Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow
Alam, Meheboob; Saha, Saikat
2014-11-01
The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.
Entanglement entropy from the holographic stress tensor
International Nuclear Information System (INIS)
Bhattacharyya, Arpan; Sinha, Aninda
2013-01-01
We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the time–time component of the Brown–York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean action methods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription. (paper)
Complete stress tensor determination by microearthquake analysis
Slunga, R.
2010-12-01
Jones 1984 found that half of the shallow strike-slip EQ in California had at least one M>2 foreshock. By the Gutenberg law this means at least 3-20 M>0 (low b-value 0.4-0.8). deformations within the crust. This was confirmed by observations in Iceland after 1990 when anew seismic network in Iceland operated by IMO started. Like the Parkfield project in California the SIL network in Iceland was established in an area predicted (Einarsson et al 1981, Stefansson and Halldorsson 1988) to be struck by major EQs within decades of years. The area of main interest have a detection threshold of M=0. A physical approach was chosen to the earthquake warning problem (Stefansson et al 1993) and therefore all microearthquakes were analyzed for FPS by the spectral amplitude method (Slunga 1981). As the shear slip is caused by the in situ stress it is logical to investigate what bounds the FPS puts on the stress tensor. McKenzie 1969 assumed that the earthquake takes place in a crust containing only one fracture, the fault plane. He found that in s uch a case only very weak constraints could be put on the stress. This was widely accepted t o be valid also for microearthquakes in the real crust and lead to methods (Angelier 1978, G ephart and Forsythe 1984 etc) to put four constraints on the stress tensor by assuming that the same stress tensor is causing the slip on four or more different fractures. Another and more realistic approach is to assume that the crust have frequent fractures with almost all orientations. In such a case one can rely on Coulomb's failure criterion for isotropic mat erial (gives four constraints) instead of the weaker Bolt's criterion (giving only one const raint). One obvious fifth constraint is to require the vertical stress to equal the lithosta tic pressure. A sixth constraint is achieved by requiring that the deviatoric elastic energy is minimized. The water pressure is also needed for the fourth constraint by Coulomb (CFS=0 ). It can be related to
Theoretical study of lithium clusters by electronic stress tensor
International Nuclear Information System (INIS)
Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo
2012-01-01
We study the electronic structure of small lithium clusters Li_n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.
Stress tensor fluctuations in de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Pérez-Nadal, Guillem; Verdaguer, Enric [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain); Roura, Albert, E-mail: guillem@ffn.ub.es, E-mail: albert.roura@aei.mpg.de, E-mail: enric.verdaguer@ub.edu [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm (Germany)
2010-05-01
The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m{sup 2}/H{sup 2}. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.
Holographic stress tensor for non-relativistic theories
International Nuclear Information System (INIS)
Ross, Simon F.; Saremi, Omid
2009-01-01
We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.
On the skew-symmetric character of the couple-stress tensor
Hadjesfandiari, Ali R.
2013-01-01
In this paper, the skew-symmetric character of the couple-stress tensor is established as the result of arguments from tensor analysis. Consequently, the couple-stress pseudo-tensor has a true vectorial character. The fundamental step in this development is that the isotropic couple-stress tensor cannot exist.
Thermodynamical inequivalence of quantum stress-energy and spin tensors
International Nuclear Information System (INIS)
Becattini, F.; Tinti, L.
2011-01-01
It is shown that different couples of stress-energy and spin tensors of quantum-relativistic fields, which would be otherwise equivalent, are in fact inequivalent if the second law of thermodynamics is taken into account. The proof of the inequivalence is based on the analysis of a macroscopic system at full thermodynamical equilibrium with a macroscopic total angular momentum and a specific instance is given for the free Dirac field, for which we show that the canonical and Belinfante stress-energy tensors are not equivalent. For this particular case, we show that the difference between the predicted angular momentum densities for a rotating system at full thermodynamical equilibrium is a quantum effect, persisting in the nonrelativistic limit, corresponding to a polarization of particles of the order of (ℎ/2π)ω/KT (ω being the angular velocity) and could in principle be measured experimentally. This result implies that specific stress-energy and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the thermodynamically right (or the right class of) tensors. We argue that the maximization of the thermodynamic potential theoretically allows us to discriminate between two different couples, yet for the present we are unable to provide a theoretical method to single out the best couple of tensors in a given quantum field theory. The existence of a nonvanishing spin tensor would have major consequences in hydrodynamics, gravity and cosmology.
Properties of the stress tensor in more than two dimensions
International Nuclear Information System (INIS)
Cappelli, A.
1988-03-01
Some aspects of conformal invariance in more than two dimensions are analysed. In this case conformal (Weyl) transformations of the metric are not realized in general by coordinate transformations. The operator product expansion of the stress tensor is investigated by means of examples in the free bosonic and fermionic theories. The effective action for the general form of the trace anomaly is built in four dimensions and the Wess-Zumino consistency conditions are discussed. This gives the anomalous transformation law of the stress tensor and the relation to the Casimir effect in the geometry R x S 3 . The explicit computation of the bosonic partition function provides a check
Stress strain tensors with their application to x-ray stress measurement
International Nuclear Information System (INIS)
Kurita, Masanori
2015-01-01
This paper describes in detail the method of obtaining the formulas of stress-strain tensor that express the directional dependence of stress-strain, that is, how these values change in response to coordinate transformation, and clarifies the preconditions for supporting both formulas. The two conversion formulas are both the second order of tensor, and the formula of strain tensor not only does not use the relational expression of stress and strain at all, but also is obtained completely independently of the formula of stress tensor. Except for the condition that the strain is very small (elastic deformation) in the conversion formula of strain, both formulas unconditionally come into effect. In other words, both formulas hold true even in the isotropic elastic body or anisotropic elastic body. It was shown that the conversion formula of strain can be derived from the conversion formula of stress using the formula of Hooke for isotropic elastic body. From these three-dimensional expressions, the two-dimensional stress-strain coordinate conversion formula that is used for Mohr's stress-strain circle was derived. It was shown that these formulas hold true for three-dimensional stress condition with stress-strain components in the three-axial direction that are not plane stress nor plane strain condition. In addition, as an application case of this theory, two-dimensional and three-dimensional X-ray stress measurements that are effective for residual stress measurement were shown. (A.O.)
Quantum stress tensor in Schwarzschild space-time
International Nuclear Information System (INIS)
Howard, K.W.; Candelas, P.
1984-01-01
The vacuum expectation value of the stress-energy tensor for the Hartle-Hawking state in Schwartzschild space-time has been calculated for the conformal scalar field. separates naturally into the sum of two terms. The first coincides with an approximate expression suggested by Page. The second term is a ''remainder'' that may be evaluated numerically. The total expression is in good qualitative agreement with Page's approximation. These results are at variance with earlier results given by Fawcett whose error is explained
Stress-tensor OPE in N=2 superconformal theories
International Nuclear Information System (INIS)
Liendo, Pedro; Ramírez, Israel; Seo, Jihye
2016-01-01
We carry out a detailed superspace analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.
Stress-tensor OPE in N=2 superconformal theories
International Nuclear Information System (INIS)
Liendo, Pedro; Ramirez, Israel; Univ. Tecnica Federico Santa Maria, Valparaiso; Seo, Jihye
2015-11-01
We carry out a detailed superspace analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.
Gravity waves from quantum stress tensor fluctuations in inflation
International Nuclear Information System (INIS)
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-01-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
Gravity waves from quantum stress tensor fluctuations in inflation
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-11-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
Stress-tensor commutators and Schwinger terms in singleton theories
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1989-06-01
We compute the commutators of the regularized quantum stress-tensor of singleton theories formulated on the boundary of a (p + 2)-dimensional anti de Sitter space (AdS p+2 ). (These are superconformal field theories on S p x S 1 ). We find that the algebra is not closed except in the case of AdS 3 . It does contain, however, the finite dimensional AdS p+2 algebra SO(p + 1,2). We also find divergent, field dependent as well as field independent Schwinger terms (i.e. the central extensions), which, however, do not lead to anomalies in the algebra of the AdS charges. We also give a simple derivation of the two-point functions for bosonic and fermionic singletons. (author). 15 refs
Stress-energy tensors for vector fields outside a static black hole
International Nuclear Information System (INIS)
Barrios, F.A.; Vaz, C.
1989-01-01
We obtain new, approximate stress-energy tensors to describe gauge fields in the neighborhood of a Schwarzschild black hole. We assume that the coefficient of ∇ 2 R in the trace anomaly is correctly given by ζ-function regularization. Our approximation differs from that of Page and of Brown and Ottewill and relies upon a new, improved ansatz for the form of the stress-energy tensor in the ultrastatic optical metric of the black hole. The Israel-Hartle-Hawking thermal tensor is constructed to be regular on the horizon and possess the correct asymptotic behavior. Our approximation of Unruh's tensor is likewise constructed to be regular on the future horizon and exhibit a luminosity which agrees with Page's numerically obtained value. Geometric expressions for the approximate tensors are given, and the approximate energy density of the thermal tensor on the horizon is compared with recent numerical estimates
TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid
Kononova, Olga; Maksudov, Farkhad; Marx, Kenneth A.; Barsegov, Valeri
2018-01-01
A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and C_α -based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid’s mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.
Realizability conditions for the turbulent stress tensor in large-eddy simulation
Vreman, A.W.; Geurts, Bernardus J.; Kuerten, Johannes G.M.
1994-01-01
The turbulent stress tensor in large-eddy simulation is examined from a theoretical point of view. Realizability conditions for the components of this tensor are derived, which hold if and only if the filter function is positive. The spectral cut-off, one of the filters frequently used in large-eddy
Characteristics of the Residual Stress tensor when filter width is larger than the Ozmidov scale
de Bragança Alves, Felipe Augusto; de Bruyn Kops, Stephen
2017-11-01
In stratified turbulence, the residual stress tensor is statistically anisotropic unless the smallest resolved length scale is smaller than the Ozmidov scale and the buoyancy Reynolds number is sufficiently high for there to exist a range of scales that is statistically isotropic. We present approximations to the residual stress tensor that are derived analytically. These approximations are evaluated by filtering data from direct numerical simulations of homogeneous stratified turbulence, with unity Prandtl number, resolved on up to 8192 × 8192 × 4096 grid points along with an isotropic homogeneous case resolved on 81923 grid points. It is found that the best possible scaling of the strain rate tensor yields a residual stress tensor (RST) that is less well statistically aligned with the exact RST than a randomly generated tensor. It is also found that, while a scaling of the strain rate tensor can dissipate the right amount of energy, it produces incorrect anisotropic dissipation, removing energy from the wrong components of the velocity vector. We find that a combination of the strain rate tensor and a tensor related to energy redistribution caused by a Newtonian fluid viscous stress yields an excellent tensorial basis for modelling the RST.
Flavour fields in steady state: stress tensor and free energy
International Nuclear Information System (INIS)
Banerjee, Avik; Kundu, Arnab; Kundu, Sandipan
2016-01-01
The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the stress tensor of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane is embedded in AdS d+1 -background, for d=2,4, and is related to conformal anomaly. For the special case of d=2, the universal factor has a striking resemblance to the well-known heat current formula in (1+1)-dimensional conformal field theory in steady-state, which endows a plausible physical interpretation to it. Interestingly, we observe a vanishing conformal anomaly in d=6.
On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity
Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia
2008-11-01
Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).
Stress tensor of a quark moving through N=4 thermal plasma
International Nuclear Information System (INIS)
Friess, Joshua J.; Gubser, Steven S.; Michalogiorgakis, Georgios; Pufu, Silviu S.
2007-01-01
We develop the linear equations that describe graviton perturbations of AdS 5 -Schwarzschild generated by a string trailing behind an external quark moving with constant velocity. Solving these equations allows us to evaluate the stress tensor in the boundary gauge theory. Components of the stress tensor exhibit directional structures in Fourier space at both large and small momenta. We comment on the possible relevance of our results to relativistic heavy-ion collisions
Conservation laws and stress-energy-momentum tensors for systems with background fields
Energy Technology Data Exchange (ETDEWEB)
Gratus, Jonathan, E-mail: j.gratus@lancaster.ac.uk [Lancaster University, Lancaster LA1 4YB (United Kingdom); The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD (United Kingdom); Obukhov, Yuri N., E-mail: yo@thp.uni-koeln.de [Institute for Theoretical Physics, University of Cologne, 50923 Koeln (Germany); Tucker, Robin W., E-mail: r.tucker@lancaster.ac.uk [Lancaster University, Lancaster LA1 4YB (United Kingdom); The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD (United Kingdom)
2012-10-15
This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.
Flat-space holography and stress tensor of Kerr black hole
Energy Technology Data Exchange (ETDEWEB)
Baghchesaraei, Omid, E-mail: omidbaghchesaraei@gmail.com [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Fareghbal, Reza, E-mail: r_fareghbal@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Izadi, Yousef, E-mail: yizadi2015@fau.edu [Department of Physics, Florida Atlantic University, Boca Raton, FL 33431 (United States)
2016-09-10
We propose a stress tensor for the Kerr black hole written in the Boyer–Lindquist coordinate. To achieve this, we use the dictionary of the Flat/CCFT correspondence and take the flat-space limit from the quasi-local stress tensor of the four-dimensional Kerr–AdS black hole. The proposed stress tensor yields the correct values for the mass and angular momentum of the Kerr black hole at spatial infinity. We also calculate some components of the energy momentum tensor of the three dimensional CCFT and show that they are consistent with the holographic calculation of the Kerr black hole. The calculation we present in this paper is another confirmation for the Flat/CCFT proposal.
Effective gravitational wave stress-energy tensor in alternative theories of gravity
International Nuclear Information System (INIS)
Stein, Leo C.; Yunes, Nicolas
2011-01-01
The inspiral of binary systems in vacuum is controlled by the stress-energy of gravitational radiation and any other propagating degrees of freedom. For gravitational waves, the dominant contribution is characterized by an effective stress-energy tensor at future null infinity. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that this tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson's. We exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then consider a wide class of theories with dynamical scalar fields coupled to higher-order curvature invariants and show that the gravitational wave stress-energy tensor still reduces to Isaacson's. The calculations presented in this paper are crucial to perform systematic tests of such modified gravity theories through the orbital decay of binary pulsars or through gravitational wave observations.
Study of the characteristics of crust stress field in East China by inversion of stress tensor
International Nuclear Information System (INIS)
Huilan, Z.; Rugang, D.
1991-12-01
This paper combines the search procedure with the optimization procedure to inverse the average stress tensor, and applies this method to study the crustal stress field using data of the solution of P wave first motion. By dealing with the data of Haicheng, Tangshan, Xingtai, Anyang, Liyang, Taiwan, Fujian and Guangdong areas, we obtain the characteristics of crust stress field of East China. The directions of the principal pressure stress always possess a small dip angle, but the azimuths vary from NEE (in north part of East China) to SEE (in the south part). This frame probably is related to the push-extrusive effects of the northwestern Pacific plate from NEE and the Philippine plate from SEE. (author). 5 refs, 8 figs, 4 tabs
Tranos, Markos D.
2018-02-01
Synthetic heterogeneous fault-slip data as driven by Andersonian compressional stress tensors were used to examine the efficiency of best-fit stress inversion methods in separating them. Heterogeneous fault-slip data are separated only if (a) they have been driven by stress tensors defining 'hybrid' compression (R constitute a necessary discriminatory tool for the establishment and comparison of two compressional stress tensors determined by a best-fit stress inversion method. The best-fit stress inversion methods are not able to determine more than one 'real' compressional stress tensor, as far as the thrust stacking in an orogeny is concerned. They can only possibly discern stress differences in the late-orogenic faulting processes, but not between the main- and late-orogenic stages.
Stress-energy tensor near a charged, rotating, evaporating black hole
International Nuclear Information System (INIS)
Hiscock, W.A.
1977-01-01
The recently developed two-dimensional stress-energy regularization techniques are applied to the two-dimensional analog of the Reissner-Nordstroem family of black-hole metrics. The calculated stress-energy tensor in all cases contains the thermal radiation discovered by Hawking. Implications for the evolution of the interior of a charged black hole are considered. The calculated stress-energy tensor is found to diverge on the inner, Cauchy, horizon. Thus the effect of quantum mechanics is to cause the Cauchy horizon to become singular. The stress-energy tensor is also calculated for the ''most reasonable'' two-dimensional analog of the Kerr-Newman family of black-hole metrics. Although the analysis is not as rigorous as in the Reissner-Nordstroem case, it appears that the correct value for the Hawking radiation also appears in this model
Estimating maize water stress by standard deviation of canopy temperature in thermal imagery
A new crop water stress index using standard deviation of canopy temperature as an input was developed to monitor crop water status. In this study, thermal imagery was taken from maize under various levels of deficit irrigation treatments in different crop growing stages. The Expectation-Maximizatio...
Boundary stress tensors for spherically-symmetric conformal Rindler observers
Energy Technology Data Exchange (ETDEWEB)
Culetu, Hristu [Ovidius University, Constanta (Romania)
2010-06-15
The boundary energy-momentum tensors for a static observer in the conformally flat Rindler geometry are considered. We find that the surface energy density is positive far from the Planck world, but that the transversal pressures are negative. The kinematical parameters associated with the nongeodesic congruence of static observers are computed. The entropy S corresponding to the degrees of freedom on the 2-surface of constant {rho} and t equals the horizon entropy of a black hole with a time-dependent mass, and the Padmanabhan expression E = 2ST is obeyed. The 2-surface shear tensor is vanishing, and the coefficient of the bulk viscosity {zeta} is 1/16 {pi}, so the negative pressure due to it acts as a surface tension.
Münch, Ingo; Neff, Patrizio; Madeo, Angela; Ghiba, Ionel-Dumitrel
2015-01-01
We show that the reasoning in favor of a symmetric couple stress tensor in Yang et al.'s introduction of the modified couple stress theory contains a gap, but we present a reasonable physical hypothesis, implying that the couple stress tensor is traceless and may be symmetric anyway. To this aim, the origin of couple stress is discussed on the basis of certain properties of the total stress itself. In contrast to classical continuum mechanics, the balance of linear momentum and the balance of...
Neutrino stress tensor regularization in two-dimensional space-time
International Nuclear Information System (INIS)
Davies, P.C.W.; Unruh, W.G.
1977-01-01
The method of covariant point-splitting is used to regularize the stress tensor for a massless spin 1/2 (neutrino) quantum field in an arbitrary two-dimensional space-time. A thermodynamic argument is used as a consistency check. The result shows that the physical part of the stress tensor is identical with that of the massless scalar field (in the absence of Casimir-type terms) even though the formally divergent expression is equal to the negative of the scalar case. (author)
International Nuclear Information System (INIS)
Brown, M.R.; Ottewill, A.C.
1986-01-01
We present the symmetric Hadamard representation for scalar and photon Feynman Green's functions. We use these representations to give a simple definition for their associated renormalized stress tensors. We investigate the connection between the accuracy of the WKB approximation and the vanishing of the trace anomaly for these fields. We show that, although for scalars there is a direct connection, this is not true for photons, and we discuss the relevance of these results to the approximation of renormalized stress tensors in static Einstein space-times
Stress tensor from the trace anomaly in Reissner-Nordstroem spacetimes
International Nuclear Information System (INIS)
Anderson, Paul R.; Mottola, Emil; Vaulin, Ruslan
2007-01-01
The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes. In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate r for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor. By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordstroem event horizons, including the extreme Q=M case. We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary. The approximation scheme based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family (0≤Q≤M) of RN horizons
On renormalisation of the quantum stress tensor in curved space-time by dimensional regularisation
International Nuclear Information System (INIS)
Bunch, T.S.
1979-01-01
Using dimensional regularisation, a prescription is given for obtaining a finite renormalised stress tensor in curved space-time. Renormalisation is carried out by renormalising coupling constants in the n-dimensional Einstein equation generalised to include tensors which are fourth order in derivatives of the metric. Except for the special case of a massless conformal field in a conformally flat space-time, this procedure is not unique. There exists an infinite one-parameter family of renormalisation ansatze differing from each other in the finite renormalisation that takes place. Nevertheless, the renormalised stress tensor for a conformally invariant field theory acquires a nonzero trace which is independent of the renormalisation ansatz used and which has a value in agreement with that obtained by other methods. A comparison is made with some earlier work using dimensional regularisation which is shown to be in error. (author)
The Topology of Symmetric Tensor Fields
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.
International Nuclear Information System (INIS)
Glowka, D.A.
1990-09-01
This report investigates the effects of borehole deviation on the useability of lined boreholes for the disposal of high-level nuclear waste at the proposed Yucca Mountain Repository in Nevada. Items that lead to constraints on borehole deviation include excessive stresses that could cause liner failure and possible binding of a waste container inside the liner during waste emplacement and retrieval operations. Liner stress models are developed for two general borehole configurations, one for boreholes drilled with a steerable bit and one for boreholes drilled with a non-steerable bit. Procedures are developed for calculating liner stresses that arise both during insertion of the liner into a borehole and during the thermal expansion process that follows waste emplacement. The effects of borehole curvature on the ability of the waste container to pass freely inside the liner without binding are also examined. Based on the results, specifications on borehole deviation allowances are developed for specific vertical and horizontal borehole configurations of current interest. 11 refs., 22 figs., 4 tabs
DEFF Research Database (Denmark)
Pessah, Martin Elias; Chan, Chi-kwan; Psaltis, Dimitrios
2006-01-01
stresses during the late times of the exponential growth of the instability is determined only by the local shear and does not depend on the initial spectrum of perturbations or the strength of the seed magnetic. Even though we derived these properties of the stress tensors for the exponential growth...... of the instability, the mean (averaged over the disc scale-height) Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the mean total stress is positive and leads to a net outward flux of angular momentum. More importantly, we show that the ratio of the Maxwell to the Reynolds...
Coordinate invariance, the differential force law, and the divergence of the stress-energy tensor
International Nuclear Information System (INIS)
Epstein, S.T.
1975-01-01
Hermitian operators linear in momenta generate coordinate transformations. The associated hypervirial theorems are written in the form of moments of a differential force law, and a connection is made with the stress-energy tensor of the Schrodinger field in configuration space
Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole
Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric
2017-07-01
We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.
Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows
Vermeulen, B.; Hoitink, A.J.F.; Sassi, M.G.
2011-01-01
We introduce a new technique to measure profiles of each term in the Reynolds stress tensor using coupled acoustic Doppler current profilers (ADCPs). The technique is based on the variance method which is extended to the case with eight acoustic beams. Methods to analyze turbulence from a single
Electromagnetic energy density and stress tensor in a warm plasma with finite flow velocity
International Nuclear Information System (INIS)
Choi, Cheong R.; Lee, Nam C.
