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

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

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

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

PubMed

Chen, Jian; Jia, Bingxi; Zhang, Kaixiang

2017-11-01

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

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

PubMed Central

Chanraud, Sandra; Zahr, Natalie; Pfefferbaum, Adolf

2010-01-01

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

Extended mimetic gravity: Hamiltonian analysis and gradient instabilities

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Kobayashi, Tsutomu

2017-11-01

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

Gravitational waves and large field inflation

NASA Astrophysics Data System (ADS)

Linde, Andrei

2017-02-01

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

A new validation technique for estimations of body segment inertia tensors: Principal axes of inertia do matter.

PubMed

Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J

2016-12-08

The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

Lattice model calculation of the strain energy density and other properties of crystalline LiCoO{sub 2}

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

Hart, F.X.; Bates, J.B.

1998-06-01

The strain energy densities for various crystalline planes of LiCoO{sub 2} were calculated from the stiffness tensors obtained from lattice model calculations using the program GULP. In addition to Coulomb and Buckingham potentials, it was necessary to include shell models for the oxygen and cobalt ions in order to obtain acceptable agreement between the observed and calculated structural parameters and high frequency dielectric constant. The strain energy densities u due to differential thermal expansion were calculated using the theoretical stiffness tensors and estimated values for the thermal expansion coefficients of LiCoO{sub 2}. For a temperature change of 675thinsp{degree}C, these rangedmore » from 0.5 to 1.3{times}10{sup 8}thinsperg/cm{sup 3} or 5 to 13thinspJ/m{sup 2} for 1-{mu}m-thick films on alumina substrates. In particular, the energies for the (003), (101), and (104) planes were ordered as u(003){gt}u(104){gt}u(101). This suggests that the strong (101) preferred orientation of LiCoO{sub 2} films ({ge}1thinsp{mu}m thick) is due to the tendency to minimize volume strain energy that arises from differential thermal expansion between the film and the substrate. Additional properties obtained from the GULP calculations include the free energy, heat capacity, and the k=0 vibrational modes. thinsp« less

First-order curvature corrections to the surface tension of multicomponent systems.

PubMed

Boltachev, Grey Sh; Baidakov, Vladimir G; Schmelzer, Jürn W P

2003-08-01

The dependence of surface tension on curvature is investigated for the case of an equilibrium phase coexistence in multicomponent systems. Employing Gibbs's method of description of heterogeneous systems, an equation is derived to determine the dependence of surface tension on curvature for widely arbitrary paths of variation of the independent thermodynamic parameters. It is supposed hereby merely that the temperature is kept constant and that the variations of the different molar fractions are such that the radius of the dividing surface varies monotonically in dependence on the change of the state parameters of the ambient phase along any of the chosen paths. In the analysis, an approach developed by Blokhuis and Bedeaux for one-component systems is utilized. It relies on the expansion of the surface free energy on curvature of the dividing surface. An equation is derived that connects the first-order correction term in the expansion with the interaction potential of the particles in the multicomponent solution and with the two-particle distribution functions in the planar interfacial layer between the two phases coexisting in equilibrium at planar interfaces. The connection of the first-order curvature correction to the surface tension and the first moment of the pressure tensor at a planar interface is analyzed as well.

Charmless hadronic B decays into a tensor meson

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

Cheng, Hai-Yang; C. N. Yang Institute for Theoretical Physics, State University of New York Stony Brook, Stony Brook, New York 11794; Yang, Kwei-Chou

2011-02-01

Two-body charmless hadronic B decays involving a tensor meson in the final state are studied within the framework of QCD factorization (QCDF). Because of the G-parity of the tensor meson, both the chiral-even and chiral-odd two-parton light-cone distribution amplitudes of the tensor meson are antisymmetric under the interchange of momentum fractions of the quark and antiquark in the SU(3) limit. Our main results are: (i) In the naieve factorization approach, the decays such as B{sup -}{yields}K{sub 2}*{sup 0}{pi}{sup -} and B{sup 0}{yields}K{sub 2}*{sup -}{pi}{sup +} with a tensor meson emitted are prohibited because a tensor meson cannot be created frommore » the local V-A or tensor current. Nevertheless, the decays receive nonfactorizable contributions in QCDF from vertex, penguin and hard spectator corrections. The experimental observation of B{sup -}{yields}K{sub 2}*{sup 0}{pi}{sup -} indicates the importance of nonfactorizable effects. (ii) For penguin-dominated B{yields}TP and TV decays, the predicted rates in naieve factorization are usually too small by 1 to 2 orders of magnitude. In QCDF, they are enhanced by power corrections from penguin annihilation and nonfactorizable contributions. (iii) The dominant penguin contributions to B{yields}K{sub 2}*{eta}{sup (')} arise from the processes: (a) b{yields}sss{yields}s{eta}{sub s} and (b) b{yields}sqq{yields}qK{sub 2}* with {eta}{sub q}=(uu+dd)/{radical}(2) and {eta}{sub s}=ss. The interference, constructive for K{sub 2}*{eta}{sup '} and destructive for K{sub 2}*{eta}, explains why {Gamma}(B{yields}K{sub 2}*{eta}{sup '})>>{Gamma}(B{yields}K{sub 2}*{eta}). (iv) We use the measured rates of B{yields}K{sub 2}*({omega},{phi}) to extract the penguin-annihilation parameters {rho}{sub A}{sup TV} and {rho}{sub A}{sup VT} and the observed longitudinal polarization fractions f{sub L}(K{sub 2}*{omega}) and f{sub L}(K{sub 2}*{phi}) to fix the phases {phi}{sub A}{sup VT} and {phi}{sub A}{sup TV}. (v) The experimental observation that f{sub T}/f{sub L}<<1 for B{yields}K{sub 2}*(1430){phi}, whereas f{sub T}/f{sub L}{approx}1 for B{yields}K{sub 2}*(1430){omega} with f{sub T} being the transverse polarization fraction, can be accommodated in QCDF, but it cannot be dynamically explained at first place. For penguin-dominated B{yields}TV decays, we find f{sub L}(K{sub 2}*{rho}){approx}f{sub L}(K{sub 2}*{omega}){approx}0.65, whereas f{sub L}(K*f{sub 2}){approx}0.93. It will be of great interest to measure f{sub L} for these modes to test QCDF. Theoretically, transverse polarization is expected to be small in tree-dominated B{yields}TV decays except for the a{sub 2}{sup -}{rho}{sup 0}, a{sub 2}{sup -}{rho}{sup +}, K{sub 2}*{sup 0}K*{sup -} and K{sub 2}*{sup 0}K*{sup 0} modes. (vi) For tree-dominated decays, their rates are usually very small except for the a{sub 2}{sup 0}({pi}{sup -},{rho}{sup -}), a{sub 2}{sup +}({pi}{sup -},{rho}{sup -}) and f{sub 2}({pi}{sup -},{rho}{sup -}) modes with branching fractions of order 10{sup -6} or even larger.« less

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

PubMed

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

2016-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Constraining the break of spatial diffeomorphism invariance with Planck data

NASA Astrophysics Data System (ADS)

Graef, L. L.; Benetti, M.; Alcaniz, J. S.

2017-07-01

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, which can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r, and the tensor spectral index, nt. If the inflation consistency relation is imposed, r=-8 nt, we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.

U (1 ) -symmetric infinite projected entangled-pair states study of the spin-1/2 square J1-J2 Heisenberg model

NASA Astrophysics Data System (ADS)

Haghshenas, R.; Sheng, D. N.

