Antisymmetric tensor generalizations of affine vector fields.

Science.gov (United States)

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.

On the skew-symmetric character of the couple-stress tensor

OpenAIRE

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.

(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

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

Science.gov (United States)

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.

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.

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.)

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.)

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...

Complete stress tensor determination by microearthquake analysis

Science.gov (United States)

Slunga, R.

2010-12-01

the depth based on the assumptions of a fractured crust, widely vary ing stress field, and a general closeness to instability as found by stress measurements (Jamison and Cook 1976). Wheather this approach is working or not is best answered by applying it to real data. This was provided by the IMO network in Iceland. Along Southern Iceland Seismic Zone (SISZ) more than 200,000 microearthquakes and a few M 5 EQs and 2 M=6.6 EQs have been recorded. The results will be presented it is obvious that the use of the stresses determined from the microearthquake recordings may significa ntly improve earthquake warnings and will make it possible to use the absolute C FS method for more deterministic predictions. Note that the microearthquake meth od only shows the part of the stress field that has caused slip. Volumes with st able stress will not show up. However stress measurements (Brown and Hoek 1978, Slunga 1988) have shown that the crustal stresses in general are close to instabi lity and microearthquake source analysis has shown that a large number of differ ent fractures become unstable within longer time windows. This may explain the e xcellent results given by the Icelandic tests of the absolute stress tensor fiel d as given by the microearthquakes. However I prefer to call this stress apparen t.

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

Science.gov (United States)

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.

A Review of Tensors and Tensor Signal Processing

Science.gov (United States)

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.

Aspects of the Antisymmetric Tensor Field

Science.gov (United States)

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.

Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow

Science.gov (United States)

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.

Vacuum expectation value of the stress tensor in an arbitrary curved background: The covariant point-separation method

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

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.

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)

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 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

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)

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.)

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.

The Topology of Three-Dimensional Symmetric Tensor Fields

Science.gov (United States)

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.

Glyph-Based Comparative Visualization for Diffusion Tensor Fields.

Science.gov (United States)

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.

The local quantum-mechanical stress tensor in Thomas-Fermi approximation and gradient expansion method

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

Photon propagators and the definition and approximation of renormalized stress tensors in curved space-time

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

TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

Science.gov (United States)

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.

On energy-momentum tensors of gravitational field

International Nuclear Information System (INIS)

Nikishov, A.I.

2001-01-01

The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru

Stress field models from Maxwell stress functions: southern California

Science.gov (United States)

Bird, Peter

2017-08-01

The lithospheric stress field is formally divided into three components: a standard pressure which is a function of elevation (only), a topographic stress anomaly (3-D tensor field) and a tectonic stress anomaly (3-D tensor field). The boundary between topographic and tectonic stress anomalies is somewhat arbitrary, and here is based on the modeling tools available. The topographic stress anomaly is computed by numerical convolution of density anomalies with three tensor Green's functions provided by Boussinesq, Cerruti and Mindlin. By assuming either a seismically estimated or isostatic Moho depth, and by using Poisson ratio of either 0.25 or 0.5, I obtain four alternative topographic stress models. The tectonic stress field, which satisfies the homogeneous quasi-static momentum equation, is obtained from particular second derivatives of Maxwell vector potential fields which are weighted sums of basis functions representing constant tectonic stress components, linearly varying tectonic stress components and tectonic stress components that vary harmonically in one, two and three dimensions. Boundary conditions include zero traction due to tectonic stress anomaly at sea level, and zero traction due to the total stress anomaly on model boundaries at depths within the asthenosphere. The total stress anomaly is fit by least squares to both World Stress Map data and to a previous faulted-lithosphere, realistic-rheology dynamic model of the region computed with finite-element program Shells. No conflict is seen between the two target data sets, and the best-fitting model (using an isostatic Moho and Poisson ratio 0.5) gives minimum directional misfits relative to both targets. Constraints of computer memory, execution time and ill-conditioning of the linear system (which requires damping) limit harmonically varying tectonic stress to no more than six cycles along each axis of the model. The primary limitation on close fitting is that the Shells model predicts very sharp

The use of Stress Tensor Discriminator Faults in separating heterogeneous fault-slip data with best-fit stress inversion methods. II. Compressional stress regimes

Science.gov (United States)

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

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

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

The modified indeterminate couple stress model: Why Yang et al.'s arguments motivating a symmetric couple stress tensor contain a gap and why the couple stress tensor may be chosen symmetric nevertheless

OpenAIRE

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...

Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.

Science.gov (United States)

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.

On the axial anomalies in external tensor fields

International Nuclear Information System (INIS)

Khudaverdyan, O.M.; Mkrtchyan, R.L.; Zurabyan, L.A.

1985-01-01

Computation of the axial anomaly for Dirac fermions in external tensor fields is studied. The sequence of the supersymmetric one-dimensional models is presented. Their supercharges are equal, after quantization, to Dirac operators in external tensor fields, and the density of Witten's partition function gives the anomaly. It is shown that action in the corresponding path integral differs from the classical one. Gaussian approximation gives the anomaly only in the case of third-rank tensor with zero exterior derivative and in that case anomaly is calculated in all dimensions. The interpretation of that field as the torsion of gravitational field and also connection with the results of Witten and Alvarez-Gaume and Atiyah-Singer index theorem are discussed

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

Vacuum expectation value of the stress-energy tensor of a 2D-gravity field and loop amplitudes for strings of noncritical dimensions

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

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.)

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

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

Migration transformation of two-dimensional magnetic vector and tensor fields

DEFF Research Database (Denmark)

Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn

2012-01-01

We introduce a new method of rapid interpretation of magnetic vector and tensor field data, based on ideas of potential field migration which extends the general principles of seismic and electromagnetic migration to potential fields. 2-D potential field migration represents a direct integral...... to the downward continuation of a well-behaved analytical function. We present case studies for imaging of SQUID-based magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from magnetic tensor field migration agree very well with both Euler deconvolution and the known...

Characteristics of the Residual Stress tensor when filter width is larger than the Ozmidov scale

Science.gov (United States)

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.

Energy-momentum tensor in quantum field theory

International Nuclear Information System (INIS)

Fujikawa, K.

1981-01-01

The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path-integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat--space-time limit, all the Ward-Takahashi identities associated with space-time transformations including the global dilatation become free from anomalies in terms of this energy-momentum tensor, reflecting the general covariance of the integral measure; the trace of this tensor is thus finite at zero momentum transfer for renormalizable theories. The Jacobian for the local conformal transformation, however, becomes nontrivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization-group b function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise

On the generally invariant Lagrangians for the metric field and other tensor fields

International Nuclear Information System (INIS)

Novotny, J.

1978-01-01

The Krupka and Trautman method for the description of all generally invariant functions of the components of geometrical object fields is applied to the invariants of second degree of the metrical field and other tensor fields. The complete system of differential identities fulfilled by the invariants mentioned is found and it is proved that these invariants depend on the tensor quantities only. (author)

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

Non-Abelian tensor gauge fields and higher-spin extension of standard model

International Nuclear Information System (INIS)

Savvidy, G.

2006-01-01

We suggest an extension of the gauge principle which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin 1,2,l. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero ''axion'' The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

arXiv Tensor to scalar ratio from single field magnetogenesis

CERN Document Server

Giovannini, Massimo

2017-08-10

The tensor to scalar ratio is affected by the evolution of the large-scale gauge fields potentially amplified during an inflationary stage of expansion. After deriving the exact evolution equations for the scalar and tensor modes of the geometry in the presence of dynamical gauge fields, it is shown that the tensor to scalar ratio is bounded from below by the dominance of the adiabatic contribution and it cannot be smaller than one thousands whenever the magnetogenesis is driven by a single inflaton field.

Tensor fields on orbits of quantum states and applications

Energy Technology Data Exchange (ETDEWEB)

Volkert, Georg Friedrich

2010-07-19

On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C{sub 0}-principal bundle H{sub 0} {yields} P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)

Tensor fields on orbits of quantum states and applications

International Nuclear Information System (INIS)

Volkert, Georg Friedrich

2010-01-01

On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C 0 -principal bundle H 0 → P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)

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

Science.gov (United States)

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).

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

The Simon and Simon-Mars tensors for stationary Einstein-Maxwell fields

International Nuclear Information System (INIS)

Bini, Donato; Cherubini, Christian; Jantzen, Robert T; Miniutti, Giovanni

2004-01-01

Modulo conventional scale factors, the Simon and Simon-Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein-Maxwell equations, the expression for the Simon tensor in the Kerr-Newman-Taub-NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing-Yano tensor

Point defects dynamics in a stress field

International Nuclear Information System (INIS)

Smetniansky de De Grande, Nelida.

1989-01-01

The dependence of anisotropic defect diffusion on stress is studied for a hexagonal close packed (hcp) material under irradiation and uniaxially stressed. The diffusion is described as a discrete process of thermally activated jumps. It is shown that the presence of an external stress field enhances the intrinsic anisotropic diffusion, being this variation determined by the defect dipole tensors' symmetry in the equilibrium and saddle point configurations. Also, the point defect diffusion equations to sinks, like edge dislocations and spherical cavities, are solved and the sink strengths are calculated. The conclusion is that the dynamics of the interaction between defects and sinks is controlled by the changes in diffusivity induced by stress fields. (Author) [es

Energy-momentum tensor in quantum field theory

International Nuclear Information System (INIS)

Fujikawa, Kazuo.

1980-12-01

The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat space-time limit, all the Ward-Takahashi identities associate with space-time transformations including the global dilatation become free from anomalies, reflecting the general covariance of the integral measure; the trace of this energy-momentum tensor is thus finite at the zero momentum transfer. The Jacobian for the local conformal transformation however becomes non-trivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at the vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization group β-function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at the vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise. (author)

Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields

International Nuclear Information System (INIS)

Anco, Stephen C.

2003-01-01

A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here

Realizability conditions for the turbulent stress tensor in large-eddy simulation

NARCIS (Netherlands)

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

Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole.

Science.gov (United States)

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.

Energy-momentum tensor of intermediate vector bosons in an external electromagnetic field

International Nuclear Information System (INIS)

Mostepanenko, V.M.; Sokolov, I.Yu.

1988-01-01

Expressions are obtained for the canonical and metric energy-momentum tensors of the vector field of intermediate bosons in an external electromagnetic field. It is shown that in the case of a gyromagnetic ratio not equal to unity the energy-momentum tensor cannot be symmetrized on its indices, and an additional term proportional to the anomalous magnetic moment appears in the conservation laws. A modification of the canonical formalism for scalar and vector fields in an external field is proposed in accordance with which the Hamiltonian density is equal to the 00 component of the energy-momentum tensor. An expression for the energy-momentum tensor of a closed system containing a gauge field of intermediate bosons and an electromagnetic field is obtained

Curvature tensors and unified field equations on SEX/sub n/

International Nuclear Information System (INIS)

Chung, K.T.; Lee, I.L.

1988-01-01

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

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

Anti-symmetric rank-two tensor matter field on superspace for NT=2

International Nuclear Information System (INIS)

Spalenza, Wesley; Ney, Wander G.; Helayel-Neto, J.A.

2004-01-01

In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N T =2 SUSY. We start off from the N T =2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables

Lorentz invariance and the zero-point stress-energy tensor

OpenAIRE

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...

Tensor categories and the mathematics of rational and logarithmic conformal field theory

International Nuclear Information System (INIS)

Huang, Yi-Zhi; Lepowsky, James

2013-01-01

We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this construction also establishes the operator product expansion for intertwining operators, which correspond to chiral vertex operators, and more generally, it establishes the logarithmic operator product expansion for logarithmic intertwining operators. We review the main ideas in the construction of the tensor product bifunctors and the associativity isomorphisms. For rational and logarithmic conformal field theories, we review the precise results that yield braided tensor categories, and in the rational case, modular tensor categories as well. In the case of rational conformal field theory, we also briefly discuss the construction of the modular tensor categories for the Wess–Zumino–Novikov–Witten models and, especially, a recent discovery concerning the proof of the fundamental rigidity property of the modular tensor categories for this important special case. In the case of logarithmic conformal field theory, we mention suitable categories of modules for the triplet W-algebras as an example of the applications of our general construction of the braided tensor category structure. (review)

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

Science.gov (United States)

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.

Visualization and processing of tensor fields

CERN Document Server

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.

Four dimensional sigma model coupled to the metric tensor field

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1980-02-01

We discuss the four dimensional nonlinear sigma model with an internal O(n) invariance coupled to the metric tensor field satisfying Einstein equations. We derive a bound on the coupling constant between the sigma field and the metric tensor using the theory of harmonic maps. A special attention is paid to Einstein spaces and some new explicit solutions of the model are constructed. (author)

Fibre bundles associated with fields of geometric objects and a structure tensor

International Nuclear Information System (INIS)

Konderak, J.

1987-08-01

A construction of a k th structure tensor of a field of geometric objects is presented here (k is a non-negative integer). For a given field σ we construct a vector bundle H k,2 (σ). The k th structure tensor is defined as a section of H k,2 (σ) generated by the torsion of σ. It is then shown that vanishing of the k th structure tensor is a necessary and sufficient condition for the field to be (k + 1)-flat. (author). 16 refs

On the equivalence among stress tensors in a gauge-fluid system

Science.gov (United States)

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.

The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity

Directory of Open Access Journals (Sweden)

František FOJTÍK

2014-06-01

Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.

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.)

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

Science.gov (United States)

Haney, Matthew M.; Hisashi Nakahara,

2016-01-01

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

Renormalization of nonabelian gauge theories with tensor matter fields

International Nuclear Information System (INIS)

Lemes, Vitor; Renan, Ricardo; Sorella, Silvio Paolo

1996-03-01

The renormalizability of a nonabelian model describing the coupling between antisymmetric second rank tensor matter fields and Yang-Mills gauge fields is discussed within the BRS algebraic framework. (author). 12 refs

Frames, the Loewner order and eigendecomposition for morphological operators on tensor fields

NARCIS (Netherlands)

van de Gronde, Jasper; Roerdink, Jos B. T. M.

2014-01-01

Rotation invariance is an important property for operators on tensor fields, but up to now, most methods for morphology on tensor fields had to either sacrifice rotation invariance, or do without the foundation of mathematical morphology: a lattice structure. Recently, we proposed a framework for

Determination of the plastic deformation and residual stress tensor distribution using surface and bulk intrinsic magnetic properties

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)

Determinations of directions of the mean stress field in Sichuan-Yunnan region from a number of focal mechanism solutions

Science.gov (United States)

Zhong, Ji-Mao; Cheng, Wan-Zheng

2006-07-01

Based on the spatial orientation and slip direction of the fault plane solutions, we present the expression of corresponding mechanical axis tensor in geographic coordinate system, and then put forward a method for calculating average mechanical axis tensor and its eigenvalues, which involves solving the corresponding eigenequation. The method for deducing mean stress field from T, B, and P axes parameters of a number of focal mechanism solutions has been verified by inverting data of mean stress fields in Fuyun region and in Tangshan region with fitting method of slip direction, and both results are consistent. To study regional average stress field, we need to choose a population of focal mechanism solutions of earthquakes in the massifs where there are significant tectonic structures. According to the focal mechanism solutions of 256 moderate-strong earthquakes occurred in 13 seismic zones of Sichuan-Yunnan region, the quantitative analysis results of stress tensor in each seismic zone have been given. The algorithm of such method is simple and convenient, which makes the method for analyzing tectonic stress field with large amount of focal mechanism solution data become quantified.

Extended pure Yang-Mills gauge theories with scalar and tensor gauge fields

International Nuclear Information System (INIS)

Gabrielli, E.

1991-01-01

The usual abelian gauge theory is extended to an interacting Yang-Mills-like theory containing vector, scalar and tensor gauge fields. These gauge fields are seen as components along the Clifford algebra basis of a gauge vector-spinorial field. Scalar fields φ naturally coupled to vector and tensor fields have been found, leading to a natural φ 4 coupling in the lagrangian. The full expression of the lagrangian for the euclidean version of the theory is given. (orig.)

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

Visualizing Tensor Normal Distributions at Multiple Levels of Detail.

Science.gov (United States)

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.

Energy-momentum tensor of the gravitational field for material spheres

International Nuclear Information System (INIS)

Sokolov, S.N.