2004-01-01
The expressions of the average of energy density and the average stress tensor of the electromagnetic field in a warm collisionless plasma moving with a finite velocity are obtained by using a microscopic method that uses the fluid description of plasma. The result contains terms involved with derivatives of the dielectric tensor with respect to the velocity, which explicitly represent the effects of the finite velocity of the medium. In the zero-velocity limit, the results reduce to the well-known expressions for a plasma at rest with temporal and spatial dispersion
Lorentz invariance and the zero-point stress-energy tensor
Visser, Matt
2016-01-01
Some 65 years ago (1951) Wolfgang Pauli noted that the net zero-point energy density could be set to zero by a carefully fine-tuned cancellation between bosons and fermions. In the current article I will argue in a slightly different direction: The zero-point energy density is only one component of the zero-point stress energy tensor, and it is this tensor quantity that is in many ways the more fundamental object of interest. I shall demonstrate that Lorentz invariance of the zero-point stres...
Stress tensor for GYM in 4p dimensions and viability of GYM-Higgs in four dimensions
International Nuclear Information System (INIS)
O'Brien, G.M.; Tchrakian, D.H.
1985-01-01
We present the stress tensor for GYM systems in 4p dimensions and give a method to compute this tensor density for a GYM-Higgs system in four dimensions. This computation is made explicitly for the first such system and its viability in four Euclidean dimensions is checked. The possibility of extracting phenomenological models from this system is analysed briefly. (Author)
Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration
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.
International Nuclear Information System (INIS)
Kaschner, R.; Graefenstein, J.; Ziesche, P.
1988-12-01
From the local momentum balance using density functional theory an expression for the local quantum-mechanical stress tensor (or stress field) σ(r) of non-relativistic Coulomb systems is found out within the Thomas-Fermi approximation and its generalizations including gradient expansion method. As an illustration the stress field σ(r) is calculated for the jellium model of the interface K-Cs, containing especially the adhesive force between the two half-space jellia. (author). 23 refs, 1 fig
Four-point correlation function of stress-energy tensors in N=4 superconformal theories
Korchemsky, G P
2015-01-01
We derive the explicit expression for the four-point correlation function of stress-energy tensors in four-dimensional N=4 superconformal theory. We show that it has a remarkably simple and suggestive form allowing us to predict a large class of four-point correlation functions involving the stress-energy tensor and other conserved currents. We then apply the obtained results on the correlation functions to computing the energy-energy correlations, which measure the flow of energy in the final states created from the vacuum by a source. We demonstrate that they are given by a universal function independent of the choice of the source. Our analysis relies only on N=4 superconformal symmetry and does not use the dynamics of the theory.
Vacuum stress tensor of a scalar field in a rectangular waveguide
International Nuclear Information System (INIS)
Rodrigues, R.B.; Svaiter, N.F.; Paola, R.D.M. de
2001-11-01
Using the heat Kernel method and the analytical continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, {T μν (vector x)} and {Θ μν (vector x)}, associated with a massless scalar field confined in the interior of an infinity long rectangular waveguide. The local depence of the renormalized energy for two special configurations when the total energy is positive and negative are presented using {T 00 (vector x)} and {Θ 00 (vector x)}. From the stress tensors we obtain the local casimir forces in all walls by introducing a particular external configuration. It is hown that this external configuration cannot give account of the edge divergences of the local forces. The local form of the forces is obtained for three special configurations. (author)
Stress tensor correlators of CCFT{sub 2} using flat-space holography
Energy Technology Data Exchange (ETDEWEB)
Asadi, Mohammad; Baghchesaraei, Omid; Fareghbal, Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-11-15
We use the correspondence between three-dimensional asymptotically flat spacetimes and two-dimensional contracted conformal field theories (CCFTs) to derive the stress tensor correlators of CCFT{sub 2}. On the gravity side we use the metric formulation instead of the Chern-Simons formulation of three-dimensional gravity. This method can also be used for the four-dimensional case, where there is no Chern-Simons formulation for the bulk theory. (orig.)
International Nuclear Information System (INIS)
Adler, S.L.; Lieberman, J.
1978-01-01
We reanalyze the problem of regularization of the stress-energy tensor for massless vector particles propating in a general background metric, using covariant point separation techniques applied to the Hadamard elementary solution. We correct an error, point out by Wald, in the earlier formulation of Adler, Lieberman, and Ng, and find a stress-energy tensor trace anomaly agreeing with that found by other regularization methods
Radiative processes for Rindler and accelerating observers and the stress-tensor detector
International Nuclear Information System (INIS)
Paola, R. De; Svaiter, N.F.
1996-04-01
It is considered a monopole detector interacting with a massive scalar field. Using the rotating wave approximation the radiative processes is discussed from the accelerated frame point of view. After this, it is obtained the Minkowski vacuum stress tensor measured by the accelerated observer using a non-gravitational stress sensor detector. Finally we analyse radiative processes of the monopole detector travelling in a world line that is inertial in the infinite past and has a constant proper acceleration in the infinite future. (author). 30 refs
An application of stress energy tensor to the vanishing theorem of differential forms
Directory of Open Access Journals (Sweden)
Kairen Cai
1988-01-01
Full Text Available The author applies the stress energy of differential forms to study the vanishing theorems of the Liouville type. It is shown that for a large class of underlying manifolds such as the Euclidean n-space, the complex n-space, and the complex hyperbolic space form, if any vector bundle valued p-form with conservative stress energy tensor is of finite norm or slowly divergent norm, then the p-form vanishes. This generalizes the recent results due to Hu and Sealey.
Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector
Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming
1996-01-01
We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.
Quantum fields interacting with colliding plane waves: the stress-energy tensor and backreaction
International Nuclear Information System (INIS)
Dorca, M.; Verdaguer, E.
1997-01-01
Following a previous work on the quantization of a massless scalar field in a space-time representing the head on collision of two plane waves which focus into a Killing-Cauchy horizon, we compute the renormalized expectation value of the stress-energy tensor of the quantum field near that horizon in the physical state which corresponds to the Minkowski vacuum before the collision of the waves. It is found that for minimally coupled and conformally coupled scalar fields the respective stress-energy tensors are unbounded in the horizon. The specific form of the divergences suggests that when the semiclassical Einstein equations describing the backreaction of the quantum fields on the space-time geometry are taken into account, the horizon will acquire a curvature singularity. Thus the Killing-Cauchy horizon which is known to be unstable under ''generic'' classical perturbations is also unstable by vacuum polarization. The calculation is done following the point-splitting regularization technique. The dynamical colliding wave space-time has four quite distinct space-time regions, namely, one flat region, two single plane wave regions, and one interaction region. Exact mode solutions of the quantum field equation cannot be found exactly, but the blueshift suffered by the initial modes in the plane wave and interaction regions makes the use of the WKB expansion a suitable method of solution. To ensure the correct regularization of the stress-energy tensor, the initial flat modes propagated into the interaction region must be given to a rather high adiabatic order of approximation. (orig.)
Cui, S. T.
The stress-stress correlation function and the viscosity of a united-atom model of liquid decane are studied by equilibrium molecular dynamics simulation using two different formalisms for the stress tensor: the atomic and the molecular formalisms. The atomic and molecular correlation functions show dramatic difference in short-time behaviour. The integrals of the two correlation functions, however, become identical after a short transient period whichis significantly shorter than the rotational relaxation time of the molecule. Both reach the same plateau value in a time period corresponding to this relaxation time. These results provide a convenient guide for the choice of the upper integral time limit in calculating the viscosity by the Green-Kubo formula.
International Nuclear Information System (INIS)
Hristoforou, E.; Svec, P. Sr.
2015-01-01
We have developed an unique method to provide the stress calibration curve in steels: performing flaw-less welding in the under examination steel, we obtained to determine the level of the local plastic deformation and the residual stress tensors. These properties where measured using both the X-ray and the neutron diffraction techniques, concerning their surface and bulk stresses type II (intra-grain stresses) respectively, as well as the stress tensor type III by using the electron diffraction technique. Measuring the distribution of these residual stresses along the length of a welded sample or structure, resulted in determining the local stresses from the compressive to tensile yield point. Local measurement of the intrinsic surface and bulk magnetic property tensors allowed for the un-hysteretic correlation. The dependence of these local magnetic tensors with the above mentioned local stress tensors, resulting in a unique and almost un-hysteretic stress calibration curve of each grade of steel. This calibration integrated the steel's mechanical and thermal history, as well as the phase transformations and the presence of precipitations occurring during the welding process.Additionally to that, preliminary results in different grade of steels reveal the existence of a universal law concerning the dependence of magnetic and magnetostrictive properties of steels on their plastic deformation and residual stress state, as they have been accumulated due to their mechanical and thermal fatigue and history. This universality is based on the unique dependence of the intrinsic magnetic properties of steels normalized with a certain magnetoelastic factor, upon the plastic deformation or residual stress state, which, in terms, is normalized with their yield point of stress. (authors)
International Nuclear Information System (INIS)
Balzar, D.; Popa, N.C.; Vogel, S.
2010-01-01
We report the complete macroscopic average strain and stress tensors for a cold-rolled uranium plate, based on the neutron TOF measurements. Both tensors were determined by the least-squares refinement of the interplanar spacings of 19 Bragg reflections. Based on the pole figures, as determined by GSAS, a triclinic sample symmetry of the uranium plate was assumed. Strain and stress are tensile in both the transverse and rolling directions and very small in the normal direction (through the thickness of the plate). Shear strain and stress components are compressive and of significant magnitude.
Limkumnerd, Surachate; Sethna, James P.
We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
Correlation functions of the chiral stress-tensor multiplet in $ \\mathcal{N}=4 $ SYM
Chicherin, Dmitry; Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P.; Mason, Lionel; Sokatchev, Emery
2015-01-01
We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N=4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N=4 SYM.
Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole.
Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten
2017-04-07
We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.
Neoclassical viscous stress tensor for non-linear MHD simulations with XTOR-2F
International Nuclear Information System (INIS)
Mellet, N.; Maget, P.; Meshcheriakov, D.; Lütjens, H.
2013-01-01
The neoclassical viscous stress tensor is implemented in the non-linear MHD code XTOR-2F (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), allowing consistent bi-fluid simulations of MHD modes, including the metastable branch of neoclassical tearing modes (NTMs) (Carrera et al 1986 Phys. Fluids 29 899–902). Equilibrium flows and bootstrap current from the neoclassical theory are formally recovered in this Chew–Goldberger–Low formulation. The non-linear behaviour of the new model is verified on a test case coming from a Tore Supra non-inductive discharge. A NTM threshold that is larger than with the previous model is obtained. This is due to the fact that the velocity is now part of the bootstrap current and that it differs from the theoretical neoclassical value. (paper)
International Nuclear Information System (INIS)
Christensen, S.M.
1976-01-01
A method known as covariant geodesic point separation is developed to calculate the vacuum expectation value of the stress tensor for a massive scalar field in an arbitrary gravitational field. The vacuum expectation value will diverge because the stress-tensor operator is constructed from products of field operators evaluated at the same space-time point. To remedy this problem, one of the field operators is taken to a nearby point. The resultant vacuum expectation value is finite and may be expressed in terms of the Hadamard elementary function. This function is calculated using a curved-space generalization of Schwinger's proper-time method for calculating the Feynman Green's function. The expression for the Hadamard function is written in terms of the biscalar of geodetic interval which gives a measure of the square of the geodesic distance between the separated points. Next, using a covariant expansion in terms of the tangent to the geodesic, the stress tensor may be expanded in powers of the length of the geodesic. Covariant expressions for each divergent term and for certain terms in the finite portion of the vacuum expectation value of the stress tensor are found. The properties, uses, and limitations of the results are discussed
Stress tensor and viscosity of water: Molecular dynamics and generalized hydrodynamics results
Bertolini, Davide; Tani, Alessandro
1995-08-01
The time correlation functions (CF's) of diagonal and off-diagonal components of the stress tensor of water have been calculated at 245 and 298 K in a molecular dynamics (MD) study on 343 molecules in the microcanonical ensemble. We present results obtained at wave number k=0 and at a few finite values of k, in the atomic and molecular formalism. In all cases, more than 98% of these functions are due to the potential term of the stress tensor. At k=0, their main features are a fast oscillatory initial decay, followed by a long-time tail more apparent in the supercooled region. Bulk and shear viscosities, calculated via Green-Kubo integration of the relevant CF at k=0, are underestimated with respect to experimental data, mainly at low temperature, but their ratio (~=2) is correctly reproduced. Both shear and bulk viscosity decrease as a function of k, the latter more rapidly, so that they become almost equal at ~=1 Å-1. Also, both viscosities drop rapidly from their maximum at ω=0. This behavior has been related to the large narrowing observed in the acoustic band, mainly in the supercooled region. The infinite frequency bulk and shear rigidity moduli have been shown to be in fair agreement with the experimental data, provided the MD value used for comparison is that corresponding to the frequency range relevant to ultrasonic measurements. The MD results of stress-stress CF's compare well with those predicted by Bertolini and Tani [Phys. Rev. E 51, 1091 (1995)] at k=0, by an application of generalized hydrodynamics [de Schepper et al., Phys. Rev. A 38, 271 (1988)] in the molecular formalism, to the same model of water (TIP4P) [Jorgensen et al., J. Chem. Phys. 79, 926 (1983)]. These CF's are essentially equal in the atomic and molecular formalism, the only minor difference being restricted to the high frequency librational region of the shear function. By a comparison of atomic and molecular results, we show here that neglecting libration has no effect on the
Energy Technology Data Exchange (ETDEWEB)
Glowka, D.A.
1990-09-01
This report investigates the effects of borehole deviation on the useability of lined boreholes for the disposal of high-level nuclear waste at the proposed Yucca Mountain Repository in Nevada. Items that lead to constraints on borehole deviation include excessive stresses that could cause liner failure and possible binding of a waste container inside the liner during waste emplacement and retrieval operations. Liner stress models are developed for two general borehole configurations, one for boreholes drilled with a steerable bit and one for boreholes drilled with a non-steerable bit. Procedures are developed for calculating liner stresses that arise both during insertion of the liner into a borehole and during the thermal expansion process that follows waste emplacement. The effects of borehole curvature on the ability of the waste container to pass freely inside the liner without binding are also examined. Based on the results, specifications on borehole deviation allowances are developed for specific vertical and horizontal borehole configurations of current interest. 11 refs., 22 figs., 4 tabs.
On the equivalence among stress tensors in a gauge-fluid system
Mitra, Arpan Krishna; Banerjee, Rabin; Ghosh, Subir
2017-12-01
In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space-time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.
Long, Zhiliang; Duan, Xujun; Xie, Bing; Du, Handan; Li, Rong; Xu, Qiang; Wei, Luqing; Zhang, Shao-xiang; Wu, Yi; Gao, Qing; Chen, Huafu
2013-09-25
Post-traumatic stress disorder (PTSD) is characterized by dysfunction of several discrete brain regions such as medial prefrontal gyrus with hypoactivation and amygdala with hyperactivation. However, alterations of large-scale whole brain topological organization of structural networks remain unclear. Seventeen patients with PTSD in motor vehicle accident survivors and 15 normal controls were enrolled in our study. Large-scale structural connectivity network (SCN) was constructed using diffusion tensor tractography, followed by thresholding the mean factional anisotropy matrix of 90 brain regions. Graph theory analysis was then employed to investigate their aberrant topological properties. Both patient and control group showed small-world topology in their SCNs. However, patients with PTSD exhibited abnormal global properties characterized by significantly decreased characteristic shortest path length and normalized characteristic shortest path length. Furthermore, the patient group showed enhanced nodal centralities predominately in salience network including bilateral anterior cingulate and pallidum, and hippocampus/parahippocamus gyrus, and decreased nodal centralities mainly in medial orbital part of superior frontal gyrus. The main limitation of this study is the small sample of PTSD patients, which may lead to decrease the statistic power. Consequently, this study should be considered an exploratory analysis. These results are consistent with the notion that PTSD can be understood by investigating the dysfunction of large-scale, spatially distributed neural networks, and also provide structural evidences for further exploration of neurocircuitry models in PTSD. © 2013 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Dappiagi, Claudio; Hack, Thomas-Paul; Pinamonti, Nicola [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik
2009-03-15
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We explicitly calculate its trace anomaly in particular. (orig.)
International Nuclear Information System (INIS)
Dappiagi, Claudio; Hack, Thomas-Paul; Pinamonti, Nicola
2009-03-01
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We explicitly calculate its trace anomaly in particular. (orig.)
Kawase, H.; Nakano, K.
2015-12-01
We investigated the characteristics of strong ground motions separated from acceleration Fourier spectra and acceleration response spectra of 5% damping calculated from weak and moderate ground motions observed by K-NET, KiK-net, and the JMA Shindokei Network in Japan using the generalized spectral inversion method. The separation method used the outcrop motions at YMGH01 as reference where we extracted site responses due to shallow weathered layers. We include events with JMA magnitude equal to or larger than 4.5 observed from 1996 to 2011. We find that our frequency-dependent Q values are comparable to those of previous studies. From the corner frequencies of Fourier source spectra, we calculate Brune's stress parameters and found a clear magnitude dependence, in which smaller events tend to spread over a wider range while maintaining the same maximum value. We confirm that this is exactly the case for several mainshock-aftershock sequences. The average stress parameters for crustal earthquakes are much smaller than those of subduction zone, which can be explained by their depth dependence. We then compared the strong motion characteristics based on the acceleration response spectra and found that the separated characteristics of strong ground motions are different, especially in the lower frequency range less than 1Hz. These differences comes from the difference between Fourier spectra and response spectra found in the observed data; that is, predominant components in high frequency range of Fourier spectra contribute to increase the response in lower frequency range with small Fourier amplitude because strong high frequency component acts as an impulse to a Single-Degree-of-Freedom system. After the separation of the source terms for 5% damping response spectra we can obtain regression coefficients with respect to the magnitude, which lead to a new GMPE as shown in Fig.1 on the left. Although stress drops for inland earthquakes are 1/7 of the subduction
Wang, Lingling; Huan, Guo; Momen, Roya; Azizi, Alireza; Xu, Tianlv; Kirk, Steven R; Filatov, Michael; Jenkins, Samantha
2017-06-29
A quantum theory of atoms in molecules (QTAIM) and stress tensor analysis was applied to analyze intramolecular interactions influencing the photoisomerization dynamics of a light-driven rotary molecular motor. For selected nonadiabatic molecular dynamics trajectories characterized by markedly different S 1 state lifetimes, the electron densities were obtained using the ensemble density functional theory method. The analysis revealed that torsional motion of the molecular motor blades from the Franck-Condon point to the S 1 energy minimum and the S 1 /S 0 conical intersection is controlled by two factors: greater numbers of intramolecular bonds before the hop-time and unusually strongly coupled bonds between the atoms of the rotor and the stator blades. This results in the effective stalling of the progress along the torsional path for an extended period of time. This finding suggests a possibility of chemical tuning of the speed of photoisomerization of molecular motors and related molecular switches by reshaping their molecular backbones to decrease or increase the degree of coupling and numbers of intramolecular bond critical points as revealed by the QTAIM/stress tensor analysis of the electron density. Additionally, the stress tensor scalar and vector analysis was found to provide new methods to follow the trajectories, and from this, new insight was gained into the behavior of the S 1 state in the vicinity of the conical intersection.
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...
International Nuclear Information System (INIS)
Levashov, V. A.
2016-01-01
It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ 1 ≥ λ 2 ≥ λ 3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ 2 /λ 1 ) and (λ 3 /λ 2 ) are essentially identical to each other in the liquids state. We also found that λ 2 tends to be equal to the geometric average of λ 1 and λ 3 . In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.
Energy Technology Data Exchange (ETDEWEB)
Levashov, V. A. [Technological Design Institute of Scientific Instrument Engineering, Novosibirsk 630058 (Russian Federation)
2016-03-07
It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ{sub 1} ≥ λ{sub 2} ≥ λ{sub 3} ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ{sub 2}/λ{sub 1}) and (λ{sub 3}/λ{sub 2}) are essentially identical to each other in the liquids state. We also found that λ{sub 2} tends to be equal to the geometric average of λ{sub 1} and λ{sub 3}. In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.
Varadhan, S R S
2016-01-01
The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
A Review of Tensors and Tensor Signal Processing
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.
Directory of Open Access Journals (Sweden)
Abolfazl Ghasemzadeh
2017-06-01
Full Text Available The phenomenon of job stress is an inevitable part of professional life and in the activities and efficiency is reflected in the organization. This study aimed to identify and predict the relationship between psychological capital and job deviation behavior through job stress regarding the moderating role of perceived organizational support. This study is correlation by using descriptive methods for applied goals. Standard questionnaire was used to collect data. 180 participants was estimated and stratified random sampling. The results showed the significance of the relationship between the variables except the relationship between deviant behaviors with psychological capital. Also, the interactive role of job stress and perceived organizational support on psychological capital and job deviation behavior was confirmed. This means that for the hospital's nurses and staffs with job stress, increasing perceived organizational support associated with enhancing psychological capital and decreasing job deviation behavior. These results emphasize necessity of recognizing interactive role of job stress and perceived organizational support in psychological capital and job deviation behavior
Deuschel, Jean-Dominique; Deuschel, Jean-Dominique
2001-01-01
This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allow
Li, Jiahui; Xu, Tianlv; Ping, Yang; van Mourik, Tanja; Früchtl, Herbert; Kirk, Steven R.; Jenkins, Samantha
2018-03-01
QTAIM and the stress tensor were used to provide a detailed analysis of the topology of the molecular graph, BCP and bond-path properties, including the new introduced helicity length H, of a Tyr-Gly dipeptide conformer subjected to a torsion with four levels of theory; MP2, M06-2X, B3LYP-D3 and B3LYP and a modest-sized basis set, 6-31+G(d). Structural effects and bonding properties are quantified and reflect differences in the BSSE and lack of inclusion of dispersion effects in the B3LYP calculations. The helicity length H demonstrated that MP2 produced a unique response to the torsion suggesting future use as a diagnostic tool.
The stress energy tensor of a locally supersymmetric quantum field on a curved spacetime
International Nuclear Information System (INIS)
Koehler, M.
1995-04-01
For an analogon of the free Wess-Zumino model on Ricci flat spacetimes, the relation between a conserved 'supercurrent' and the point-separated improved energy momentum tensor is investigated and a similar relation as on Minkowski space is established. The expectation value of the latter in any globally Hadamard product state is found to be a priori finite in the coincidence limit if the theory is massive. On arbitrary globally hyperbolic spacetimes the 'supercurrent' is shown to be a well defined operator valued distribution on the GNS Hilbertspace of any globally Hadamard product state. Viewed as a new field, all n-point distributions exist, giving a new example for a Wightman field on that manifold. Moreover, it is shown that this field satisfies a new wave front set spectrum condition in a nontrivial way. (orig.)