2018-05-01

We develop an improved variant of U (1 ) -symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground-state phase diagram of the spin-1 /2 square J1-J2 Heisenberg model. In order to improve the accuracy of the ansatz, we discuss a simple strategy to select automatically relevant symmetric sectors and also introduce an optimization method to treat second-neighbor interactions more efficiently. We show that variational ground-state energies of the model obtained by the U (1 ) -symmetric iPEPS ansatz (for a fixed bond dimension D ) set a better upper bound, improving previous tensor-network-based results. By studying the finite-D scaling of the magnetically order parameter, we find a Néel phase for J2/J1<0.53 . For 0.53

Conditional High-Order Boltzmann Machines for Supervised Relation Learning.

PubMed

Huang, Yan; Wang, Wei; Wang, Liang; Tan, Tieniu

2017-09-01

Relation learning is a fundamental problem in many vision tasks. Recently, high-order Boltzmann machine and its variants have shown their great potentials in learning various types of data relation in a range of tasks. But most of these models are learned in an unsupervised way, i.e., without using relation class labels, which are not very discriminative for some challenging tasks, e.g., face verification. In this paper, with the goal to perform supervised relation learning, we introduce relation class labels into conventional high-order multiplicative interactions with pairwise input samples, and propose a conditional high-order Boltzmann Machine (CHBM), which can learn to classify the data relation in a binary classification way. To be able to deal with more complex data relation, we develop two improved variants of CHBM: 1) latent CHBM, which jointly performs relation feature learning and classification, by using a set of latent variables to block the pathway from pairwise input samples to output relation labels and 2) gated CHBM, which untangles factors of variation in data relation, by exploiting a set of latent variables to multiplicatively gate the classification of CHBM. To reduce the large number of model parameters generated by the multiplicative interactions, we approximately factorize high-order parameter tensors into multiple matrices. Then, we develop efficient supervised learning algorithms, by first pretraining the models using joint likelihood to provide good parameter initialization, and then finetuning them using conditional likelihood to enhance the discriminant ability. We apply the proposed models to a series of tasks including invariant recognition, face verification, and action similarity labeling. Experimental results demonstrate that by exploiting supervised relation labels, our models can greatly improve the performance.

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

PubMed

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

2011-05-01

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

Observable cosmological vector mode in the dark ages

NASA Astrophysics Data System (ADS)

Saga, Shohei

2016-09-01

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

Stochastic Representations of Seismic Anisotropy: Verification of Effective Media Models and Application to the Continental Crust

NASA Astrophysics Data System (ADS)

Song, X.; Jordan, T. H.

2017-12-01

The seismic anisotropy of the continental crust is dominated by two mechanisms: the local (intrinsic) anisotropy of crustal rocks caused by the lattice-preferred orientation of their constituent minerals, and the geometric (extrinsic) anisotropy caused by the alignment and layering of elastic heterogeneities by sedimentation and deformation. To assess the relative importance of these mechanisms, we have applied Jordan's (GJI, 2015) self-consistent, second-order theory to compute the effective elastic parameters of stochastic media with hexagonal local anisotropy and small-scale 3D heterogeneities that have transversely isotropic (TI) statistics. The theory pertains to stochastic TI media in which the eighth-order covariance tensor of the elastic moduli can be separated into a one-point variance tensor that describes the local anisotropy in terms of a anisotropy orientation ratio (ξ from 0 to ∞), and a two-point correlation function that describes the geometric anisotropy in terms of a heterogeneity aspect ratio (η from 0 to ∞). If there is no local anisotropy, then, in the limiting case of a horizontal stochastic laminate (η→∞), the effective-medium equations reduce to the second-order equations derived by Backus (1962) for a stochastically layered medium. This generalization of the Backus equations to 3D stochastic media, as well as the introduction of local, stochastically rotated anisotropy, provides a powerful theory for interpreting the anisotropic signatures of sedimentation and deformation in continental environments; in particular, the parameterizations that we propose are suitable for tomographic inversions. We have verified this theory through a series high-resolution numerical experiments using both isotropic and anisotropic wave-propagation codes.

Noncommutative spherically symmetric spacetimes at semiclassical order

NASA Astrophysics Data System (ADS)

Fritz, Christopher; Majid, Shahn

2017-07-01

Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\

Application of Effective Medium Theory to the Three-Dimensional Heterogeneity of Mantle Anisotropy

NASA Astrophysics Data System (ADS)

Song, X.; Jordan, T. H.

2015-12-01

A self-consistent theory for the effective elastic parameters of stochastic media with small-scale 3D heterogeneities has been developed using a 2nd-order Born approximation to the scattered wavefield (T. H. Jordan, GJI, in press). Here we apply the theory to assess how small-scale variations in the local anisotropy of the upper mantle affect seismic wave propagation. We formulate a anisotropic model in which the local elastic properties are specified by a constant stiffness tensor with hexagonal symmetry of arbitrary orientation. This orientation is guided by a Gaussian random vector field with transversely isotropic (TI) statistics. If the outer scale of the statistical variability is small compared to a wavelength, then the effective seismic velocities are TI and depend on two parameters, a horizontal-to-vertical orientation ratio ξ and a horizontal-to-vertical aspect ratio, η. If ξ = 1, the symmetry axis is isotropically distributed; if ξ < 1, it is vertical biased (bipolar distribution), and if ξ > 1, it is horizontally biased (girdle distribution). If η = 1, the heterogeneity is geometrically isotropic; as η à∞, the medium becomes a horizontal stochastic laminate; as η à0, the medium becomes a vertical stochastic bundle. Using stiffness tensors constrained by laboratory measurements of mantle xenoliths, we explore the dependence of the effective P and S velocities on ξ and η. The effective velocities are strongly controlled by the orientation ratio ξ; e.g., if the hexagonal symmetry axis of the local anisotropy is the fast direction of propagation, then vPH > vPV and vSH > vSV for ξ > 1. A more surprising result is the 2nd-order insensitivity of the velocities to the heterogeneity aspect ratio η. Consequently, the geometrical anisotropy of upper-mantle heterogeneity significantly enhances seismic-wave anisotropy only through local variations in the Voigt-averaged velocities, which depend primarily on rock composition and not deformation history.

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

NASA Astrophysics Data System (ADS)

Khoromskaia, Venera; Khoromskij, Boris N.

2014-12-01

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

Video denoising using low rank tensor decomposition

NASA Astrophysics Data System (ADS)

Gui, Lihua; Cui, Gaochao; Zhao, Qibin; Wang, Dongsheng; Cichocki, Andrzej; Cao, Jianting

2017-03-01

Reducing noise in a video sequence is of vital important in many real-world applications. One popular method is block matching collaborative filtering. However, the main drawback of this method is that noise standard deviation for the whole video sequence is known in advance. In this paper, we present a tensor based denoising framework that considers 3D patches instead of 2D patches. By collecting the similar 3D patches non-locally, we employ the low-rank tensor decomposition for collaborative filtering. Since we specify the non-informative prior over the noise precision parameter, the noise variance can be inferred automatically from observed video data. Therefore, our method is more practical, which does not require knowing the noise variance. The experimental on video denoising demonstrates the effectiveness of our proposed method.

Moment-Tensor Spectra of Source Physics Experiments (SPE) Explosions in Granite

NASA Astrophysics Data System (ADS)

Yang, X.; Cleveland, M.