1990-01-01

Density of the energy-momentum tensor of a gravitational field which can be defined in the general relativity theory with the help of ideas of the relativistic gravitational theory is found for the case of material spheres. A relationship of this quantity with the Riemann tensor R αβγδ is discussed

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.

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

Science.gov (United States)

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.

Stress field modelling from digital geological map data

Science.gov (United States)

Albert, Gáspár; Barancsuk, Ádám; Szentpéteri, Krisztián

2016-04-01

To create a model for the lithospheric stress a functional geodatabase is required which contains spatial and geodynamic parameters. A digital structural-geological map is a geodatabase, which usually contains enough attributes to create a stress field model. Such a model is not accurate enough for engineering-geological purposes because simplifications are always present in a map, but in many cases maps are the only sources for a tectonic analysis. The here presented method is designed for field geologist, who are interested to see the possible realization of the stress field over the area, on which they are working. This study presents an application which can produce a map of 3D stress vectors from a kml-file. The core application logic is implemented on top of a spatially aware relational database management system. This allows rapid and geographically accurate analysis of the imported geological features, taking advantage of standardized spatial algorithms and indexing. After pre-processing the map features in a GIS, according to the Type-Property-Orientation naming system, which was described in a previous study (Albert et al. 2014), the first stage of the algorithm generates an irregularly spaced point cloud by emitting a pattern of points within a user-defined buffer zone around each feature. For each point generated, a component-wise approximation of the tensor field at the point's position is computed, derived from the original feature's geodynamic properties. In a second stage a weighted moving average method calculates the stress vectors in a regular grid. Results can be exported as geospatial data for further analysis or cartographic visualization. Computation of the tensor field's components is based on the implementation of the Mohr diagram of a compressional model, which uses a Coulomb fracture criterion. Using a general assumption that the main principal stress must be greater than the stress from the overburden, the differential stress is

From stochastic completion fields to tensor voting

NARCIS (Netherlands)

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

Numerical evaluation of the tensor bispectrum in two field inflation

Energy Technology Data Exchange (ETDEWEB)

Raveendran, Rathul Nath [The Institute of Mathematical Sciences, HBNI, CIT Campus, Chennai, 600113 India (India); Sriramkumar, L., E-mail: rathulnr@imsc.res.in, E-mail: sriram@physics.iitm.ac.in [Department of Physics, Indian Institute of Technology Madras, Chennai, 600036 India (India)

2017-07-01

We evaluate the dimensionless non-Gaussianity parameter h {sub NL}, that characterizes the amplitude of the tensor bispectrum, numerically for a class of two field inflationary models such as double inflation, hybrid inflation and aligned natural inflation. We compare the numerical results with the slow roll results which can be obtained analytically. In the context of double inflation, we also investigate the effects on h {sub NL} due to curved trajectories in the field space. We explicitly examine the validity of the consistency relation governing the tensor bispectrum in the squeezed limit. Lastly, we discuss the contribution to h {sub NL} due to the epoch of preheating in two field models.

Numerical evaluation of the tensor bispectrum in two field inflation

International Nuclear Information System (INIS)

Raveendran, Rathul Nath; Sriramkumar, L.

2017-01-01

We evaluate the dimensionless non-Gaussianity parameter h NL , that characterizes the amplitude of the tensor bispectrum, numerically for a class of two field inflationary models such as double inflation, hybrid inflation and aligned natural inflation. We compare the numerical results with the slow roll results which can be obtained analytically. In the context of double inflation, we also investigate the effects on h NL due to curved trajectories in the field space. We explicitly examine the validity of the consistency relation governing the tensor bispectrum in the squeezed limit. Lastly, we discuss the contribution to h NL due to the epoch of preheating in two field models.

Anti-symmetric rank-two tensor matter field on superspace for N{sub T}=2

Energy Technology Data Exchange (ETDEWEB)

Spalenza, Wesley; Ney, Wander G; Helayel-Neto, J A

2004-05-06

In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N{sub T}=2 SUSY. We start off from the N{sub T}=2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables.

Bowen-York tensors

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

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.

Dilaton and second-rank tensor fields as supersymmetric compensators

International Nuclear Information System (INIS)

Nishino, Hitoshi; Rajpoot, Subhash

2007-01-01

We formulate a supersymmetric theory in which both a dilaton and a second-rank tensor play roles of compensators. The basic off-shell multiplets are a linear multiplet (B μν ,χ,φ) and a vector multiplet (A μ ,λ;C μνρ ), where φ and B μν are, respectively, a dilaton and a second-rank tensor. The third-rank tensor C μνρ in the vector multiplet is ''dual'' to the conventional D field with 0 on-shell or 1 off-shell degree of freedom. The dilaton φ is absorbed into one longitudinal component of A μ , making it massive. Initially, B μν has 1 on-shell or 3 off-shell degrees of freedom, but it is absorbed into the longitudinal components of C μνρ . Eventually, C μνρ with 0 on-shell or 1 off-shell degree of freedom acquires in total 1 on-shell or 4 off-shell degrees of freedom, turning into a propagating massive field. These basic multiplets are also coupled to chiral multiplets and a supersymmetric Dirac-Born-Infeld action. Some of these results are also reformulated in superspace. The proposed mechanism may well provide a solution to the long-standing puzzle of massless dilatons and second-rank tensors in supersymmetric models inspired by string theory

Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

Science.gov (United States)

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

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

Science.gov (United States)

Sato, N.; Yoshida, Z.

2018-02-01

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

Strain and stress tensors of rolled uranium plate by Rietveld refinement of TOF neutron-diffraction data

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.

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

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.

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

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.

Electron Gas Dynamic Conductivity Tensor on the Nanotube Surface in Magnetic Field

Directory of Open Access Journals (Sweden)

A. M. Ermolaev

2011-01-01

Full Text Available Kubo formula was derived for the electron gas conductivity tensor on the nanotube surface in longitudinal magnetic field considering spatial and time dispersion. Components of the degenerate and nondegenerate electron gas conductivity tensor were calculated. The study has showed that under high electron density, the conductivity undergoes oscillations of de Haas-van Alphen and Aharonov-Bohm types with the density of electrons and magnetic field changes.

Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory

International Nuclear Information System (INIS)

Pons, Josep M.

2011-01-01

In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. With this baggage on board, we next discuss in detail, for Poincare invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincare symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincare. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincare invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved background.

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...

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

Science.gov (United States)

Kiehn, R. M.

1976-01-01

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

Torsion tensor and covector in a unified field theory

International Nuclear Information System (INIS)

Chernikov, N.A.

1976-01-01

The Einstein unified field theory is used to solve a tensor equation to provide the unambiguous definition of affine connectedness. In the process of solving the Einstein equation limitations imposed by symmetry on the tensor and the torsion covector as well as on affine connectedness are elucidated. It is demonstrated that in a symmetric case the connectedness is unambiguously determined by the Einstein equation. By means of the Riemann geometry a formula for the torsion covector is derived. The equivalence of Einstein equations to those of the nonlinear Born-Infeld electrodynamics is proved

Trace anomaly of the stress-energy tensor for massless vector particles propagating in a general background metric

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

A Third-Rank Tensor Field Based on a U(1) Gauge Theory in Loop Space

OpenAIRE

Shinichi, DEGUCHI; Tadahito, NAKAJIMA; Department of Physics and Atomic Energy Research Institute College of Science and Technology; Department of Physics and Atomic Energy Research Institute College of Science and Technology

1995-01-01

We derive the Stueckelberg formalism extended to a third-rank tensor field from a U(1) gauge theory in loop space, the space of all loops in space-time. The third-rank tensor field is regarded as a constrained U(1) gauge field on the loop space.

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

Science.gov (United States)

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

2018-05-01

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

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

Science.gov (United States)

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

2002-01-01

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

Four-point correlation function of stress-energy tensors in N=4 superconformal theories

CERN Document Server

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.

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

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.

Restrictions on Possible Forms of Classical Matter Fields Carrying no Energy

International Nuclear Information System (INIS)

Sokolowski, L.M.

2004-01-01

It is postulated in general relativity that the matter energy-momentum tensor vanishes if and only if all the matter fields vanish. In classical Lagrangian field theory the energy and momentum density are described by the variational (symmetric) energy-momentum tensor (named the stress tensor) and a priori it might occur that for some systems the tensor is identically to zero for all field configurations whereas evolution of the system is subject to deterministic Lagrange equations of motion. Such a system would not generate its own gravitational field. To check if these systems can exist in the framework of classical field theory we find a relationship between the stress tensor and the Euler operator (i.e. the Lagrange field equations). We prove that if a system of interacting scalar fields (the number of fields cannot exceed the spacetime dimension d) or a single vector field (in spacetimes with d even) has the stress tensor such that its divergence is identically zero (i.e. ''on and of shell''), then the Lagrange equations of motion hold identically too. These systems have then no propagation equations at all and should be regarded as unphysical. Thus nontrivial field equations require the stress tensor be nontrivial too. This relationship between vanishing (of divergence) of the stress tensor and of the Euler operator breaks down if the number of fields is greater than d. We show on concrete examples that a system of n > d interacting scalars or two interacting vector fields can have the stress tensor equal identically to zero while their propagation equations are nontrivial. This means that non-self-gravitating (and yet detectable) field systems are in principle admissible. Their equations of motion are, however, in some sense degenerate. We also show, that for a system of arbitrary number of interacting scalar fields or for a single vector field (in some specific spacetimes in the latter case), if the stress tensor is not identically zero, then it cannot

Mapping residual stress fields from Vickers hardness indents using Raman microprobe spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Sparks, R.G.; Enloe, W.S.; Paesler, M.A.

1988-12-01

Micro-Raman spectroscopy is used to map the residual stress fields in the vicinity of Vickers hardness indents. Both 514.5 and 488.0 nm, light is used to excite the effect and the resulting shifted and broadened Raman peaks are analyzed using computer deconvolution. Half-wave plates are used to vary the orientation of the incident later light`s polarization state with respect to crystal orientation. The Raman scattered light is then analyzed for polarization dependences which are indicative of the various components of the Raman scattering tensor. Such studies can yield valuable information about the orientation of stress components in a well known stress field. The results can then be applied to the determination of stress components in machined semiconductor materials.

Energy momentum tensor in theories with scalar field

International Nuclear Information System (INIS)

Joglekar, S.D.

1992-01-01

The renormalization of energy momentum tensor in theories with scalar fields and two coupling constants is considered. The need for addition of an improvement term is shown. Two possible forms for the improvement term are: (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 derived from an action that is a finite function of bare quantities), (ii) One in which the improvement coefficient is a finite quantity, i.e. finite function of the renormalized quantities are considered. Four possible model of such theories are (i) Scalar Q.E.D. (ii) Non-Abelian theory with scalars, (iii) Yukawa theory, (iv) A model with two scalars. In all these theories a negative conclusion is established: neither forms for the improvement terms lead to a finite energy momentum tensor. Physically this means that when interaction with external gravity is incorporated in such a model, additional experimental input in the form of root mean square mass radius must be given to specify the theory completely, and the flat space parameters are insufficient. (author). 12 refs

Diffusion tensor image registration using hybrid connectivity and tensor features.

Science.gov (United States)

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.

Modified weak energy condition for the energy momentum tensor in quantum field theory

International Nuclear Information System (INIS)

Latorre, J.

1998-01-01

The weak energy condition is known to fail in general when applied to expectation values of the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states vertical stroke ψ right angle for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural restriction on vertical stroke ψ right angle is suggested and illustrated by two quantum mechanical examples based on a simple perturbed harmonic oscillator Hamiltonian. The proposed alternative quantum weak energy condition is applied to states formed by the action of the scalar, vector and the energy momentum tensor operators on the vacuum. We assume conformal invariance in order to determine almost uniquely three-point functions involving the energy momentum tensor in terms of a few parameters. The positivity conditions lead to non-trivial inequalities for these parameters. They are satisfied in free field theories, except in one case for dimensions close to two. Further restrictions on vertical stroke ψ right angle are suggested which remove this problem. The inequalities which follow from considering the state formed by applying the energy momentum tensor to the vacuum are shown to imply that the coefficient of the topological term in the expectation value of the trace of the energy momentum tensor in an arbitrary curved space background is positive, in accord with calculations in free field theories. (orig.)

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

Science.gov (United States)

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.

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

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)

Energy-momentum tensor for a Casimir apparatus in a weak gravitational field

International Nuclear Information System (INIS)

Bimonte, Giuseppe; Calloni, Enrico; Esposito, Giampiero; Rosa, Luigi

2006-01-01

The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane-parallel conducting plates is derived. We use Fermi coordinates and work to first order in the constant acceleration parameter. A perturbative expansion, to this order, of the Green functions involved and of the energy-momentum tensor is derived by means of the covariant geodesic point-splitting procedure. In correspondence to the Green functions satisfying mixed and gauge-invariant boundary conditions, and Ward identities, the energy-momentum tensor is covariantly conserved and satisfies the expected relation between gauge-breaking and ghost parts, while a new simple formula for the trace anomaly is obtained to first order in the constant acceleration. A more systematic derivation is therefore obtained of the theoretical prediction according to which the Casimir device in a weak gravitational field will experience a tiny push in the upwards direction

Hamiltonian quantization of self-dual tensor fields and a bosonic Nielsen-Ninomiya theorem

International Nuclear Information System (INIS)

Tang Waikeung

1989-01-01

The quantization of self-dual tensor fields is carried out following the procedure of Batalin and Fradkin. The (anti) self-duality constraints (either fermionic or bosonic) in the action leads to the gravitational anomaly. In the process of gauge fixing, the impossibility of the co-existence of a positive hamiltonian and covariant action is shown. A version of the Nielsen-Ninomiya theorem applies to self-dual tensor fields viz. the lattice version of the theory shows species doubling with zero net chirality. (orig.)

Tensorial analysis of Eshelby stresses in 3D supercooled liquids

Science.gov (United States)

Lemaître, Anaël

2015-10-01

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

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)

Analysis of fracture patterns and local stress field variations in fractured reservoirs

Science.gov (United States)

Deckert, Hagen; Drews, Michael; Fremgen, Dominik; Wellmann, J. Florian

2010-05-01

independently estimated regional stress tensor is put as a boundary condition into the BE Model. The computed BE model allows to recognize local 3D stress tensor perturbations caused by the larger faults that act as mechanical inhomogeneities. The geometry of the fracture network from field work together with the local stress tensors derived from the 3D BE models allows examining normal and shear stresses on single fractures in different domains of the investigated area. This in turn is used to evaluate, which of the fractures might preferably act as fluid conduits by describing the dilation potential of single fractures. The combination of an improved understanding of the fracture network along with local stress tensors variations from mechanical models will provide a sound evaluation of fluid pathways in fractured reservoirs. In future applications the accurate investigation of large discontinuity pattern in outcrops might be used for a better mathematical definition of fracture networks which could be implemented into numerical simulations of fluid flow.

Large tensor mode, field range bound and consistency in generalized G-inflation

International Nuclear Information System (INIS)

Kunimitsu, Taro; Suyama, Teruaki; Watanabe, Yuki; Yokoyama, Jun'ichi

2015-01-01

We systematically show that in potential driven generalized G-inflation models, quantum corrections coming from new physics at the strong coupling scale can be avoided, while producing observable tensor modes. The effective action can be approximated by the tree level action, and as a result, these models are internally consistent, despite the fact that we introduced new mass scales below the energy scale of inflation. Although observable tensor modes are produced with sub-strong coupling scale field excursions, this is not an evasion of the Lyth bound, since the models include higher-derivative non-canonical kinetic terms, and effective rescaling of the field would result in super-Planckian field excursions. We argue that the enhanced kinetic term of the inflaton screens the interactions with other fields, keeping the system weakly coupled during inflation

Large tensor mode, field range bound and consistency in generalized G-inflation

Energy Technology Data Exchange (ETDEWEB)

Kunimitsu, Taro; Suyama, Teruaki; Watanabe, Yuki; Yokoyama, Jun' ichi, E-mail: kunimitsu@resceu.s.u-tokyo.ac.jp, E-mail: suyama@resceu.s.u-tokyo.ac.jp, E-mail: watanabe@resceu.s.u-tokyo.ac.jp, E-mail: yokoyama@resceu.s.u-tokyo.ac.jp [Research Center for the Early Universe, Graduate School of Science, The University of Tokyo, Tokyo 113-0033 (Japan)

2015-08-01

We systematically show that in potential driven generalized G-inflation models, quantum corrections coming from new physics at the strong coupling scale can be avoided, while producing observable tensor modes. The effective action can be approximated by the tree level action, and as a result, these models are internally consistent, despite the fact that we introduced new mass scales below the energy scale of inflation. Although observable tensor modes are produced with sub-strong coupling scale field excursions, this is not an evasion of the Lyth bound, since the models include higher-derivative non-canonical kinetic terms, and effective rescaling of the field would result in super-Planckian field excursions. We argue that the enhanced kinetic term of the inflaton screens the interactions with other fields, keeping the system weakly coupled during inflation.