A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2018-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new
Towards the Irving-Kirkwood limit of the mechanical stress tensor
Smith, E. R.; Heyes, D. M.; Dini, D.
2017-06-01
The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V =ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ =1.0 , a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.
The radiation stress and beaches; El tensor de radiacion y las playas
Energy Technology Data Exchange (ETDEWEB)
Lechuga Alvaro, A. [Ministerio de Fomento (Spain)
1998-06-01
In this paper we summarize the main characteristics of the radiation stress on shallow water and its relation ship with the sediment transport. After Longuet-Higguins and Stewart presented the concept and applications of the radiation stress there have been several studies showing some aspects of the integral characteristics of the wave nonlinearity. First of all we describe the radiation stress and its components when we change coordinates. Thirdly we generalize the coordinates using the differential operators in orthogonal curvilinear coordinates. The problem is strongly simplified and also is the sedimentary circulation and dynamics. A quick look at the term of the equation shows us the main characteristics of sediment transports both in deep and shallow water. Some conclusions can be drawn of it. (Author)
Eden, Burkhard; Korchemsky, Gregory P; Sokatchev, Emery
2012-01-01
We present a construction of the integrand of the correlation function of four stress-tensor multiplets in N=4 SYM at weak coupling. It does not rely on Feynman diagrams and makes use of the recently discovered symmetry of the integrand under permutations of external and integration points. This symmetry holds for any gauge group, so it can be used to predict the integrand both in the planar and non-planar sectors. We demonstrate the great efficiency of graph-theoretical tools in the systematic study of the possible permutation symmetric integrands. We formulate a general ansatz for the correlation function as a linear combination of all relevant graph topologies, with arbitrary coefficients. Powerful restrictions on the coefficients come from the analysis of the logarithmic divergences of the correlation function in two singular regimes: Euclidean short-distance and Minkowski light-cone limits. We demonstrate that the planar integrand is completely fixed by the procedure up to six loops and probably beyond. ...
Brugger, Peter; Katul, Gabriel G.; De Roo, Frederik; Kröniger, Konstantin; Rotenberg, Eyal; Rohatyn, Shani; Mauder, Matthias
2018-05-01
Anisotropy in the turbulent stress tensor, which forms the basis of invariant analysis, is conducted using velocity time series measurements collected in the canopy sublayer (CSL) and the atmospheric surface layer (ASL). The goal is to assess how thermal stratification and surface roughness conditions simultaneously distort the scalewise relaxation towards isotropic state from large to small scales when referenced to homogeneous turbulence. To achieve this goal, conventional invariant analysis is extended to allow scalewise information about relaxation to isotropy in physical (instead of Fourier) space to be incorporated. The proposed analysis shows that the CSL is more isotropic than its ASL counterpart at large, intermediate, and small (or inertial) scales irrespective of the thermal stratification. Moreover, the small (or inertial) scale anisotropy is more prevalent in the ASL when compared to the CSL, a finding that cannot be fully explained by the intensity of the mean velocity gradient acting on all scales. Implications to the validity of scalewise Rotta and Lumley models for return to isotropy as well as advantages to using barycentric instead of anisotropy invariant maps for such scalewise analysis are discussed.
Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point
International Nuclear Information System (INIS)
Giribet, Gaston; Goya, Andres; Leston, Mauricio
2011-01-01
Chiral gravity admits asymptotically AdS 3 solutions that are not locally equivalent to AdS 3 ; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally AdS 3 solutions to chiral gravity is relevant to understanding the quantum theory. Here, we discuss a special family of nonlocally AdS 3 solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally AdS 3 solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote AdS 3 space without being locally equivalent to it appear. Defining the boundary stress tensor for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.
International Nuclear Information System (INIS)
Danilov, G.S.
1995-01-01
It is shown that, in the theory of free noncritical strings, there are no modular-invariant partition functions on surfaces of higher genus. This is due to the fact that the vacuum expectation value of the stress-energy tensor is singular in the fundamental region on the complex plane in which Riemann surfaces are mapped. The above singularity is associated with a nonzero vacuum expectation value of the 2D-gravity field. 15 refs
Puelacher, Christian; Wagener, Max; Abächerli, Roger; Honegger, Ursina; Lhasam, Nundsin; Schaerli, Nicolas; Prêtre, Gil; Strebel, Ivo; Twerenbold, Raphael; Boeddinghaus, Jasper; Nestelberger, Thomas; Rubini Giménez, Maria; Hillinger, Petra; Wildi, Karin; Sabti, Zaid; Badertscher, Patrick; Cupa, Janosch; Kozhuharov, Nikola; du Fay de Lavallaz, Jeanne; Freese, Michael; Roux, Isabelle; Lohrmann, Jens; Leber, Remo; Osswald, Stefan; Wild, Damian; Zellweger, Michael J; Mueller, Christian; Reichlin, Tobias
2017-07-01
Exercise ECG stress testing is the most widely available method for evaluation of patients with suspected myocardial ischemia. Its major limitation is the relatively poor accuracy of ST-segment changes regarding ischemia detection. Little is known about the optimal method to assess ST-deviations. A total of 1558 consecutive patients undergoing bicycle exercise stress myocardial perfusion imaging (MPI) were enrolled. Presence of inducible myocardial ischemia was adjudicated using MPI results. The diagnostic value of ST-deviations for detection of exercise-induced myocardial ischemia was systematically analyzed 1) for each individual lead, 2) at three different intervals after the J-point (J+40ms, J+60ms, J+80ms), and 3) at different time points during the test (baseline, maximal workload, 2min into recovery). Exercise-induced ischemia was detected in 481 (31%) patients. The diagnostic accuracy of ST-deviations was highest at +80ms after the J-point, and at 2min into recovery. At this point, ST-amplitude showed an AUC of 0.63 (95% CI 0.59-0.66) for the best-performing lead I. The combination of ST-amplitude and ST-slope in lead I did not increase the AUC. Lead I reached a sensitivity of 37% and a specificity of 83%, with similar sensitivity to manual ECG analysis (34%, p=0.31) but lower specificity (90%, pST-deviations is highest when evaluated at +80ms after the J-point, and at 2min into recovery. Copyright © 2017 Elsevier B.V. All rights reserved.
(Ln-bar, g)-spaces. Special tensor fields
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces
Weinsaft, Jonathan W; Manoushagian, Shant J; Patel, Taral; Shakoor, Aqsa; Kim, Robert J; Mirchandani, Sunil; Lin, Fay; Wong, Franklin J; Szulc, Massimiliano; Okin, Peter M; Kligfield, Paul D; Min, James K
2009-01-01
To assess the utility of stress electrocardiography (ECG) for identifying the presence and severity of obstructive coronary artery disease (CAD) defined by coronary computed tomographic angiography (CCTA) among patients with normal nuclear myocardial perfusion imaging (MPI). The study population comprised 119 consecutive patients with normal MPI who also underwent CCTA (interval 3.5+/-3.8 months). Stress ECG was performed at the time of MPI. CCTA and MPI were interpreted using established scoring systems, and CCTA was used to define the presence and extent of CAD, which was quantified by a coronary artery jeopardy score. Within this population, 28 patients (24%) had obstructive CAD identified by CCTA. The most common CAD pattern was single-vessel CAD (61%), although proximal vessel involvement was present in 46% of patients. Patients with CAD were nearly three times more likely to have positive standard test responses (1 mm ST-segment deviation) than patients with patent coronary arteries (36 vs. 13%, P=0.007). In multivariate analysis, a positive ST-segment test response was an independent marker for CAD (odds ratio: 2.02, confidence interval: 1.09-3.78, P=0.03) even after adjustment for a composite of clinical cardiac risk factors (odds ratio: 1.85, confidence interval: 1.05-3.23, P=0.03). Despite uniformly normal MPI, mean coronary jeopardy score was three-fold higher among patients with positive compared to those with negative ST-segment response to exercise or dobutamine stress (1.9+/-2.7 vs. 0.5+/-1.4, P=0.03). Stress-induced ST-segment deviation is an independent marker for obstructive CAD among patients with normal MPI. A positive stress ECG identifies patients with a greater anatomic extent of CAD as quantified by coronary jeopardy score.
International Nuclear Information System (INIS)
Mozharovskaya, T.N.
1984-01-01
A programme and procedure are given to study 08Kh18N9 steel at 600 deg C and 15Kh2MFA steel at 550 deg C for creep and long-term strength at different parameters of proportional loading as well as at different parameters under loading in two-link irregular trajectories. This makes it possible to estimate the effect of the kind of a stress deviator, history and prehistory of loading on plastic deformation in creep and on failure under long-term loading
Energy Technology Data Exchange (ETDEWEB)
Mozharovskaya, T N [AN Ukrainskoj SSR, Kiev. Inst. Problem Prochnosti
1984-11-01
A programme and procedure are given to study 08Kh18N9 steel at 600 deg C and 15Kh2MFA steel at 550 deg C for creep and long-term strength at different parameters of proportional loading as well as at different parameters under loading in two-link irregular trajectories. This makes it possible to estimate the effect of the kind of a stress deviator, history and prehistory of loading on plastic deformation in creep and on failure under long-term loading.
Hamilton, Nicholas; Cal, Raúl Bayoán
2015-01-01
A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean
International Nuclear Information System (INIS)
Buchner, Abel-John; Kitsios, Vassili; Atkinson, Callum; Soria, Julio; Lozano-Durán, Adrián
2016-01-01
Previous works have shown that momentum transfer in the wall–normal direction within turbulent wall–bounded flows occurs primarily within coherent structures defined by regions of intense Reynolds stress [1]. Such structures may be classified into wall–attached and wall–detached structures with the latter being typically weak, small–scale, and isotropically oriented, while the former are larger and carry most of the Reynolds stresses. The mean velocity fluctuation within each structure may also be used to separate structures by their dynamic properties. This study aims to extract information regarding the scales, kinematics and dynamics of these structures within the topological framework of the invariants of the velocity gradient tensor (VGT). The local topological characteristics of these intense Reynolds stress structures are compared to the topological characteristics of vortex clusters defined by the discriminant of the velocity gradient tensor. The alignment of vorticity with the principal strain directions within these structures is also determined, and the implications of these findings are discussed. (paper)
International Nuclear Information System (INIS)
Chesler, Paul M.; Yaffe, Laurence G.
2008-01-01
The stress-energy tensor of a quark moving through a strongly-coupled N=4 supersymmetric Yang-Mills plasma, at large N c , is evaluated using gauge/string duality. The accuracy with which the resulting wake, in position space, is reproduced by hydrodynamics is examined. Remarkable agreement is found between hydrodynamics and the complete result down to distances less than 2/T away from the quark. In performing the gravitational analysis, we use a relatively simple formulation of the bulk to boundary problem in which the linearized Einstein field equations are fully decoupled. Our analysis easily generalizes to other sources in the bulk.
Directory of Open Access Journals (Sweden)
Andreas Eckert
2015-02-01
Full Text Available The advanced tensor based concept of pore pressure-stress coupling is used to provide pre-injection analytical estimates of the maximum sustainable pore pressure change, ΔPc, for fluid injection scenarios into generic anticline geometries. The heterogeneous stress distribution for different prevailing stress regimes in combination with the Young's modulus (E contrast between the injection layer and the cap rock and the interbedding friction coefficient, μ, may result in large spatial and directional differences of ΔPc. A single value characterizing the cap rock as for horizontal layered injection scenarios is not obtained. It is observed that a higher Young's modulus in the cap rock and/or a weak mechanical coupling between layers amplifies the maximum and minimum ΔPc values in the valley and limb, respectively. These differences in ΔPc imposed by E and μ are further amplified by different stress regimes. The more compressional the stress regime is, the larger the differences between the maximum and minimum ΔPc values become. The results of this study show that, in general compressional stress regimes yield the largest magnitudes of ΔPc and extensional stress regimes provide the lowest values of ΔPc for anticline formations. Yet this conclusion has to be considered with care when folded anticline layers are characterized by flexural slip and the friction coefficient between layers is low, i.e. μ = 0.1. For such cases of weak mechanical coupling, ΔPc magnitudes may range from 0 MPa to 27 MPa, indicating imminent risk of fault reactivation in the cap rock.
Chicherin, Dmitry
2017-03-09
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators differ only slightly from those for the chiral correlators. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper \\cite{PartI}. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.
The Distance Standard Deviation
Edelmann, Dominic; Richards, Donald; Vogel, Daniel
2017-01-01
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. New representations for the distance standard deviation are obtained in terms of Gini's mean difference and in terms of the moments of spacings of order statistics. Inequalities for the distance variance are derived, proving that the distance standard deviation is bounded above by the classical standard deviation and by Gini's mean difference. Further, it is ...
DEFF Research Database (Denmark)
Vaage-Nilsen, M; Rasmussen, Verner; Sørum, C
1999-01-01
or descending ST-segment depression of >/=0.15 mV during Holter monitoring or at the exercise test, respectively. Furthermore, the specificity was 0.95 when a horizontal or downsloping ST-segment depression of 0.1 mV was displayed in both the Holter and exercise electrocardiographic recording system......BACKGROUND: Although ST-segment deviation has been evaluated and used during many years both on continuous electrocardiographic Holter monitoring and during exercise stress testing, considerable controversy still remains concerning the prevalence and diagnostic significance of fortuitously...... discovered ST-segment deviation in asymptomatic healthy persons. METHODS AND RESULTS: The occurrence of ST-segment deviation was studied in a population of 63 clinically healthy male subjects 51 to 75 years of age, with the use of 24-hour Holter monitoring and exercise stress testing. The subjects were...
Tensor Transpose and Its Properties
Pan, Ran
2014-01-01
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Segmentation Using Symmetry Deviation
DEFF Research Database (Denmark)
Hollensen, Christian; Højgaard, L.; Specht, L.
2011-01-01
of the CT-scans into a single atlas. Afterwards the standard deviation of anatomical symmetry for the 20 normal patients was evaluated using non-rigid registration and registered onto the atlas to create an atlas for normal anatomical symmetry deviation. The same non-rigid registration was used on the 10...... hypopharyngeal cancer patients to find anatomical symmetry and evaluate it against the standard deviation of the normal patients to locate pathologic volumes. Combining the information with an absolute PET threshold of 3 Standard uptake value (SUV) a volume was automatically delineated. The overlap of automated....... The standard deviation of the anatomical symmetry, seen in figure for one patient along CT and PET, was extracted for normal patients and compared with the deviation from cancer patients giving a new way of determining cancer pathology location. Using the novel method an overlap concordance index...
Tensor rank is not multiplicative under the tensor product
DEFF Research Database (Denmark)
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2018-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2018-01-01
textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2017-01-01
textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in
Taguchi, Y-H
2017-12-21
Although post-traumatic stress disorder (PTSD) is primarily a mental disorder, it can cause additional symptoms that do not seem to be directly related to the central nervous system, which PTSD is assumed to directly affect. PTSD-mediated heart diseases are some of such secondary disorders. In spite of the significant correlations between PTSD and heart diseases, spatial separation between the heart and brain (where PTSD is primarily active) prevents researchers from elucidating the mechanisms that bridge the two disorders. Our purpose was to identify genes linking PTSD and heart diseases. In this study, gene expression profiles of various murine tissues observed under various types of stress or without stress were analyzed in an integrated manner using tensor decomposition (TD). Based upon the obtained features, ∼ 400 genes were identified as candidate genes that may mediate heart diseases associated with PTSD. Various gene enrichment analyses supported biological reliability of the identified genes. Ten genes encoding protein-, DNA-, or mRNA-interacting proteins-ILF2, ILF3, ESR1, ESR2, RAD21, HTT, ATF2, NR3C1, TP53, and TP63-were found to be likely to regulate expression of most of these ∼ 400 genes and therefore are candidate primary genes that cause PTSD-mediated heart diseases. Approximately 400 genes in the heart were also found to be strongly affected by various drugs whose known adverse effects are related to heart diseases and/or fear memory conditioning; these data support the reliability of our findings. TD-based unsupervised feature extraction turned out to be a useful method for gene selection and successfully identified possible genes causing PTSD-mediated heart diseases.
International Nuclear Information System (INIS)
Phan, Thien Q.; Levine, Lyle E.; Lee, I-Fang; Xu, Ruqing; Tischler, Jonathan Z.; Huang, Yi; Langdon, Terence G.; Kassner, Michael E.
2016-01-01
Synchrotron X-ray microbeam diffraction was used to measure the full elastic long range internal strain and stress tensors of low dislocation density regions within the submicrometer grain/subgrain structure of equal-channel angular pressed (ECAP) aluminum alloy AA1050 after 1, 2, and 8 passes using route B C . This is the first time that full tensors were measured in plastically deformed metals at this length scale. The maximum (most tensile or least compressive) principal elastic strain directions for the unloaded 1 pass sample for the grain/subgrain interiors align well with the pressing direction, and are more random for the 2 and 8 pass samples. The measurements reported here indicate that the local stresses and strains become increasingly isotropic (homogenized) with increasing ECAP passes using route B C . The average maximum (in magnitude) LRISs are −0.43 σ a for 1 pass, −0.44 σ a for 2 pass, and 0.14 σ a for the 8 pass sample. These LRISs are larger than those reported previously because those earlier measurements were unable to measure the full stress tensor. Significantly, the measured stresses are inconsistent with the two-component composite model.
Ye, Qian; Lin, Haoze
2017-07-01
Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.
International Nuclear Information System (INIS)
Ye, Qian; Lin, Haoze
2017-01-01
Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space , if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function. (paper)
Tensor rank is not multiplicative under the tensor product
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2017-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...
International Nuclear Information System (INIS)
Laraufie, Romain; Deck, Sébastien
2013-01-01
Highlights: • Present various Reynolds stresses reconstruction methods from a RANS-SA flow field. • Quantify the accuracy of the reconstruction methods for a wide range of Reynolds. • Evaluate the capabilities of the overall process (Reconstruction + SEM). • Provide practical guidelines to realize a streamwise RANS/LES (or WMLES) transition. -- Abstract: Hybrid or zonal RANS/LES approaches are recognized as the most promising way to accurately simulate complex unsteady flows under current computational limitations. One still open issue concerns the transition from a RANS to a LES or WMLES resolution in the stream-wise direction, when near wall turbulence is involved. Turbulence content has then to be prescribed at the transition to prevent from turbulence decay leading to possible flow relaminarization. The present paper aims to propose an efficient way to generate this switch, within the flow, based on a synthetic turbulence inflow condition, named Synthetic Eddy Method (SEM). As the knowledge of the whole Reynolds stresses is often missing, the scope of this paper is focused on generating the quantities required at the SEM inlet from a RANS calculation, namely the first and second order statistics of the aerodynamic field. Three different methods based on two different approaches are presented and their capability to accurately generate the needed aerodynamic values is investigated. Then, the ability of the combination SEM + Reconstruction method to manufacture well-behaved turbulence is demonstrated through spatially developing flat plate turbulent boundary layers. In the mean time, important intrinsic features of the Synthetic Eddy method are pointed out. The necessity of introducing, within the SEM, accurate data, with regards to the outer part of the boundary layer, is illustrated. Finally, user’s guidelines are given depending on the Reynolds number based on the momentum thickness, since one method is suitable for low Reynolds number while the
Tensor gauge condition and tensor field decomposition
Zhu, Ben-Chao; Chen, Xiang-Song
2015-10-01
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
Tensor structure for Nori motives
Barbieri-Viale, Luca; Huber, Annette; Prest, Mike
2018-01-01
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
Tensor eigenvalues and their applications
Qi, Liqun; Chen, Yannan
2018-01-01
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)
2016-07-01
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.
DEFF Research Database (Denmark)
Rocha, Vera; Van Praag, Mirjam; Carneiro, Anabela
This paper studies three related questions: To what extent otherwise similar startups employ different quantities and qualities of human capital at the moment of entry? How persistent are initial human capital choices over time? And how does deviating from human capital benchmarks influence firm......, founders human capital, and the ownership structure of startups (solo entrepreneurs versus entrepreneurial teams). We then study the survival implications of exogenous deviations from these benchmarks, based on spline models for survival data. Our results indicate that (especially negative) deviations from...... the benchmark can be substantial, are persistent over time, and hinder the survival of firms. The implications may, however, vary according to the sector and the ownership structure at entry. Given the stickiness of initial choices, wrong human capital decisions at entry turn out to be a close to irreversible...
Sirlin, Samuel W.
1993-01-01
Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.
Local Tensor Radiation Conditions For Elastic Waves
DEFF Research Database (Denmark)
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...
Barberi, G.; Cammarata, L.; Cocina, O.; Maiolino, V.; Musumeci, C.; Privitera, E.
2003-04-01
Late on the night of October 26, 2002, a bi-lateral eruption started on both the eastern and the southeastern flanks of Mt. Etna. The opening of the eruptive fracture system on the NE sector and the reactivation of the 2001 fracture system, on the S sector, were accompanied by a strong seismic swarm recorded between October 26 and 28 and by sharp increase of volcanic tremor amplitude. After this initial phase, on October 29 another seismogenetic zone became active in the SE sector of the volcano. At present (January 2003) the eruption is still in evolution. During the whole period a total of 862 earthquakes (Md≫1) was recorded by the local permanent seismic network run by INGV - Sezione di Catania. The maximum magnitude observed was Md=4.4. We focus our attention on 55 earthquakes with magnitude Md≫ 3.0. The dataset consists of accurate digital pickings of P- and S-phases including first-motion polarities. Firstly earthquakes were located using a 1D velocity model (Hirn et alii, 1991), then events were relocated by using two different 3D velocity models (Aloisi et alii, 2002; Patane et alii, 2002). Results indicate that most of earthquakes are located to the east of the Summit Craters and to northeast of them. Fault plane solutions (FPS) obtained show prevalent strike-slip rupture mechanisms. The suitable FPSs were considered for the application of Gephart and Forsyth`s algorithm in order to evaluate seismic stress field characteristics. Taking into account the preliminary results we propose a kinematic model of the eastern flank eastward movement in response of the intrusion processes in the central part of the volcano. References Aloisi M., Cocina O., Neri G., Orecchio B., Privitera E. (2002). Seismic tomography of the crust underneath the Etna volcano, Sicily. Physics of the Earth and Planetary Interiors 4154, pp. 1-17 Hirn A., Nercessian A., Sapin M., Ferrucci F., Wittlinger G. (1991). Seismic heterogeneity of Mt. Etna: structure and activity. Geophys. J
International Nuclear Information System (INIS)
Giginyak, F.F.; Dragunov, Yu.G.; Mozharovskaya, T.N.; Titov, V.F.