2016-12-01

We perform frequency-domain moment tensor inversions of Source Physics Experiments (SPE) explosions conducted in granite during Phase I of the experiment. We test the sensitivity of source moment-tensor spectra to factors such as the velocity model, selected dataset and smoothing and damping parameters used in the inversion to constrain the error bound of inverted source spectra. Using source moments and corner frequencies measured from inverted source spectra of these explosions, we develop a new explosion P-wave source model that better describes observed source spectra of these small and over-buried chemical explosions detonated in granite than classical explosion source models derived mainly from nuclear-explosion data. In addition to source moment and corner frequency, we analyze other features in the source spectra to investigate their physical causes.

Generalized Grueneisen tensor from solid nonlinearity parameters

NASA Technical Reports Server (NTRS)

Cantrell, J. H., Jr.

1980-01-01

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

Moment Tensor Inversion of the 1998 Aiquile Earthquake Using Long-period surface waves

NASA Astrophysics Data System (ADS)

Wang, H.

2016-12-01

On 22nd May 1998 at 04:49(GMT), an earthquake of magnitude Mw = 6.6 struck the Aiquile region of Bolivia, causing 105 deaths and significant damage to the nearby towns of Hoyadas and Pampa Grande. This was the largest shallow earthquake (15 km depth) in Bolivia in over 50 years, and was felt as far Sucre, approximately 100 km away. In this report, a centroid moment tensor (CMT) inversion is carried using body waves and surface waves from 1998 Aiquile earthquake with 1-D and 3-D earth models to obtain the source model parameters and moment tensor, which are the values will be subsequently compared against the Global Centroid Moment Tensor Catalog(GCMT). Also, the excitation kernels could be gained and synthetic data can be created with different earth models. The two method for calculating synthetic seismograms are SPECFEM3D Globe which is based on shear wave mantle model S40RTS and crustal model CRUST 2.0, and AxiSEM which is based on PREM 1-D earth Model. Within the report, the theory behind the CMT inversion was explained and the source parameters gained from the inversion can be used to reveal the tectonics of the source of this earthquake, these information could be helpful in assessing seismic hazard and overall tectonic regime of this region. Furthermore, results of synthetic seismograms and the solution of inversion are going to be used to assess two models.

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

NASA Astrophysics Data System (ADS)

Groote, S.; Körner, J. G.

2017-12-01

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

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

ERIC Educational Resources Information Center

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

2012-01-01

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

Interaction of non-Abelian tensor gauge fields

NASA Astrophysics Data System (ADS)

Savvidy, George

2018-01-01

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

Diffusion in shear flow

NASA Astrophysics Data System (ADS)

Dufty, J. W.

1984-09-01

Diffusion of a tagged particle in a fluid with uniform shear flow is described. The continuity equation for the probability density describing the position of the tagged particle is considered. The diffusion tensor is identified by expanding the irreversible part of the probability current to first order in the gradient of the probability density, but with no restriction on the shear rate. The tensor is expressed as the time integral of a nonequilibrium autocorrelation function for the velocity of the tagged particle in its local fluid rest frame, generalizing the Green-Kubo expression to the nonequilibrium state. The tensor is evaluated from results obtained previously for the velocity autocorrelation function that are exact for Maxwell molecules in the Boltzmann limit. The effects of viscous heating are included and the dependence on frequency and shear rate is displayed explicitly. The mode-coupling contributions to the frequency and shear-rate dependent diffusion tensor are calculated.

Exact example of backreaction of small scale inhomogeneities in cosmology

NASA Astrophysics Data System (ADS)

Green, Stephen; Wald, Robert

2013-04-01

We construct a one-parameter family of polarized vacuum Gowdy spacetimes on a torus. In the limit as the parameter N goes to infinity, the metric uniformly approaches a smooth ``background metric.'' However, spacetime derivatives of the metric do not approach a limit. As a result, we find that the background metric itself is not a solution of the vacuum Einstein equation. Rather, it is a solution of the Einstein equation with an ``effective stress-energy tensor,'' which is traceless and satisfies the weak energy condition. This is an explicit example of backreaction due to small scale inhomogeneities. We comment on the non-vacuum case, where we have proven in previous work that, provided the matter stress-energy tensor satisfies the weak energy condition, no additional backreaction is possible.

On the role of the transformation eigenstrain in the growth or shrinkage of spheroidal isotropic precipitations

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

Fischer, F.D.; Boehm, H.J.

The jumps of the strain and stress tensors on the surface of elastic homogeneous or inhomogeneous ellipsoidal inclusions embedded in an elastic matrix are obtained from results reported in the literature. They are used to derive closed-form expressions for the thermodynamic force in such matrix-inclusion systems that are subjected to a generally defined homogeneous transformation eigenstrain. A detailed study is presented for an isotropic spheroidal inclusion in an isotropic matrix in which the most important parameters are the inclusion's aspect ratio {alpha} and an eigenstrain triaxiality parameter d-bar. The fluctuations of the thermodynamic force are investigated for a set ofmore » specific transformation eigenstrain tensors and are presented for inclusion shapes ranging from disk-like to fiber-like spheroids.« less

Determination of atomic site susceptibility tensors from neutron diffraction data on polycrystalline samples.

PubMed

Gukasov, A; Brown, P J

2010-12-22

Polarized neutron diffraction can provide information about the atomic site susceptibility tensor χ(ij) characterizing the magnetic response of individual atoms to an external magnetic field (Gukasov and Brown 2002 J. Phys.: Condens. Mater. 14 8831). The six independent atomic susceptibility parameters (ASPs) can be determined from polarized neutron flipping ratio measurements on single crystals and visualized as magnetic ellipsoids which are analogous to the thermal ellipsoids obtained from atomic displacement parameters (ADPs). We demonstrate now that the information about local magnetic susceptibility at different magnetic sites in a crystal can also be obtained from polarized and unpolarized neutron diffraction measurements on magnetized powder samples. The validity of the method is illustrated by the results of such measurements on a polycrystalline sample of Tb(2)Sn(2)O(7).

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

PubMed

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

2018-02-09

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

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

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

NASA Astrophysics Data System (ADS)

Aragón, Alejandro M.

2014-06-01

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

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

NASA Astrophysics Data System (ADS)

Aragón, Alejandro M.

2014-11-01

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

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

NASA Astrophysics Data System (ADS)

Matyjasek, Jerzy; Sadurski, Paweł; Telecka, Małgorzata

2014-04-01

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

Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

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

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

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

Simultaneous Tensor Decomposition and Completion Using Factor Priors.

PubMed

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

2013-08-27

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

Dark matter scenarios with multiple spin-2 fields

NASA Astrophysics Data System (ADS)

González Albornoz, N. L.; Schmidt-May, Angnis; von Strauss, Mikael

2018-01-01

We study ghost-free multimetric theories for (N+1) tensor fields with a coupling to matter and maximal global symmetry group SN×(Z2)N. Their mass spectra contain a massless mode, the graviton, and N massive spin-2 modes. One of the massive modes is distinct by being the heaviest, the remaining (N‑1) massive modes are simply identical copies of each other. All relevant physics can therefore be understood from the case N=2. Focussing on this case, we compute the full perturbative action up to cubic order and derive several features that hold to all orders in perturbation theory. The lighter massive mode does not couple to matter and neither of the massive modes decay into massless gravitons. We propose the lighter massive particle as a candidate for dark matter and investigate its phenomenology in the parameter region where the matter coupling is dominated by the massless graviton. The relic density of massive spin-2 can originate from a freeze-in mechanism or from gravitational particle production, giving rise to two different dark matter scenarios. The allowed parameter regions are very different from those in scenarios with only one massive spin-2 field and more accessible to experiments.