Site characterization and validation - stress field in the SCV block and around the validation drift. Stage 3

International Nuclear Information System (INIS)

McKinnon, S.; Carr, P.

1990-04-01

The results of previous stress measurement and stress modelling programmes carried out in the vicinity of the SCV block have been reviewed. Collectively, the results show that the stress field is influenced by the presence of the old mine excavations, and the measurements can be divided into near-field and far-field locations. The near-field measurements denote the extent and magnitude of the mining induced stresses while the far-field measurements reflect virgin conditions. Because of large scatter in the previous data, additional stress measurements were carried out using the CSIRO hollow inclusion cell. Combining all measurements, an estimate of the virgin stress tensor was made. Three-dimensional stress modelling was carried out using the program BEFE to determine the state of stress in the SCV block, and around the validation drift. This modelling showed that most of the SCV block is in a virgin stress field. Stresses acting on the fracture zones in the SCV block will be due only to the virgin stress field and induced stresses from the validation drift. (orig.)

Study of the tensor correlation in oxygen isotopes using mean-field-type and shell model methods

International Nuclear Information System (INIS)

Sugimoto, Satoru

2007-01-01

The tensor force plays important roles in nuclear structure. Recently, we have developed a mean-field-type model which can treat the two-particle-two-hole correlation induced by the tensor force. We applied the model to sub-closed-shell oxygen isotopes and found that an sizable attractive energy comes from the tensor force. We also studied the tensor correlation in 16O using a shell model including two-particle-two-hole configurations. In this case, quite a large attractive energy is obtained for the correlation energy from the tensor force

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

Science.gov (United States)

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.

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

On the computation of the demagnetization tensor field for an arbitrary particle shape using a Fourier space approach

International Nuclear Information System (INIS)

Beleggia, M.; Graef, M. de

2003-01-01

A method is presented to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. By means of a Fourier space approach it is possible to compute analytically the Fourier representation of the demagnetization tensor field for a given shape. Then, specifying the direction of the uniform magnetization, the demagnetizing field and the magnetostatic energy associated with the particle can be evaluated. In some particular cases, the real space representation is computable analytically. In general, a numerical inverse fast Fourier transform is required to perform the inversion. As an example, the demagnetization tensor field for the tetrahedron will be given

A GENERALIZED DIFFUSION TENSOR FOR FULLY ANISOTROPIC DIFFUSION OF ENERGETIC PARTICLES IN THE HELIOSPHERIC MAGNETIC FIELD

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.

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

Science.gov (United States)

Benedetti, Dario; Gurau, Razvan

2018-05-01

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

Lagrangian analysis of vector and tensor fields: Algorithmic foundations and applications in medical imaging and computational fluid dynamics

OpenAIRE

Ding, Zi'ang

2016-01-01

Both vector and tensor fields are important mathematical tools used to describe the physics of many phenomena in science and engineering. Effective vector and tensor field visualization techniques are therefore needed to interpret and analyze the corresponding data and achieve new insight into the considered problem. This dissertation is concerned with the extraction of important structural properties from vector and tensor datasets. Specifically, we present a unified approach for the charact...

Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows

NARCIS (Netherlands)

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

On the energy-momentum tensors for field theories in spaces with affine connection and metric

International Nuclear Information System (INIS)

Manoff, S.

1991-01-01

Generalized covariant Bianchi type identities are obtained and investigated for Lagrangian densities, depending on co- and contravariant tensor fields and their first and second covariant derivatives in spaces with affine connection and metric (L n -space). The notions of canonical, generalized canonical, symmetric and variational energy-momentum tensor are introduced and necessary and sufficient conditions for the existence of the symmetric energy-momentum tensor as a local conserved quantity are obtained. 19 refs.; 1 tab

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

Science.gov (United States)

Dvoeglazov, V. V.

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

Microscopic 57 Fe electric-field-gradient and anisotropic mean-squared-displacement tensors: ferrous chloride tetrahydrate

International Nuclear Information System (INIS)

Bull, James N.; Fitchett, Christopher M.; Tennant, W. Craighead

2010-01-01

This paper reports the determination of the electric-field-gradient and mean-squared-displacement tensors in 57 Fe symmetry-related sites of 1-bar Laue class in monoclinic FeCl 2 .4H 2 O at room temperature by single-crystal Mössbauer spectroscopy. Contrary to all previous work, the mean-squared-displacement matrix (tensor), , is not constrained to be isotropic resulting in the determination of physically meaningful estimates of microscopic (local) electric-field gradient (efg) and tensors. As a consequence of anisotropy in the tensor the absorber recoilless fractions are also anisotropic. As expected of a low-symmetry site, Laue class 1-bar in this case, no two principal axes of the efg and tensors are coaxial, within the combined errors in the two. Further, no principal direction of the efg tensor seems related to bond directions in the unit cell. Within error, and in agreement with an earlier study of sodium nitroprusside, it appears that the tensor principal directions lie close to the crystallographic axes suggesting that they are determined by long wavelength (phonon) vibrations in the crystal rather than by approximate local symmetry about the 57 Fe nucleus. Concurrent with the Mössbauer measurements, we determined as part of a new X-ray structural determination, precise atomic displacement parameters (ADPs) leading to an alternative determination of the matrix (tensor). The average of the eigenvalues of the Mössbauer-determined exceeds that of the average of the X-ray-determined eigenvalues by a factor of around 2.2. Assuming isotropic absorber recoilless fractions leads to substantially the same (macroscopic) efg tensor as had been determined in earlier work. Taking 1/3 x the trace of the anisotropic absorber recoilless fractions leads to an isotropic value of 0.304 in good agreement with earlier single crystal studies where isotropy was assumed.

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

Science.gov (United States)

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

2011-01-01

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

An application of stress energy tensor to the vanishing theorem of differential forms

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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.

Currents and the energy-momentum tensor in classical field theory: a fresh look at an old problem

International Nuclear Information System (INIS)

Forger, Michael; Roemer, Hartmann

2004-01-01

We give a comprehensive review of various methods to define currents and the energy-momentum tensor in classical field theory, with emphasis on a geometric point of view. The necessity of 'improving' the expressions provided by the canonical Noether procedure is addressed and given an adequate geometric framework. The main new ingredient is the explicit formulation of a principle of 'ultralocality' with respect to the symmetry generators, which is shown to fix the ambiguity inherent in the procedure of improvement and guide it towards a unique answer: when combined with the appropriate splitting of the fields into sectors, it leads to the well-known expressions for the current as the variational derivative of the matter field Lagrangian with respect to the gauge field and for the energy-momentum tensor as the variational derivative of the matter field Lagrangian with respect to the metric tensor. In the second case, the procedure is shown to work even when the matter field Lagrangian depends explicitly on the curvature, thus establishing the correct relation between scale invariance, in the form of local Weyl invariance 'on shell', and tracelessness of the energy-momentum tensor, required for a consistent definition of the concept of a conformal field theory

TensorLy: Tensor Learning in Python

NARCIS (Netherlands)

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.

Tensors for physics

CERN Document Server

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-...

Can Effective Field Theory of inflation generate large tensor-to-scalar ratio within Randall–Sundrum single braneworld?

International Nuclear Information System (INIS)

Choudhury, Sayantan

2015-01-01

In this paper my prime objective is to explain the generation of large tensor-to-scalar ratio from the single field sub-Planckian inflationary paradigm within Randall–Sundrum (RS) single braneworld scenario in a model independent fashion. By explicit computation I have shown that the effective field theory prescription of brane inflation within RS single brane setup is consistent with sub-Planckian excursion of the inflaton field, which will further generate large value of tensor-to-scalar ratio, provided the energy density for inflaton degrees of freedom is high enough compared to the brane tension in high energy regime. Finally, I have mentioned the stringent theoretical constraint on positive brane tension, cut-off of the quantum gravity scale and bulk cosmological constant to get sub-Planckian field excursion along with large tensor-to-scalar ratio as recently observed by BICEP2 or at least generates the tensor-to-scalar ratio consistent with the upper bound of Planck (2013 and 2015) data and Planck+BICEP2+Keck Array joint constraint

Anisotropy of the Reynolds stress tensor in the wakes of wind turbine arrays in Cartesian arrangements with counter-rotating rotors

Science.gov (United States)

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

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

Monodimensional estimation of maximum Reynolds shear stress in the downstream flow field of bileaflet valves.

Science.gov (United States)

Grigioni, Mauro; Daniele, Carla; D'Avenio, Giuseppe; Barbaro, Vincenzo

2002-05-01

Turbulent flow generated by prosthetic devices at the bloodstream level may cause mechanical stress on blood particles. Measurement of the Reynolds stress tensor and/or some of its components is a mandatory step to evaluate the mechanical load on blood components exerted by fluid stresses, as well as possible consequent blood damage (hemolysis or platelet activation). Because of the three-dimensional nature of turbulence, in general, a three-component anemometer should be used to measure all components of the Reynolds stress tensor, but this is difficult, especially in vivo. The present study aimed to derive the maximum Reynolds shear stress (RSS) in three commercially available prosthetic heart valves (PHVs) of wide diffusion, starting with monodimensional data provided in vivo by echo Doppler. Accurate measurement of PHV flow field was made using laser Doppler anemometry; this provided the principal turbulence quantities (mean velocity, root-mean-square value of velocity fluctuations, average value of cross-product of velocity fluctuations in orthogonal directions) needed to quantify the maximum turbulence-related shear stress. The recorded data enabled determination of the relationship, the Reynolds stresses ratio (RSR) between maximum RSS and Reynolds normal stress in the main flow direction. The RSR was found to be dependent upon the local structure of the flow field. The reported RSR profiles, which permit a simple calculation of maximum RSS, may prove valuable during the post-implantation phase, when an assessment of valve function is made echocardiographically. Hence, the risk of damage to blood constituents associated with bileaflet valve implantation may be accurately quantified in vivo.

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

TensorLy: Tensor Learning in Python

OpenAIRE

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...

Stress field reconstruction in an active mudslide

Science.gov (United States)

Baroň, Ivo; Kernstocková, Markéta; Melichar, Rostislav

2017-07-01

Meso-scale structures from gravitational slope deformation observed in landslides and deep-seated gravitational slope failures are very similar to those of endogenous ones. Therefore we applied palaeostress analysis of fault-slip data for reconstructing the stress field of an active mudslide in Pechgraben, Austria. This complex compound landslide has developed in clayey colluvium and shale and was activated after a certain period of dormancy in June 2013. During the active motion on June 12, 2013, 73 fault-slip traces at 9 locations were measured within the landslide body. The heterogeneous fault-slip data were processed in term of palaeostresses, the reconstructed palaeostress tensor being characterized by the orientations of the three principal stress axes and the stress ratio (which provides the shape of the stress ellipsoid). The results of the palaeostress analysis were compared to airborne laser scan digital terrain models that revealed dynamics and superficial displacements of the moving mass prior and after our survey. The results were generally in good agreement with the observed landslide displacement pattern and with the anticipated stress regime according to Mohr-Coulomb failure criteria and Anderson's theory. The compressional regime was mostly registered at the toe in areas, where a compressional stress field is expected during previous mass-movement stages, or at margins loaded by subsequent landslide bodies from above. On the other hand, extension regimes were identified at the head scarps of secondary slides, subsequently on bulged ridges at the toe and in the zone of horst-and-graben structures in the lower central part of the main landslide body, where the basal slip surface probably had locally convex character. Strike-slip regimes, as well as oblique normal or oblique reverse regimes were observed at the lateral margins of the landslide bodies. The directions of principal stresses could be used as markers of landslide movement directions

Equations of motion for anisotropic nonlinear elastic continuum in gravitational field

International Nuclear Information System (INIS)

Sokolov, S.N.

1994-01-01

Equations of motion for anisotropic nonlinear elastic continuum in the gravitational field are written in the form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors frozen in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given. 47 refs

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

Science.gov (United States)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

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

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

Science.gov (United States)

Crenshaw, Michael E.

2017-08-01

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

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

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

Improved modeling techniques for turbomachinery flow fields

Energy Technology Data Exchange (ETDEWEB)

Lakshminarayana, B. [Pennsylvania State Univ., University Park, PA (United States); Fagan, J.R. Jr. [Allison Engine Company, Indianapolis, IN (United States)

1995-10-01

This program has the objective of developing an improved methodology for modeling turbomachinery flow fields, including the prediction of losses and efficiency. Specifically, the program addresses the treatment of the mixing stress tensor terms attributed to deterministic flow field mechanisms required in steady-state Computational Fluid Dynamic (CFD) models for turbo-machinery flow fields. These mixing stress tensors arise due to spatial and temporal fluctuations (in an absolute frame of reference) caused by rotor-stator interaction due to various blade rows and by blade-to-blade variation of flow properties. These tasks include the acquisition of previously unavailable experimental data in a high-speed turbomachinery environment, the use of advanced techniques to analyze the data, and the development of a methodology to treat the deterministic component of the mixing stress tensor. Penn State will lead the effort to make direct measurements of the momentum and thermal mixing stress tensors in high-speed multistage compressor flow field in the turbomachinery laboratory at Penn State. They will also process the data by both conventional and conditional spectrum analysis to derive momentum and thermal mixing stress tensors due to blade-to-blade periodic and aperiodic components, revolution periodic and aperiodic components arising from various blade rows and non-deterministic (which includes random components) correlations. The modeling results from this program will be publicly available and generally applicable to steady-state Navier-Stokes solvers used for turbomachinery component (compressor or turbine) flow field predictions. These models will lead to improved methodology, including loss and efficiency prediction, for the design of high-efficiency turbomachinery and drastically reduce the time required for the design and development cycle of turbomachinery.

Tensor calculus for physics a concise guide

CERN Document Server

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...

Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors.

Science.gov (United States)

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 Galileons and gravity

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.

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

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.

The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs

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...

Averaged null energy condition and difference inequalities in quantum field theory

International Nuclear Information System (INIS)

Yurtsever, U.

1995-01-01

For a large class of quantum states, all local (pointwise) energy conditions widely used in relativity are violated by the renormalized stress-energy tensor of a quantum field. In contrast, certain nonlocal positivity constraints on the quantum stress-energy tensor might hold quite generally, and this possibility has received considerable attention in recent years. In particular, it is now known that the averaged null energy condition, the condition that the null-null component of the stress-energy tensor integrated along a complete null geodesic is non-negative for all states, holds quite generally in a wide class of spacetimes for a minimally coupled scalar field. Apart from the specific class of spacetimes considered (mainly two-dimensional spacetimes and four-dimensional Minkowski space), the most significant restriction on this result is that the null geodesic over which the average is taken must be achronal. Recently, Ford and Roman have explored this restriction in two-dimensional flat spacetime, and discovered that in a flat cylindrical space, although the stress energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (nonachronal) null geodesics, when the ''Casimir-vacuum'' contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ''difference inequalities.'' Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary (globally hyperbolic) two-dimensional spacetime, using the same techniques as those we relied on to prove the ANEC in an earlier paper with Wald. I begin with an overview of averaged energy conditions in quantum field theory

Incompressible Steady Flow with Tensor Conductivity Leaving a Transverse Magnetic Field

International Nuclear Information System (INIS)

Witalis, E.A.

1965-12-01

The straight channel flow of an inviscid, incompressible fluid with tensor conductivity is considered when the flow leaves a region of constant transverse magnetic field. The channel walls are taken to be insulating, and an eddy current system arises. This is investigated by the method of magnetic field analysis as given by Witalis. The spatial distribution of magnetic field and ohmic power loss, both parallel and transverse to the flow, are given as functions of the Hall parameter with consideration also to the magnetic Reynolds number of the fluid. MHD power generator aspects of this problem and the results are discussed

Incompressible Steady Flow with Tensor Conductivity Leaving a Transverse Magnetic Field

Energy Technology Data Exchange (ETDEWEB)

Witalis, E A

1965-12-15

The straight channel flow of an inviscid, incompressible fluid with tensor conductivity is considered when the flow leaves a region of constant transverse magnetic field. The channel walls are taken to be insulating, and an eddy current system arises. This is investigated by the method of magnetic field analysis as given by Witalis. The spatial distribution of magnetic field and ohmic power loss, both parallel and transverse to the flow, are given as functions of the Hall parameter with consideration also to the magnetic Reynolds number of the fluid. MHD power generator aspects of this problem and the results are discussed.