1993-01-01
The results of the experimental investigations into creep and long-term strength of heat-resistant steels 15Kh2MFA and 15Kh2NMFA in the initial state and after heat-treatment simulating the metal irradiation embrittlement at the end of the product service date under static loading at the complex stress state and at high temperatures are presented. The experimentally substantiated equations of state describing creep and long-term stability of materials taking into account the type of the stress state are derived. (author)
International Nuclear Information System (INIS)
Beig, Robert; Krammer, Werner
2004-01-01
For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York
INDICATIVE MODEL OF DEVIATIONS IN PROJECT
Directory of Open Access Journals (Sweden)
Олена Борисівна ДАНЧЕНКО
2016-02-01
Full Text Available The article shows the process of constructing the project deviations indicator model. It based on a conceptual model of project deviations integrated management (PDIM. During the project different causes (such as risks, changes, problems, crises, conflicts, stress lead to deviations of integrated project indicators - time, cost, quality, and content. For a more detailed definition of where in the project deviations occur and how they are dangerous for the whole project, it needs to develop an indicative model of project deviations. It allows identifying the most dangerous deviations that require PDIM. As a basis for evaluation of project's success has been taken famous model IPMA Delta. During the evaluation, IPMA Delta estimated project management competence of organization in three modules: I-Module ("Individuals" - a self-assessment personnel, P-module ("Projects" - self-assessment of projects and/or programs, and O-module ("Organization" - used to conduct interviews with selected people during auditing company. In the process of building an indicative model of deviations in the project, the first step is the assessment of project management in the organization by IPMA Delta. In the future, built cognitive map and matrix of system interconnections of the project, which conducted simulations and built a scale of deviations for the selected project. They determined a size and place of deviations. To identify the detailed causes of deviations in the project management has been proposed to use the extended system of indicators, which is based on indicators of project management model Project Excellence. The proposed indicative model of deviations in projects allows to estimate the size of variation and more accurately identify the place of negative deviations in the project and provides the project manager information for operational decision making for the management of deviations in the implementation of the project
International Nuclear Information System (INIS)
Xi Yibin; Liu Kang; Zhe Xia; Mu Yunfeng; Yin Hong; Huan Yi; Yang Xiaobin; Du Ping
2013-01-01
Objective: To study the changes of the brain white matter microstructure at the acute stage of posttraumatic stress disorder (PTSD) resulting from a single-prolonged stress. Methods: DTI scans were performed on 17 survivors buried more than 190 h in Shanxi Wangjialing mine disaster and 17 cases of normal controls using Siemens 3.0 T MR. The differences of the FA values measured from the whole brain DTI between the two groups were analyzed based on tract based spatial statistics (TBSS). FA data were statistically compared between the two groups based on nonparametric random permutation test (RPT), and the brain areas of the PTSD patients with abnormal FA were defined. Results: Compared with control group, FA values in the PTSD (at acute stage) group decreased in genu, rostral body of corpus callosum, and increased in the left thalamic and corticospinal tract region of bilateral corona radiata and the posterior limb of the left internal capsule, the left cerebral peduncle. The differences were statistically significant (P < 0.01 TFCE-corrected). Conclusions: TBSS is a comprehensive and accurate method for evaluating the changes of whole brain DTI in PTSD cases. The fiber structural abnormalities in the genu, rostral body of bilateral corpus callosum, anterior radiation of left thalamic may be due to stress. TBSS can provide a more objective basis for the early diagnosis and intervention of PTSD. (authors)
Detecting deviating behaviors without models
Lu, X.; Fahland, D.; van den Biggelaar, F.J.H.M.; van der Aalst, W.M.P.; Reichert, M.; Reijers, H.A.
2016-01-01
Deviation detection is a set of techniques that identify deviations from normative processes in real process executions. These diagnostics are used to derive recommendations for improving business processes. Existing detection techniques identify deviations either only on the process instance level
Categorical Tensor Network States
Directory of Open Access Journals (Sweden)
Jacob D. Biamonte
2011-12-01
Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
International Nuclear Information System (INIS)
Wit, B. de; Rocek, M.
1982-01-01
We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)
Time integration of tensor trains
Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart
2014-01-01
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...
Vector-tensor interaction of gravitation
Energy Technology Data Exchange (ETDEWEB)
Zhang Yuan-zhong; Guo han-ying
1982-11-01
In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.
Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
Visualizing the Sample Standard Deviation
Sarkar, Jyotirmoy; Rashid, Mamunur
2017-01-01
The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This…
Group Cohesiveness, Deviation, Stress, and Conformity
1993-08-11
Cola number of cups, __ Chocolate, cocoa, wine, beer/ alcohol , decaffeinated coffee. Breads containing raisins, prunes, orange peel , banana , or...conforming in order to get the group to accept them. In a study using a similar procedure, Kiesler and Corbin (1965) found that commitment to continue as...second lession, we’ll have subjects actually interact in a group problem solving task , so you’ll get a first hand view of each other’s ways of
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
Large deviations and idempotent probability
Puhalskii, Anatolii
2001-01-01
In the view of many probabilists, author Anatolii Puhalskii''s research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak convergence results.Large Deviations and Idempotent Probability expounds upon the recent methodology of building large deviation theory along the lines of weak convergence theory. The author develops an idempotent (or maxitive) probability theory, introduces idempotent analogues of martingales (maxingales), Wiener and Poisson processes, and Ito differential equations, and studies their properties. The large deviation principle for stochastic processes is formulated as a certain type of convergence of stochastic processes to idempotent processes. The author calls this large deviation convergence.The approach to establishing large deviation convergence uses novel com...
Lazzeretti, Paolo
2018-04-01
It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.
Fidelity deviation in quantum teleportation
Bang, Jeongho; Ryu, Junghee; Kaszlikowski, Dagomir
2018-01-01
We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel---we here consider the so-called Werner channel. To characterize our resu...
Tensor spaces and exterior algebra
Yokonuma, Takeo
1992-01-01
This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
Tensor analysis for physicists
Schouten, J A
1989-01-01
This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...
Generalized dielectric permittivity tensor
International Nuclear Information System (INIS)
Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.
1986-01-01
The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form
Killing tensors and conformal Killing tensors from conformal Killing vectors
International Nuclear Information System (INIS)
Rani, Raffaele; Edgar, S Brian; Barnes, Alan
2003-01-01
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)
2017-03-13
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.
Tensors, relativity, and cosmology
Dalarsson, Mirjana
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
International Nuclear Information System (INIS)
Malyshev, C
2007-01-01
A translational gauge approach of the Einstein type is proposed for obtaining the stresses that are due to non-singular screw dislocation. The stress distribution of the second order around the screw dislocation is classically known for the hollow circular cylinder with traction-free external and internal boundaries. The inner boundary surrounds the dislocation's core, which is not captured by the conventional solution. The present gauge approach enables us to continue the classically known quadratic stresses inside the core. The gauge equation is chosen in the Hilbert-Einstein form, and it plays the role of non-conventional incompatibility law. The stress function method is used, and it leads to the modified stress potential given by two constituents: the conventional one, say, the 'background' and a short-ranged gauge contribution. The latter just causes additional stresses, which are localized. The asymptotic properties of the resulting stresses are studied. Since the gauge contributions are short-ranged, the background stress field dominates sufficiently far from the core. The outer cylinder's boundary is traction-free. At sufficiently moderate distances, the second-order stresses acquire regular continuation within the core region, and the cut-off at the core does not occur. Expressions for the asymptotically far stresses provide self-consistently new length scales dependent on the elastic parameters. These lengths could characterize an exteriority of the dislocation core region
International Nuclear Information System (INIS)
Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A
2011-01-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.
2011-08-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle s...
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas
2016-01-01
Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.
The evolution of tensor polarization
International Nuclear Information System (INIS)
Huang, H.; Lee, S.Y.; Ratner, L.
1993-01-01
By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
Computer generation of random deviates
International Nuclear Information System (INIS)
Cormack, John
1991-01-01
The need for random deviates arises in many scientific applications. In medical physics, Monte Carlo simulations have been used in radiology, radiation therapy and nuclear medicine. Specific instances include the modelling of x-ray scattering processes and the addition of random noise to images or curves in order to assess the effects of various processing procedures. Reliable sources of random deviates with statistical properties indistinguishable from true random deviates are a fundamental necessity for such tasks. This paper provides a review of computer algorithms which can be used to generate uniform random deviates and other distributions of interest to medical physicists, along with a few caveats relating to various problems and pitfalls which can occur. Source code listings for the generators discussed (in FORTRAN, Turbo-PASCAL and Data General ASSEMBLER) are available on request from the authors. 27 refs., 3 tabs., 5 figs
Diffusion tensor image registration using hybrid connectivity and tensor features.
Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang
2014-07-01
Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.
Gogny interactions with tensor terms
Energy Technology Data Exchange (ETDEWEB)
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...
Association between septal deviation and sinonasal papilloma.
Nomura, Kazuhiro; Ogawa, Takenori; Sugawara, Mitsuru; Honkura, Yohei; Oshima, Hidetoshi; Arakawa, Kazuya; Oshima, Takeshi; Katori, Yukio
2013-12-01
Sinonasal papilloma is a common benign epithelial tumor of the sinonasal tract and accounts for 0.5% to 4% of all nasal tumors. The etiology of sinonasal papilloma remains unclear, although human papilloma virus has been proposed as a major risk factor. Other etiological factors, such as anatomical variations of the nasal cavity, may be related to the pathogenesis of sinonasal papilloma, because deviated nasal septum is seen in patients with chronic rhinosinusitis. We, therefore, investigated the involvement of deviated nasal septum in the development of sinonasal papilloma. Preoperative computed tomography or magnetic resonance imaging findings of 83 patients with sinonasal papilloma were evaluated retrospectively. The side of papilloma and the direction of septal deviation showed a significant correlation. Septum deviated to the intact side in 51 of 83 patients (61.4%) and to the affected side in 18 of 83 patients (21.7%). Straight or S-shaped septum was observed in 14 of 83 patients (16.9%). Even after excluding 27 patients who underwent revision surgery and 15 patients in whom the papilloma touched the concave portion of the nasal septum, the concave side of septal deviation was associated with the development of sinonasal papilloma (p = 0.040). The high incidence of sinonasal papilloma in the concave side may reflect the consequences of the traumatic effects caused by wall shear stress of the high-velocity airflow and the increased chance of inhaling viruses and pollutants. The present study supports the causative role of human papilloma virus and toxic chemicals in the occurrence of sinonasal papilloma.
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
Fidelity deviation in quantum teleportation
Bang, Jeongho; Ryu, Junghee; Kaszlikowski, Dagomir
2018-04-01
We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel—we here consider the so-called Werner channel. To characterize our results, we introduce a 2D space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.
Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.
2017-01-01
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...
The tensor distribution function.
Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M
2009-01-01
Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.
Deviations from Newton's law in supersymmetric large extra dimensions
International Nuclear Information System (INIS)
Callin, P.; Burgess, C.P.
2006-01-01
Deviations from Newton's inverse-squared law at the micron length scale are smoking-gun signals for models containing supersymmetric large extra dimensions (SLEDs), which have been proposed as approaches for resolving the cosmological constant problem. Just like their non-supersymmetric counterparts, SLED models predict gravity to deviate from the inverse-square law because of the advent of new dimensions at sub-millimeter scales. However SLED models differ from their non-supersymmetric counterparts in three important ways: (i) the size of the extra dimensions is fixed by the observed value of the dark energy density, making it impossible to shorten the range over which new deviations from Newton's law must be seen; (ii) supersymmetry predicts there to be more fields in the extra dimensions than just gravity, implying different types of couplings to matter and the possibility of repulsive as well as attractive interactions; and (iii) the same mechanism which is purported to keep the cosmological constant naturally small also keeps the extra-dimensional moduli effectively massless, leading to deviations from general relativity in the far infrared of the scalar-tensor form. We here explore the deviations from Newton's law which are predicted over micron distances, and show the ways in which they differ and resemble those in the non-supersymmetric case
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Standard Deviation for Small Samples
Joarder, Anwar H.; Latif, Raja M.
2006-01-01
Neater representations for variance are given for small sample sizes, especially for 3 and 4. With these representations, variance can be calculated without a calculator if sample sizes are small and observations are integers, and an upper bound for the standard deviation is immediate. Accessible proofs of lower and upper bounds are presented for…
Tensor Factorization for Low-Rank Tensor Completion.
Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao
2018-03-01
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.
Herman, Matthew W.; Herrmann, Robert B.; Benz, Harley M.; Furlong, Kevin P.
2014-01-01
On September 3, 2010, a MW 7.0 (U.S. Geological Survey moment magnitude) earthquake ruptured across the Canterbury Plains in South Island, New Zealand. Since then, New Zealand GNS Science has recorded over 10,000 aftershocks ML 2.0 and larger, including three destructive ~ MW 6.0 earthquakes near Christchurch. We treat the Canterbury earthquake sequence as an intraplate earthquake sequence, and compare its kinematics to an Andersonian model for fault slip in a uniform stress field. We determined moment magnitudes and double couple solutions for 150 earthquakes having MW 3.7 and larger through the use of a waveform inversion technique using data from broadband seismic stations on South Island, New Zealand. The majority (126) of these double couple solutions have strike-slip focal mechanisms, with right-lateral slip on ENE fault planes or equivalently left-lateral slip on SSE fault planes. The remaining focal mechanisms indicate reverse faulting, except for two normal faulting events. The strike-slip segments have compatible orientations for slip in a stress field with a horizontal σ1 oriented ~ N115°E, and horizontal σ3. The preference for right lateral strike-slip earthquakes suggests that these structures are inherited from previous stages of deformation. Reverse slip is interpreted to have occurred on previously existing structures in regions with an absence of existing structures optimally oriented for strike-slip deformation. Despite the variations in slip direction and faulting style, most aftershocks had nearly the same P-axis orientation, consistent with the regional σ1. There is no evidence for significant changes in these stress orientations throughout the Canterbury earthquake sequence.
Tensor Train Neighborhood Preserving Embedding
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2018-05-01
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.
Notes on super Killing tensors
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-03-14
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
48 CFR 801.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations. 801... Individual deviations. (a) Authority to authorize individual deviations from the FAR and VAAR is delegated to... nature of the deviation. (d) The DSPE may authorize individual deviations from the FAR and VAAR when an...
48 CFR 2001.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 2001... Individual deviations. In individual cases, deviations from either the FAR or the NRCAR will be authorized... deviations clearly in the best interest of the Government. Individual deviations must be authorized in...
Ruhl, C. J.; Smith, K. D.
2012-12-01
well as available and developed short-period focal mechanisms are compiled to evaluate the stress field to assess mechanisms of slip accommodation. Based on the complex distribution of fault orientations, the stress field varies locally northward from the SWL throughout the MD; however, in many cases, fault plane alignments can be isolated from high-precision locations, providing better constraints on stress and slip orientations.
Typesafe Abstractions for Tensor Operations
Chen, Tongfei
2017-01-01
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.
Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
Deviations in human gut microbiota
DEFF Research Database (Denmark)
Casén, C; Vebø, H C; Sekelja, M
2015-01-01
microbiome profiling. AIM: To develop and validate a novel diagnostic test using faecal samples to profile the intestinal microbiota and identify and characterise dysbiosis. METHODS: Fifty-four DNA probes targeting ≥300 bacteria on different taxonomic levels were selected based on ability to distinguish......, and potential clinically relevant deviation in the microbiome from normobiosis. This model was tested in different samples from healthy volunteers and IBS and IBD patients (n = 330) to determine the ability to detect dysbiosis. RESULTS: Validation confirms dysbiosis was detected in 73% of IBS patients, 70...
Killing-Yano tensors and Nambu mechanics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3
Large deviations and portfolio optimization
Sornette, Didier
Risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as, more or less consciously, in our everyday life. We present a discussion of the characterization of risks and of the optimization of portfolios that starts from a simple illustrative model and ends by a general functional integral formulation. A major item is that risk, usually thought of as one-dimensional in the conventional mean-variance approach, has to be addressed by the full distribution of losses. Furthermore, the time-horizon of the investment is shown to play a major role. We show the importance of accounting for large fluctuations and use the theory of Cramér for large deviations in this context. We first treat a simple model with a single risky asset that exemplifies the distinction between the average return and the typical return and the role of large deviations in multiplicative processes, and the different optimal strategies for the investors depending on their size. We then analyze the case of assets whose price variations are distributed according to exponential laws, a situation that is found to describe daily price variations reasonably well. Several portfolio optimization strategies are presented that aim at controlling large risks. We end by extending the standard mean-variance portfolio optimization theory, first within the quasi-Gaussian approximation and then using a general formulation for non-Gaussian correlated assets in terms of the formalism of functional integrals developed in the field theory of critical phenomena.
Core Polarization and Tensor Coupling Effects on Magnetic Moments of Hypernuclei
International Nuclear Information System (INIS)
Jiang-Ming, Yao; Jie, Meng; Hong-Feng, Lü; Greg, Hillhouse
2008-01-01
Effects of core polarization and tensor coupling on the magnetic moments in Λ 13 C, Λ 17 O, and Λ 41 Ca Λ-hypernuclei are studied by employing the Dirac equation with scalar, vector and tensor potentials. It is found that the effect of core polarization on the magnetic moments is suppressed by Λ tensor coupling. The Λ tensor potential reduces the spin-orbit splitting of p Λ states considerably. However, almost the same magnetic moments are obtained using the hyperon wavefunction obtained via the Dirac equation either with or without the A tensor potential in the electromagnetic current vertex. The deviations of magnetic moments for p Λ states from the Schmidt values are found to increase with nuclear mass number. (nuclear physics)
MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-10-01
Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.
X-ray strain tensor imaging: FEM simulation and experiments with a micro-CT.
Kim, Jae G; Park, So E; Lee, Soo Y
2014-01-01
In tissue elasticity imaging, measuring the strain tensor components is necessary to solve the inverse problem. However, it is impractical to measure all the tensor components in ultrasound or MRI elastography because of their anisotropic spatial resolution. The objective of this study is to compute 3D strain tensor maps from the 3D CT images of a tissue-mimicking phantom. We took 3D micro-CT images of the phantom twice with applying two different mechanical compressions to it. Applying the 3D image correlation technique to the CT images under different compression, we computed 3D displacement vectors and strain tensors at every pixel. To evaluate the accuracy of the strain tensor maps, we made a 3D FEM model of the phantom, and we computed strain tensor maps through FEM simulation. Experimentally obtained strain tensor maps showed similar patterns to the FEM-simulated ones in visual inspection. The correlation between the strain tensor maps obtained from the experiment and the FEM simulation ranges from 0.03 to 0.93. Even though the strain tensor maps suffer from high level noise, we expect the x-ray strain tensor imaging may find some biomedical applications such as malignant tissue characterization and stress analysis inside the tissues.
Estimation of the magnetic field gradient tensor using the Swarm constellation
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Finlay, Chris; Olsen, Nils
2014-01-01
For the first time, part of the magnetic field gradient tensor is estimated in space by the Swarm mission. We investigate the possibility of a more complete estimation of the gradient tensor exploiting the Swarm constellation. The East-West gradients can be approximated by observations from...... deviations compared to conventional vector observations at almost all latitudes. Analytical and numerical analysis of the spectral properties of the gradient tensor shows that specific combinations of the East-West and North-South gradients have almost identical signal content to the radial gradient...
Efficient tensor completion for color image and video recovery: Low-rank tensor train
Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.
2016-01-01
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 tensor tra...
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
48 CFR 1301.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations... DEPARTMENT OF COMMERCE ACQUISITION REGULATIONS SYSTEM Deviations From the FAR 1301.403 Individual deviations. The designee authorized to approve individual deviations from the FAR is set forth in CAM 1301.70. ...
48 CFR 301.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Individual deviations. 301... ACQUISITION REGULATION SYSTEM Deviations From the FAR 301.403 Individual deviations. Contracting activities shall prepare requests for individual deviations to either the FAR or HHSAR in accordance with 301.470. ...
48 CFR 1501.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 1501.403 Section 1501.403 Federal Acquisition Regulations System ENVIRONMENTAL PROTECTION AGENCY GENERAL GENERAL Deviations 1501.403 Individual deviations. Requests for individual deviations from the FAR and the...
48 CFR 501.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Individual deviations. 501... Individual deviations. (a) An individual deviation affects only one contract action. (1) The Head of the Contracting Activity (HCA) must approve an individual deviation to the FAR. The authority to grant an...
48 CFR 1201.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations... FEDERAL ACQUISITION REGULATIONS SYSTEM 70-Deviations From the FAR and TAR 1201.403 Individual deviations... Executive Service (SES) official or that of a Flag Officer, may authorize individual deviations (unless (FAR...
48 CFR 401.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Individual deviations. 401... AGRICULTURE ACQUISITION REGULATION SYSTEM Deviations From the FAR and AGAR 401.403 Individual deviations. In individual cases, deviations from either the FAR or the AGAR will be authorized only when essential to effect...
48 CFR 2401.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 2401... DEVELOPMENT GENERAL FEDERAL ACQUISITION REGULATION SYSTEM Deviations 2401.403 Individual deviations. In individual cases, proposed deviations from the FAR or HUDAR shall be submitted to the Senior Procurement...
48 CFR 2801.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 2801... OF JUSTICE ACQUISITION REGULATIONS SYSTEM Deviations From the FAR and JAR 2801.403 Individual deviations. Individual deviations from the FAR or the JAR shall be approved by the head of the contracting...
Black holes in vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: r.kase@rs.tus.ac.jp, E-mail: masato.minamitsuji@tecnico.ulisboa.pt, E-mail: shinji@rs.kagu.tus.ac.jp [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2017-08-01
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 and 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.
Tensor Product of Polygonal Cell Complexes
Chien, Yu-Yen
2017-01-01
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.
The Einstein tensor characterizing some Riemann spaces
International Nuclear Information System (INIS)
Rahman, M.S.
1993-07-01
A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
Tensor Completion Algorithms in Big Data Analytics
Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia
2017-01-01
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...
Nonlocal elasticity tensors in dislocation and disclination cores
International Nuclear Information System (INIS)
Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.
2017-01-01
We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.
Development of the Tensoral Computer Language
Ferziger, Joel; Dresselhaus, Eliot
1996-01-01
The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.
Energy-momentum tensor and definition of particle states for Robertson-Walker space-time
International Nuclear Information System (INIS)
Brown, M.R.; Dutton, C.R.
1978-01-01
A new regularization scheme is developed for calculating expectation values of the energy-momentum tensor of a quantized scalar field in Robertson-Walker space-times. Using this regularized stress tensor we consider a definition for the vacuum state of the scalar field on any initial hypersurface. Asymptotic methods are developed to investigate the structure of both the divergent and finite terms of the stress tensor when evaluated in this state. The conformal anomaly is discussed in the context of this model. It does not naturally enter into the analysis and we argue that its inclusion is unnecessary
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
The reinterpretation of standard deviation concept
Ye, Xiaoming
2017-01-01
Existing mathematical theory interprets the concept of standard deviation as the dispersion degree. Therefore, in measurement theory, both uncertainty concept and precision concept, which are expressed with standard deviation or times standard deviation, are also defined as the dispersion of measurement result, so that the concept logic is tangled. Through comparative analysis of the standard deviation concept and re-interpreting the measurement error evaluation principle, this paper points o...