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.

Classical stability of sudden and big rip singularities

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

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

2009-08-15

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

Stress Energy tensor in LCFT and the Logarithmic Sugawara construction

NASA Astrophysics Data System (ADS)

Kogan, Ian I.; Nichols, Alexander

2002-01-01

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c = -2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra.

Towards real-time regional earthquake simulation I: real-time moment tensor monitoring (RMT) for regional events in Taiwan

NASA Astrophysics Data System (ADS)

Lee, Shiann-Jong; Liang, Wen-Tzong; Cheng, Hui-Wen; Tu, Feng-Shan; Ma, Kuo-Fong; Tsuruoka, Hiroshi; Kawakatsu, Hitoshi; Huang, Bor-Shouh; Liu, Chun-Chi

2014-01-01

We have developed a real-time moment tensor monitoring system (RMT) which takes advantage of a grid-based moment tensor inversion technique and real-time broad-band seismic recordings to automatically monitor earthquake activities in the vicinity of Taiwan. The centroid moment tensor (CMT) inversion technique and a grid search scheme are applied to obtain the information of earthquake source parameters, including the event origin time, hypocentral location, moment magnitude and focal mechanism. All of these source parameters can be determined simultaneously within 117 s after the occurrence of an earthquake. The monitoring area involves the entire Taiwan Island and the offshore region, which covers the area of 119.3°E to 123.0°E and 21.0°N to 26.0°N, with a depth from 6 to 136 km. A 3-D grid system is implemented in the monitoring area with a uniform horizontal interval of 0.1° and a vertical interval of 10 km. The inversion procedure is based on a 1-D Green's function database calculated by the frequency-wavenumber (fk) method. We compare our results with the Central Weather Bureau (CWB) catalogue data for earthquakes occurred between 2010 and 2012. The average differences between event origin time and hypocentral location are less than 2 s and 10 km, respectively. The focal mechanisms determined by RMT are also comparable with the Broadband Array in Taiwan for Seismology (BATS) CMT solutions. These results indicate that the RMT system is realizable and efficient to monitor local seismic activities. In addition, the time needed to obtain all the point source parameters is reduced substantially compared to routine earthquake reports. By connecting RMT with a real-time online earthquake simulation (ROS) system, all the source parameters will be forwarded to the ROS to make the real-time earthquake simulation feasible. The RMT has operated offline (2010-2011) and online (since January 2012 to present) at the Institute of Earth Sciences (IES), Academia Sinica (http://rmt.earth.sinica.edu.tw). The long-term goal of this system is to provide real-time source information for rapid seismic hazard assessment during large earthquakes.

Matrix product states for su(2) invariant quantum spin chains

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Fledderjohann, Andreas; Klümper, Andreas

2016-08-01

A systematic and compact treatment of arbitrary su(2) invariant spin-s quantum chains with nearest-neighbour interactions is presented. The ground-state is derived in terms of matrix product states (MPS). The fundamental MPS calculations consist of taking products of basic tensors of rank 3 and contractions thereof. The algebraic su(2) calculations are carried out completely by making use of Wigner calculus. As an example of application, the spin-1 bilinear-biquadratic quantum chain is investigated. Various physical quantities are calculated with high numerical accuracy of up to 8 digits. We obtain explicit results for the ground-state energy, entanglement entropy, singlet operator correlations and the string order parameter. We find an interesting crossover phenomenon in the correlation lengths.

Vortex lattices and defect-mediated viscosity reduction in active liquids

NASA Astrophysics Data System (ADS)

Slomka, Jonasz; Dunkel, Jorn

2016-11-01

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

Geometry-dependent viscosity reduction in sheared active fluids

NASA Astrophysics Data System (ADS)

Słomka, Jonasz; Dunkel, Jörn

2017-04-01

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

Chiral vacuum fluctuations in quantum gravity.

PubMed

Magueijo, João; Benincasa, Dionigi M T

2011-03-25

We examine tensor perturbations around a de Sitter background within the framework of Ashtekar's variables and its cousins parameterized by the Immirzi parameter γ. At the classical level we recover standard cosmological perturbation theory, with illuminating insights. Quantization leads to real novelties. In the low energy limit we find a second quantized theory of gravitons which displays different vacuum fluctuations for right and left gravitons. Nonetheless right and left gravitons have the same (positive) energies, resolving a number of paradoxes suggested in the literature. The right-left asymmetry of the vacuum fluctuations depends on γ and the ordering of the Hamiltonian constraint, and it would leave a distinctive imprint in the polarization of the cosmic microwave background, thus opening quantum gravity to observational test.

Molecular dynamics simulations on PGLa using NMR orientational constraints.

PubMed

Sternberg, Ulrich; Witter, Raiker

2015-11-01

NMR data obtained by solid state NMR from anisotropic samples are used as orientational constraints in molecular dynamics simulations for determining the structure and dynamics of the PGLa peptide within a membrane environment. For the simulation the recently developed molecular dynamics with orientational constraints technique (MDOC) is used. This method introduces orientation dependent pseudo-forces into the COSMOS-NMR force field. Acting during a molecular dynamics simulation these forces drive molecular rotations, re-orientations and folding in such a way that the motional time-averages of the tensorial NMR properties are consistent with the experimentally measured NMR parameters. This MDOC strategy does not depend on the initial choice of atomic coordinates, and is in principle suitable for any flexible and mobile kind of molecule; and it is of course possible to account for flexible parts of peptides or their side-chains. MDOC has been applied to the antimicrobial peptide PGLa and a related dimer model. With these simulations it was possible to reproduce most NMR parameters within the experimental error bounds. The alignment, conformation and order parameters of the membrane-bound molecule and its dimer were directly derived with MDOC from the NMR data. Furthermore, this new approach yielded for the first time the distribution of segmental orientations with respect to the membrane and the order parameter tensors of the dimer systems. It was demonstrated the deuterium splittings measured at the peptide to lipid ratio of 1/50 are consistent with a membrane spanning orientation of the peptide.

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

DTIC Science & Technology

2007-11-08

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

New methods for interpretation of magnetic vector and gradient tensor data I: eigenvector analysis and the normalised source strength

NASA Astrophysics Data System (ADS)

Clark, David A.

2012-09-01

Acquisition of magnetic gradient tensor data is likely to become routine in the near future. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for several elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalised source strength (NSS), calculated from the eigenvalues, is a particularly useful rotational invariant that peaks directly over 3D compact sources, 2D compact sources, thin sheets and contacts, and is independent of magnetisation direction. In combination the NSS and its vector gradient determine source locations uniquely. NSS analysis can be extended to other useful models, such as vertical pipes, by calculating eigenvalues of the vertical derivative of the gradient tensor. Inversion based on the vector gradient of the NSS over the Tallawang magnetite deposit obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Besides the geological applications, the algorithms for the dipole model are readily applicable to the detection, location and characterisation (DLC) of magnetic objects, such as naval mines, unexploded ordnance, shipwrecks, archaeological artefacts, and buried drums.