New topological invariants for non-abelian antisymmetric tensor fields from extended BRS algebra

International Nuclear Information System (INIS)

Boukraa, S.; Maillet, J.M.; Nijhoff, F.

1988-09-01

Extended non-linear BRS and Gauge transformations containing Lie algebra cocycles, and acting on non-abelian antisymmetric tensor fields are constructed in the context of free differential algebras. New topological invariants are given in this framework. 6 refs

QTAIM and Stress Tensor Characterization of Intramolecular Interactions Along Dynamics Trajectories of a Light-Driven Rotary Molecular Motor.

Science.gov (United States)

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.

Current density tensors

Science.gov (United States)

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.

The invariant polarisation-tensor field for deuterons in storage rings and the Bloch equation for the polarisation-tensor density

International Nuclear Information System (INIS)

Barber, D.P.

2015-10-01

I extend and update earlier work, summarised in an earlier paper (D.P. Barber, M. Voigt, AIP Conference Proceedings 1149 (28)), whereby the invariant polarisation-tensor field (ITF) for deuterons in storage rings was introduced to complement the invariant spin field (ISF). Taken together, the ITF and the ISF provide a definition of the equilibrium spin density-matrix field which, in turn, offers a clean framework for describing equilibrium spin-1 ensembles in storage rings. I show how to construct the ITF by stroboscopic averaging, I give examples, I discuss adiabatic invariance and I introduce a formalism for describing the effect of noise and damping.

Energy-momentum tensor in theories with scalar fields and two coupling constants. I. Non-Abelian case

International Nuclear Information System (INIS)

Joglekar, S.D.; Misra, A.

1989-01-01

In this paper, we generalize our earlier discussion of renormalization of the energy-momentum tensor in scalar QED to that in non-Abelian gauge theories involving scalar fields. 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 derived 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/)

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

International Nuclear Information System (INIS)

Ikhdair, Sameer M.; Hamzavi, Majid

2013-01-01

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

Geometric decomposition of the conformation tensor in viscoelastic turbulence

Science.gov (United States)

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.

Symmetric energy-momentum tensor in Maxwell, Yang-Mills, and Proca theories obtained using only Noether's theorem

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)

Voltage tensor for a plasma in high frequency electromagnetic and constant electric fields in the presence of collisions

International Nuclear Information System (INIS)

Vigdorchik, N.E.

1978-01-01

The voltage tensor expression is obtained for plasma placed in a HF electromagnetic and constant electric fields. The kinetic equations with allowance for collisions are initial. Weakly ionized and completely ionized plasmas are considered. The voltage tensor for completely ionized plasma differs essentially from that for transparent media

Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors

OpenAIRE

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...

A pseudospectral matrix method for time-dependent tensor fields on a spherical shell

International Nuclear Information System (INIS)

Brügmann, Bernd

2013-01-01

We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the double Fourier method, we employ a filter to address time-step limitations and certain stability issues. We find that a tensor filter based on spin-weighted spherical harmonics is successful, while two simplified, non-spin-weighted filters do not lead to stable evolutions. The derivatives and the filter are implemented by matrix multiplication for efficiency. A key technical point is the construction of a matrix multiplication method for the spin-weighted spherical harmonic filter. As example for the efficient parallelization of the double Fourier, spin-weighted filter method we discuss an implementation on a GPU, which achieves a speed-up of up to a factor of 20 compared to a single core CPU implementation

Gauge theories, duality relations and the tensor hierarchy

International Nuclear Information System (INIS)

Bergshoeff, Eric A.; Hohm, Olaf; Hartong, Jelle; Huebscher, Mechthild; OrtIn, Tomas

2009-01-01

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.

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

Science.gov (United States)

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.

Energy momentum tensor and marginal deformations in open string field theory

International Nuclear Information System (INIS)

Sen, Ashoke

2004-01-01

Marginal boundary deformations in a two dimensional conformal field theory correspond to a family of classical solutions of the equations of motion of open string field theory. In this paper we develop a systematic method for relating the parameter labelling the marginal boundary deformation in the conformal field theory to the parameter labelling the classical solution in open string field theory. This is done by first constructing the energy-momentum tensor associated with the classical solution in open string field theory using Noether method, and then comparing this to the answer obtained in the conformal field theory by analysing the boundary state. We also use this method to demonstrate that in open string field theory the tachyon lump solution on a circle of radius larger than one has vanishing pressure along the circle direction, as is expected for a co-dimension one D-brane. (author)

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

Science.gov (United States)

Stepanova, L. V.

2017-12-01

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

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.)

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

Science.gov (United States)

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.

Symmetric energy-momentum tensor in Maxwell, Yang-Mills, and Proca theories obtained using only Noether's theorem

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)

The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields

Energy Technology Data Exchange (ETDEWEB)

Basile, Thomas [Group of Mechanics and Gravitation, Physique théorique et mathématique,University of Mons - UMONS,20 Place du Parc, 7000 Mons (Belgium); Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche du CNRS,Fédération de Recherche Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Bonezzi, Roberto; Boulanger, Nicolas [Group of Mechanics and Gravitation, Physique théorique et mathématique,University of Mons - UMONS,20 Place du Parc, 7000 Mons (Belgium)

2017-04-11

A first-order differential equation is provided for a one-form, spin-s connection valued in the two-row, width-(s−1) Young tableau of GL(5). The connection is glued to a zero-form identified with the spin-s Cotton tensor. The usual zero-Cotton equation for a symmetric, conformal spin-s tensor gauge field in 3D is the flatness condition for the sum of the GL(5) spin-s and background connections. This presentation of the equations allows to reformulate in a compact way the cohomological problem studied in https://arxiv.org/abs/1511.07389, featuring the spin-s Schouten tensor. We provide full computational details for spin 3 and 4 and present the general spin-s case in a compact way.

Analysis of stress fields and elastic energies in the vicinity of nanograin boundaries using the disclination approach

Science.gov (United States)

Sukhanov, Ivan I.; Ditenberg, Ivan A.

2017-12-01

The paper provides a theoretical analysis of elastic stresses and elastic energy distribution in nanostructured metal materials in the vicinity of nanograin boundaries with a high partial disclination density. The analysis demonstrates the stress field distribution in disclination grain boundary configurations as a function of nanograin size, taking into account the superposition of these stresses in screening the disclination pile-ups. It is found that the principal stress tensor components reach maximum values only in disclination planes P ≈ E/25 and that the stress gradients peak at nodal points ∂P/∂x ≈ 0.08E nm-1. The shear stress components are localized within the physical grain size, and the specific elastic energy distribution for such configurations reveals characteristic local maxima which can be the cause for physical broadening of nanograin boundaries.

Einstein gravity 3-point functions from conformal field theory

Science.gov (United States)

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein

2017-12-01

We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈 T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

Antisymmetric tensor Zp gauge symmetries in field theory and string theory

International Nuclear Information System (INIS)

Berasaluce-González, Mikel; Ramírez, Guillermo; Uranga, Angel M.

2014-01-01

We consider discrete gauge symmetries in D dimensions arising as remnants of broken continuous gauge symmetries carried by general antisymmetric tensor fields, rather than by standard 1-forms. The lagrangian for such a general Z p gauge theory can be described in terms of a r-form gauge field made massive by a (r−1)-form, or other dual realizations, that we also discuss. The theory contains charged topological defects of different dimensionalities, generalizing the familiar charged particles and strings in D=4. We describe realizations in string theory compactifications with torsion cycles, or with background field strength fluxes. We also provide examples of non-abelian discrete groups, for which the group elements are associated with charged objects of different dimensionality

Tensor algebra over Hilbert space: Field theory in classical phase space

International Nuclear Information System (INIS)

Matos Neto, A.; Vianna, J.D.M.

1984-01-01

It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt

Characterizing the Potential for Injection-Induced Fault Reactivation Through Subsurface Structural Mapping and Stress Field Analysis, Wellington Field, Sumner County, Kansas

Science.gov (United States)

Schwab, Drew R.; Bidgoli, Tandis S.; Taylor, Michael H.

2017-12-01

Kansas, like other parts of the central U.S., has experienced a recent increase in seismicity. Correlation of these events with brine disposal operations suggests pore fluid pressure increases are reactivating preexisting faults, but rigorous evaluation at injection sites is lacking. Here we determine the suitability of CO2 injection into the Cambrian-Ordovician Arbuckle Group for long-term storage and into a Mississippian reservoir for enhanced oil recovery in Wellington Field, Sumner County, Kansas. To determine the potential for injection-induced earthquakes, we map subsurface faults and estimate in situ stresses, perform slip and dilation tendency analyses to identify well-oriented faults relative to the estimated stress field, and determine the pressure changes required to induce slip at reservoir and basement depths. Three-dimensional seismic reflection data reveal 12 near-vertical faults, mostly striking NNE, consistent with nodal planes from moment tensor solutions from recent earthquakes in the region. Most of the faults cut both reservoirs and several clearly penetrate the Precambrian basement. Drilling-induced fractures (N = 40) identified from image logs and inversion of earthquake moment tensor solutions (N = 65) indicate that the maximum horizontal stress is approximately EW. Slip tendency analysis indicates that faults striking <020° are stable under current reservoir conditions, whereas faults striking 020°-049° may be prone to reactivation with increasing pore fluid pressure. Although the proposed injection volume (40,000 t) is unlikely to reactive faults at reservoir depths, high-rate injection operations could reach pressures beyond the critical threshold for slip within the basement, as demonstrated by the large number of injection-induced earthquakes west of the study area.

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

Science.gov (United States)

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

2018-05-01

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

a tensor theory of gravitation in a curved metric on a flat background

International Nuclear Information System (INIS)

Drummond, J.E.

1979-01-01

A theory of gravity is proposed using a tensor potential for the field on a flat metric. This potential cannot be isolated by local observations, but some details can be deduced from measurements at a distance. The requirement that the field equations for the tensor potential shall be deducible from an action integral, that the action and field equations are gauge invariant, and, conversely, that the Lagrangian in the action integral can be integrated from the field equations leads to Einstein's field equations. The requirement that the field energy-momentum tensor exists leads to a constraint on the tensor potential. If the constraint is a differential gauge condition, then it can only be the Hilbert condition giving a unique background tensor, metric tensor and tensor potential. For a continuous field inside a solid sphere the metric must be homogeneous in the spatial coordinates, and the associated field energy-momentum tensor has properties consistent with Newtonian dynamics. (author)

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)

Algebraic and computational aspects of real tensor ranks

CERN Document Server

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...

The Physical Interpretation of the Lanczos Tensor

OpenAIRE

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...

Electromagnetic Field Theory in (N+1)-Space-Time : AModern Time-Domain Tensor/Array Introduction

NARCIS (Netherlands)

De Hoop, A.T.

2012-01-01

In this paper, a modern time-domain introduction is presented for electromagnetic field theory in (N+1)-spacetime. It uses a consistent tensor/array notation that accommodates the description of electromagnetic phenomena in N-dimensional space (plus time), a requirement that turns up in present-day

Analyzing vortex breakdown flow structures by assignment of colors to tensor invariants.

Science.gov (United States)

Rütten, Markus; Chong, Min S

2006-01-01

Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.

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 ...

Radiation reaction for the classical relativistic spinning particle in scalar, tensor and linearized gravitational fields

International Nuclear Information System (INIS)

Barut, A.O.; Cruz, M.G.

1992-08-01

We use the method of analytic continuation of the equation of motion including the self-fields to evaluate the radiation reaction for a classical relativistic spinning point particle in interaction with scalar, tensor and linearized gravitational fields in flat spacetime. In the limit these equations reduce to those of spinless particles. We also show the renormalizability of these theories. (author). 10 refs

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...

Development of the Tensoral Computer Language

Science.gov (United States)

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.

Photon polarization tensor in the light front field theory at zero and finite temperatures

International Nuclear Information System (INIS)

Silva, Charles da Rocha; Perez, Silvana; Strauss, Stefan

2012-01-01

Full text: In recent years, light front quantized field theories have been successfully generalized to finite temperature. The light front frame was introduced by Dirac , and the quantization of field theories on the null-plane has found applications in many branches of physics. In order to obtain the thermal contribution, we consider the hard thermal loop approximation. This technique was developed by Braaten and Pisarski for the thermal quantum field theory at equal times and is particularly useful to extract the leading thermal contributions to the amplitudes in perturbative quantum field theories. In this work, we consider the light front quantum electrodynamics in (3+1) dimensions and evaluate the photon polarization tensor at one loop for both zero and finite temperatures. In the first case, we apply the dimensional regularization method to extract the finite contribution and find the transverse structure for the amplitude in terms of the light front coordinates. The result agrees with one-loop covariant calculation. For the thermal corrections, we generalize the hard thermal loop approximation to the light front and calculate the dominant temperature contribution to the polarization tensor, consistent with the Ward identity. In both zero as well as finite temperature calculations, we use the oblique light front coordinates. (author)

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...

Gauge theories, duality relations and the tensor hierarchy

NARCIS (Netherlands)

Bergshoeff, Eric A.; Hartong, Jelle; Hohm, Olaf; Huebscher, Mechthild; Ortin, Tomas; Hübscher, Mechthild

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of

On the energy-momentum tensor in Moyal space

International Nuclear Information System (INIS)

Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois

2015-01-01

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

Correlation Between Fracture Network Properties and Stress Variability in Geological Media

Science.gov (United States)

Lei, Qinghua; Gao, Ke

2018-05-01

We quantitatively investigate the stress variability in fractured geological media under tectonic stresses. The fracture systems studied include synthetic fracture networks following power law length scaling and natural fracture patterns based on outcrop mapping. The stress field is derived from a finite-discrete element model, and its variability is analyzed using a set of mathematical formulations that honor the tensorial nature of stress data. We show that local stress perturbation, quantified by the Euclidean distance of a local stress tensor to the mean stress tensor, has a positive, linear correlation with local fracture intensity, defined as the total fracture length per unit area within a local sampling window. We also evaluate the stress dispersion of the entire stress field using the effective variance, that is, a scalar-valued measure of the overall stress variability. The results show that a well-connected fracture system under a critically stressed state exhibits strong local and global stress variabilities.

Stress-energy tensor of a quark moving through a strongly-coupled N=4 supersymmetric Yang-Mills plasma: Comparing hydrodynamics and AdS/CFT duality

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.

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

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

Measuring the stress field around an evolving crack in tensile deformed Mg AZ31 using three-dimensional X-ray diffraction

DEFF Research Database (Denmark)

Oddershede, Jette; Camin, Bettina; Schmidt, Søren

2012-01-01

The stress field around a notch in a coarse grained Mg AZ31 sample has been measured under tensile load using the individual grains as probes in an in situ high energy synchrotron diffraction experiment. The experimental set-up, a variant of three-dimensional X-ray diffraction microscopy, allows...... the position, orientation and full stress tensor of each illuminated grain to be determined and, hence, enables the study of evolving stress fields in coarse grained materials with a spatial resolution equal to the grain size. Grain resolved information like this is vital for understanding what happens when...... the traditional continuum mechanics approach breaks down and fracture is governed by local heterogeneities (e.g. phase or stress differences) between grains. As a first approximation the results obtained were averaged through the thickness of the sample and compared with an elastic–plastic continuum finite...

Dirac vacuum: Acceleration and external-field effects

International Nuclear Information System (INIS)

Jauregui, R.; Torres, M.; Hacyan, S.

1991-01-01

The quantization of the massive spin-1/2 field in Rindler coordinates is considered, including the effects of a background magnetic field. We calculate the expectation values of conserved quantities such as the stress-energy tensor, current density, and spin distribution, as detected by an accelerated observer. The ratio of the energy and particle densities is given by a Fermi-Dirac distribution, but the spectrum of these quantities takes in general a complicated form that cannot be simply interpreted as a thermal spectrum. For the free-particle case the spectrum of the energy-stress tensor has a Fermi-Dirac form only in the massless limit. In the presence of the magnetic field the Dirac vacuum is magnetized and exhibits plasmalike properties

Quantum fields in curved space

International Nuclear Information System (INIS)

Birrell, N.D.; Davies, P.C.W.