Teh, Irvin; McClymont, Darryl; Zdora, Marie-Christine; Whittington, Hannah J; Davidoiu, Valentina; Lee, Jack; Lygate, Craig A; Rau, Christoph; Zanette, Irene; Schneider, Jürgen E
2017-03-10
Diffusion tensor imaging (DTI) is widely used to assess tissue microstructure non-invasively. Cardiac DTI enables inference of cell and sheetlet orientations, which are altered under pathological conditions. However, DTI is affected by many factors, therefore robust validation is critical. Existing histological validation is intrinsically flawed, since it requires further tissue processing leading to sample distortion, is routinely limited in field-of-view and requires reconstruction of three-dimensional volumes from two-dimensional images. In contrast, synchrotron radiation imaging (SRI) data enables imaging of the heart in 3D without further preparation following DTI. The objective of the study was to validate DTI measurements based on structure tensor analysis of SRI data. One isolated, fixed rat heart was imaged ex vivo with DTI and X-ray phase contrast SRI, and reconstructed at 100 μm and 3.6 μm isotropic resolution respectively. Structure tensors were determined from the SRI data and registered to the DTI data. Excellent agreement in helix angles (HA) and transverse angles (TA) was observed between the DTI and structure tensor synchrotron radiation imaging (STSRI) data, where HA DTI-STSRI = -1.4° ± 23.2° and TA DTI-STSRI = -1.4° ± 35.0° (mean ± 1.96 standard deviation across all voxels in the left ventricle). STSRI confirmed that the primary eigenvector of the diffusion tensor corresponds with the cardiomyocyte long-axis across the whole myocardium. We have used STSRI as a novel and high-resolution gold standard for the validation of DTI, allowing like-with-like comparison of three-dimensional tissue structures in the same intact heart free of distortion. This represents a critical step forward in independently verifying the structural basis and informing the interpretation of cardiac DTI data, thereby supporting the further development and adoption of DTI in structure-based electro-mechanical modelling and routine clinical
Theoretical study of the relativistic molecular rotational g-tensor
Energy Technology Data Exchange (ETDEWEB)
Aucar, I. Agustín, E-mail: agustin.aucar@conicet.gov.ar; Gomez, Sergio S., E-mail: ssgomez@exa.unne.edu.ar [Institute for Modeling and Technological Innovation, IMIT (CONICET-UNNE) and Faculty of Exact and Natural Sciences, Northeastern University of Argentina, Avenida Libertad 5400, W3404AAS Corrientes (Argentina); Giribet, Claudia G.; Ruiz de Azúa, Martín C. [Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)
2014-11-21
An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.
Theoretical study of the relativistic molecular rotational g-tensor
International Nuclear Information System (INIS)
Aucar, I. Agustín; Gomez, Sergio S.; Giribet, Claudia G.; Ruiz de Azúa, Martín C.
2014-01-01
An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH + (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH + systems. Only for the sixth-row Rn atom a significant deviation of this relation is found
Introducing the Mean Absolute Deviation "Effect" Size
Gorard, Stephen
2015-01-01
This paper revisits the use of effect sizes in the analysis of experimental and similar results, and reminds readers of the relative advantages of the mean absolute deviation as a measure of variation, as opposed to the more complex standard deviation. The mean absolute deviation is easier to use and understand, and more tolerant of extreme…
48 CFR 201.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 3 2010-10-01 2010-10-01 false Individual deviations. 201.403 Section 201.403 Federal Acquisition Regulations System DEFENSE ACQUISITION REGULATIONS SYSTEM... Individual deviations. (1) Individual deviations, except those described in 201.402(1) and paragraph (2) of...
48 CFR 3401.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 7 2010-10-01 2010-10-01 false Individual deviations. 3401.403 Section 3401.403 Federal Acquisition Regulations System DEPARTMENT OF EDUCATION ACQUISITION REGULATION GENERAL ED ACQUISITION REGULATION SYSTEM Deviations 3401.403 Individual deviations. An individual...
48 CFR 1.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 1 2010-10-01 2010-10-01 false Individual deviations. 1.403 Section 1.403 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION GENERAL FEDERAL ACQUISITION REGULATIONS SYSTEM Deviations from the FAR 1.403 Individual deviations. Individual...
48 CFR 3001.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 7 2010-10-01 2010-10-01 false Individual deviations... from the FAR and HSAR 3001.403 Individual deviations. Unless precluded by law, executive order, or other regulation, the HCA is authorized to approve individual deviation (except with respect to (FAR) 48...
48 CFR 601.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Individual deviations. 601.403 Section 601.403 Federal Acquisition Regulations System DEPARTMENT OF STATE GENERAL DEPARTMENT OF STATE ACQUISITION REGULATIONS SYSTEM Deviations from the FAR 601.403 Individual deviations. The...
48 CFR 1901.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 1901.403 Section 1901.403 Federal Acquisition Regulations System BROADCASTING BOARD OF GOVERNORS GENERAL... Individual deviations. Deviations from the IAAR or the FAR in individual cases shall be authorized by the...
48 CFR 2501.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 2501.403 Section 2501.403 Federal Acquisition Regulations System NATIONAL SCIENCE FOUNDATION GENERAL FEDERAL ACQUISITION REGULATIONS SYSTEM Deviations From the FAR 2501.403 Individual deviations. Individual...
The tensor rank of tensor product of two three-qubit W states is eight
Chen, Lin; Friedland, Shmuel
2017-01-01
We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.
The Standard Deviation of Launch Vehicle Environments
Yunis, Isam
2005-01-01
Statistical analysis is used in the development of the launch vehicle environments of acoustics, vibrations, and shock. The standard deviation of these environments is critical to accurate statistical extrema. However, often very little data exists to define the standard deviation and it is better to use a typical standard deviation than one derived from a few measurements. This paper uses Space Shuttle and expendable launch vehicle flight data to define a typical standard deviation for acoustics and vibrations. The results suggest that 3dB is a conservative and reasonable standard deviation for the source environment and the payload environment.
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....
Confinement through tensor gauge fields
International Nuclear Information System (INIS)
Salam, A.; Strathdee, J.
1977-12-01
Using the 0(3,2)-symmetric de Sitter solution of Einstein's equation describing a strongly interacting tensor field it is shown that hadronic bags confining quarks can be represented as de Sitter ''micro-universes'' with radii given 1/R 2 =lambdak 2 /6. Here k 2 and lambda are the strong coupling and the ''cosmological'' constant which apear in the Einstein equation used. Surprisingly the energy spectrum for the two-body hadronic states is the same as that for a harmonic oscillator potential, though the wave functions are completely different. The Einstein equation can be extended to include colour for the tensor fields
Tensor product of quantum logics
Pulmannová, Sylvia
1985-01-01
A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.
The 'gravitating' tensor in the dualistic theory
International Nuclear Information System (INIS)
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
Tensor calculus for physics a concise guide
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
Mean template for tensor-based morphometry using deformation tensors.
Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M
2007-01-01
Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.
Deviations from thermal equilibrium in plasmas
International Nuclear Information System (INIS)
Burm, K.T.A.L.
2004-01-01
A plasma system in local thermal equilibrium can usually be described with only two parameters. To describe deviations from equilibrium two extra parameters are needed. However, it will be shown that deviations from temperature equilibrium and deviations from Saha equilibrium depend on one another. As a result, non-equilibrium plasmas can be described with three parameters. This reduction in parameter space will ease the plasma describing effort enormously
Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
Tensor-based spatiotemporal saliency detection
Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen
2018-03-01
This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
Bridging scales of crustal stress patterns using the new World Stress Map
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
Efficient Tensor Strategy for Recommendation
Directory of Open Access Journals (Sweden)
Aboagye Emelia Opoku
2017-07-01
Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.
... can be life-saving. But chronic stress can cause both physical and mental harm. There are at least three different types of stress: Routine stress related to the pressures of work, family, and other daily responsibilities Stress brought about ...
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
Spherical Tensor Calculus for Local Adaptive Filtering
Reisert, Marco; Burkhardt, Hans
In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.
A new Weyl-like tensor of geometric origin
Vishwakarma, Ram Gopal
2018-04-01
A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
International Nuclear Information System (INIS)
Costa, Miguel S.; Hansen, Tobias; Penedones, João; Trevisani, Emilio
2016-01-01
In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length l_1 of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in l_1 for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
Energy Technology Data Exchange (ETDEWEB)
Costa, Miguel S. [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Theory Division, Department of Physics, CERN, CH-1211 Genève 23 (Switzerland); Hansen, Tobias [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg (Germany); Penedones, João [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Theory Division, Department of Physics, CERN, CH-1211 Genève 23 (Switzerland); Fields and Strings Laboratory, Institute of Physics, EPFL, CH-1015 Lausanne (Switzerland); Trevisani, Emilio [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)
2016-07-05
In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length l{sub 1} of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in l{sub 1} for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
Costa, Miguel S.; Penedones, João; Trevisani, Emilio
2016-01-01
In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
Comparing Standard Deviation Effects across Contexts
Ost, Ben; Gangopadhyaya, Anuj; Schiman, Jeffrey C.
2017-01-01
Studies using tests scores as the dependent variable often report point estimates in student standard deviation units. We note that a standard deviation is not a standard unit of measurement since the distribution of test scores can vary across contexts. As such, researchers should be cautious when interpreting differences in the numerical size of…
FINDING STANDARD DEVIATION OF A FUZZY NUMBER
Fokrul Alom Mazarbhuiya
2017-01-01
Two probability laws can be root of a possibility law. Considering two probability densities over two disjoint ranges, we can define the fuzzy standard deviation of a fuzzy variable with the help of the standard deviation two random variables in two disjoint spaces.
Exploring Students' Conceptions of the Standard Deviation
delMas, Robert; Liu, Yan
2005-01-01
This study investigated introductory statistics students' conceptual understanding of the standard deviation. A computer environment was designed to promote students' ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an…
48 CFR 1401.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations. 1401.403 Section 1401.403 Federal Acquisition Regulations System DEPARTMENT OF THE INTERIOR GENERAL DEPARTMENT OF THE INTERIOR ACQUISITION REGULATION SYSTEM Deviations from the FAR and DIAR 1401.403 Individual...
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Deviations. 226.4 Section 226.4 Foreign Relations AGENCY FOR INTERNATIONAL DEVELOPMENT ADMINISTRATION OF ASSISTANCE AWARDS TO U.S. NON-GOVERNMENTAL ORGANIZATIONS General § 226.4 Deviations. The Office of Management and Budget (OMB) may grant exceptions for...
41 CFR 115-1.110 - Deviations.
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviations. 115-1.110 Section 115-1.110 Public Contracts and Property Management Federal Property Management Regulations System (Continued) ENVIRONMENTAL PROTECTION AGENCY 1-INTRODUCTION 1.1-Regulation System § 115-1.110 Deviations...
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviation. 105-1.110 Section 105-1.110 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.110 Deviation. (a...
2010-07-01
... 41 Public Contracts and Property Management 2 2010-07-01 2010-07-01 true Deviation. 101-1.110 Section 101-1.110 Public Contracts and Property Management Federal Property Management Regulations System FEDERAL PROPERTY MANAGEMENT REGULATIONS GENERAL 1-INTRODUCTION 1.1-Regulation System § 101-1.110 Deviation...
Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.
Li, Wei; Liu, Chunlei
2013-10-01
Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.
Tensor Fields for Use in Fractional-Order Viscoelasticity
Freed, Alan D.; Diethelm, Kai
2003-01-01
To be able to construct viscoelastic material models from fractional0order differentegral equations that are applicable for 3D finite-strain analysis requires definitions for fractional derivatives and integrals for symmetric tensor fields, like stress and strain. We define these fields in the body manifold. We then map them ito spatial fields expressed in terms of an Eulerian or Lagrangian reference frame where most analysts prefer to solve boundary problems.
Tensor voting for robust color edge detection
Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec
2014-01-01
The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ...
The Physical Interpretation of the Lanczos Tensor
Roberts, Mark D.
1999-01-01
The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...
Robust estimation of adaptive tensors of curvature by tensor voting.
Tong, Wai-Shun; Tang, Chi-Keung
2005-03-01
Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.
Antisymmetric tensor generalizations of affine vector fields.
Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro
2016-02-01
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
Entanglement transitions induced by large deviations
Bhosale, Udaysinh T.
2017-12-01
The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.
Extended vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2017-01-01
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.
Scalar-tensor linear inflation
Energy Technology Data Exchange (ETDEWEB)
Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)
2017-04-01
We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.
Mukherjee, Pratik; Miller, Jeffrey H; Shimony, Joshua S; Philip, Joseph V; Nehra, Deepika; Snyder, Abraham Z; Conturo, Thomas E; Neil, Jeffrey J; McKinstry, Robert C
2002-10-01
Conventional MR imaging findings of human brain development are thought to result from decreasing water content, increasing macromolecular concentration, and myelination. We use diffusion-tensor MR imaging to test theoretical models that incorporate hypotheses regarding how these maturational processes influence water diffusion in developing gray and white matter. Experimental data were derived from diffusion-tensor imaging of 167 participants, ages 31 gestational weeks to 11 postnatal years. An isotropic diffusion model was applied to the gray matter of the basal ganglia and thalamus. A model that assumes changes in the magnitude of diffusion while maintaining cylindrically symmetric anisotropy was applied to the white matter of the corpus callosum and internal capsule. Deviations of the diffusion tensor from the ideal model predictions, due to measurement noise, were estimated by using Monte Carlo simulations. Developing gray matter of the basal ganglia and developing white matter of the internal capsule and corpus callosum largely conformed to theory, with only small departures from model predictions in older children. However, data from the thalamus substantially diverged from predicted values, with progressively larger deviations from the model with increasing participant age. Changes in water diffusion during maturation of central gray and white matter structures can largely be explained by theoretical models incorporating simple assumptions regarding the influence of brain water content and myelination, although deviations from theory increase as the brain matures. Diffusion-tensor MR imaging is a powerful method for studying the process of brain development, with both scientific and clinical applications.
TERMINOLOGY MANAGEMENT FRAMEWORK DEVIATIONS IN PROJECTS
Directory of Open Access Journals (Sweden)
Олена Борисівна ДАНЧЕНКО
2015-05-01
Full Text Available The article reviews new approaches to managing projects deviations (risks, changes, problems. By offering integrated control these parameters of the project and by analogy with medical terminological systems building a new system for managing terminological variations in the projects. With an improved method of triads system definitions are analyzed medical terms that make up terminological basis. Using the method of analogy proposed new definitions for managing deviations in projects. By using triad integrity built a new system triad in project management, which will subsequently also analogous to develop a new methodology of deviations in projects.
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
Sparse alignment for robust tensor learning.
Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming
2014-10-01
Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.
Shape anisotropy: tensor distance to anisotropy measure
Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.
2011-03-01
Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.
Transposes, L-Eigenvalues and Invariants of Third Order Tensors
Qi, Liqun
2017-01-01
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...
Transport Coefficients from Large Deviation Functions
Gao, Chloe Ya; Limmer, David T.
2017-01-01
We describe a method for computing transport coefficients from the direct evaluation of large deviation functions. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which are scaled cumulant generating functions analogous to the free energies. A diffusion Monte Carlo algorithm is used to evaluate th...
An absolute deviation approach to assessing correlation.
Gorard, S.
2015-01-01
This paper describes two possible alternatives to the more traditional Pearson’s R correlation coefficient, both based on using the mean absolute deviation, rather than the standard deviation, as a measure of dispersion. Pearson’s R is well-established and has many advantages. However, these newer variants also have several advantages, including greater simplicity and ease of computation, and perhaps greater tolerance of underlying assumptions (such as the need for linearity). The first alter...
The large deviations theorem and ergodicity
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions
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.
The large deviation approach to statistical mechanics
International Nuclear Information System (INIS)
Touchette, Hugo
2009-01-01
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
The large deviation approach to statistical mechanics
Touchette, Hugo
2009-07-01
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein’s theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
Iwasaki, Tohru; Furukawa, Tetsuo
2016-05-01
In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.
Applications of tensor functions in creep mechanics
International Nuclear Information System (INIS)
Betten, J.
1991-01-01
Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM)
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.
Liu, Haofei; Sun, Wei
2017-08-01
Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.
On improving the efficiency of tensor voting
Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim
2011-01-01
This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v...
Schrimpf, Martin
2016-01-01
Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...
Efficient Low Rank Tensor Ring Completion
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2017-01-01
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana...
The Riemann-Lovelock Curvature Tensor
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D
The 1/ N Expansion of Tensor Models with Two Symmetric Tensors
Gurau, Razvan
2018-06-01
It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.
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.
Dictionary-Based Tensor Canonical Polyadic Decomposition
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.
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif
2007-01-01
Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
SASAKURA, NAOKI
2010-01-01
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...
The tensor network theory library
Al-Assam, S.; Clark, S. R.; Jaksch, D.
2017-09-01
In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
Dirac tensor with heavy photon
Energy Technology Data Exchange (ETDEWEB)
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
Transport Coefficients from Large Deviation Functions
Directory of Open Access Journals (Sweden)
Chloe Ya Gao
2017-10-01
Full Text Available We describe a method for computing transport coefficients from the direct evaluation of large deviation functions. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which are scaled cumulant generating functions analogous to the free energies. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green–Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.
Transport Coefficients from Large Deviation Functions
Gao, Chloe; Limmer, David
2017-10-01
We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which is a scaled cumulant generating function analogous to the free energy. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green-Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.
PoDMan: Policy Deviation Management
Directory of Open Access Journals (Sweden)
Aishwarya Bakshi
2017-07-01
Full Text Available Whenever an unexpected or exceptional situation occurs, complying with the existing policies may not be possible. The main objective of this work is to assist individuals and organizations to decide in the process of deviating from policies and performing a non-complying action. The paper proposes utilizing software agents as supportive tools to provide the best non-complying action while deviating from policies. The article also introduces a process in which the decision on the choice of non-complying action can be made. The work is motivated by a real scenario observed in a hospital in Norway and demonstrated through the same settings.
... taking care of an aging parent. With mental stress, the body pumps out hormones to no avail. Neither fighting ... with type 1 diabetes. This difference makes sense. Stress blocks the body from releasing insulin in people with type 2 ...
3D reconstruction of tensors and vectors
International Nuclear Information System (INIS)
Defrise, Michel; Gullberg, Grant T.
2005-01-01
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields
SAMPLE STANDARD DEVIATION(s) CHART UNDER THE ASSUMPTION OF MODERATENESS AND ITS PERFORMANCE ANALYSIS
Kalpesh S. Tailor
2017-01-01
Moderate distribution proposed by Naik V.D and Desai J.M., is a sound alternative of normal distribution, which has mean and mean deviation as pivotal parameters and which has properties similar to normal distribution. Mean deviation (δ) is a very good alternative of standard deviation (σ) as mean deviation is considered to be the most intuitively and rationally defined measure of dispersion. This fact can be very useful in the field of quality control to construct the control limits of the c...
Raman scattering tensors of tyrosine.
Tsuboi, M; Ezaki, Y; Aida, M; Suzuki, M; Yimit, A; Ushizawa, K; Ueda, T
1998-01-01
Polarized Raman scattering measurements have been made of a single crystal of L-tyrosine by the use of a Raman microscope with the 488.0-nm exciting beam from an argon ion laser. The L-tyrosine crystal belongs to the space group P2(1)2(1)2(1) (orthorhombic), and Raman scattering intensities corresponding to the aa, bb, cc, ab and ac components of the crystal Raman tensor have been determined for each prominent Raman band. A similar set of measurements has been made of L-tyrosine-d4, in which four hydrogen atoms on the benzene ring are replaced by deuterium atoms. The effects of NH3-->ND3 and OH-->OD on the Raman spectrum have also been examined. In addition, depolarization ratios of some bands of L-tyrosine in aqueous solutions of pH 13 and pH 1 were examined. For comparison with these experimental results, on the other hand, ab initio molecular orbital calculations have been made of the normal modes of vibration and their associated polarizability oscillations of the L-tyrosine molecule. On the basis of these experimental data and by referring to the results of the calculations, discussions have been presented on the Raman tensors associated to some Raman bands, including those at 829 cm-1 (benzene ring breathing), 642 cm-1 (benzene ring deformation), and 432 cm-1 (C alpha-C beta-C gamma bending).
A robust standard deviation control chart
Schoonhoven, M.; Does, R.J.M.M.
2012-01-01
This article studies the robustness of Phase I estimators for the standard deviation control chart. A Phase I estimator should be efficient in the absence of contaminations and resistant to disturbances. Most of the robust estimators proposed in the literature are robust against either diffuse
Evolutionary implications of genetic code deviations
International Nuclear Information System (INIS)
Chela Flores, J.
1986-07-01
By extending the standard genetic code into a temperature dependent regime, we propose a train of molecular events leading to alternative coding. The first few examples of these deviations have already been reported in some ciliated protozoans and Gram positive bacteria. A possible range of further alternative coding, still within the context of universality, is pointed out. (author)
48 CFR 201.404 - Class deviations.
2010-10-01
..., and the Defense Logistics Agency, may approve any class deviation, other than those described in 201...) Diminish any preference given small business concerns by the FAR or DFARS; or (D) Extend to requirements imposed by statute or by regulations of other agencies such as the Small Business Administration and the...
Bodily Deviations and Body Image in Adolescence
Vilhjalmsson, Runar; Kristjansdottir, Gudrun; Ward, Dianne S.
2012-01-01
Adolescents with unusually sized or shaped bodies may experience ridicule, rejection, or exclusion based on their negatively valued bodily characteristics. Such experiences can have negative consequences for a person's image and evaluation of self. This study focuses on the relationship between bodily deviations and body image and is based on a…
Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
Klima, Matej [Czech Technical Univ. in Prague, Praha (Czech Republic); Kucharik, MIlan [Czech Technical Univ. in Prague, Praha (Czech Republic); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Velechovsky, Jan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-06
We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J_{2} invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J_{2} invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.
Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
International Nuclear Information System (INIS)
Senovilla, Jose M M
2010-01-01
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 track communication)
Constraints on the tensor-to-scalar ratio for non-power-law models
International Nuclear Information System (INIS)
Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M.P.
2013-01-01
Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby and Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: r LD = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Tensor Network Quantum Virtual Machine (TNQVM)
Energy Technology Data Exchange (ETDEWEB)
2016-11-18
There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.
Tensor product varieties and crystals. GL case
Malkin, Anton
2001-01-01
The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.
Differential invariants for higher-rank tensors. A progress report
International Nuclear Information System (INIS)
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
Beyond Low Rank: A Data-Adaptive Tensor Completion Method
Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning
2017-01-01
Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no...