Mutated hilltop inflation revisited

NASA Astrophysics Data System (ADS)

Pal, Barun Kumar

2018-05-01

In this work we re-investigate pros and cons of mutated hilltop inflation. Applying Hamilton-Jacobi formalism we solve inflationary dynamics and find that inflation goes on along the {W}_{-1} branch of the Lambert function. Depending on the model parameter mutated hilltop model renders two types of inflationary solutions: one corresponds to small inflaton excursion during observable inflation and the other describes large field inflation. The inflationary observables from curvature perturbation are in tune with the current data for a wide range of the model parameter. The small field branch predicts negligible amount of tensor to scalar ratio r˜ O(10^{-4}), while the large field sector is capable of generating high amplitude for tensor perturbations, r˜ O(10^{-1}). Also, the spectral index is almost independent of the model parameter along with a very small negative amount of scalar running. Finally we find that the mutated hilltop inflation closely resembles the α -attractor class of inflationary models in the limit of α φ ≫ 1.

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.

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.

Polymer Fluid Dynamics: Continuum and Molecular Approaches.

PubMed

Bird, R B; Giacomin, A J

2016-06-07

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

Constraining the break of spatial diffeomorphism invariance with Planck data

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

Graef, L.L.; Benetti, M.; Alcaniz, J.S., E-mail: leilagraef@on.br, E-mail: micolbenetti@on.br, E-mail: alcaniz@on.br

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, whichmore » can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r , and the tensor spectral index, n {sub t} . If the inflation consistency relation is imposed, r =−8 n {sub t} , we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.« less

New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions.

PubMed

Bonhomme, Christian; Gervais, Christel; Coelho, Cristina; Pourpoint, Frédérique; Azaïs, Thierry; Bonhomme-Coury, Laure; Babonneau, Florence; Jacob, Guy; Ferrari, Maude; Canet, Daniel; Yates, Jonathan R; Pickard, Chris J; Joyce, Siân A; Mauri, Francesco; Massiot, Dominique

2010-12-01

In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), β-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, β-HMX and α-NTO are explosive compounds. Copyright © 2010 John Wiley & Sons, Ltd.

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

NASA Astrophysics Data System (ADS)

Alvizuri, Celso R.

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

Obtaining orthotropic elasticity tensor using entries zeroing method.

NASA Astrophysics Data System (ADS)

Gierlach, Bartosz; Danek, Tomasz

2017-04-01

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

The Invar tensor package: Differential invariants of Riemann

NASA Astrophysics Data System (ADS)

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

2008-10-01

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

Pryce-Hoyle Tensor in a Combined Einstein-Cartan-Brans-Dicke Model

NASA Astrophysics Data System (ADS)

Berman, Marcelo Samuel

2009-03-01

In addition to introducing matter injection through a scalar field determined by Pryce-Hoyle tensor, we also combine it with a BCDE (Brans-Dicke-Einstein-Cartan) theory with lambda-term developed earlier by Berman (Astrophys. Space Sci. 314:79-82, 2008), for inflationary scenario. It involves a variable cosmological constant, which decreases with time, jointly with energy density, cosmic pressure, shear, vorticity, and Hubble’s parameter, while the scale factor, total spin and scalar field increase exponentially. The post-inflationary fluid resembles a perfect one, though total spin grows, but not the angular speed (Berman, in Astrophys. Space Sci. 312:275, 2007). The Pryce-Hoyle tensor, which can measured by the number of injected particles per unit proper volume and time, as well as shear and vorticity, can be neglected in the aftermath of inflation (“no-hair”).

What is the right formalism to search for resonances?

NASA Astrophysics Data System (ADS)

Mikhasenko, M.; Pilloni, A.; Nys, J.; Albaladejo, M.; Fernández-Ramírez, C.; Jackura, A.; Mathieu, V.; Sherrill, N.; Skwarnicki, T.; Szczepaniak, A. P.

2018-03-01

Hadron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B→ ψ π K and B→ \\bar{D}π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

An Integrated Tensorial Approach for Quantifying Porous, Fractured Rocks

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Electro-optical parameters of bond polarizability model for aluminosilicates.

PubMed

Smirnov, Konstantin S; Bougeard, Daniel; Tandon, Poonam

2006-04-06

Electro-optical parameters (EOPs) of bond polarizability model (BPM) for aluminosilicate structures were derived from quantum-chemical DFT calculations of molecular models. The tensor of molecular polarizability and the derivatives of the tensor with respect to the bond length are well reproduced with the BPM, and the EOPs obtained are in a fair agreement with available experimental data. The parameters derived were found to be transferable to larger molecules. This finding suggests that the procedure used can be applied to systems with partially ionic chemical bonds. The transferability of the parameters to periodic systems was tested in molecular dynamics simulation of the polarized Raman spectra of alpha-quartz. It appeared that the molecular Si-O bond EOPs failed to reproduce the intensity of peaks in the spectra. This limitation is due to large values of the longitudinal components of the bond polarizability and its derivative found in the molecular calculations as compared to those obtained from periodic DFT calculations of crystalline silica polymorphs by Umari et al. (Phys. Rev. B 2001, 63, 094305). It is supposed that the electric field of the solid is responsible for the difference of the parameters. Nevertheless, the EOPs obtained can be used as an initial set of parameters for calculations of polarizability related characteristics of relevant systems in the framework of BPM.

Tensor scale-based fuzzy connectedness image segmentation

NASA Astrophysics Data System (ADS)

Saha, Punam K.; Udupa, Jayaram K.

2003-05-01

Tangible solutions to image segmentation are vital in many medical imaging applications. Toward this goal, a framework based on fuzzy connectedness was developed in our laboratory. A fundamental notion called "affinity" - a local fuzzy hanging togetherness relation on voxels - determines the effectiveness of this segmentation framework in real applications. In this paper, we introduce the notion of "tensor scale" - a recently developed local morphometric parameter - in affinity definition and study its effectiveness. Although, our previous notion of "local scale" using the spherical model successfully incorporated local structure size into affinity and resulted in measureable improvements in segmentation results, a major limitation of the previous approach was that it ignored local structural orientation and anisotropy. The current approach of using tensor scale in affinity computation allows an effective utilization of local size, orientation, and ansiotropy in a unified manner. Tensor scale is used for computing both the homogeneity- and object-feature-based components of affinity. Preliminary results of the proposed method on several medical images and computer generated phantoms of realistic shapes are presented. Further extensions of this work are discussed.

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

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

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

Identifying isotropic events using a regional moment tensor inversion

DOE PAGES

Ford, Sean R.; Dreger, Douglas S.; Walter, William R.

2009-01-17

We calculate the deviatoric and isotropic source components for 17 explosions at the Nevada Test Site, as well as 12 earthquakes and 3 collapses in the surrounding region of the western United States, using a regional time domain full waveform inversion for the complete moment tensor. The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination between explosions, earthquakes, and collapses. Confidence regions of the model parameters are estimated from the data misfit by assuming normally distributed parameter values. Wemore » investigate the sensitivity of the resolved parameters of an explosion to imperfect Earth models, inaccurate event depths, and data with low signal-to-noise ratio (SNR) assuming a reasonable azimuthal distribution of stations. In the band of interest (0.02–0.10 Hz) the source-type calculated from complete moment tensor inversion is insensitive to velocity model perturbations that cause less than a half-cycle shift (<5 s) in arrival time error if shifting of the waveforms is allowed. The explosion source-type is insensitive to an incorrect depth assumption (for a true depth of 1 km), and the goodness of fit of the inversion result cannot be used to resolve the true depth of the explosion. Noise degrades the explosive character of the result, and a good fit and accurate result are obtained when the signal-to-noise ratio is greater than 5. We assess the depth and frequency dependence upon the resolved explosive moment. As the depth decreases from 1 km to 200 m, the isotropic moment is no longer accurately resolved and is in error between 50 and 200%. Furthermore, even at the most shallow depth the resultant moment tensor is dominated by the explosive component when the data have a good SNR.« less

Searching the Force Field Electrostatic Multipole Parameter Space.