1982-01-01

The book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Quantum field theory in Minkowski space, quantum field theory in curved spacetime, flat spacetime examples, curved spacetime examples, stress-tensor renormalization, applications of renormalization techniques, quantum black holes and interacting fields are all discussed in detail. (U.K.)

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 J₂ 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 J₂ 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.

Tensor algebra and tensor analysis for engineers with applications to continuum mechanics

CERN Document Server

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.

A multivector derivative approach to Lagrangian field theory

International Nuclear Information System (INIS)

Lasenby, A.; Gull, S.; Doran, C.

1993-01-01

A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether's theorem is found which is appropriate to both discrete and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-energy and angular-momentum tensors are derived, with spinors and vectors treated in a unified way. It is demonstrated that the antisymmetric terms in the stress-energy tensor are crucial to the correct treatment of angular momentum. The multivector derivative is extended to provide a functional calculus for linear functions which is more compact and more powerful than previous formalisms. This is demonstrated in a reformulation of the functional derivative with respect to the metric, which is then used to recover the full canonical stress-energy tensor. Unlike conventional formalisms, which result in a symmetric stress-energy tensor, this reformulation retains the potentially important antisymmetric contribution. 23 refs

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

(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

Local topology via the invariants of the velocity gradient tensor within vortex clusters and intense Reynolds stress structures in turbulent channel flow

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)

A variational principle giving gravitational 'superpotentials', the affine connection, Riemann tensor, and Einstein field equations

International Nuclear Information System (INIS)

Stachel, J.

1977-01-01

A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor Rsub(μνkappalambda) in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational 'superpotentials' closely connected with the Komar conservation laws (Phys. Rev.; 113:934 (1959)). Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational 'superpotentials'. (author)

Tensors and their applications

CERN Document Server

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

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

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

NARCIS (Netherlands)

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

Tensor rank is not multiplicative under the tensor product

OpenAIRE

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...

Tensor surgery and tensor rank

NARCIS (Netherlands)

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

NARCIS (Netherlands)

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

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...

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

Science.gov (United States)

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.

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)

Tensor B mode and stochastic Faraday mixing

CERN Document Server

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 Excitations in Nambu - Jona-Lasinio Model

CERN Document Server

Chizhov, M V

1996-01-01

It is shown that in the one-flavour NJL model the vector and axial-vector quasiparticles described by the antisymmetric tensor field are generated. These excitations have tensor interactions with quarks in contrast to usual vector ones. Phenomenological applications are discussed.

Dissecting CFT Correlators and String Amplitudes. Conformal Blocks and On-Shell Recursion for General Tensor Fields

International Nuclear Information System (INIS)

Hansen, Tobias

2015-07-01

This thesis covers two main topics: the tensorial structure of quantum field theory correlators in general spacetime dimensions and a method for computing string theory scattering amplitudes directly in target space. In the first part tensor structures in generic bosonic CFT correlators and scattering amplitudes are studied. To this end arbitrary irreducible tensor representations of SO(d) (traceless mixed-symmetry tensors) are encoded in group invariant polynomials, by contracting with sets of commuting and anticommuting polarization vectors which implement the index symmetries of the tensors. The tensor structures appearing in CFT d correlators can then be inferred by studying these polynomials in a d + 2 dimensional embedding space. It is shown with an example how these correlators can be used to compute general conformal blocks describing the exchange of mixed-symmetry tensors in four-point functions, which are crucial for advancing the conformal bootstrap program to correlators of operators with spin. Bosonic string theory lends itself as an ideal example for applying the same methods to scattering amplitudes, due to its particle spectrum of arbitrary mixed-symmetry tensors. This allows in principle the definition of on-shell recursion relations for string theory amplitudes. A further chapter introduces a different target space definition of string scattering amplitudes. As in the case of on-shell recursion relations, the amplitudes are expressed in terms of their residues via BCFW shifts. The new idea here is that the residues are determined by use of the monodromy relations for open string theory, avoiding the infinite sums over the spectrum arising in on-shell recursion relations. Several checks of the method are presented, including a derivation of the Koba-Nielsen amplitude in the bosonic string. It is argued that this method provides a target space definition of the complete S-matrix of string theory at tree-level in a at background in terms of a small

Horizontal rotation of the local stress field in response to magmatic activity: Evidence from case studies and modeling

Science.gov (United States)

Roman, D. C.

2003-12-01

A complete understanding of the initiation, evolution, and termination of volcanic eruptions requires reliable monitoring techniques to detect changes in the conduit system during periods of activity, as well as corresponding knowledge of conduit structure and of magma physical properties. Case studies of stress field orientation prior to, during, and after magmatic activity can be used to relate changes in stress field orientation to the state of the magmatic conduit system. These relationships may be tested through modeling of induced stresses. Here I present evidence from case studies and modeling that horizontal rotation of the axis of maximum compressive stress at an active volcano indicates pressurization of a magmatic conduit, and that this rotation, when observed, may also be indicative of the physical properties of the ascending magma. Changes in the local stress field orientation during the 1992 eruption sequence at Crater Peak (Mt. Spurr), Alaska were analyzed by calculating and inverting subsets of over 150 fault-plane solutions. Local stress tensors for four time periods, corresponding approximately to changes in activity at the volcano, were calculated based on the misfit of individual fault-plane solutions to a regional stress tensor. Results indicate that for nine months prior to the eruption, local maximum compressive stress was oriented perpendicular to regional maximum compressive stress. A similar horizontal rotation was observed beginning in November of 1992, coincident with an episode of elevated earthquake and tremor activity indicating intrusion of magma into the conduit. During periods of quiescence the local stress field was similar to the regional stress field. Similar horizontal rotations have been observed at Mt. Ruapehu, New Zealand (Miller and Savage 2001, Gerst 2003), Usu Volcano, Japan (Fukuyama et al. 2001), Unzen Volcano, Japan (Umakoshi et al. 2001), and Mt. St. Helens Volcano, USA (Moran 1994) in conjunction with eruptive

Quantum field theory in spaces with closed time-like curves

International Nuclear Information System (INIS)

Boulware, D.G.

1992-01-01

Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon

Tensor Factorization for Low-Rank Tensor Completion.

Science.gov (United States)

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

2018-03-01

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

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

Science.gov (United States)

Wu, Bofeng; Huang, Chao-Guang

2018-04-01

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

Energy-momentum tensor in thermal strong-field QED with unstable vacuum

Energy Technology Data Exchange (ETDEWEB)

Gavrilov, S P [Department of General and Experimental Physics, Herzen State Pedagogical University of Russia, Moyka emb. 48, 191186 St Petersburg (Russian Federation); Gitman, D M [Instituto de Fisica, Universidade de Sao Paulo, CP 66318, CEP 05315-970 Sao Paulo, SP (Brazil)], E-mail: gavrilovsergeyp@yahoo.com, E-mail: gitman@dfn.if.usp.br

2008-04-25

The mean value of the one-loop energy-momentum tensor in thermal QED with an electric-like background that creates particles from vacuum is calculated. The problem is essentially different from calculations of effective actions (similar to the action of Heisenberg-Euler) in backgrounds that respect the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and the duration over which one can neglect the back-reaction of created particles are established.

Energy-momentum tensor in thermal strong-field QED with unstable vacuum

International Nuclear Information System (INIS)

Gavrilov, S P; Gitman, D M

2008-01-01

The mean value of the one-loop energy-momentum tensor in thermal QED with an electric-like background that creates particles from vacuum is calculated. The problem is essentially different from calculations of effective actions (similar to the action of Heisenberg-Euler) in backgrounds that respect the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and the duration over which one can neglect the back-reaction of created particles are established

From the Berlin "Entwurf" Field Equations to the Einstein Tensor III: March 1916

OpenAIRE

Weinstein, Galina

2012-01-01

I discuss Albert Einstein's 1916 General Theory of Relativity. I show that in Einstein's 1916 review paper, "the Foundation of the General Theory of Relativity", he derived his November 25, 1915 field equations with an additional term on the right hand side involving the trace of the energy-momentum tensor (he posed the condition square root -g=1) using the equations he presented on November 4, 1915. Series of papers: Final paper.

Stress tensor and viscosity of water: Molecular dynamics and generalized hydrodynamics results

Science.gov (United States)

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

Traversible wormholes and the negative-stress-energy problem in the nonsymmetric gravitational theory

International Nuclear Information System (INIS)

Moffat, J.W.; Svoboda, T.

1991-01-01

The stress-energy tensor for a a general spherically symmetric matter distribution in the nonsymmetric gravitational theory (NGT) is determined using a heuristic argument. Using this tensor and the NGT field equations, it is shown that a wormhole threaded with matter must necessarily have a radial tension greater than the mass-energy density in the throat region. Hence, as in general relativity, a traversible wormhole in NGT must contain matter with a negative stress energy

Probing Earth's State of Stress

Science.gov (United States)

Delorey, A. A.; Maceira, M.; Johnson, P. A.; Coblentz, D. D.

2016-12-01

The state of stress in the Earth's crust is a fundamental physical property that controls both engineered and natural systems. Engineered environments including those for hydrocarbon, geothermal energy, and mineral extraction, as well those for storage of wastewater, carbon dioxide, and nuclear fuel are as important as ever to our economy and environment. Yet, it is at spatial scales relevant to these activities where stress is least understood. Additionally, in engineered environments the rate of change in the stress field can be much higher than that of natural systems. In order to use subsurface resources more safely and effectively, we need to understand stress at the relevant temporal and spatial scales. We will present our latest results characterizing the state of stress in the Earth at scales relevant to engineered environments. Two important components of the state of stress are the orientation and magnitude of the stress tensor, and a measure of how close faults are to failure. The stress tensor at any point in a reservoir or repository has contributions from both far-field tectonic stress and local density heterogeneity. We jointly invert seismic (body and surface waves) and gravity data for a self-consistent model of elastic moduli and density and use the model to calculate the contribution of local heterogeneity to the total stress field. We then combine local and plate-scale contributions, using local indicators for calibration and ground-truth. In addition, we will present results from an analysis of the quantity and pattern of microseismicity as an indicator of critically stressed faults. Faults are triggered by transient stresses only when critically stressed (near failure). We show that tidal stresses can trigger earthquakes in both tectonic and reservoir environments and can reveal both stress and poroelastic conditions.

Continuity equations for bound electromagnetic field and the electromagnetic energy-momentum tensor

International Nuclear Information System (INIS)

Kholmetskii, A L; Missevitch, O V; Yarman, T

2011-01-01

We analyze the application of the Poynting theorem to the bound (velocity-dependent) electromagnetic (EM) field and show that an often-used arbitrary elimination of the term of self-interaction in the product j·E (where j is the current density and E the electric field) represents, in general, an illegitimate operation, which leads to incorrect physical consequences. We propose correct ways of eliminating the terms of self-interaction from the Poynting theorem to transform it into the form that is convenient for problems with bound EM field, which yield the continuity equations for the proper EM energy density, the interaction part of EM energy density and the total EM energy density of bound fields, respectively. These equations indicate the incompleteness of the common EM energy-momentum tensor, and in our analysis, we find a missed term in its structure, which makes its trace non-vanished. Some implications of these results are discussed, in particular, in view of the notion of EM mass of charged particles.

Reynolds and Maxwell stress measurements in the reversed field pinch experiment Extrap-T2R

Science.gov (United States)

Vianello, N.; Antoni, V.; Spada, E.; Spolaore, M.; Serianni, G.; Cavazzana, R.; Bergsåker, H.; Cecconello, M.; Drake, J. R.

2005-08-01

The complete Reynolds stress (RS) has been measured in the edge region of the Extrap-T2R reversed field pinch experiment. The RS exhibits a strong gradient in the region where a high E × B shear takes place. Experimental results show this gradient to be almost entirely due to the electrostatic contribution. This has been interpreted as experimental evidence of flow generation via turbulence mechanism. The scales involved in flow generation are deduced from the frequency decomposition of RS tensor. They are found related to magnetohydrodynamic activity but are different with respect to the scales responsible for turbulent transport.

Reynolds and Maxwell stress measurements in the reversed field pinch experiment Extrap-T2R

International Nuclear Information System (INIS)

Vianello, N.; Antoni, V.; Spada, E.; Spolaore, M.; Serianni, G.; Cavazzana, R.; Bergsaaker, H.; Cecconello, M.; Drake, J.R.

2005-01-01

The complete Reynolds stress (RS) has been measured in the edge region of the Extrap-T2R reversed field pinch experiment. The RS exhibits a strong gradient in the region where a high E x B shear takes place. Experimental results show this gradient to be almost entirely due to the electrostatic contribution. This has been interpreted as experimental evidence of flow generation via turbulence mechanism. The scales involved in flow generation are deduced from the frequency decomposition of RS tensor. They are found related to magnetohydrodynamic activity but are different with respect to the scales responsible for turbulent transport

Mean template for tensor-based morphometry using deformation tensors.

Science.gov (United States)

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.

Couplings of self-dual tensor multiplet in six dimensions

NARCIS (Netherlands)

Bergshoeff, E.; Sezgin, E.; Sokatchev, E.

1996-01-01

The (1, 0) supersymmetry in six dimensions admits a tensor multiplet which contains a second-rank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to a Yang–Mills multiplet, in the absence of supergravity. The

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/)....

Composite antisymmetric tensor bosons in a four-fermion interaction model

International Nuclear Information System (INIS)

Dmitrasinovic, V.

2000-01-01

We discuss the phenomenological consequences of the U A (1) symmetry-breaking two-flavour four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the 'duality' symmetry of this interaction. Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (a) Four antisymmetric tensor and four AS pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (b) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (c) The mixing of massive AS tensor fields with vector fields leads to two sets of spin-1 states. The second set of spin-1 mesons is heavy and has not been observed. Moreover, at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the AS tensor interaction. The tachyonic state also shows up as a pole in the space-like region of the electromagnetic form factors. (d) The mixing of axial-vector fields with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift is negligible. (e) The AS tensor version of the Veneziano-Witten U A (1) symmetry-breaking interaction does not lead to tachyons, or any AS tensor field propagation to leading order in N C . (author)

Comments on conformal Killing vector fields and quantum field theory

International Nuclear Information System (INIS)

Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.

1982-01-01

We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in stress-energy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantum-mechanical measurements made by noninertial observers moving through flat space

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

Science.gov (United States)

Chen, Y.; Huang, L.

2017-12-01

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

Synchrotron X-ray microbeam diffraction measurements of full elastic long range internal strain and stress tensors in commercial-purity aluminum processed by multiple passes of equal-channel angular pressing

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.

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

Energy Technology Data Exchange (ETDEWEB)

Germán, Gabriel [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP (United Kingdom); Herrera-Aguilar, Alfredo [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apdo. postal J-48, CP 72570, Puebla, Pue., México (Mexico); Hidalgo, Juan Carlos [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apdo. postal 48-3, 62251 Cuernavaca, Morelos, México (Mexico); Sussman, Roberto A., E-mail: gabriel@fis.unam.mx, E-mail: aherrera@ifuap.buap.mx, E-mail: hidalgo@fis.unam.mx, E-mail: sussman@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. postal 70-543, 04510 México D. F., México (Mexico)

2016-05-01

We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter ε(φ) and its derivatives ε'(φ) and ε''(φ), thereby extracting general conditions on the tensor-to-scalar ratio r and the running n {sub sk} at φ {sub H} where the perturbations are produced, some 50–60 e -folds before the end of inflation. We find quite generally that for models where ε(φ) develops a maximum, a relatively large r is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter ξ{sub 2}(φ). To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic ε(φ) decreasing during most part of inflation. Since at φ {sub H} the slow-roll parameter ε(φ) is increasing, we thus require that ε(φ) develops a maximum for φ > φ {sub H} after which ε(φ) decrease to small values where most e -folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion Δφ {sub e} ≡ |φ {sub H} −φ {sub e} | is obtained with a sufficiently thin profile for ε(φ) which, however, should not conflict with the second slow-roll parameter η(φ). As a consequence of this analysis we find bounds for Δφ {sub e} , r {sub H} and for the scalar spectral index n {sub sH} . Finally we provide examples where these considerations are explicitly realised.

Mass generation for Abelian spin-1 particles via a symmetric tensor

International Nuclear Information System (INIS)

Dalmazi, D.; Mendonça, E.L.