Unique characterization of the Bel-Robinson tensor
International Nuclear Information System (INIS)
Bergqvist, G; Lankinen, P
2004-01-01
We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors
Tensor completion and low-n-rank tensor recovery via convex optimization
International Nuclear Information System (INIS)
Gandy, Silvia; Yamada, Isao; Recht, Benjamin
2011-01-01
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
A recursive reduction of tensor Feynman integrals
International Nuclear Information System (INIS)
Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.
2009-07-01
We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)
On Lovelock analogs of the Riemann tensor
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.
Morphometric study of tensor of vastus intermedius in South Indian population.
Veeramani, Raveendranath; Gnanasekaran, Dhivyalakshmi
2017-03-01
Tensor of vastus intermedius is a newly discovered muscle located between vastus lateralis and vastus intermedius. The purpose of this study was to investigate the detailed morphology of tensor of vastus intermedius, specifically to provide data pertaining to the attachments, innervations, variation in the types and its morphometry in South Indian population. The tensor of vastus intermedius was studied in thirty six cadaveric lower limbs using macrodissection techniques. The origin of the muscle was from upper part of intertrochanteric line and anterior part of greater trochanter of femur inserted to medial aspect of upper border of patella. The muscle was classified into four types based on the origin and also the aponeurosis course with independent type (type 1) being common. The mean and standard deviation of the length of tensor of vastus intermedius and aponeurosis were 145.40±37.55 mm and 193.55±42.32 mm, respectively. The results of the study suggest that tensor of vastus intermedius is variable and the information provided regarding the attachments, types and quantitative data will contribute to the existing knowledge of the muscle.
International Nuclear Information System (INIS)
Effenberger, F.; Fichtner, H.; Scherer, K.; Barra, S.; Kleimann, J.; Strauss, R. D.
2012-01-01
The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e., one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the diffusion tensor from this local to a global frame, in which the Parker transport equation for energetic particles is usually formulated and solved. Particularly, we generalize the transformation formulae to allow for an explicit choice of two principal local perpendicular diffusion axes. This generalization includes the 'traditional' diffusion tensor in the special case of isotropic perpendicular diffusion. For the local frame, we describe the motivation for the choice of the Frenet-Serret trihedron, which is related to the intrinsic magnetic field geometry. We directly compare the old and the new tensor elements for two heliospheric magnetic field configurations, namely the hybrid Fisk and Parker fields. Subsequently, we examine the significance of the different formulations for the diffusion tensor in a standard three-dimensional model for the modulation of galactic protons. For this, we utilize a numerical code to evaluate a system of stochastic differential equations equivalent to the Parker transport equation and present the resulting modulated spectra. The computed differential fluxes based on the new tensor formulation deviate from those obtained with the 'traditional' one (only valid for isotropic perpendicular diffusion) by up to 60% for energies below a few hundred MeV depending on heliocentric distance.
Tensor Minkowski Functionals: first application to the CMB
Energy Technology Data Exchange (ETDEWEB)
Ganesan, Vidhya [Indian Institute of Astrophysics, Koramangala II Block, Bangalore 560 034 (India); Chingangbam, Pravabati, E-mail: vidhya@iiap.res.in, E-mail: prava@iiap.res.in [Indian Institute of Science, C.V. Raman Ave, Bangalore 560 012 (India)
2017-06-01
Tensor Minkowski Functionals (TMFs) are tensor generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze the Cosmic Microwave Background (CMB) radiation. They encapsulate information about the shapes of structures and the orientation of distributions of structures. We focus on one of the TMFs, namely W {sub 2}{sup 1,1}, which is the (1,1) rank tensor generalization of the genus. The ratio of the eigenvalues of the average of W {sub 2}{sup 1,1} over all structures, α, encodes the net orientation of the structures; and the average of the ratios of the eigenvalues of W {sub 2}{sup 1,1} for each structure, β, encodes the net intrinsic anisotropy of the structures. We have developed a code that computes W {sub 2}{sup 1,1}, and from it α and β, for a set of structures on the 2-dimensional Euclidean plane. We use it to compute α and β as functions of chosen threshold levels for simulated Gaussian and isotropic CMB temperature and E mode fields. We obtain the value of α to be one for both temperature and E mode, which means that we recover the statistical isotropy of density fluctuations that we input in the simulations. We find that the standard ΛCDM model predicts a charateristic shape of β for temperature and E mode as a function of the threshold, and the average over thresholds is β∼ 0.62 for temperature and β∼ 0.63 for E mode. Accurate measurements of α and β can be used to test the standard model of cosmology and to search for deviations from it. For this purpose we compute α and β for temperature and E mode data of various data sets from PLANCK mission. We compare the values measured from observed data with those obtained from simulations to which instrument beam and noise characteristics of the 44GHz frequency channel have been added (which are provided as part of the PLANCK data release). We find very good agreement of β and α between all
Stress transmission in planar disordered solid foams
International Nuclear Information System (INIS)
Blumenfeld, Raphael
2003-01-01
Stress transmission in planar open-cell cellular solids is analysed using a recent theory developed for marginally rigid granular assemblies. This is made possible by constructing a one-to-one mapping between the two systems. General trivalent networks are mapped onto assemblies of rough grains, while networks where Plateau rules are observed, are mapped onto assemblies of smooth grains. The constitutive part of the stress transmission equations couples the stress directly to the local rotational disorder of the cellular structure via a new fabric tensor. An intriguing consequence of the analysis is that the stress field can be determined in terms of the microstructure alone independent of stress-strain information. This redefines the problem of structure-property relationship in these materials and poses questions on the relations between this formalism and elasticity theory. The deviation of the stress transmission equations from those of conventional solids has been interpreted in the context of granular assemblies as a new state of solid matter and the relevance of this interpretation to the state of matter of cellular solids is discussed
Examining the consistency relations describing the three-point functions involving tensors
International Nuclear Information System (INIS)
Sreenath, V.; Sriramkumar, L.
2014-01-01
It is well known that the non-Gaussianity parameter f NL characterizing the scalar bi-spectrum can be expressed in terms of the scalar spectral index in the squeezed limit, a property that is referred to as the consistency relation. In contrast to the scalar bi-spectrum, the three-point cross-correlations involving scalars and tensors and the tensor bi-spectrum have not received adequate attention, which can be largely attributed to the fact that the tensors had remained undetected at the level of the power spectrum until very recently. The detection of the imprints of the primordial tensor perturbations by BICEP2 and its indication of a rather high tensor-to-scalar ratio, if confirmed, can open up a new window for understanding the tensor perturbations, not only at the level of the power spectrum, but also in the realm of non-Gaussianities. In this work, we consider the consistency relations associated with the three-point cross-correlations involving scalars and tensors as well as the tensor bi-spectrum in inflationary models driven by a single, canonical, scalar field. Characterizing the cross-correlations in terms of the dimensionless non-Gaussianity parameters C NL R and C NL γ that we had introduced earlier, we express the consistency relations governing the cross-correlations as relations between these non-Gaussianity parameters and the scalar or tensor spectral indices, in a fashion similar to that of the purely scalar case. We also discuss the corresponding relation for the non-Gaussianity parameter h NL used to describe the tensor bi-spectrum. We analytically establish these consistency relations explicitly in the following two situations: a simple example involving a specific case of power law inflation and a non-trivial scenario in the so-called Starobinsky model that is governed by a linear potential with a sharp change in its slope. We also numerically verify the consistency relations in three types of inflationary models that permit deviations from
Deviations from LTE in a stellar atmosphere
International Nuclear Information System (INIS)
Kalkofen, W.; Klein, R.I.; Stein, R.F.
1979-01-01
Deviations from LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient b is smaller than unity when the radiative cross section αsub(ν) grows with frequency ν faster than ν 2 ; b exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of αsub(ν). Overpopulation (b > 1) always implies that the kinetic temperature in the statistical equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature. (author)
Deviations from LTE in a stellar atmosphere
Kalkofen, W.; Klein, R. I.; Stein, R. F.
1979-01-01
Deviations for LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient is smaller than unity when the radiative cross section grows with frequency faster than with the square of frequency; it exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of the radiative cross section. Overpopulation always implies that the kinetic temperature in the statistical-equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.
Note onset deviations as musical piece signatures.
Serrà, Joan; Özaslan, Tan Hakan; Arcos, Josep Lluis
2013-01-01
A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.
Note onset deviations as musical piece signatures.
Directory of Open Access Journals (Sweden)
Joan Serrà
Full Text Available A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.
Hearing protector performance and standard deviation.
Williams, W; Dillon, H
2005-01-01
The attenuation performance of a hearing protector is used to estimate the protected exposure level of the user. The aim is to reduce the exposed level to an acceptable value. Users should expect the attenuation to fall within a reasonable range of values around a norm. However, an analysis of extensive test data indicates that there is a negative relationship between attenuation performance and the standard deviation. This result is deduced using a variation in the method of calculating a single number rating of attenuation that is more amenable to drawing statistical inferences. As performance is typically specified as a function of the mean attenuation minus one or two standard deviations from the mean to ensure that greater than 50% of the wearer population are well protected, the implication of increasing standard deviation with decreasing attenuation found in this study means that a significant number of users are, in fact, experiencing over-protection. These users may be disinclined to use their hearing protectors because of an increased feeling of acoustic isolation. This problem is exacerbated in areas with lower noise levels.
Top Yukawa deviation in extra dimension
International Nuclear Information System (INIS)
Haba, Naoyuki; Oda, Kin-ya; Takahashi, Ryo
2009-01-01
We suggest a simple one-Higgs-doublet model living in the bulk of five-dimensional spacetime compactified on S 1 /Z 2 , in which the top Yukawa coupling can be smaller than the naive standard-model expectation, i.e. the top quark mass divided by the Higgs vacuum expectation value. If we find only single Higgs particle at the LHC and also observe the top Yukawa deviation, our scenario becomes a realistic candidate beyond the standard model. The Yukawa deviation comes from the fact that the wave function profile of the free physical Higgs field can become different from that of the vacuum expectation value, due to the presence of the brane-localized Higgs potentials. In the Brane-Localized Fermion scenario, we find sizable top Yukawa deviation, which could be checked at the LHC experiment, with a dominant Higgs production channel being the WW fusion. We also study the Bulk Fermion scenario with brane-localized Higgs potential, which resembles the Universal Extra Dimension model with a stable dark matter candidate. We show that both scenarios are consistent with the current electroweak precision measurements.
Dislocations, the elastic energy momentum tensor and crack propagation
International Nuclear Information System (INIS)
Lung, Chi-wei
1979-07-01
Based upon dislocation theory, some stress intensity factors can be calculated for practical cases. The results obtained by this method have been found to agree fairly well with the results obtained by the conventional fracture mechanics. The elastic energy momentum tensor has been used to calculate the force acting on the crack tip. A discussion on the kinetics of migration of impurities to the crack tip was given. It seems that the crack tip sometimes may be considered as a singularity in an elastic field and the fundamental law of classical field theory is applicable on the problem in fracture of materials. (author)
International Nuclear Information System (INIS)
Montesinos, M.; Flores, E.
2006-01-01
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)
Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.
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.
Tensor network method for reversible classical computation
Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.
2018-03-01
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.
On improving the efficiency of tensor voting.
Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim
2011-11-01
This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.
Conformal field theories and tensor categories. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics
2014-08-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Conformal field theories and tensor categories. Proceedings
International Nuclear Information System (INIS)
Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph
2014-01-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Tensor harmonic analysis on homogenous space
International Nuclear Information System (INIS)
Wrobel, G.
1997-01-01
The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
Scalable Tensor Factorizations with Missing Data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.
2010-01-01
of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP...... is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
2015-01-01
From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Tensor products of higher almost split sequences
Pasquali, Andrea
2015-01-01
We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suit...
Scalable tensor factorizations for incomplete data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.
2011-01-01
to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP...... experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP...
Quantum energy-momentum tensor in space-time with time-like killing vector
International Nuclear Information System (INIS)
Frolov, V.P.; Zel'nikov, A.I.
1987-01-01
An approximate expression for the vacuum and thermal average μν > ren of the stress-energy tensor of conformal massless fields in static Ricci-flat space-times is constructed. The application of this approximation to the space-time of a Schwarzschild black hole and its relation to the Page-Brown-Ottewill approximation are briefly discussed. (orig.)
Standard deviation of scatterometer measurements from space.
Fischer, R. E.
1972-01-01
The standard deviation of scatterometer measurements has been derived under assumptions applicable to spaceborne scatterometers. Numerical results are presented which show that, with sufficiently long integration times, input signal-to-noise ratios below unity do not cause excessive degradation of measurement accuracy. The effects on measurement accuracy due to varying integration times and changing the ratio of signal bandwidth to IF filter-noise bandwidth are also plotted. The results of the analysis may resolve a controversy by showing that in fact statistically useful scatterometer measurements can be made from space using a 20-W transmitter, such as will be used on the S-193 experiment for Skylab-A.
General projective relativity and the vector-tensor gravitational field
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
Tucker tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander
2018-04-20
Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments
TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow
Hafner, Danijar; Davidson, James; Vanhoucke, Vincent
2017-01-01
We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...
DEFF Research Database (Denmark)
Keller, Hanne Dauer
2015-01-01
Kapitlet handler om stress som følelse, og det trækker primært på de få kvalitative undersøgelser, der er lavet af stressforløb.......Kapitlet handler om stress som følelse, og det trækker primært på de få kvalitative undersøgelser, der er lavet af stressforløb....
Fledderus, M.
2012-01-01
Twee op de vijf UT-studenten hebben last van ernstige studiestress, zo erg zelfs dat het ze in hun privéleven belemmert. Die cijfers komen overeen met het landelijk beeld van stress onder studenten. Samen met 14 andere universiteits- en hogeschoolbladen enquêteerde UT Nieuws bijna 5500 studenten. Opvallend is dat mannelijke studenten uit Twente zich veel minder druk lijken te maken over hun studie. Onder vrouwen ligt de stress juist erg hoog ten opzichte van het landelijk gemiddelde.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
2016-01-01
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...
Energy-momentum tensor in scalar QED
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1988-01-01
We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE
Unsupervised Tensor Mining for Big Data Practitioners.
Papalexakis, Evangelos E; Faloutsos, Christos
2016-09-01
Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
Potentials for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory; Murchadha, Niall Ó
2014-01-01
In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)
Correlators in tensor models from character calculus
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Loop optimization for tensor network renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Algebraic classification of the conformal tensor
International Nuclear Information System (INIS)
Ares de Parga, Gonzalo; Chavoya, O.; Lopez B, J.L.; Ovando Z, Gerardo
1989-01-01
Starting from the Petrov matrix method, we deduce a new algorithm (adaptable to computers), within the Newman-Penrose formalism, to obtain the algebraic type of the Weyl tensor in general relativity. (author)
Effects of tensor forces in nuclei
International Nuclear Information System (INIS)
Tanihata, Isao
2013-01-01
Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Allan deviation analysis of financial return series
Hernández-Pérez, R.
2012-05-01
We perform a scaling analysis for the return series of different financial assets applying the Allan deviation (ADEV), which is used in the time and frequency metrology to characterize quantitatively the stability of frequency standards since it has demonstrated to be a robust quantity to analyze fluctuations of non-stationary time series for different observation intervals. The data used are opening price daily series for assets from different markets during a time span of around ten years. We found that the ADEV results for the return series at short scales resemble those expected for an uncorrelated series, consistent with the efficient market hypothesis. On the other hand, the ADEV results for absolute return series for short scales (first one or two decades) decrease following approximately a scaling relation up to a point that is different for almost each asset, after which the ADEV deviates from scaling, which suggests that the presence of clustering, long-range dependence and non-stationarity signatures in the series drive the results for large observation intervals.
Computation of standard deviations in eigenvalue calculations
International Nuclear Information System (INIS)
Gelbard, E.M.; Prael, R.
1990-01-01
In Brissenden and Garlick (1985), the authors propose a modified Monte Carlo method for eigenvalue calculations, designed to decrease particle transport biases in the flux and eigenvalue estimates, and in corresponding estimates of standard deviations. Apparently a very similar method has been used by Soviet Monte Carlo specialists. The proposed method is based on the generation of ''superhistories'', chains of histories run in sequence without intervening renormalization of the fission source. This method appears to have some disadvantages, discussed elsewhere. Earlier numerical experiments suggest that biases in fluxes and eigenvalues are negligibly small, even for very small numbers of histories per generation. Now more recent experiments, run on the CRAY-XMP, tend to confirm these earlier conclusions. The new experiments, discussed in this paper, involve the solution of one-group 1D diffusion theory eigenvalue problems, in difference form, via Monte Carlo. Experiments covered a range of dominance ratios from ∼0.75 to ∼0.985. In all cases flux and eigenvalue biases were substantially smaller than one standard deviation. The conclusion that, in practice, the eigenvalue bias is negligible has strong theoretical support. (author)
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
Estimation of Uncertainties of Full Moment Tensors
2017-10-06
For our moment tensor inversions, we use the ‘cut-and-paste’ ( CAP ) code of Zhu and Helmberger (1996) and Zhu and Ben-Zion (2013), with some...modifications. For the misfit function we use an L1 norm Silwal and Tape (2016), and we incorporate the number of misfitting polarities into the waveform... norm of the eigenvalue triple provides the magnitude of the moment tensor, leaving two free parameters to define the source type. In the same year
Superconformal tensor calculus in five dimensions
International Nuclear Information System (INIS)
Fujita, Tomoyuki; Ohashi, Keisuke
2001-01-01
We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)
Goldsborough, Peter
2016-01-01
Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...
Geometrical foundations of tensor calculus and relativity
Schuller , Frédéric; Lorent , Vincent
2006-01-01
Manifolds, particularly space curves: basic notions 1 The first groundform, the covariant metric tensor 11 The second groundform, Meusnier's theorem 19 Transformation groups in the plane 28 Co- and contravariant components for a special affine transformation in the plane 29 Surface vectors 32 Elements of tensor calculus 36 Generalization of the first groundform to the space 46 The covariant (absolute) derivation 57 Examples from elasticity theory 61 Geodesic lines 63 Main curvatur...
Diffusion tensor MRI: clinical applications
International Nuclear Information System (INIS)
Meli, Francisco; Romero, Carlos; Carpintiero, Silvina; Salvatico, Rosana; Lambre, Hector; Vila, Jose
2005-01-01
Purpose: To evaluate the usefulness of diffusion-tensor imaging (DTI) on different neurological diseases, and to know if this technique shows additional information than conventional Magnetic Resonance Imaging (MRI). Materials and method: Eight patients, with neurological diseases (five patients with brain tumors, one with multiple sclerosis (MS), one with variant Creutzfeldt-Jakob disease (vCJD) and the other with delayed CO intoxication were evaluated. A MR scanner of 1.5 T was used and conventional sequences and DTI with twenty-five directions were done. Quantitative maps were gotten, where the fractional anisotropy (FA) through regions of interest (ROIs) in specific anatomic area were quantified (i.e.: internal and external capsules, frontal and temporal bundles, corpus fibers). Results: In the patients with brain tumors, there was a decrease of FA on intra and peritumoral fibers. Some of them had a disruption in their pattern. In patients with MS and CO intoxication, partial interruption along white matter bundles was demonstrated. However, a 'mismatch' between the findings of FLAIR, Diffusion-weighted images (DWI) and DTI, in the case of CO intoxication, was seen. Conclusions: DTI gave more information compared to conventional sequences about ultrastructural brain tissue in almost all the diseases above mentioned. Therefore, there is a work in progress about DTI acquisition, to evaluate a new technique, called tractography. (author)
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
Directory of Open Access Journals (Sweden)
İhsan Çaça
2004-01-01
Full Text Available We evaluated the correlation with success rates and deviation type and degree inhorizontal concomitant deviations. 104 horizontal concomitan strabismus cases whowere operated in our clinic between January 1994 – December 2000 were included in thestudy. 56 cases undergone recession-resection procedure in the same eye 19 cases twomuscle recession and one muscle resection, 20 cases two muscle recession, 9 cases onlyone muscle recession. 10 ± prism diopter deviation in postoperative sixth monthexamination was accepted as surgical success.Surgical success rate was 90% and 89.3% in the cases with deviation angle of 15-30and 31-50 prism diopter respectively. Success rate was 78.9% if the angle was more than50 prism diopter. According to strabismus type when surgical success rate examined; inalternan esotropia 88.33%, in alternan exotropia 84.6%, in monocular esotropia 88%and in monocular exotropia 83.3% success was fixed. Statistically significant differencewas not found between strabismus type and surgical success rate. The binocular visiongaining rate was found as 51.8% after the treatment of cases.In strabismus surgery, preoperative deviation angle was found to be an effectivefactor on the success rate.
Transmission-type angle deviation microscopy
International Nuclear Information System (INIS)
Chiu, M.-H.; Lai, C.-W.; Tan, C.-T.; Lai, C.-F.
2008-01-01
We present a new microscopy technique that we call transmission angle deviation microscopy (TADM). It is based on common-path heterodyne interferometry and geometrical optics. An ultrahigh sensitivity surface plasmon resonance (SPR) angular sensor is used to expand dynamic measurement ranges and to improve the axial resolution in three-dimensional optical microscopy. When transmitted light is incident upon a specimen, the beam converges or diverges because of refractive and/or surface height variations. Advantages include high axial resolution (∼32 nm), nondestructive and noncontact measurement, and larger measurement ranges (± 80 μm) for a numerical aperture of 0.21in a transparent measurement medium. The technique can be used without conductivity and pretreatment
Investigating deviations from norms in court interpreting
DEFF Research Database (Denmark)
Dubslaff, Friedel; Martinsen, Bodil
Since Shlesinger (1989) discussed the applicability of translational norms to the field of interpreting, a number of scholars have advocated the use of this concept as a frame of reference in interpreting research (e.g. Harris 1990, Schjoldager 1994, 1995, Jansen 1995, Gile 1999, Garzone 2002). Due...... for the study, we intend to conduct interviews instead. The purpose of the study is to investigate deviations from translational norms in court interpreting. More specifically, we aim to identify and describe instances of deviant behaviour on the part of the interpreters, discuss signs of possible deviant...... speaking these languages. This example does not immediately indicate that Translation Studies might be able to contribute to, for example, an improvement of the training situation for the group of court interpreters mentioned above. However, in our opinion, there is reason to believe that TS can make...
Phylogenetic rooting using minimal ancestor deviation.