PubMed

Jakobsen, Sofie; Jensen, Frank

2016-04-12

We show by tensor decomposition analyses that the molecular electrostatic potential for amino acid peptide models has an effective rank less than twice the number of atoms. This rank indicates the number of parameters that can be derived from the electrostatic potential in a statistically significant way. Using this as a guideline, we investigate different strategies for deriving a reduced set of atomic charges, dipoles, and quadrupoles capable of reproducing the reference electrostatic potential with a low error. A full combinatorial search of selected parameter subspaces for N-methylacetamide and a cysteine peptide model indicates that there are many different parameter sets capable of providing errors close to that of the global minimum. Among the different reduced multipole parameter sets that have low errors, there is consensus that atoms involved in π-bonding require higher order multipole moments. The possible correlation between multipole parameters is investigated by exhaustive searches of combinations of up to four parameters distributed in all possible ways on all possible atomic sites. These analyses show that there is no advantage in considering combinations of multipoles compared to a simple approach where the importance of each multipole moment is evaluated sequentially. When combined with possible weighting factors related to the computational efficiency of each type of multipole moment, this may provide a systematic strategy for determining a computational efficient representation of the electrostatic component in force field calculations.

FAST TRACK COMMUNICATION Determination of atomic site susceptibility tensors from neutron diffraction data on polycrystalline samples

NASA Astrophysics Data System (ADS)

Gukasov, A.; Brown, P. J.

2010-12-01

Polarized neutron diffraction can provide information about the atomic site susceptibility tensor χij characterizing the magnetic response of individual atoms to an external magnetic field (Gukasov and Brown 2002 J. Phys.: Condens. Mater. 14 8831). The six independent atomic susceptibility parameters (ASPs) can be determined from polarized neutron flipping ratio measurements on single crystals and visualized as magnetic ellipsoids which are analogous to the thermal ellipsoids obtained from atomic displacement parameters (ADPs). We demonstrate now that the information about local magnetic susceptibility at different magnetic sites in a crystal can also be obtained from polarized and unpolarized neutron diffraction measurements on magnetized powder samples. The validity of the method is illustrated by the results of such measurements on a polycrystalline sample of Tb2Sn2O7.

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

NASA Astrophysics Data System (ADS)

Liu, Tan; Zhang, Xing; Zhao, Wen

2018-02-01

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

Diffusive sensitivity to muscle architecture: a magnetic resonance diffusion tensor imaging study of the human calf.

PubMed

Galbán, Craig J; Maderwald, Stefan; Uffmann, Kai; de Greiff, Armin; Ladd, Mark E

2004-12-01

The aim of this study was to examine the diffusive properties of adjacent muscles at rest, and to determine the relationship between diffusive and architectural properties, which are task-specific to muscles. The principle, second, and third eigenvalues, trace of the diffusion tensor, and two anisotropic parameters, ellipsoid eccentricity (e) and fractional anisotropy (FA), of various muscles in the human calf were calculated by diffusion tensor imaging (DTI). Linear correlations of the calculated parameters to the muscle physiological cross-sectional area (PCSA), which is proportional to maximum muscle force, were performed to ascertain any linear relation between muscle architecture and diffusivity. Images of the left calf were acquired from six healthy male volunteers. Seven muscles were investigated in this study. These comprised the soleus, lateral gastrocnemius, medial gastrocnemius, posterior tibialis, anterior tibialis, extensor digitorum longus, and peroneus longus. All data were presented as the mean and standard error of the mean (SEM). In general, differences in diffusive parameter values occurred primarily between functionally different muscles. A strong correlation was also found between PCSA and the third eigenvalue, e, and FA. A mathematical derivation revealed a linear relationship between PCSA and the third eigenvalue as a result of their dependence on the average radius of all fibers within a single muscle. These findings demonstrated the ability of DTI to differentiate between functionally different muscles in the same region of the body on the basis of their diffusive properties.

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.

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.

Autonomous Appliance Scheduling System for Residential Energy Management in the Smart Grid

NASA Astrophysics Data System (ADS)

Martinez-Pabon, Madeline D.

Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. There are strong evidences that in physics the fields are fundamental entities of nature and not particles. If this is the case then topological defects (TDs) might play the role of fundamental particles. An adequate testing ground to study and gain fundamental understanding of TDs are nematic liquid crystals. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We analyze the impact of extrinsic and intrinsic curvature on positions of topological defects (TDs) in two-dimensional (2D) nematic films. We demonstrate that both these curvature contributions are commonly present and are expected to be weighted by comparable elastic constants. A simple Landau-de Gennes approach in terms of tensor nematic order parameter is used to numerically demonstrate impact of the curvatures on position of TDs on 2D ellipsoidal nematic shells. In particular, in oblate ellipsoids the extrinsic and intrinsic elastic terms enforce conflicting tendencies to positions of TDs. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs (defect,antidefect) on curved surfaces and/or presence of relevant "impurities" (e.g. nanoparticles). For this purpose, we define an effective topological charge Deltameff consisting of real, virtual and smeared curvature topological charges within a surface patch Deltazeta identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Deltam eff ≠ 0 on surfaces composed of Deltazeta exhibiting significantly different values of spatially averaged K. For non-zero Deltameff, we estimate a critical depinning threshold to form pairs (defect,antidefect) using the electrostatic analogy. Effectively two-dimensional (2D) closed films exhibiting in-plane orientational ordering (ordered shells) might be an instrumental for the realization of scaled crystals. In them ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs) within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e. linkers) which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose it is of interest to develop simple and robust mechanism via which one could control position and number of TDs in such atoms. In this thesis we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically effciency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could effciently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter. Red blood cells (erythrocytes) are present in almost all vertebrates and their main function is the transport oxygen to the body tissues. Erythrocyte shape plays an important role in its functionality. In almost all mammals in normal conditions erythrocytes adopt a disk-like (discocyte) shape which optimizes their flow properties in large vessels and capillaries. The experimental values of the relative volume v of stable discocyte shapes range in a relatively broad window. However, these experimental observations are not fully supported by existing theoretical membrane-shape models. In this thesis we developed theoretical model of erythrocyte membrane by using a hybrid Helfrich-Landau type mesoscopic approach, taking into account in-plane membrane ordering. We demonstrate that the derived extrinsic membrane energy term, which strongly depends on the local orientations of the molecules, is essential for the predicted broadening of the range of the relative volumes corresponding to the stable discocyte shapes, which is otherwise very narrow if only intrinsic curvature energy term dominates. A fingerprint of the importance of the extrinsic/deviatoric curvature energy term are the locations of topological defects (TDs) within a curved membrane.

Multiple Echo Diffusion Tensor Acquisition Technique (MEDITATE) on a 3T clinical scanner

PubMed Central

Baete, Steven H.; Cho, Gene; Sigmund, Eric E.