2012-01-01

In the topologically massive BF model (TMBF) the photon becomes massive via coupling to an antisymmetric tensor, without breaking the U(1) gauge symmetry. There is no need of a Higgs field. The TMBF model is dual to a first-order (in derivatives) formulation of the Maxwell-Proca theory where the antisymmetric field plays the role of an auxiliary field. Since the Maxwell-Proca theory also admits a first-order version which makes use of an auxiliary symmetric tensor, we investigate here a possible generalization of the TMBF model where the photon acquires mass via coupling to a symmetric tensor. We show that it is indeed possible to build up dual models to the Maxwell-Proca theory where the U(1) gauge symmetry is manifest without Higgs field, but after a local field redefinition the vector field eats up the trace of the symmetric tensor and becomes massive. So the explicit U(1) symmetry can be removed unlike the TMBF model.

EINSTEIN EQUATIONS FOR TETRAD FIELDS ECUACIONES DE EINSTEIN PARA CAMPOS TETRADOS

Directory of Open Access Journals (Sweden)

Héctor Torres-Silva

2008-11-01

Full Text Available Every metric tensor can be expressed by the inner product of tetrad fields. We prove that Einstein's equations for these fields have the same form as the stress-energy tensor of electromagnetism if the total external current . Using the Evans' unified field theory, we show that the true unification of gravity and electromagnetism is with source-free Maxwell equations.Todo tensor métrico puede ser expresado por el producto interno de campos tetrados. Se prueba que las ecuaciones de Einstein para esos campos tienen la misma forma que el tensor electromagnético de momento-energía si la corriente externa total es igual a cero. Usando la teoría de campo unificado de Evans se muestra que la verdadera unificación de la gravedad y el electromagnetismo es con las ecuaciones de Maxwell sin fuentes.

Effective field theory approaches for tensor potentials

Energy Technology Data Exchange (ETDEWEB)

Jansen, Maximilian

2016-11-14

Effective field theories are a widely used tool to study physical systems at low energies. We apply them to systematically analyze two and three particles interacting via tensor potentials. Two examples are addressed: pion interactions for anti D{sup 0}D{sup *0} scattering to dynamically generate the X(3872) and dipole interactions for two and three bosons at low energies. For the former, the one-pion exchange and for the latter, the long-range dipole force induce a tensor-like structure of the potential. We apply perturbative as well as non-perturbative methods to determine low-energy observables. The X(3872) is of major interest in modern high-energy physics. Its exotic characteristics require approaches outside the range of the quark model for baryons and mesons. Effective field theories represent such methods and provide access to its peculiar nature. We interpret the X(3872) as a hadronic molecule consisting of neutral D and D{sup *} mesons. It is possible to apply an effective field theory with perturbative pions. Within this framework, we address chiral as well as finite volume extrapolations for low-energy observables, such as the binding energy and the scattering length. We show that the two-point correlation function for the D{sup *0} meson has to be resummed to cure infrared divergences. Moreover, next-to-leading order coupling constants, which were introduced by power counting arguments, appear to be essential to renormalize the scattering amplitude. The binding energy as well as the scattering length display a moderate dependence on the light quark masses. The X(3872) is most likely deeper bound for large light quark masses. In a finite volume on the other hand, the binding energy significantly increases. The dependence on the light quark masses and the volume size can be simultaneously obtained. For bosonic dipoles we apply a non-perturbative, numerical approach. We solve the Lippmann-Schwinger equation for the two-dipole system and the Faddeev

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

Science.gov (United States)

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

2017-01-01

We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches. Copyright © 2016. Published by Elsevier Inc.

THE FIELD OF RECENT TECTONIC STRESSES IN CENTRAL AND SOUTH-EASTERN ASIA

Directory of Open Access Journals (Sweden)

Yu. L. Rebetsky

2014-01-01

Full Text Available  The publication presents results of the study aimed at reconstruction of recent crustal stresses for Central and South-Eastern Asia with application of the method of cataclastic analysis of displacements caused by ruptures, which was proposed by Yu.L. Rebetsky. Two sources of seismic data were referred to: (1 the catalog comprising data from publications covering the period from 1904 to 1992, and (2 the Global Centroid Moment Tensor (CMT Database of earthquake mechanisms (http://earthquake.usgs.gov/eqarchives/sopor, which covers the period from 1978 to 2010. The method of cataclastic analysis in its earliest version was applied in 1996 and 1997 when seismic data from the first catalog were analyzed, and it yielded only parameters of stress ellipsoids; the reconstructions were published in a Russian-Chinese journal (it does not exist now. In this paper, these reconstructions are presented in new graphical formats of GIS. Data from the Global CMT Database were analyzed by the method of cataclastic analysis in the new revision with application of its stages 1 and 2. Based on the calculations, orientations of axes of principal stresses, types of ellipsoids, correlations between spherical and deviatoric components of stress tensors, and reduced stresses were determined. The two sets of reconstructions are compared in this paper. The catalog of earthquake focal mechanisms for the period from 1904 to 1992 consolidated information provided by different authors, and thus focal data for many seismic events were highly inconsistent; therefore, the reliability of reconstructions based on such data seems to be lower than that on the basis the Global CMT Database for the period from 1978 to 2010. Some of the reconstructed stress tensor parameters are mapped. For the areas which data are given in the Global CMT Database and considered as more reliable, mapping is based on stress parameters calculated from such data. For the areas that are not covered by the

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.

Retinal Vessel Segmentation via Structure Tensor Coloring and Anisotropy Enhancement

Directory of Open Access Journals (Sweden)

Mehmet Nergiz

2017-11-01

Full Text Available Retinal vessel segmentation is one of the preliminary tasks for developing diagnosis software systems related to various retinal diseases. In this study, a fully automated vessel segmentation system is proposed. Firstly, the vessels are enhanced using a Frangi Filter. Afterwards, Structure Tensor is applied to the response of the Frangi Filter and a 4-D tensor field is obtained. After decomposing the Eigenvalues of the tensor field, the anisotropy between the principal Eigenvalues are enhanced exponentially. Furthermore, this 4-D tensor field is converted to the 3-D space which is composed of energy, anisotropy and orientation and then a Contrast Limited Adaptive Histogram Equalization algorithm is applied to the energy space. Later, the obtained energy space is multiplied by the enhanced mean surface curvature of itself and the modified 3-D space is converted back to the 4-D tensor field. Lastly, the vessel segmentation is performed by using Otsu algorithm and tensor coloring method which is inspired by the ellipsoid tensor visualization technique. Finally, some post-processing techniques are applied to the segmentation result. In this study, the proposed method achieved mean sensitivity of 0.8123, 0.8126, 0.7246 and mean specificity of 0.9342, 0.9442, 0.9453 as well as mean accuracy of 0.9183, 0.9442, 0.9236 for DRIVE, STARE and CHASE_DB1 datasets, respectively. The mean execution time of this study is 6.104, 6.4525 and 18.8370 s for the aforementioned three datasets respectively.

A single action for the scalar-tensor theory of gravity

International Nuclear Information System (INIS)

Roxburgh, I.W.

1977-01-01

The standard form of the scalar-tensor theory gives eleven equations for eleven unknowns, the metric tensor Gsub(ij) and the scalar field phi. Here the scalar field is eliminated to produce a theory that has just ten equations for ten unknown gsub(ij). The resulting expression for the action of fields and matter is contained completely in a single expression. (author)

Seismotectonics of the Armutlu peninsula (Marmara Sea, NW Turkey) from geological field observation and regional moment tensor inversion

Science.gov (United States)

Kinscher, J.; Krüger, F.; Woith, H.; Lühr, B. G.; Hintersberger, E.; Irmak, T. S.; Baris, S.

2013-11-01

The Armutlu peninsula, located in the eastern Marmara Sea, coincides with the western end of the rupture of the 17 August 1999, İzmit MW 7.6 earthquake which is the penultimate event of an apparently westward migrating series of strong and disastrous earthquakes along the NAFZ during the past century. We present new seismotectonic data of this key region in order to evaluate previous seismotectonic models and their implications for seismic hazard assessment in the eastern Marmara Sea. Long term kinematics were investigated by performing paleo strain reconstruction from geological field investigations by morphotectonic and kinematic analysis of exposed brittle faults. Short term kinematics were investigated by inverting for the moment tensor of 13 small to moderate recent earthquakes using surface wave amplitude spectra. Our results confirm previous models interpreting the eastern Marmara Sea Region as an active transtensional pull-apart environment associated with significant NNE-SSW extension and vertical displacement. At the northern peninsula, long term deformation pattern did not change significantly since Pliocene times contradicting regional tectonic models which postulate a newly formed single dextral strike slip fault in the Marmara Sea Region. This area is interpreted as a horsetail splay fault structure associated with a major normal fault segment that we call the Waterfall Fault. Apart from the Waterfall Fault, the stress strain relation appears complex associated with a complicated internal fault geometry, strain partitioning, and reactivation of pre-existing plane structures. At the southern peninsula, recent deformation indicates active pull-apart tectonics constituted by NE-SW trending dextral strike slip faults. Earthquakes generated by stress release along large rupture zones seem to be less probable at the northern, but more probable at the southern peninsula. Additionally, regional seismicity appears predominantly driven by plate boundary

Homogeneous collapsing star: Tensor and vector harmonics for matter and field asymmetries

International Nuclear Information System (INIS)

Gerlach, U.H.; Sengupta, U.K.

1978-01-01

For the space-time of the interior of a homogeneous collapsing star complete sets of orthogonal vector and tensor harmonics are presented. Their relationship to the set of vector and tensor harmonics for a generic spherically symmetric space-time is exhibited

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 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.

Continuity equations for bound electromagnetic field and the electromagnetic energy-momentum tensor

Energy Technology Data Exchange (ETDEWEB)

Kholmetskii, A L [Department of Physics, Belarusian State University, 4 Nezavisimosti Avenue, 220030 Minsk (Belarus); Missevitch, O V [Institute for Nuclear Problems, Belarusian State University, 11 Bobruiskaya Street, 220030 Minsk (Belarus); Yarman, T, E-mail: khol123@yahoo.com [Department of Engineering, Okan University, Akfirat, Istanbul, Turkey and Savronik, Eskisehir (Turkey)

2011-05-01

We analyze the application of the Poynting theorem to the bound (velocity-dependent) electromagnetic (EM) field and show that an often-used arbitrary elimination of the term of self-interaction in the product j{center_dot}E (where j is the current density and E the electric field) represents, in general, an illegitimate operation, which leads to incorrect physical consequences. We propose correct ways of eliminating the terms of self-interaction from the Poynting theorem to transform it into the form that is convenient for problems with bound EM field, which yield the continuity equations for the proper EM energy density, the interaction part of EM energy density and the total EM energy density of bound fields, respectively. These equations indicate the incompleteness of the common EM energy-momentum tensor, and in our analysis, we find a missed term in its structure, which makes its trace non-vanished. Some implications of these results are discussed, in particular, in view of the notion of EM mass of charged particles.

A forgotten argument by Gordon uniquely selects Abraham's tensor as the energy-momentum tensor for the electromagnetic field in homogeneous, isotropic matter

International Nuclear Information System (INIS)

Antoci, S.; Mihich, L.

1997-01-01

Given the present status of the problem of the electromagnetic energy tensor in matter, there is perhaps use in recalling a forgotten argument given in 1923 by W. Gordon. Let us consider a material medium which is homogeneous and isotropic when observed in its rest frame. For such a medium, Gordon's argument allows to reduce the above-mentioned problem to an analogous one, defined in a general relativistic vacuum. For the latter problem the form of the Lagrangian is known already, hence the determination of the energy tensor is a straightforward matter. One just performs the Hamiltonian derivative of the Lagrangian chosen in this way with respect to the true metric g ik . Abraham's tensor is thus selected as the electromagnetic energy tensor for a medium which is homogeneous and isotropic in its rest frame

Quantum field theory near surfaces of discontinuity

International Nuclear Information System (INIS)

Onishi, H.T.

1981-01-01

This work deals with the problem of a quantized scalar field propagating near a surface of discontinuity. The proper time formalism is employed to express the Green's function and stress tensor as proper time integrals of a transformation function. The transformation function is calculated by a WKB approximation which exhibits the essential singularities generated by the high frequency behavior of waves propagating near the surface. Two singularities are present, the usual direct singularity and an additional reflected singularity generated by the high frequency behavior of waves reflected by the discontinuity. The stress tensor is calculated by dimensional continuation. The results are employed to analyze energy generated by the surface

The simplicial Ricci tensor

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.

The simplicial Ricci tensor

Science.gov (United States)

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.

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

Science.gov (United States)

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

2015-09-01

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

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.

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

Science.gov (United States)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-06-01

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

Elastic constants of stressed and unstressed materials in the phase-field crystal model

Science.gov (United States)

Wang, Zi-Le; Huang, Zhi-Feng; Liu, Zhirong

2018-04-01

A general procedure is developed to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase-field crystal (PFC) models. It is found that for a complete description of system response to elastic deformation, the variations of all the quantities of lattice wave vectors, their density amplitudes (including the corresponding anisotropic variation and degeneracy breaking), the average atomic density, and system volume should be incorporated. The quantitative and qualitative results of elastic constant calculations highly depend on the physical interpretation of the density field used in the model, and also importantly, on the intrinsic pressure that usually pre-exists in the model system. A formulation based on thermodynamics is constructed to account for the effects caused by constant pre-existing stress during the homogeneous elastic deformation, through the introducing of a generalized Gibbs free energy and an effective finite strain tensor used for determining the elastic constants. The elastic properties of both solid and liquid states can be well produced by this unified approach, as demonstrated by an analysis for the liquid state and numerical evaluations for the bcc solid phase. The numerical calculations of bcc elastic constants and Poisson's ratio through this method generate results that are consistent with experimental conditions, and better match the data of bcc Fe given by molecular dynamics simulations as compared to previous work. The general theory developed here is applicable to the study of different types of stressed or unstressed material systems under elastic deformation.

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

Science.gov (United States)

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.

Hydrogen bond interactions in sulfamerazine: DFT study of the O-17, N-14, and H-2 electric field gradient tensors

International Nuclear Information System (INIS)

Aghazadeh, Mustafa; Mirzaei, Mahmoud

2008-01-01

Hydrogen bond (HB) interactions are studied in the real crystalline structure of sulfamerazine by density functional theory (DFT) calculations of the electric field gradient (EFG) tensors at the sites of O-17, N-14, and H-2 nuclei. One-molecule (single) and four-molecule (cluster) models of sulfamerazine are created by available crystal coordinates and the EFG tensors are calculated in both models to indicate the influence of HB interactions on the tensors. Directly relate to the experiments, the calculated EFG tensors are converted to the experimentally measurable nuclear quadrupole resonance (NQR) parameters, quadrupole coupling constant (qcc) and asymmetry parameter (η Q ). The evaluated NQR parameters reveal that due to contribution of the target molecule to N-H...N and N-H...O types of HB interactions, the EFG tensors at the sites of various nuclei are influenced from single model to the target molecule in cluster. Additionally, O2, N4, and H2 nuclei of the target molecule are significantly influenced by HB interactions, consequently, they have the major contributions to HB interactions in cluster model of sulfamerazine. The calculations are performed employing B3LYP method and 6-311++G** basis set using GAUSSIAN 98 suite of program

Ryu-Takayanagi formula for symmetric random tensor networks

Science.gov (United States)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

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

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)

Correlation functions of the chiral stress-tensor multiplet in $ \\mathcal{N}=4 $ SYM

CERN Document Server

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.

A Closed-Form Solution to Tensor Voting: Theory and Applications

OpenAIRE

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

2016-01-01

We prove a closed-form solution to tensor voting (CFTV): given a point set in any dimensions, our closed-form solution provides an exact, continuous and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence...

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

Science.gov (United States)

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 tensor calculus and matter coupling of the alternative minimal auxiliary field formulation of N = 1 supergravity

International Nuclear Information System (INIS)

Sohnius, M.; West, P.

1982-01-01

The tensor calculus for the new alternative minimal auxiliary field formulation of N = 1 supergravity is given. It is used to construct the couplings of this formulation of supergravity to matter. These couplings are found to be different, in several respects to those of the old minimal formulation of N = 1 supergravity. (orig.)

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

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

CERN Document Server

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.

Energy momentum tensor in local causal perturbation theory

International Nuclear Information System (INIS)

Prange, D.