Tria, Fernando Domingues Kümmel; Landan, Giddy; Dagan, Tal
2017-06-19
Ancestor-descendent relations play a cardinal role in evolutionary theory. Those relations are determined by rooting phylogenetic trees. Existing rooting methods are hampered by evolutionary rate heterogeneity or the unavailability of auxiliary phylogenetic information. Here we present a rooting approach, the minimal ancestor deviation (MAD) method, which accommodates heterotachy by using all pairwise topological and metric information in unrooted trees. We demonstrate the performance of the method, in comparison to existing rooting methods, by the analysis of phylogenies from eukaryotes and prokaryotes. MAD correctly recovers the known root of eukaryotes and uncovers evidence for the origin of cyanobacteria in the ocean. MAD is more robust and consistent than existing methods, provides measures of the root inference quality and is applicable to any tree with branch lengths.
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
14 CFR 21.609 - Approval for deviation.
2010-01-01
... deviation. (a) Each manufacturer who requests approval to deviate from any performance standard of a TSO shall show that the standards from which a deviation is requested are compensated for by factors or... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Approval for deviation. 21.609 Section 21...
International Nuclear Information System (INIS)
Hoegl, A.
1996-01-01
This study investigates how, from a legal point of view, deviations in radiation protection measurements should be treated in comparisons between measured results and limits stipulated by nuclear legislation or goods transport regulations. A case-by-case distinction is proposed which is based on the legal concequences of the respective measurement. Commentaries on nuclear law contain no references to the legal assessment of deviating measurements in radiation protection. The examples quoted in legal commentaries on civil and criminal proceedings of the way in which errors made in measurements for speed control and determinations of the alcohol content in the blood are to be taken into account, and a commentary on ozone legislation, are examined for analogies with radiation protection measurements. Leading cases in the nuclear field are evaluated in the light of the requirements applying in case of deviations in measurements. The final section summarizes the most important findings and conclusions. (orig.) [de
Fledderus, M.
2012-01-01
Twee op de vijf UT-studenten hebben last van ernstige studiestress, zo erg zelfs dat het ze in hun privéleven belemmert. Die cijfers komen overeen met het landelijk beeld van stress onder studenten. Samen met 14 andere universiteits- en hogeschoolbladen enquêteerde UT Nieuws bijna 5500 studenten.
Marin Quintero, Maider J.
2013-01-01
The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…
Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.
Tensor network state correspondence and holography
Singh, Sukhwinder
2018-01-01
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)
2007-02-15
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)
Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions
International Nuclear Information System (INIS)
Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.
2007-01-01
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)
Deviation from Standard Inflationary Cosmology and the Problems in Ekpyrosis
Tseng, Chien-Yao
There are two competing models of our universe right now. One is Big Bang with inflation cosmology. The other is the cyclic model with ekpyrotic phase in each cycle. This paper is divided into two main parts according to these two models. In the first part, we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes ( alma*l'm') of the spherical-harmonic coefficients. We then provide a model and study the two-point correlation of a massless scalar (the inflaton) when the stress tensor contains the energy density from an infinitely long straight cosmic string in addition to a cosmological constant. Finally, we discuss if inflation can reconcile with the Liouville's theorem as far as the fine-tuning problem is concerned. In the second part, we find several problems in the cyclic/ekpyrotic cosmology. First of all, quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of scale-free power spectrum in ekpyrotic/cyclic universe model requires more inspection. Secondly, we find that the usual mechanism to solve fine-tuning problems is not compatible with eternal universe which contains infinitely many cycles in both direction of time. Therefore, all fine-tuning problems including the flatness problem still asks for an explanation in any generic cyclic models.
Energy Technology Data Exchange (ETDEWEB)
Kim, Tae Ho; Kim, Jin Eun [Dept. of Chemistry (BK21 plus) and Research Institute of Natural Science, Gyeongsang National University, Jinju (Korea, Republic of); Lee, Kang Yeol [School of Mechanical Engineering, Korea University, Seoul (Korea, Republic of)
2016-11-15
Simultaneous multiple data set fits of all transition peaks of {sup 133}Cs nuclei enabled us to obtain accurate cesium-133 nuclear magnetic resonance (NMR) parameters and Euler angles between the principal axis systems of the chemical shift (CS) and quadrupole coupling (Q) tensors of {sup 133}Cs nuclei in Cs{sub 2}CrO{sub 4} . Although in a previous study of Cs{sub 2}CrO{sub 4} by Power et al. (W. P. Power, S. Mooibroek, R. E. Wasylishen, T. S. Cameron, J. Phys. Chem. 1994, 98, 1552), one central transition was observed for cesium sites 1 and 2 in the {sup 133}Cs NMR spectra and one Euler angle between the CS tensors and Q tensors was obtained as 52° and 7° for cesium sites 1 and 2, respectively, the present single-crystal {sup 133}Cs NMR measurements found two Euler angles (10(2)°, 51.9(1)°, 0°) for site 1 and two central transition peaks for site 2. Three principal components of the CS tensor for Cs1 are oriented along the crystallographic a, b, and c axes, whereas none of the principal components of the Q tensor for Cs1 are oriented along the crystal axes. The principal component V{sub 22} of the Q tensor for Cs1 is tilted 10° from the b axis in the bc plane, and the other two components are not located in the ac plane. Therefore, we have found that the requirement that “the quadrupole coupling tensor for a nucleus located in a mirror plane has one principal axis perpendicular to the mirror plane” cannot be applied to Cs1. On the other hand, δ{sub 11} and V{sub 22} for Cs2 are aligned along the b axis, and the other components of the CS and Q tensors deviate at an angle of 1.4(1)° and 10.1(1)°, respectively, from the a and c axes in the ac plane. A distortion-free powder {sup 133}Cs NMR spectrum of Cs{sub 2}CrO{sub 4} was measured using a solid-state spin echo technique.
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
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 and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, 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 the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the 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 the 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. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Susceptibility Tensor Imaging (STI) of the Brain
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
Off-shell N = 2 tensor supermultiplets
International Nuclear Information System (INIS)
Wit, Bernard de; Saueressig, Frank
2006-01-01
A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given
International Nuclear Information System (INIS)
Huf, P A; Carminati, J
2015-01-01
In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)
Energy-momentum tensor in the fermion-pairing model
International Nuclear Information System (INIS)
Kawati, S.; Miyata, H.
1980-01-01
The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory
(Ln-bar, g)-spaces. Ordinary and tensor differentials
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces
Seismic sensitivity of normal-mode coupling to Lorentz stresses in the Sun
Hanasoge, Shravan M.
2017-09-01
Understanding the governing mechanism of solar magnetism remains an outstanding challenge in astrophysics. Seismology is the most compelling technique to infer the internal properties of the Sun and stars. Waves in the Sun, nominally acoustic, are sensitive to the emergence and cyclical strengthening of magnetic field, evidenced by measured changes in resonant oscillation frequencies that are correlated with the solar cycle. The inference of internal Lorentz stresses from these measurements has the potential to significantly advance our appreciation of the dynamo. Indeed, seismological inverse theory for the Sun is well understood for perturbations in composition, thermal structure and flows but, is not fully developed for magnetism, owing to the complexity of the ideal magnetohydrodynamic (MHD) equation. Invoking first-Born perturbation theory to characterize departures from spherically symmetric hydrostatic models of the Sun and applying the notation of generalized spherical harmonics, we calculate sensitivity functions of seismic measurements to the general time-varying Lorentz stress tensor. We find that eigenstates of isotropic (I.e. acoustic only) background models are dominantly sensitive to isotropic deviations in the stress tensor and much more weakly than anisotropic stresses (and therefore challenging to infer). The apple cannot fall far from the tree.
Federated Tensor Factorization for Computational Phenotyping
Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian
2017-01-01
Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
Exploring extra dimensions through inflationary tensor modes
Im, Sang Hui; Nilles, Hans Peter; Trautner, Andreas
2018-03-01
Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the "clockwork mechanism". The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of "remote inflation", where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.
On an uninterpretated tensor in Dirac's theory
International Nuclear Information System (INIS)
Costa de Beauregard, O.
1989-01-01
Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity [fr
The Riemann-Lovelock curvature tensor
International Nuclear Information System (INIS)
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)
International Nuclear Information System (INIS)
Martins, Rene V.; Margulies, Lawrence; Schmidt, Soeren; Poulsen, Henning F.; Leffers, Torben
2004-01-01
First results are presented on the simultaneous observation of the elastic strain tensor as a function of load of 10 individual grains, deeply embedded in the bulk of a polycrystalline Al tensile sample. The experimental technique is based on the use of focused high energy synchrotron radiation in transmission geometry. After each load step diffraction patterns are collected with a large-area X-ray detector system for a series of different angular and lateral sample positions. An automated indexing routine was used to assign sets of diffraction spots to individual grains. The strain tensor components as well as the individual grain position within the sample were then fitted from the diffraction spot positions. A maximum tensile load of 48 MPa was applied. Deviations in strain of up to 600 x 10 -6 are observed between respective strain components of individual grains
Diffusion tensor smoothing through weighted Karcher means
Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie
2014-01-01
Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264
Aspects of the Antisymmetric Tensor Field
Lahiri, Amitabha
1991-02-01
With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.
Tensor hypercontraction. II. Least-squares renormalization
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.
Diffusion tensor imaging in spinal cord compression
International Nuclear Information System (INIS)
Wang, Wei; Qin, Wen; Hao, Nanxin; Wang, Yibin; Zong, Genlin
2012-01-01
Background Although diffusion tensor imaging has been successfully applied in brain research for decades, several main difficulties have hindered its extended utilization in spinal cord imaging. Purpose To assess the feasibility and clinical value of diffusion tensor imaging and tractography for evaluating chronic spinal cord compression. Material and Methods Single-shot spin-echo echo-planar DT sequences were scanned in 42 spinal cord compression patients and 49 healthy volunteers. The mean values of the apparent diffusion coefficient and fractional anisotropy were measured in region of interest at the cervical and lower thoracic spinal cord. The patients were divided into two groups according to the high signal on T2WI (the SCC-HI group and the SCC-nHI group for with or without high signal). A one-way ANOVA was used. Diffusion tensor tractography was used to visualize the morphological features of normal and impaired white matter. Results There were no statistically significant differences in the apparent diffusion coefficient and fractional anisotropy values between the different spinal cord segments of the normal subjects. All of the patients in the SCC-HI group had increased apparent diffusion coefficient values and decreased fractional anisotropy values at the lesion level compared to the normal controls. However, there were no statistically significant diffusion index differences between the SCC-nHI group and the normal controls. In the diffusion tensor imaging maps, the normal spinal cord sections were depicted as fiber tracts that were color-encoded to a cephalocaudal orientation. The diffusion tensor images were compressed to different degrees in all of the patients. Conclusion Diffusion tensor imaging and tractography are promising methods for visualizing spinal cord tracts and can provide additional information in clinical studies in spinal cord compression
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.
Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben
2017-08-02
It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.
Seismic moment tensor for anisotropic media: implication for Non-double-couple earthquakes
Cai, X.; Chen, X.; Chen, Y.; Cai, M.
2008-12-01
It is often found that the inversion results of seismic moment tensor from real seismic recorded data show the trace of seismic moment tensor M is not zero, a phenomenon called non-double-couple earthquake sources mechanism. Recently we have derived the analytical expressions of M in transversely isotropic media with the titled axis of symmetry and the results shows even only pure shear-motion of fault can lead to the implosive components determined by several combined anisotropic elastic constants. Many non-double-couple earthquakes from observations often appear in volcanic and geothermal areas (Julian, 1998), where there exist a mount of stress-aligned fluid-saturated parallel vertical micro-cracks identical to transversely isotropic media (Crampin, 2008), this stress-aligned crack will modify the seismic moment tensor. In another word, non-double-couple earthquakes don't mean to have a seismic failure movement perpendicular to the fault plane, while traditional research of seismic moment tensor focus on the case of isotropy, which cannot provide correct interpretation of seismic source mechanism. Reference: Julian, B.R., Miller, A.D. and Foulger, G.R., 1998. Non-double-couple earthquakes,1. Theory, Rev. Geophys., 36, 525¨C549. Crampin,S., Peacock,S., 2008, A review of the current understanding of seismic shear-wave splitting in the Earth's crust and common fallacies in interpretation, wave motion, 45,675-722
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...
Improving Tensor Based Recommenders with Clustering
DEFF Research Database (Denmark)
Leginus, Martin; Dolog, Peter; Zemaitis, Valdas
2012-01-01
Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD),...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...
Tensor modes in pure natural inflation
Nomura, Yasunori; Yamazaki, Masahito
2018-05-01
We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.
Chambers, David W
2008-01-01
We all experience stress as a regular, and sometimes damaging and sometimes useful, part of our daily lives. In our normal ups and downs, we have our share of exhaustion, despondency, and outrage--matched with their corresponding positive moods. But burnout and workaholism are different. They are chronic, dysfunctional, self-reinforcing, life-shortening habits. Dentists, nurses, teachers, ministers, social workers, and entertainers are especially susceptible to burnout; not because they are hard-working professionals (they tend to be), but because they are caring perfectionists who share control for the success of what they do with others and perform under the scrutiny of their colleagues (they tend to). Workaholics are also trapped in self-sealing cycles, but the elements are ever-receding visions of control and using constant activity as a barrier against facing reality. This essay explores the symptoms, mechanisms, causes, and successful coping strategies for burnout and workaholism. It also takes a look at the general stress response on the physiological level and at some of the damage American society inflicts on itself.
3D asthenopia in horizontal deviation.
Kim, Seung-Hyun; Suh, Young-Woo; Yun, Cheol-Min; Yoo, Eun-Joo; Yeom, Ji-Hyun; Cho, Yoonae A
2013-05-01
This study was conducted to investigate the asthenopic symptoms in patients with exotropia and esotropia while watching stereoscopic 3D (S3D) television (TV). A total 77 subjects who more than 9 years of age were enrolled in this study. We divided them into three groups; Thirty-four patients with exodeviation (Exo group), 11 patients with esodeviation (Eso group) and 32 volunteers with normal binocular vision (control group). The S3D images were shown to all patients with S3D high-definition TV for a period of 20 min. Best corrected visual acuity, refractive errors, angle of strabismus, stereopsis test and history of strabismus surgery, were evaluated. After watching S3D TV for 20 min, a survey of subjective symptoms was conducted with a questionnaire to evaluate the degree of S3D perception and asthenopic symptoms such as headache, dizziness and ocular fatigue while watching 3D TV. The mean amounts of deviation in the Exo group and Eso group were 11.2 PD and 7.73PD, respectively. Mean stereoacuity was 102.7 arc sec in the the Exo group and 1389.1 arc sec in the Eso group. In the control group, it was 41.9 arc sec. Twenty-nine patients in the Exo group showed excellent stereopsis (≤60 arc sec at near), but all 11 subjects of the Eso group showed 140 arc sec or worse and showed more decreased 3D perception than the Exo and the control group (p Kruskal-Wallis test). The Exo group reported more eye fatigue (p Kruskal-Wallis test) than the Eso and the control group. However, the scores of ocular fatigue in the patients who had undergone corrective surgery were less than in the patients who had not in the Exo group (p Kruskal-Wallis test) and the amount of exodeviation was not correlated with the asthenopic symptoms (dizziness, r = 0.034, p = 0.33; headache, r = 0.320, p = 0.119; eye fatigue, r = 0.135, p = 0.519, Spearman rank correlation test, respectively). Symptoms of 3D asthenopia were related to the presence of exodeviation but not to esodeviation. This may
Tucker Tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander; Keyes, David E.; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G.
2018-01-01
in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matern- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence
9 CFR 318.308 - Deviations in processing.
2010-01-01
...) Deviations in processing (or process deviations) must be handled according to: (1)(i) A HACCP plan for canned...) of this section. (c) [Reserved] (d) Procedures for handling process deviations where the HACCP plan... accordance with the following procedures: (a) Emergency stops. (1) When retort jams or breakdowns occur...
7 CFR 400.204 - Notification of deviation from standards.
2010-01-01
... 7 Agriculture 6 2010-01-01 2010-01-01 false Notification of deviation from standards. 400.204... Contract-Standards for Approval § 400.204 Notification of deviation from standards. A Contractor shall advise the Corporation immediately if the Contractor deviates from the requirements of these standards...
A Visual Model for the Variance and Standard Deviation
Orris, J. B.
2011-01-01
This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object--in particular, as a square. A series of displays show how the standard deviation is the size of the average square.
21 CFR 330.11 - NDA deviations from applicable monograph.
2010-04-01
... 21 Food and Drugs 5 2010-04-01 2010-04-01 false NDA deviations from applicable monograph. 330.11... EFFECTIVE AND NOT MISBRANDED Administrative Procedures § 330.11 NDA deviations from applicable monograph. A new drug application requesting approval of an OTC drug deviating in any respect from a monograph that...
41 CFR 109-1.110-50 - Deviation procedures.
2010-07-01
... best interest of the Government; (3) If applicable, the name of the contractor and identification of... background information which will contribute to a full understanding of the desired deviation. (b)(1... authorized to grant deviations to the DOE-PMR. (d) Requests for deviations from the FPMR will be coordinated...
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-03-05
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-01-01
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Concatenated image completion via tensor augmentation and completion
Bengua, Johann A.; Tuan, Hoang D.; Phien, Ho N.; Do, Minh N.
2016-01-01
This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor,...
Norm of the Riemannian Curvature Tensor
Indian Academy of Sciences (India)
We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...
Abelian tensor models on the lattice
Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi
2018-04-01
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.
Tensor squeezed limits and the Higuchi bound
Energy Technology Data Exchange (ETDEWEB)
Bordin, Lorenzo [SISSA, via Bonomea 265, 34136, Trieste (Italy); Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Mirbabayi, Mehrdad [Institute for Advanced Study, Princeton, NJ 08540 (United States); Noreña, Jorge, E-mail: lbordin@sissa.it, E-mail: creminel@ictp.it, E-mail: mehrdadm@ias.edu, E-mail: jorge.norena@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Universidad 330, Curauma, Valparaíso (Chile)
2016-09-01
We point out that tensor consistency relations—i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum—are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: de Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor consistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) graviton exchange contribution to the scalar four-point function; (b) quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.
Fermionic topological quantum states as tensor networks
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.
Higher-order tensors in diffusion imaging
Schultz, T.; Fuster, A.; Ghosh, A.; Deriche, R.; Florack, L.M.J.; Lim, L.H.; Westin, C.-F.; Vilanova, A.; Burgeth, B.
2014-01-01
Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Introduction to vector and tensor analysis
Wrede, Robert C
1972-01-01
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
Positivity of linear maps under tensor powers
Energy Technology Data Exchange (ETDEWEB)
Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Reeb, David, E-mail: reeb.qit@gmail.com [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Institute for Theoretical Physics, Leibniz Universität Hannover, 30167 Hannover (Germany)
2016-01-15
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 transpose 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.
An introduction to diffusion tensor image analysis.
O'Donnell, Lauren J; Westin, Carl-Fredrik
2011-04-01
Diffusion tensor magnetic resonance imaging (DTI) is a relatively new technology that is popular for imaging the white matter of the brain. This article provides a basic and broad overview of DTI to enable the reader to develop an intuitive understanding of these types of data, and an awareness of their strengths and weaknesses. Copyright © 2011 Elsevier Inc. All rights reserved.
Primordial tensor modes from quantum corrected inflation
DEFF Research Database (Denmark)
Joergensen, Jakob; Sannino, Francesco; Svendsen, Ole
2014-01-01
. Finally we confront these theories with the Planck and BICEP2 data. We demonstrate that the discovery of primordial tensor modes by BICEP2 require the presence of sizable quantum departures from the $\\phi^4$-Inflaton model for the non-minimally coupled scenario which we parametrize and quantify. We...
From stochastic completion fields to tensor voting
Almsick, van M.A.; Duits, R.; Franken, E.M.; Haar Romenij, ter B.M.; Olsen, O.F.; Florack, L.M.J.; Kuijper, A.
2005-01-01
Several image processing algorithms imitate the lateral interaction of neurons in the visual striate cortex V1 to account for the correlations along contours and lines. Here we focus on two methodologies: tensor voting by Guy and Medioni, and stochastic completion fields by Mumford, Williams and
Positivity of linear maps under tensor powers
International Nuclear Information System (INIS)
Müller-Hermes, Alexander; Wolf, Michael M.; Reeb, David
2016-01-01
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 transpose 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
Dark energy in scalar-tensor theories
International Nuclear Information System (INIS)
Moeller, J.
2007-12-01
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Tensors in image processing and computer vision
De Luis García, Rodrigo; Tao, Dacheng; Li, Xuelong
2009-01-01
Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the developments in this branch of signal processing, offering research and discussions by experts in the area. It is suitable for advanced students working in the area of computer vision and image processing.
Tensor B mode and stochastic Faraday mixing
Giovannini, Massimo
2014-01-01
This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...
Tensor operators in R-matrix approach
International Nuclear Information System (INIS)
Bytsko, A.G.; Rossijskaya Akademiya Nauk, St. Petersburg
1995-12-01
The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of U q (sl(n)) (in particular, for n=2) is discussed in more detail. (orig.)
Tensors, differential forms, and variational principles
Lovelock, David
1989-01-01
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
Itskov, Mikhail
2015-01-01
This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir
2016-08-01
In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.
The nonabelian tensor square of a bieberbach group with ...
African Journals Online (AJOL)
The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor ...
[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].
Xu, Yonghong; Gao, Shangce; Hao, Xiaofei
2016-04-01
Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.
Tensor based structure estimation in multi-channel images
DEFF Research Database (Denmark)
Schou, Jesper; Dierking, Wolfgang; Skriver, Henning
2000-01-01
. In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...
Relativistic particles with spin and antisymmetric tensor fields
International Nuclear Information System (INIS)
Sandoval Junior, L.
1990-09-01
A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)
Efficient MATLAB computations with sparse and factored tensors.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)
2006-12-01
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...
Energy Technology Data Exchange (ETDEWEB)
Montesinos, M. [CINVESTAV-IPN, 07360 Mexico D.F. (Mexico); Flores, E. [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)]. E-mail: merced@fis.cinvestav.mx
2006-07-01
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)
Experimental investigation of acoustic emissions and their moment tensors in rock during failure
Czech Academy of Sciences Publication Activity Database
Aker, E.; Kühn, D.; Vavryčuk, Václav; Soldal, M.; Oye, V.
2014-01-01
Roč. 70, September (2014), s. 286-295 ISSN 1365-1609 R&D Projects: GA ČR(CZ) GAP210/12/1491 EU Projects: European Commission(XE) 230669 - AIM Institutional support: RVO:67985530 Keywords : acoustic emissions * focal mechanisms * moment tensors * rock fracturing * hoop stresses * laboratory experiment Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 1.686, year: 2014
Massless and massive quanta resulting from a mediumlike metric tensor
International Nuclear Information System (INIS)
Soln, J.
1985-01-01
A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.
Glyph-Based Comparative Visualization for Diffusion Tensor Fields.
Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna
2016-01-01
Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.
Tensoral for post-processing users and simulation authors
Dresselhaus, Eliot
1993-01-01
The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.