2013-01-01

This paper describes the concepts and implementation of an MRI method, Multiple Echo Diffusion Tensor Acquisition Technique (MEDITATE), which is capable of acquiring apparent diffusion tensor maps in two scans on a 3T clinical scanner. In each MEDITATE scan, a set of RF-pulses generates multiple echoes whose amplitudes are diffusion-weighted in both magnitude and direction by a pattern of diffusion gradients. As a result, two scans acquired with different diffusion weighting strengths suffice for accurate estimation of diffusion tensor imaging (DTI)-parameters. The MEDITATE variation presented here expands previous MEDITATE approaches to adapt to the clinical scanner platform, such as exploiting longitudinal magnetization storage to reduce T2-weighting. Fully segmented multi-shot Cartesian encoding is used for image encoding. MEDITATE was tested on isotropic (agar gel), anisotropic diffusion phantoms (asparagus), and in vivo skeletal muscle in healthy volunteers with cardiac-gating. Comparisons of accuracy were performed with standard twice-refocused spin echo (TRSE) DTI in each case and good quantitative agreement was found between diffusion eigenvalues, mean diffusivity, and fractional anisotropy derived from TRSE-DTI and from the MEDITATE sequence. Orientation patterns were correctly reproduced in both isotropic and anisotropic phantoms, and approximately so for in vivo imaging. This illustrates that the MEDITATE method of compressed diffusion encoding is feasible on the clinical scanner platform. With future development and employment of appropriate view-sharing image encoding this technique may be used in clinical applications requiring time-sensitive acquisition of DTI parameters such as dynamical DTI in muscle. PMID:23828606

Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations

NASA Astrophysics Data System (ADS)

Madsen, Niels Kristian; Godtliebsen, Ian H.; Losilla, Sergio A.; Christiansen, Ove

2018-01-01

A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.

A 2D forward and inverse code for streaming potential problems

NASA Astrophysics Data System (ADS)

Soueid Ahmed, A.; Jardani, A.; Revil, A.

2013-12-01

The self-potential method corresponds to the passive measurement of the electrical field in response to the occurrence of natural sources of current in the ground. One of these sources corresponds to the streaming current associated with the flow of the groundwater. We can therefore apply the self- potential method to recover non-intrusively some information regarding the groundwater flow. We first solve the forward problem starting with the solution of the groundwater flow problem, then computing the source current density, and finally solving a Poisson equation for the electrical potential. We use the finite-element method to solve the relevant partial differential equations. In order to reduce the number of (petrophysical) model parameters required to solve the forward problem, we introduced an effective charge density tensor of the pore water, which can be determined directly from the permeability tensor for neutral pore waters. The second aspect of our work concerns the inversion of the self-potential data using Tikhonov regularization with smoothness and weighting depth constraints. This approach accounts for the distribution of the electrical resistivity, which can be independently and approximately determined from electrical resistivity tomography. A numerical code, SP2DINV, has been implemented in Matlab to perform both the forward and inverse modeling. Three synthetic case studies are discussed.

Classical theory of radiating strings

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Minutia Tensor Matrix: A New Strategy for Fingerprint Matching

PubMed Central

Fu, Xiang; Feng, Jufu

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2018-05-01

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

Extended scalar-tensor theories of gravity

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

Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo

2016-04-21

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

Self-accelerating universe in scalar-tensor theories after GW170817

NASA Astrophysics Data System (ADS)

Crisostomi, Marco; Koyama, Kazuya

2018-04-01

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

Normal stress differences and beyond-Navier-Stokes hydrodynamics

NASA Astrophysics Data System (ADS)

Alam, Meheboob; Saha, Saikat

2017-06-01

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

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

NASA Astrophysics Data System (ADS)

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

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

Hydrodynamics of isotropic and liquid crystalline active polymer solutions.

PubMed

Ahmadi, Aphrodite; Marchetti, M C; Liverpool, T B

2006-12-01

We describe the large-scale collective behavior of solutions of polar biofilaments and stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization, and alignment tensor obtained by coarse-graining the Smoluchovski equation. The possible homogeneous and inhomogeneous states of the systems are obtained as stable solutions of the dynamical equations and are characterized in terms of experimentally accessible parameters. We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.

Communication: Appearance of undershoots in start-up shear: Experimental findings captured by tumbling-snake dynamics

NASA Astrophysics Data System (ADS)

Stephanou, Pavlos S.; Schweizer, Thomas; Kröger, Martin

2017-04-01

Our experimental data unambiguously show (i) a damping behavior (the appearance of an undershoot following the overshoot) in the transient shear viscosity of a concentrated polymeric solution, and (ii) the absence of a corresponding behavior in the transient normal stress coefficients. Both trends are shown to be quantitatively captured by the bead-link chain kinetic theory for concentrated polymer solutions and entangled polymer melts proposed by Curtiss and Bird, supplemented by a non-constant link tension coefficient that we relate to the nematic order parameter. The observed phenomena are attributed to the tumbling behavior of the links, triggered by rotational fluctuations, on top of reptation. Using model parameters deduced from stationary data, we calculate the transient behavior of the stress tensor for this "tumbling-snake" model after startup of shear flow efficiently via simple Brownian dynamics. The unaltered method is capable of handling arbitrary homogeneous flows and has the promising capacity to improve our understanding of the transient behavior of concentrated polymer solutions.

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

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2000-01-01

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

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed

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

2008-07-23

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

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

NASA Astrophysics Data System (ADS)

Miao, Xijiang; Mukhopadhyay, Rishi; Valafar, Homayoun

2008-10-01

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

Black holes in vector-tensor theories

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

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

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

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

PubMed Central

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

2017-01-01

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

Fluid Registration of Diffusion Tensor Images Using Information Theory

PubMed Central

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

2008-01-01

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

Inertial sensor and method of use

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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.

Symmetries of the Space of Linear Symplectic Connections

NASA Astrophysics Data System (ADS)

Fox, Daniel J. F.

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Kornbluth, Mordechai; Marianetti, Chris

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

Effective description of higher-order scalar-tensor theories

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

Langlois, David; Mancarella, Michele; Vernizzi, Filippo

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

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

Park, Jong-Kyu; Logan, Nikolas C.

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Stress modeling in colloidal dispersions undergoing non-viscometric flows

NASA Astrophysics Data System (ADS)

Dolata, Benjamin; Zia, Roseanna

2017-11-01

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

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

PubMed Central

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

2016-01-01

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

High-order perturbations of a spherical collapsing star

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

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

2010-11-15

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

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

What is the right formalism to search for resonances?

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

Mikhasenko, M.; Pilloni, A.; Nys, J.

Hmore » adron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. ereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B → ψ π K and B → D ¯ π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.« less

What is the right formalism to search for resonances?

DOE PAGES

Mikhasenko, M.; Pilloni, A.; Nys, J.; ...

2018-03-17

Hmore » adron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. ereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B → ψ π K and B → D ¯ π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.« less

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

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

Zeile, J.R.