2001-01-01

We study the energy momentum tensor in the Bogolyubov-Epstein-Glaser approach to perturbation theory. It is found to be locally conserved for a class of theories containing to derivated fields in the interaction. For the massless φ 4 -theory we derive the trace anomaly of the improved tensor. (orig.)

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

Science.gov (United States)

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

2012-11-01

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

Inductive Framework for Multi-Aspect Streaming Tensor Completion with Side Information

OpenAIRE

Nimishakavi, Madhav; Mishra, Bamdev; Gupta, Manish; Talukdar, Partha

2018-01-01

Low-rank tensor completion is a well-studied problem and has applications in various fields. However, in many real-world applications the data is dynamic, i.e., the tensor grows as new data arrives. Besides the tensor, in many real-world scenarios, side information is also available in the form of matrices which also grow. Existing work on dynamic tensor completion do not incorporate side information and most of the previous work is based on the assumption that the tensor grows only in one mo...

A dielectric tensor for magnetoplasmas comprising components with generalized Lorentzian distributions

International Nuclear Information System (INIS)

Mace, R.L.

1996-01-01

We report on a new form for the dielectric tensor for a plasma containing superthermal particles. The individual particle components are modelled by 3-dimensional isotropic kappa, or generalized Lorentzian, distributions with arbitrary real-valued index κ. The new dielectric tensor is valid for arbitrary wavevectors. The dielectric tensor, which resembles Trubnikov's dielectric tensor for a relativistic plasma, is compared with the familiar Maxwellian form. When the dielectric tensor is used in the plasma dispersion relation for waves propagating parallel to the magnetic field it reproduces previously derived dispersion relations for various electromagnetic and electrostatic waves in plasmas modelled by Lorentzian particle distributions. Within the constraints of propagation parallel to the ambient magnetic field, we extend the above results to incorporate loss-cone Lorentzian particle distributions, which have important applications in laboratory mirror devices, as well as in space and astrophysical environments. (orig.)

What have we learned from quantum field theory in curved space-time

International Nuclear Information System (INIS)

Fulling, S.A.

1984-01-01

The paper reviews the quantum field theory in curved space-time. Field quantization in gravitational backgrounds; particle creation by black holes; Hawking radiation; quantum field theory in curved space-time; covariant renormalization of the stress-energy-momentum tensor; quantum field theory and quantum gravity; are all discussed. (U.K.)

Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.

Science.gov (United States)

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.

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.

Tensor categories and endomorphisms of von Neumann algebras with applications to quantum field theory

CERN Document Server

Bischoff, Marcel; Longo, Roberto; Rehren, Karl-Henning

2015-01-01

C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).

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

Importance of Force Decomposition for Local Stress Calculations in Biomembrane Molecular Simulations.

Science.gov (United States)

Vanegas, Juan M; Torres-Sánchez, Alejandro; Arroyo, Marino

2014-02-11

Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.

A new solution of Einstein's vacuum field equations

Indian Academy of Sciences (India)

The motivation for the new solution ensues ... terms of singularity, does not seem to work universally as there also exist other solutions of eq. ..... the field equations and not necessarily a contribution to the energy–stress tensor, rather just.

Numerical simulations of plasma equilibrium in a one-dimensional current sheet with a nonzero normal magnetic field component

International Nuclear Information System (INIS)

Mingalev, O. V.; Mingalev, I. V.; Malova, Kh. V.; Zelenyi, L. M.

2007-01-01

The force balance in a thin collisionless current sheet in the Earth's magnetotail with a given constant magnetic field component B z across the sheet is numerically studied for the first time in a self-consistent formulation of the problem. The current sheet is produced by oppositely directed plasma flows propagating from the periphery of the sheet toward the neutral plane. A substantially improved version of a macroparticle numerical model is used that makes it possible to simulate on the order of 10 7 macroparticles even with a personal computer and to calculate equilibrium configurations with a sufficiently low discrete noise level in the first-and second-order moments of the distribution function, which determine the stress tensor elements. Quasisteady configurations were calculated numerically for several sets of plasma parameters in some parts of the magnetotail. The force balance in the sheet was checked by calculating the longitudinal and transverse pressures as well as the elements of the full stress tensor. The stress tensor in the current sheet is found to be nondiagonal and to differ appreciably from the gyrotropic stress tensor in the Chew-Goldberger-Low model, although the Chew-Goldberger-Low theory and numerical calculations yield close results for large distances from the region of reversed magnetic field

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

Energy Technology Data Exchange (ETDEWEB)

Jurco, Branislav [Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute, Prague (Czech Republic); Saemann, Christian [Maxwell Institute for Mathematical Sciences, Department of Mathematics, Heriot-Watt University, Edinburgh (United Kingdom); Wolf, Martin [Department of Mathematics, University of Surrey, Guildford (United Kingdom)

2016-08-15

We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general class of (higher) spaces comprising presentable differentiable stacks, as e.g. orbifolds. We start off with a self-contained review on simplicial sets as models of (∞, 1)-categories. We then discuss principal bundles in terms of simplicial maps and their homotopies. We explain in detail a differentiation procedure, suggested by Severa, that maps higher groupoids to L{sub ∞}-algebroids. Generalising this procedure, we define connections for higher groupoid bundles. As an application, we obtain six-dimensional superconformal field theories via a Penrose-Ward transform of higher groupoid bundles over a twistor space. This construction reduces the search for non-Abelian self-dual tensor field equations in six dimensions to a search for the appropriate (higher) gauge structure. The treatment aims to be accessible to theoretical physicists. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

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

International Nuclear Information System (INIS)

Jurco, Branislav; Saemann, Christian; Wolf, Martin

2016-01-01

We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general class of (higher) spaces comprising presentable differentiable stacks, as e.g. orbifolds. We start off with a self-contained review on simplicial sets as models of (∞, 1)-categories. We then discuss principal bundles in terms of simplicial maps and their homotopies. We explain in detail a differentiation procedure, suggested by Severa, that maps higher groupoids to L ∞ -algebroids. Generalising this procedure, we define connections for higher groupoid bundles. As an application, we obtain six-dimensional superconformal field theories via a Penrose-Ward transform of higher groupoid bundles over a twistor space. This construction reduces the search for non-Abelian self-dual tensor field equations in six dimensions to a search for the appropriate (higher) gauge structure. The treatment aims to be accessible to theoretical physicists. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

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

Science.gov (United States)

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.

The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces

International Nuclear Information System (INIS)

Bergqvist, Goeran; Eriksson, Ingemar

2007-01-01

In this paper, we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces

Algebraic Rainich conditions for the fourth rank tensor V

International Nuclear Information System (INIS)

So, Lau Loi

2011-01-01

Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor B αβμν , a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor B αβμν fulfill these conditions, but so also does our recently proposed tensor V αβμν , which has many of the desirable properties of B αβμν . For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors, B αβμν and V αβμν , which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions.

Tensor modes in pure natural inflation

Science.gov (United States)

Nomura, Yasunori; Yamazaki, Masahito

2018-05-01

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

Volume illustration of muscle from diffusion tensor images.

Science.gov (United States)

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

2009-01-01

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

The normal conformal Cartan connection and the Bach tensor

International Nuclear Information System (INIS)

Korzynski, Mikolaj; Lewandowski, Jerzy

2003-01-01

The goal of this paper is to express the Bach tensor of a four-dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang-Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach tensor. As an example we study the case of a CNC connection which admits a twisting covariantly constant twistor field. This class of conformal geometries of this property is known as given by the Fefferman metric tensors. We use our result to calculate the Bach tensor of an arbitrary Fefferman metric and show that it is proportional to the tensorial square of the four-fold eigenvector of the Weyl tensor. Finally, we solve the Yang-Mills equations imposed on the CNC connection for all the homogeneous Fefferman metrics. The only solution is the Nurowski-Plebanski metric

Methods for the Determination of Currents and Fields in Steady Two-Dimensional MHD Flow With Tensor Conductivity

International Nuclear Information System (INIS)

Witalis, E.A.

1965-12-01

Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given

Methods for the Determination of Currents and Fields in Steady Two-Dimensional MHD Flow With Tensor Conductivity

Energy Technology Data Exchange (ETDEWEB)

Witalis, E A

1965-12-15

Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given.

Coordinate independent expression for transverse trace-free tensors

International Nuclear Information System (INIS)

Conboye, Rory

2016-01-01

The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. Quantum Grav. 31 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector. (paper)

Tensor polarized deuteron targets for intermediate energy physics experiments

International Nuclear Information System (INIS)

Meyer, W.; Schilling, E.

1985-03-01

At intermediate energies measurements from a tensor polarized deuteron target are being prepared for the following reactions: the photodisintegration of the deuteron, the elastic pion-deuteron scattering and the elastic electron-deuteron scattering. The experimental situation of the polarization experiments for these reactions is briefly discussed in section 2. In section 3 the definitions of the deuteron polarization and the possibilities to determine the vector and tensor polarization are given. Present tensor polarization values and further improvements in this field are reported in section 4. (orig.)

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

Science.gov (United States)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

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

Massive quantum field theory in two-dimensional Robertson-Walker space-time

International Nuclear Information System (INIS)

Bunch, T.S.; Christensen, S.M.; Fulling, S.A.

1978-01-01

The stress tensor of a massive scalar field, as an integral over normal modes (which are not mere plane waves), is regularized by covariant point separation. When the expectation value in a Parker-Fulling adiabatic vacuum state is expanded in the limit of small curvature-to-mass ratios, the series coincides in each order with the Schwinger-DeWitt-Christensen proper-time expansion. The renormalization ansatz suggested by these expansions (which applies to arbitrary curvature-to-mass ratios and arbitrary quantum state) can be implemented at the integrand level for practical computations. The renormalized tensor (1) passes in the massless limit, for appropriate choice of state, to the known vacuum stress of a massless field, (2) agrees with the explicit results of Bernard and Duncan for a special model, and (3) has a nonzero vacuum expectation value in the two-dimensional ''Milne universe'' (flat space in hyperbolic coordinates). Following Wald, we prove that the renormalized tensor is conserved and point out that there is no arbitrariness in the renormalization procedure. The general approach of this paper is applicable to four-dimensional models

Fourth meeting entitled “Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data”

CERN Document Server

Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

2014-01-01

Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...

X-ray strain tensor imaging: FEM simulation and experiments with a micro-CT.

Science.gov (United States)

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.

General equilibrium second-order hydrodynamic coefficients for free quantum fields

Science.gov (United States)

Buzzegoli, M.; Grossi, E.; Becattini, F.

2017-10-01

We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called "Kubo formulae". We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term.

(2, 0) tensor multiplets and conformal supergravity in D = 6

NARCIS (Netherlands)

Bergshoeff, Eric; Sezgin, Ergin; Proeyen, Antoine Van

1999-01-01

We construct the supercurrent multiplet that contains the energy–momentum tensor of the (2, 0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2, 0) Weyl multiplet.

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.

Efficient tensor completion for color image and video recovery: Low-rank tensor train

OpenAIRE

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...

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.

Physical stress, mass, and energy for non-relativistic matter

Science.gov (United States)

Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.

2017-06-01

For theories of relativistic matter fields there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for non-relativistic matter theories. We point out that while the physical non-relativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. We also provide computations of these quantities for some simple non-relativistic actions.

Diffusion tensor imaging of the human skeletal muscle: contributions and applications

International Nuclear Information System (INIS)

Neji, Radhouene

2010-01-01

In this thesis, we present several techniques for the processing of diffusion tensor images. They span a wide range of tasks such as estimation and regularization, clustering and segmentation, as well as registration. The variational framework proposed for recovering a tensor field from noisy diffusion weighted images exploits the fact that diffusion data represent populations of fibers and therefore each tensor can be reconstructed using a weighted combination of tensors lying in its neighborhood. The segmentation approach operates both at the voxel and the fiber tract levels. It is based on the use of Mercer kernels over Gaussian diffusion probabilities to model tensor similarity and spatial interactions, allowing the definition of fiber metrics that combine information from spatial localization and diffusion tensors. Several clustering techniques can be subsequently used to segment tensor fields and fiber tractographies. Moreover, we show how to develop supervised extensions of these algorithms. The registration algorithm uses probability kernels in order to match moving and target images. The deformation consistency is assessed using the distortion induced in the distances between neighboring probabilities. Discrete optimization is used to seek an optimum of the defined objective function. The experimental validation is done over a dataset of manually segmented diffusion images of the lower leg muscle for healthy and diseased subjects. The results of the techniques developed throughout this thesis are promising. (author)

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

Energy momentum tensor and operator product expansion in local causal perturbation theory

International Nuclear Information System (INIS)

Prange, D.

2000-09-01

We derive new examples for algebraic relations of interacting fields in local perturbative quantum field theory. The fundamental building blocks in this approach are time ordered products of free (composed) fields. We give explicit formulas for the construction of Poincare covariant ones, which were already known to exist through cohomological arguments. For a large class of theories the canonical energy momentum tensor is shown to be conserved. Classical theories without dimensionful couplings admit an improved tensor that is additionally traceless. On the example of φ 4 -theory we discuss the improved tensor in the quantum theory. Its trace receives an anomalous contribution due to its conservation. Moreover, we define an interacting bilocal normal product for scalar theories. This leads to an operator product expansion of two time ordered fields. (orig.) [de

Tensor eigenvalues and their applications

CERN Document Server

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.

Boundary effects in quantum field theory

International Nuclear Information System (INIS)

Deutsch, D.; Candelas, P.

1979-01-01

Electromagnetic and scalar fields are quantized in the region near an arbitrary smooth boundary, and the renormalized expectation value of the stress-energy tensor is calculated. The energy density is found to diverge as the boundary is approached. For nonconformally invariant fields it varies, to leading order, as the inverse fourth power of the distance from the boundary. For conformally invariant fields the coefficient of this leading term is zero, and the energy density varies as the inverse cube of the distance. An asymptotic series for the renormalized stress-energy tensor is developed as far as the inverse-square term in powers of the distance. Some criticisms are made of the usual approach to this problem, which is via the ''renormalized mode sum energy,'' a quantity which is generically infinite. Green's-function methods are used in explicit calculations, and an iterative scheme is set up to generate asymptotic series for Green's functions near a smooth boundary. Contact is made with the theory of the asymptotic distribution of eigenvalues of the Laplacian operator. The method is extended to nonflat space-times and to an example with a nonsmooth boundary

CTCP temperature fields and stresses

Directory of Open Access Journals (Sweden)

Minjiang Zhang

2017-11-01

Full Text Available Cross-tensioned concrete pavements (CTCPs are used in the construction of continuous Portland cement concrete pavements. They eliminate the need for transverse joints and also restrict cracking of the pavement. A CTCP consists of three components, namely, the CTCP slab, the sand sliding layer (SSL, and the cement-stabilized macadam base, from top to down. The retard-bonded tendons (RBTs of the CTCP slab are arranged diagonally. In the present study, a detailed 3D finite element model was developed and used to examine the temperature fields and stresses of a CTCP by thermal-mechanical coupling analysis, and the results were compared with field measurements. The model investigations revealed that, under typical cloudless summer conditions, the temperature field of the CTCP varied nonlinearly with both time and depth. The resultant step-type temperature gradient of the CTCP represents a significant deviation from that of a conventional pavement and impacts the thermal contact resistance of the SSL. It was found that the SSL could effectively reduce the temperature stresses in the CTCP, and that the residual temperature stresses were effectively resisted by the staged cross-tensioned RBTs. The potential problem areas in the vicinity of the temperature stresses were also investigated by the finite element method and field tests. Keywords: Portland cement concrete pavement, Prestressed concrete pavement, Temperature stress, Temperature field, Finite element method, Retard-bonded tendon

Stress-stress correlator in ϕ 4 theory: poles or a cut?

Science.gov (United States)

Moore, Guy D.

2018-05-01

We explore the analytical properties of the traceless stress tensor 2-point function at zero momentum and small frequency (relevant for shear viscosity and hydrodynamic response) in hot, weakly coupled λ ϕ 4 theory. We show that, rather than one or a small number of poles, the correlator has a cut along the negative imaginary frequency axis. We briefly discuss this result's relevance for constructing 2'nd order hydrodynamic models of hot relativistic field theories.

Multivariate Tensor-based Brain Anatomical Surface Morphometry via Holomorphic One-Forms

OpenAIRE

Wang, Yalin; Chan, Tony F.; Toga, Arthur W.; Thompson, Paul M.