Energy-momentum tensor of the electromagnetic field
International Nuclear Information System (INIS)
Horndeski, G.W.; Wainwright, J.
1977-01-01
In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
International Nuclear Information System (INIS)
Cariglia, Marco
2004-01-01
In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
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.
Early universe with modified scalar-tensor theory of gravity
Mandal, Ranajit; Sarkar, Chandramouli; Sanyal, Abhik Kumar
2018-05-01
Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.
Accurate thermoelastic tensor and acoustic velocities of NaCl
Energy Technology Data Exchange (ETDEWEB)
Marcondes, Michel L., E-mail: michel@if.usp.br [Physics Institute, University of Sao Paulo, Sao Paulo, 05508-090 (Brazil); Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Shukla, Gaurav, E-mail: shukla@physics.umn.edu [School of Physics and Astronomy, University of Minnesota, Minneapolis, 55455 (United States); Minnesota supercomputer Institute, University of Minnesota, Minneapolis, 55455 (United States); Silveira, Pedro da [Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Wentzcovitch, Renata M., E-mail: wentz002@umn.edu [Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Minnesota supercomputer Institute, University of Minnesota, Minneapolis, 55455 (United States)
2015-12-15
Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor by using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.
Wang, Chun; Zheng, Yi; Chang, Hua-Hua
2014-01-01
With the advent of web-based technology, online testing is becoming a mainstream mode in large-scale educational assessments. Most online tests are administered continuously in a testing window, which may post test security problems because examinees who take the test earlier may share information with those who take the test later. Researchers have proposed various statistical indices to assess the test security, and one most often used index is the average test-overlap rate, which was further generalized to the item pooling index (Chang & Zhang, 2002, 2003). These indices, however, are all defined as the means (that is, the expected proportion of common items among examinees) and they were originally proposed for computerized adaptive testing (CAT). Recently, multistage testing (MST) has become a popular alternative to CAT. The unique features of MST make it important to report not only the mean, but also the standard deviation (SD) of test overlap rate, as we advocate in this paper. The standard deviation of test overlap rate adds important information to the test security profile, because for the same mean, a large SD reflects that certain groups of examinees share more common items than other groups. In this study, we analytically derived the lower bounds of the SD under MST, with the results under CAT as a benchmark. It is shown that when the mean overlap rate is the same between MST and CAT, the SD of test overlap tends to be larger in MST. A simulation study was conducted to provide empirical evidence. We also compared the security of MST under the single-pool versus the multiple-pool designs; both analytical and simulation studies show that the non-overlapping multiple-pool design will slightly increase the security risk.
Tensor modes on the string theory landscape
International Nuclear Information System (INIS)
Westphal, Alexander
2012-06-01
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Tensor modes on the string theory landscape
Energy Technology Data Exchange (ETDEWEB)
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
International Nuclear Information System (INIS)
Kibler, M.; Grenet, G.
1979-07-01
The SU 2 unit tensor operators tsub(k,α) are studied. In the case where the spinor point group G* coincides with U 1 , then tsub(k α) reduces up to a constant to the Wigner-Racah-Schwinger tensor operator tsub(kqα), an operator which produces an angular momentum state. One first investigates those general properties of tsub(kα) which are independent of their realization. The tsub(kα) in terms of two pairs of boson creation and annihilation operators are realized. This leads to look at the Schwinger calculus relative to one angular momentum of two coupled angular momenta. As a by-product, a procedure is given for producing recursion relationships between SU 2 Wigner coefficients. Finally, some of the properties of the Wigner and Racah operators for an arbitrary compact group and the SU 2 coupling coefficients are studied
Heterodyne Angle Deviation Interferometry in Vibration and Bubble Measurements
Ming-Hung Chiu; Jia-Ze Shen; Jian-Ming Huang
2016-01-01
We proposed heterodyne angle deviation interferometry (HADI) for angle deviation measurements. The phase shift of an angular sensor (which can be a metal film or a surface plasmon resonance (SPR) prism) is proportional to the deviation angle of the test beam. The method has been demonstrated in bubble and speaker’s vibration measurements in this paper. In the speaker’s vibration measurement, the voltage from the phase channel of a lock-in amplifier includes the vibration level and frequency. ...
Large deviations for noninteracting infinite-particle systems
International Nuclear Information System (INIS)
Donsker, M.D.; Varadhan, S.R.S.
1987-01-01
A large deviation property is established for noninteracting infinite particle systems. Previous large deviation results obtained by the authors involved a single I-function because the cases treated always involved a unique invariant measure for the process. In the context of this paper there is an infinite family of invariant measures and a corresponding infinite family of I-functions governing the large deviations
Quantum uncertainty relation based on the mean deviation
Sharma, Gautam; Mukhopadhyay, Chiranjib; Sazim, Sk; Pati, Arun Kumar
2018-01-01
Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present alternative forms of uncertainty relations, in both state dependent and state independent forms, based on the mean deviation. We illustrate the robustness of this formulation in situations where the standard deviation based uncertainty relation is inapplica...
Two examples of non strictly convex large deviations
De Marco, Stefano; Jacquier, Antoine; Roome, Patrick
2016-01-01
We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.
Tensor Networks and Quantum Error Correction
Ferris, Andrew J.; Poulin, David
2014-07-01
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Old tensor mesons in QCD sum rules
International Nuclear Information System (INIS)
Aliev, T.M.; Shifman, M.A.
1981-01-01
Tensor mesons f, A 2 and A 3 are analyzed within the framework of QCD sum rules. The effects of gluon and quark condensate is accounted for phenomenologically. Accurate estimates of meson masses and coupling constants of the lowest-lying states are obtained. It is shown that the masses are reproduced within theoretical uncertainty of about 80 MeV. The coupling of f meson to the corresponding quark current is determined. The results are in good aqreement with experimental data [ru
Energy-momentum-tensor in quantumelectrodynamics
Energy Technology Data Exchange (ETDEWEB)
Schott, T
1974-01-01
This work deals with the operator properties of the energy-momentum-tensor (ET) in the framework of quantum electrodynamics. The principles of construction of the ET are discussed for quantized fields in the Schwinger variation principle. Dealing with the conserved quantities for quantized fields operator problems are coming up in the Coulomb gauge because Dirac- and Maxwellfield do not commute completely. Further on contemporary commutators of the ET components are investigated mutually. Finally non-canonical methods are developed.
Embryo Cell Membranes Reconstruction by Tensor Voting
Michelin , Gaël; Guignard , Léo; Fiuza , Ulla-Maj; Malandain , Grégoire
2014-01-01
International audience; Image-based studies of developing organs or embryos produce a huge quantity of data. To handle such high-throughput experimental protocols, automated computer-assisted methods are highly desirable. This article aims at designing an efficient cell segmentation method from microscopic images. The proposed approach is twofold: first, cell membranes are enhanced or extracted by the means of structure-based filters, and then perceptual grouping (i.e. tensor voting) allows t...
Sasakian manifolds with purely transversal Bach tensor
Ghosh, Amalendu; Sharma, Ramesh
2017-10-01
We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2 n (2 n +1 ) , equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).
Anisotropic diffusion tensor applied to temporal mammograms
DEFF Research Database (Denmark)
Karemore, Gopal; Brandt, Sami; Sporring, Jon
2010-01-01
changes related to specific effects like Hormonal Replacement Therapy (HRT) and aging. Given effect-grouped patient data, we demonstrated how anisotropic diffusion tensor and its coherence features computed in an anatomically oriented breast coordinate system followed by statistical learning...
Numerical CP Decomposition of Some Difficult Tensors
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2017-01-01
Roč. 317, č. 1 (2017), s. 362-370 ISSN 0377-0427 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Small matrix multiplication * Canonical polyadic tensor decomposition * Levenberg-Marquardt method Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385. pdf
Experimental status of scalar and tensor mesons
International Nuclear Information System (INIS)
Von Dombrowski, S.
1997-01-01
The recent discoveries of a 0 (1450) and f 0 (1370)/f 0 (1500) in antiproton-proton annihilation at rest shed new light on the interpretation of light scalar mesons. The properties of f 0 (1500) match the expectations of a scalar glueball mixed with nearby qq states. New decay modes of the ξ(2230) are reported in radiative J/Ψ decays, pointing also towards a (tensor) glueball nature of this state. Results from different experiments are discussed and compared. (orig.)
Bayesian approach to magnetotelluric tensor decomposition
Czech Academy of Sciences Publication Activity Database
Červ, Václav; Pek, Josef; Menvielle, M.
2010-01-01
Roč. 53, č. 2 (2010), s. 21-32 ISSN 1593-5213 R&D Projects: GA AV ČR IAA200120701; GA ČR GA205/04/0746; GA ČR GA205/07/0292 Institutional research plan: CEZ:AV0Z30120515 Keywords : galvanic distortion * telluric distortion * impedance tensor * basic procedure * inversion * noise Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 0.336, year: 2010
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
Electrical tensor Green functions for cylindrical waveguides
International Nuclear Information System (INIS)
Prijmenko, S.D.; Papkovich, V.G.; Khizhnyak, N.A.
1988-01-01
Formation of electrical tensor Green functions for cylindrical waveguides is considered. Behaviour of these functions in the source region is studied. Cases of electrical tensor Green functions for vector potential G E (r-vector, r'-vector) and electric field G e (r-vector, r'-vector) are analysed. When forming G E (r-vector, r'-vector), its dependence on lateral coordinates is taken into account by means of two-dimensional fundamental vector Hansen functions, several methods are used to take into account the dependence on transverse coordinate. When forming G e (r-vector, r'-vector) we use the fact that G E (r-vector, r'-vector) and G e (r-vector, r'-vector) are the generalized functions. It is shown that G e (r-vector, r'-vector) behaviour in the source region is defined by a singular term, which properties are described by the delta-function. Two variants of solving the problem of defining singular and regular sides of tensor function G E (r-vector, r'-vector) are presented. 23 refs
Tensor integrand reduction via Laurent expansion
Energy Technology Data Exchange (ETDEWEB)
Hirschi, Valentin [SLAC, National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025-7090 (United States); Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)
2016-06-09
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MADLOOP, which is part of the public MADGRAPH5{sub A}MC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CUTTOOLS, SAMURAI, IREGI, PJFRY++ and GOLEM95. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool GOLEM95 which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.
Liu, Chunlei; Murphy, Nicole E.; Li, Wei
2012-01-01
Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987
Tensor interaction in heavy-ion scattering. Pt. 1
International Nuclear Information System (INIS)
Nishioka, H.; Johnson, R.C.
1985-01-01
The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power anti Tsub(2q) have certain relations with each other for each type of tensor interaction (Tsub(R), Tsub(P) and Tsub(L) types). The predicted relations between the anti Tsub(2q) are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for 7 Li and 23 Na elastic scattering from 58 Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a Tsub(P)- or Tsub(L)-type tensor interaction in polarized heavy-ion scattering. The presence of a Tsub(P)-type tensor interaction is suggested by measured anti T 20 /anti T 22 ratios for 7 Li + 58 Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail. (orig.)
Tensor network decompositions in the presence of a global symmetry
International Nuclear Information System (INIS)
Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre
2010-01-01
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.
International Nuclear Information System (INIS)
Provata, A.; Katsaloulis, P.; Verganelakis, D.A.
2012-01-01
Highlights: ► Calculation of human brain multifractal spectra. ► Calculations are based on Diffusion Tensor MRI Images. ► Spectra are modelled by coupled Ikeda map dynamics. ► Coupled lattice Ikeda maps model well only positive multifractal spectra. ► Appropriately modified coupled lattice Ikeda maps give correct spectra. - Abstract: The multifractal spectra of 3d Diffusion Tensor Images (DTI) obtained by magnetic resonance imaging of the human brain are studied. They are shown to deviate substantially from artificial brain images with the same white matter intensity. All spectra, obtained from 12 healthy subjects, show common characteristics indicating non-trivial moments of the intensity. To model the spectra the dynamics of the chaotic Ikeda map are used. The DTI multifractal spectra for positive q are best approximated by 3d coupled Ikeda maps in the fully developed chaotic regime. The coupling constants are as small as α = 0.01. These results reflect not only the white tissue non-trivial architectural complexity in the human brain, but also demonstrate the presence and importance of coupling between neuron axons. The architectural complexity is also mirrored by the deviations in the negative q-spectra, where the rare events dominate. To obtain a good agreement in the DTI negative q-spectrum of the brain with the Ikeda dynamics, it is enough to slightly modify the most rare events of the coupled Ikeda distributions. The representation of Diffusion Tensor Images with coupled Ikeda maps is not unique: similar conclusions are drawn when other chaotic maps (Tent, Logistic or Henon maps) are employed in the modelling of the neuron axons network.
Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.
Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M
2017-08-01
Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.
Perception of midline deviations in smile esthetics by laypersons.
Ferreira, Jamille Barros; Silva, Licínio Esmeraldo da; Caetano, Márcia Tereza de Oliveira; Motta, Andrea Fonseca Jardim da; Cury-Saramago, Adriana de Alcantara; Mucha, José Nelson
2016-01-01
To evaluate the esthetic perception of upper dental midline deviation by laypersons and if adjacent structures influence their judgment. An album with 12 randomly distributed frontal view photographs of the smile of a woman with the midline digitally deviated was evaluated by 95 laypersons. The frontal view smiling photograph was modified to create from 1 mm to 5 mm deviations in the upper midline to the left side. The photographs were cropped in two different manners and divided into two groups of six photographs each: group LCN included the lips, chin, and two-thirds of the nose, and group L included the lips only. The laypersons performed the rate of each smile using a visual analog scale (VAS). Wilcoxon test, Student's t-test and Mann-Whitney test were applied, adopting a 5% level of significance. Laypersons were able to perceive midline deviations starting at 1 mm. Statistically significant results (p< 0.05) were found for all multiple comparisons of the values in photographs of group LCN and for almost all comparisons in photographs of group L. Comparisons between the photographs of groups LCN and L showed statistically significant values (p< 0.05) when the deviation was 1 mm. Laypersons were able to perceive the upper dental midline deviations of 1 mm, and above when the adjacent structures of the smiles were included. Deviations of 2 mm and above when the lips only were included. The visualization of structures adjacent to the smile demonstrated influence on the perception of midline deviation.
Statistics as Unbiased Estimators: Exploring the Teaching of Standard Deviation
Wasserman, Nicholas H.; Casey, Stephanie; Champion, Joe; Huey, Maryann
2017-01-01
This manuscript presents findings from a study about the knowledge for and planned teaching of standard deviation. We investigate how understanding variance as an unbiased (inferential) estimator--not just a descriptive statistic for the variation (spread) in data--is related to teachers' instruction regarding standard deviation, particularly…
Moderate deviations principles for the kernel estimator of ...
African Journals Online (AJOL)
Abstract. The aim of this paper is to provide pointwise and uniform moderate deviations principles for the kernel estimator of a nonrandom regression function. Moreover, we give an application of these moderate deviations principles to the construction of condence regions for the regression function. Resume. L'objectif de ...
Generation of deviation parameters for amino acid singlets, doublets ...
Indian Academy of Sciences (India)
We present a new method, secondary structure prediction by deviation parameter (SSPDP) for predicting the secondary structure of proteins from amino acid sequence. Deviation parameters (DP) for amino acid singlets, doublets and triplets were computed with respect to secondary structural elements of proteins based on ...
38 CFR 36.4304 - Deviations; changes of identity.
2010-07-01
... identity. 36.4304 Section 36.4304 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS... Deviations; changes of identity. A deviation of more than 5 percent between the estimates upon which a... change in the identity of the property upon which the original appraisal was based, will invalidate the...
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, P.; van Doorn, E.A.
2001-01-01
The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, Pauline; van Doorn, Erik A.
2002-01-01
he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
Sensitivity Analysis of Deviation Source for Fast Assembly Precision Optimization
Directory of Open Access Journals (Sweden)
Jianjun Tang
2014-01-01
Full Text Available Assembly precision optimization of complex product has a huge benefit in improving the quality of our products. Due to the impact of a variety of deviation source coupling phenomena, the goal of assembly precision optimization is difficult to be confirmed accurately. In order to achieve optimization of assembly precision accurately and rapidly, sensitivity analysis of deviation source is proposed. First, deviation source sensitivity is defined as the ratio of assembly dimension variation and deviation source dimension variation. Second, according to assembly constraint relations, assembly sequences and locating, deviation transmission paths are established by locating the joints between the adjacent parts, and establishing each part’s datum reference frame. Third, assembly multidimensional vector loops are created using deviation transmission paths, and the corresponding scalar equations of each dimension are established. Then, assembly deviation source sensitivity is calculated by using a first-order Taylor expansion and matrix transformation method. Finally, taking assembly precision optimization of wing flap rocker as an example, the effectiveness and efficiency of the deviation source sensitivity analysis method are verified.
Towards a large deviation theory for strongly correlated systems
International Nuclear Information System (INIS)
Ruiz, Guiomar; Tsallis, Constantino
2012-01-01
A large-deviation connection of statistical mechanics is provided by N independent binary variables, the (N→∞) limit yielding Gaussian distributions. The probability of n≠N/2 out of N throws is governed by e −Nr , r related to the entropy. Large deviations for a strong correlated model characterized by indices (Q,γ) are studied, the (N→∞) limit yielding Q-Gaussians (Q→1 recovers a Gaussian). Its large deviations are governed by e q −Nr q (∝1/N 1/(q−1) , q>1), q=(Q−1)/(γ[3−Q])+1. This illustration opens the door towards a large-deviation foundation of nonextensive statistical mechanics. -- Highlights: ► We introduce the formalism of relative entropy for a single random binary variable and its q-generalization. ► We study a model of N strongly correlated binary random variables and their large-deviation probabilities. ► Large-deviation probability of strongly correlated model exhibits a q-exponential decay whose argument is proportional to N, as extensivity requires. ► Our results point to a q-generalized large deviation theory and suggest a large-deviation foundation of nonextensive statistical mechanics.
Limiting values of large deviation probabilities of quadratic statistics
Jeurnink, Gerardus A.M.; Kallenberg, W.C.M.
1990-01-01
Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation
45 CFR 63.19 - Budget revisions and minor deviations.
2010-10-01
... 45 Public Welfare 1 2010-10-01 2010-10-01 false Budget revisions and minor deviations. 63.19 Section 63.19 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION GRANT PROGRAMS... Budget revisions and minor deviations. Pursuant to § 74.102(d) of this title, paragraphs (b)(3) and (b)(4...
Refraction in Terms of the Deviation of the Light.
Goldberg, Fred M.
1985-01-01
Discusses refraction in terms of the deviation of light. Points out that in physics courses where very little mathematics is used, it might be more suitable to describe refraction entirely in terms of the deviation, rather than by introducing Snell's law. (DH)
Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation
Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan
2018-03-01
Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.
[The crooked nose: correction of dorsal and caudal septal deviations].
Foda, H M T
2010-09-01
The deviated nose represents a complex cosmetic and functional problem. Septal surgery plays a central role in the successful management of the externally deviated nose. This study included 800 patients seeking rhinoplasty to correct external nasal deviations; 71% of these suffered from variable degrees of nasal obstruction. Septal surgery was necessary in 736 (92%) patients, not only to improve breathing, but also to achieve a straight, symmetric external nose. A graduated surgical approach was adopted to allow correction of the dorsal and caudal deviations of the nasal septum without weakening its structural support to the nasal dorsum or nasal tip. The approach depended on full mobilization of deviated cartilage, followed by straightening of the cartilage and its fixation in the corrected position by using bony splinting grafts through an external rhinoplasty approach.
Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.
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.
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
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
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2011-01-01
An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...
Radiative corrections in a vector-tensor model
International Nuclear Information System (INIS)
Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.
2006-01-01
In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field
Abboud, A; Kirchlechner, C; Keckes, J; Conka Nurdan, T; Send, S; Micha, J S; Ulrich, O; Hartmann, R; Strüder, L; Pietsch, U
2017-06-01
The full strain and stress tensor determination in a triaxially stressed single crystal using X-ray diffraction requires a series of lattice spacing measurements at different crystal orientations. This can be achieved using a tunable X-ray source. This article reports on a novel experimental procedure for single-shot full strain tensor determination using polychromatic synchrotron radiation with an energy range from 5 to 23 keV. Microbeam X-ray Laue diffraction patterns were collected from a copper micro-bending beam along the central axis (centroid of the cross section). Taking advantage of a two-dimensional energy-dispersive X-ray detector (pnCCD), the position and energy of the collected Laue spots were measured for multiple positions on the sample, allowing the measurement of variations in the local microstructure. At the same time, both the deviatoric and hydrostatic components of the elastic strain and stress tensors were calculated.
Supergravity tensor calculus in 5D from 6D
International Nuclear Information System (INIS)
Kugo, Taichiro; Ohashi, Keisuke
2000-01-01
Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)
Mesh Denoising based on Normal Voting Tensor and Binary Optimization
Yadav, S. K.; Reitebuch, U.; Polthier, K.
2016-01-01
This paper presents a tensor multiplication based smoothing algorithm that follows a two step denoising method. Unlike other traditional averaging approaches, our approach uses an element based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stoc...
Comparison of two global digital algorithms for Minkowski tensor estimation
DEFF Research Database (Denmark)
The geometry of real world objects can be described by Minkowski tensors. Algorithms have been suggested to approximate Minkowski tensors if only a binary image of the object is available. This paper presents implementations of two such algorithms. The theoretical convergence properties...... are confirmed by simulations on test sets, and recommendations for input arguments of the algorithms are given. For increasing resolutions, we obtain more accurate estimators for the Minkowski tensors. Digitisations of more complicated objects are shown to require higher resolutions....
Properties of the tensor correlation in He isotopes
International Nuclear Information System (INIS)
Myo, Takayuki; Sugimoto, Satoru; Kato, Kiyoshi; Toki, Hiroshi; Ikeda, Kiyomi
2006-01-01
We investigate the roles of the tensor correlation on the structures of 4,5 He. For 4 He, we take the high angular momentum states as much as possible with the 2p2h excitations of the shell model type method to describe the tensor correlation. Three specific configurations are found to be favored for the tensor correlation. This correlation is also important to describe the scattering phenomena of the 4 He+nsystem including the higher partial waves consistently
A General Expression for the Quartic Lovelock Tensor
Briggs, C. C.
1997-01-01
A general expression is given for the quartic Lovelock tensor in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection. In addition, expressions are given (in the appendix) for the coefficient of the quartic Lovelock Lagrangian as well as for lower-order Lovelock tensors and Lovelock Lagrangian coefficients.
Energy-momentum tensor in the quantum field theory
International Nuclear Information System (INIS)
Azakov, S.I.
1977-01-01
An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor
Joint Tensor Feature Analysis For Visual Object Recognition.
Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po
2015-11-01
Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms.
The Topology of Three-Dimensional Symmetric Tensor Fields
Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus
1994-01-01
We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.