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

Observational constraints on monomial warm inflation

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

Visinelli, Luca, E-mail: Luca.Visinelli@studio.unibo.it

Warm inflation is, as of today, one of the best motivated mechanisms for explaining an early inflationary period. In this paper, we derive and analyze the current bounds on warm inflation with a monomial potential U ∝ φ {sup p} , using the constraints from the PLANCK mission. In particular, we discuss the parameter space of the tensor-to-scalar ratio r and the potential coupling λ of the monomial warm inflation in terms of the number of e-folds. We obtain that the theoretical tensor-to-scalar ratio r ∼ 10{sup −8} is much smaller than the current observational constrain r ∼< 0.12, despitemore » a relatively large value of the field excursion Δ φ ∼ 0.1 M {sub Pl}. Warm inflation thus eludes the Lyth bound set on the tensor-to-scalar ratio by the field excursion.« less

Spin-Flipping Polarized Deuterons At COSY

NASA Astrophysics Data System (ADS)

Yonehara, K.; Krisch, A. D.; Morozov, V. S.; Raymond, R. S.; Wong, V. K.; Bechstedt, U.; Gebel, R.; Lehrach, A.; Lorenz, B.; Maier, R.; Prasuhn, D.; Schnase, A.; Stockhorst, H.; Eversheim, D.; Hinterberger, F.; Rohdjess, H.; Ulbrich, K.; Scobel, W.

2004-02-01

We recently stored a 1.85 GeV/c vertically polarized deuteron beam in the COSY Ring in Jülich; we then spin-flipped it by ramping a new air-core rf dipole's frequency through an rf-induced spin resonance to manipulate the polarization direction of the deuteron beam. We first experimentally determined the resonance's frequency and set the dipole's rf voltage to its maximum; then we varied its frequency ramp time and frequency range. We used the EDDA detector to measure the vector and tensor polarization asymmetries. We have not yet extracted the deuteron's tensor polarization spin-flip parameters from the measured data, since our short run did not provide adequate tensor analyzing-power data at 1.85 GeV/c. However, with a 100 Hz frequency ramp and our longest ramp time of 400 s, the deuterons' vector polarization spin-flip efficiency was 48±1%.

Quantum-metric contribution to the pair mass in spin-orbit-coupled Fermi superfluids

NASA Astrophysics Data System (ADS)

Iskin, M.

2018-03-01

As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which corresponds to the Berry curvature measuring the emergent gauge field in momentum space. Here, we first derive the Ginzburg-Landau theory near the critical superfluid transition temperature and then identify and analyze the geometric effects on the effective mass tensor of the Cooper pairs. By showing that the quantum-metric contribution accounts for a sizable fraction of the pair mass in a surprisingly large parameter regime throughout the BCS-Bose-Einstein condensate crossover, we not only reveal the physical origin of its governing role in the superfluid density tensor but also hint at its plausible roles in many other observables.

Conflation: a new type of accelerated expansion

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

Fertig, Angelika; Lehners, Jean-Luc; Mallwitz, Enno

2016-08-31

In the framework of scalar-tensor theories of gravity, we construct a new kind of cosmological model that conflates inflation and ekpyrosis. During a phase of conflation, the universe undergoes accelerated expansion, but with crucial differences compared to ordinary inflation. In particular, the potential energy is negative, which is of interest for supergravity and string theory where both negative potentials and the required scalar-tensor couplings are rather natural. A distinguishing feature of the model is that, for a large parameter range, it does not significantly amplify adiabatic scalar and tensor fluctuations, and in particular does not lead to eternal inflation andmore » the associated infinities. We also show how density fluctuations in accord with current observations may be generated by adding a second scalar field to the model. Conflation may be viewed as complementary to the recently proposed anamorphic universe of Ijjas and Steinhardt.« less

Road detection in SAR images using a tensor voting algorithm

NASA Astrophysics Data System (ADS)

Shen, Dajiang; Hu, Chun; Yang, Bing; Tian, Jinwen; Liu, Jian

2007-11-01

In this paper, the problem of the detection of road networks in Synthetic Aperture Radar (SAR) images is addressed. Most of the previous methods extract the road by detecting lines and network reconstruction. Traditional algorithms such as MRFs, GA, Level Set, used in the progress of reconstruction are iterative. The tensor voting methodology we proposed is non-iterative, and non-sensitive to initialization. Furthermore, the only free parameter is the size of the neighborhood, related to the scale. The algorithm we present is verified to be effective when it's applied to the road extraction using the real Radarsat Image.

Structural Assembly of Multidomain Proteins and Protein Complexes Guided by the Overall Rotational Diffusion Tensor

PubMed Central

Ryabov, Yaroslav; Fushman, David

2008-01-01

We present a simple and robust approach that uses the overall rotational diffusion tensor as a structural constraint for domain positioning in multidomain proteins and protein-protein complexes. This method offers the possibility to use NMR relaxation data for detailed structure characterization of such systems provided the structures of individual domains are available. The proposed approach extends the concept of using long-range information contained in the overall rotational diffusion tensor. In contrast to the existing approaches, we use both the principal axes and principal values of protein’s rotational diffusion tensor to determine not only the orientation but also the relative positioning of the individual domains in a protein. This is achieved by finding the domain arrangement in a molecule that provides the best possible agreement with all components of the overall rotational diffusion tensor derived from experimental data. The accuracy of the proposed approach is demonstrated for two protein systems with known domain arrangement and parameters of the overall tumbling: the HIV-1 protease homodimer and Maltose Binding Protein. The accuracy of the method and its sensitivity to domain positioning is also tested using computer-generated data for three protein complexes, for which the experimental diffusion tensors are not available. In addition, the proposed method is applied here to determine, for the first time, the structure of both open and closed conformations of Lys48-linked di-ubiquitin chain, where domain motions render impossible accurate structure determination by other methods. The proposed method opens new avenues for improving structure characterization of proteins in solution. PMID:17550252

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).

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Serial proton MR spectroscopy and diffusion tensor imaging in infantile Balo's concentric sclerosis.

PubMed

Dreha-Kulaczewski, Steffi F; Helms, Gunther; Dechent, Peter; Hofer, Sabine; Gärtner, Jutta; Frahm, Jens

2009-02-01

Proton magnetic resonance spectroscopy (MRS) and diffusion tensor imaging (DTI) yield different parameters for characterizing the evolution of a demyelinating white matter disease. The purpose was to elucidate biochemical and microstructural changes in Balo's concentric sclerosis lesions and to correlate the findings with the clinical course. Localized short-echo time MRS and DTI were performed over 6 years in a left occipital lesion of a female patient (age at onset 13.8 years) with Balo's concentric sclerosis. A right homonym hemianopsia persisted. Metabolite patterns were in line with initial active demyelination followed by gliosis and partial recovery of neuroaxonal metabolites. Fractional anisotropy and mean diffusivity of tissue water remained severely altered. Fiber tracking confirmed a disruption in the geniculo-calcarine tract as well as involvement of the corpus callosum. MRS and DTI depict complementary parameters, but DTI seems to correlate better with clinical symptoms.

Source Parameters for Moderate Earthquakes in the Zagros Mountains with Implications for the Depth Extent of Seismicity

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

Adams, A; Brazier, R; Nyblade, A

2009-02-23

Six earthquakes within the Zagros Mountains with magnitudes between 4.9 and 5.7 have been studied to determine their source parameters. These events were selected for study because they were reported in open catalogs to have lower crustal or upper mantle source depths and because they occurred within an area of the Zagros Mountains where crustal velocity structure has been constrained by previous studies. Moment tensor inversion of regional broadband waveforms have been combined with forward modeling of depth phases on short period teleseismic waveforms to constrain source depths and moment tensors. Our results show that all six events nucleated withinmore » the upper crust (<11 km depth) and have thrust mechanisms. This finding supports other studies that call into question the existence of lower crustal or mantle events beneath the Zagros Mountains.« less