2009-01-01

Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer’s Disease (AD; 26 subjects), lateral ventricula...

Perturbations of ultralight vector field dark matter

Energy Technology Data Exchange (ETDEWEB)

Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez [Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid (Spain)

2017-02-13

We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with k{sup 2}≪Hma, we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with k{sup 2}≫Hma, we get a wave-like behaviour in which the sound speed is non-vanishing and of order c{sub s}{sup 2}≃k{sup 2}/m{sup 2}a{sup 2}. This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ−Ψ)/Φ∼c{sub s}{sup 2}. Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ∼c{sub s}{sup 2}. This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.

Tensor Transpose and Its Properties

OpenAIRE

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.

Structure of the Einstein tensor for class-1 embedded space time

Energy Technology Data Exchange (ETDEWEB)

Krause, J [Universidad Central de Venezuela, Caracas

1976-04-11

Continuing previous work, some features of the flat embedding theory of class-1 curved space-time are further discussed. In the two-metric formalism provided by the embedding approach the Gauss tensor obtains as the flat-covariant gradient of a fundamental vector potential. The Einstein tensor is then examined in terms of the Gauss tensor. It is proved that the Einstein tensor is divergence free in flat space-time, i.e. a true Lorentz-covariant conservation law for the Einstein tensor is shown to hold. The form of the Einstein tensor in flat space-time also appears as a canonical energy-momentum tensor of the vector potential. The corresponding Lagrangian density, however, does not provide us with a set of field equations for the fundamental vector potential; indeed, the Euler-Lagrange ''equations'' collapse to a useless identity, while the Lagrangian density has the form of a flat divergence.

CONSTRAINTS ON SCALAR AND TENSOR PERTURBATIONS IN PHENOMENOLOGICAL AND TWO-FIELD INFLATION MODELS: BAYESIAN EVIDENCES FOR PRIMORDIAL ISOCURVATURE AND TENSOR MODES

Energy Technology Data Exchange (ETDEWEB)

Vaeliviita, Jussi [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, N-0315 Oslo (Norway); Savelainen, Matti; Talvitie, Marianne; Kurki-Suonio, Hannu; Rusak, Stanislav, E-mail: jussi.valiviita@astro.uio.no [Department of Physics and Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FIN-00014 University of Helsinki (Finland)

2012-07-10

We constrain cosmological models where the primordial perturbations have an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the power spectra of primordial perturbations are parameterized with amplitudes and spectral indices, and a slow-roll two-field inflation approach where slow-roll parameters are used as primary parameters, determining the spectral indices and the tensor-to-scalar ratio. In the phenomenological case, with CMB data, the upper limit to the CDM isocurvature fraction is {alpha} < 6.4% at k = 0.002 Mpc{sup -1} and 15.4% at k = 0.01 Mpc{sup -1}. The non-adiabatic contribution to the CMB temperature variance is -0.030 < {alpha}{sub T} < 0.049 at the 95% confidence level. Including the supernova (SN) (or large-scale structure) data, these limits become {alpha} < 7.0%, 13.7%, and -0.048 < {alpha}{sub T} < 0.042 (or {alpha} < 10.2%, 16.0%, and -0.071 < {alpha}{sub T} < 0.024). The CMB constraint on the tensor-to-scalar ratio, r < 0.26 at k = 0.01 Mpc{sup -1}, is not affected by the non-adiabatic modes. In the slow-roll two-field inflation approach, the spectral indices are constrained close to 1. This leads to tighter limits on the isocurvature fraction; with the CMB data {alpha} < 2.6% at k = 0.01 Mpc{sup -1}, but the constraint on {alpha}{sub T} is not much affected, -0.058 < {alpha}{sub T} < 0.045. Including SN (or LSS) data, these limits become {alpha} < 3.2% and -0.056 < {alpha}{sub T} < 0.030 (or {alpha} < 3.4% and -0.063 < {alpha}{sub T} < -0.008). In addition to the generally correlated models, we study also special cases where the adiabatic and isocurvature modes are uncorrelated or fully (anti)correlated. We calculate Bayesian evidences (model probabilities) in 21 different non-adiabatic cases and compare them to the corresponding adiabatic models, and find that in all cases the data support the pure adiabatic model.

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

Science.gov (United States)

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

2018-05-01

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

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

Science.gov (United States)

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S

2017-05-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.

A tensor approach to the estimation of hydraulic conductivities in ...

African Journals Online (AJOL)

Based on the field measurements of the physical properties of fractured rocks, the anisotropic properties of hydraulic conductivity (HC) of the fractured rock aquifer can be assessed and presented using a tensor approach called hydraulic conductivity tensor. Three types of HC values, namely point value, axial value and flow ...

Tensor network state correspondence and holography

Science.gov (United States)

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.

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

Science.gov (United States)

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

From static to rotating to conformal static solutions: rotating imperfect fluid wormholes with(out) electric or magnetic field

Energy Technology Data Exchange (ETDEWEB)

Azreg-Ainou, Mustapha [Baskent University, Department of Mathematics, Ankara (Turkey)

2014-05-15

We derive a shortcut stationary metric formula for generating imperfect fluid rotating solutions, in Boyer-Lindquist coordinates, from spherically symmetric static ones. We explore the properties of the curvature scalar and stress-energy tensor for all types of rotating regular solutions we can generate without restricting ourselves to specific examples of regular solutions (regular black holes or wormholes). We show through examples how it is generally possible to generate an imperfect fluid regular rotating solution via radial coordinate transformations. We derive rotating wormholes that are modeled as imperfect fluids and discuss their physical properties. These are independent on the way the stress-energy tensor is interpreted. A solution modeling an imperfect fluid rotating loop black hole is briefly discussed. We then specialize to the recently discussed stable exotic dust Ellis wormhole as emerged in a source-free radial electric or magnetic field, and we generate its, conjecturally stable, rotating counterpart. This turns out to be an exotic imperfect fluid wormhole, and we determine the stress-energy tensor of both the imperfect fluid and the electric or magnetic field. (orig.)

From static to rotating to conformal static solutions: rotating imperfect fluid wormholes with(out) electric or magnetic field

International Nuclear Information System (INIS)

Azreg-Ainou, Mustapha

2014-01-01

We derive a shortcut stationary metric formula for generating imperfect fluid rotating solutions, in Boyer-Lindquist coordinates, from spherically symmetric static ones. We explore the properties of the curvature scalar and stress-energy tensor for all types of rotating regular solutions we can generate without restricting ourselves to specific examples of regular solutions (regular black holes or wormholes). We show through examples how it is generally possible to generate an imperfect fluid regular rotating solution via radial coordinate transformations. We derive rotating wormholes that are modeled as imperfect fluids and discuss their physical properties. These are independent on the way the stress-energy tensor is interpreted. A solution modeling an imperfect fluid rotating loop black hole is briefly discussed. We then specialize to the recently discussed stable exotic dust Ellis wormhole as emerged in a source-free radial electric or magnetic field, and we generate its, conjecturally stable, rotating counterpart. This turns out to be an exotic imperfect fluid wormhole, and we determine the stress-energy tensor of both the imperfect fluid and the electric or magnetic field. (orig.)

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

Science.gov (United States)

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

2018-02-01

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

The tensor rank of tensor product of two three-qubit W states is eight

OpenAIRE

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.

NW transverse fault system in Southern Bogota, Colombia: New seismologic and structural evidences derived from focal mechanisms and stress field determination

Science.gov (United States)

Angel Amaya, J.; Fierro Morales, J.; Ordoñez Potes, M.; Blanco, M.

2012-12-01

We present new seismological, morphotectonic and structural data of the Southern Bogota area. The goals of the study were to characterize the NW transverse fault system and to evaluate its effect on seismic wave's generation and propagation. The data set included epicenters of the RSNC (Red Sismologica Nacional de Colombia) catalog over the period 1993-2012, historical description of seismic events (period 1644-1921), structural field data (scale 1:100000) and remote sensors interpretation. The methodology included the structural analysis of over 476 faults having a known sense of offset by using a least squares iterative inversion outlined by Angelier (1984) to determinate the mean deviatoric principal stress tensor. Preliminary conclusions showed that both propagation medium and direction are determined by the structural and mechanic conditions of the Southern Bogota Shear Zone (SBSZ) defined by Fierro & Angel, (2008) as a NW-SE oblique-slip fault zone within sinistral and normal regimes. Based on both data sources (focal mechanism and field structural data) we attempted to reconstruct the stress field starting with a strike slip faulting stress regime (S2 vertical), the solution yielded a ENE-WSW orientation for horizontal principal stress (S1). It is hypothesized that the NW oblique-slip fault zone may generate and/or propagate seismic waves, as a local source, implying local hazard to Bogota the capital city of Colombia with over 8 million habitants.

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.)

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.)

Continuum mechanics for engineers

CERN Document Server

Mase, G Thomas; Mase, George E

2009-01-01

Continuum TheoryContinuum MechanicsStarting OverNotationEssential MathematicsScalars, Vectors and Cartesian TensorsTensor Algebra in Symbolic Notation - Summation ConventionIndicial NotationMatrices and DeterminantsTransformations of Cartesian TensorsPrincipal Values and Principal DirectionsTensor Fields, Tensor CalculusIntegral Theorems of Gauss and StokesStress PrinciplesBody and Surface Forces, Mass DensityCauchy Stress PrincipleThe Stress TensorForce and Moment Equilibrium; Stress Tensor SymmetryStress Transformation LawsPrincipal Stresses; Principal Stress DirectionsMaximum and Minimum Stress ValuesMohr's Circles For Stress Plane StressDeviator and Spherical Stress StatesOctahedral Shear StressKinematics of Deformation and MotionParticles, Configurations, Deformations and MotionMaterial and Spatial CoordinatesLangrangian and Eulerian DescriptionsThe Displacement FieldThe Material DerivativeDeformation Gradients, Finite Strain TensorsInfinitesimal Deformation TheoryCompatibility EquationsStretch RatiosRot...

Active stress field and seismotectonic features in Intra-Carpathian region of Romania

Science.gov (United States)

Oros, Eugen; Popa, Mihaela; Diaconescu, Mihai; Radulian, Mircea

2017-04-01

The Romanian Intra-Carpathian Region is located on the eastern half of Tisa-Dacia geodynamic block from the Neogene Carpathian-Pannonian Basin. The distribution of seismicity displays clear clusters and narrower zones with seismogenic potential confirmed by the damaging earthquakes recoded in the region, e.g. July 01, 1829 (Mw=6.2), October 10, 1834 (Mw=5.6), January 26, 1916 (Mw=6.4), July 12, 1991 (Mw=5.7), December 2, 1991 (Mw=5.5). The state of recent stress and deformation appears to be controlled by the interaction of plate-boundary and intraplate forces, which include the counterclockwise rotation and N-NE-directed indentation of the Adria microplate and buoyancy forces associated with differential topography and lithospheric heterogeneities. The stress field and tectonic regime are investigated at regional and local scales by the formal inversion of focal mechamisms. There can be observed short-scale lateral changes of i) tectonic regimes from compressive (reverse and strike-slip faultings) to pure extensive (normal faultings) and ii) variation of stress directions (SHmax) from NE-SW to EW and WNW-ESE towards Southern Carpathians and NS within Easter Carpathians. The changes in stress directions occur over a distance that is comparable to or smaller than the thickness of the lithosphere. A comparative analysis of stress tensor with GPS velocity/displacememt vectors shows variations from paralellism to orthogonality, suggesting different mechanisms of crustal deformations.The major seismic activity (Mw≥5.0) appears to be generally concentrated along the faults systems bordering de Tisa-Dacia Block, intersections of faults of different ages, internal shear zones and with the border of the former structural terrains, old rifts and neostructures.

Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors

International Nuclear Information System (INIS)

Ramos, Tomas; Rubilar, Guillermo F.; Obukhov, Yuri N.

2011-01-01

Highlights: → The definition of the momentum of light inside matter is studied. → Fully relativistic analysis of the dielectric 'Einstein box' thought experiment. → Minkowski, Abraham and the total energy-momentum tensors are derived in detail. → Some assumptions hidden in the usual Einstein box argument are identified. → The Abraham momentum is not uniquely selected as the momentum of light in this case. - Abstract: We analyse the 'Einstein box' thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.

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

Science.gov (United States)

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.

Stress field of a dislocating inclined fault

Energy Technology Data Exchange (ETDEWEB)

Huang, F.; Wang, T.

1980-02-01

Analytical expressions are derived for the stress field caused by a rectangular dislocating fault of an arbitrary dip in a semi-infinite elastic medium for the case of unequal Lame constants. The results of computations for the stress fields on the ground surface of an inclined strike-slip and an inclined dip-slip fault are represented by contour maps. The effects of Poisson Ratio of the medium, the dip angle, upper and lower boundaries of the faults on the stress field at surface have been discussed. As an application, the contour maps for shear stress and hydrostatic stress of near fields of the Tonghai (1970), Haicheng (1975) and Tangshan (1976) earthquakes have been calculated and compared with the spatial distributions of strong aftershocks of these earthquakes. It is found that most of the strong aftershocks are distributed in the regions of tensional stress, where the hydrostatic stress is positive.

On the backreaction of scalar and spinor quantum fields in curved spacetimes

International Nuclear Information System (INIS)

Hack, Thomas-Paul

2010-10-01

In the first instance, the present work is concerned with generalising constructions and results in quantum field theory on curved spacetimes from the well-known case of the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra of observables of the Dirac field is constructed in the algebraic framework. This algebra contains normal-ordered Wick polynomials in particular, and an extended analysis of one of its elements, the stress-energy tensor, is performed. Based on detailed calculations of the Hadamard coe?cients of the Dirac field, it is found that a local, covariant, and covariantly conserved construction of the stress-energy tensor is possible. Additionally, the mathematically sound Hadamard regularisation prescription of the stress-energy tensor is compared to the mathematically less rigorous DeWitt-Schwinger regularisation. It is found that both prescriptions are essentially equivalent, particularly, it turns out to be possible to formulate the DeWitt-Schwinger prescription in a well-defined way. While the aforementioned results hold in generic curved spacetimes, particular attention is also devoted to a specific class of Robertson-Walker spacetimes with a lightlike Big Bang hypersurface. Employing holographic methods, Hadamard states for the Klein-Gordon and the Dirac field are constructed. These states are preferred in the sense that they constitute asymptotic equilibrium states in the limit to the Big Bang hypersurface. Finally, solutions of the semiclassical Einstein equation for quantum fields of arbitrary spin are analysed in the flat Robertson-Walker case. One finds that these solutions explain the measured supernova Ia data as good as the ΛCDM model. Hence, one arrives at a natural explanation of dark energy and a simple quantum model of cosmological dark matter. (orig.)

On the backreaction of scalar and spinor quantum fields in curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Hack, Thomas-Paul

2010-10-15

In the first instance, the present work is concerned with generalising constructions and results in quantum field theory on curved spacetimes from the well-known case of the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra of observables of the Dirac field is constructed in the algebraic framework. This algebra contains normal-ordered Wick polynomials in particular, and an extended analysis of one of its elements, the stress-energy tensor, is performed. Based on detailed calculations of the Hadamard coe?cients of the Dirac field, it is found that a local, covariant, and covariantly conserved construction of the stress-energy tensor is possible. Additionally, the mathematically sound Hadamard regularisation prescription of the stress-energy tensor is compared to the mathematically less rigorous DeWitt-Schwinger regularisation. It is found that both prescriptions are essentially equivalent, particularly, it turns out to be possible to formulate the DeWitt-Schwinger prescription in a well-defined way. While the aforementioned results hold in generic curved spacetimes, particular attention is also devoted to a specific class of Robertson-Walker spacetimes with a lightlike Big Bang hypersurface. Employing holographic methods, Hadamard states for the Klein-Gordon and the Dirac field are constructed. These states are preferred in the sense that they constitute asymptotic equilibrium states in the limit to the Big Bang hypersurface. Finally, solutions of the semiclassical Einstein equation for quantum fields of arbitrary spin are analysed in the flat Robertson-Walker case. One finds that these solutions explain the measured supernova Ia data as good as the {lambda}CDM model. Hence, one arrives at a natural explanation of dark energy and a simple quantum model of cosmological dark matter. (orig.)

Non-Abelian formulation of a vector-tensor gauge theory with topological coupling

International Nuclear Information System (INIS)

Barcelos Neto, J.; Cabo, A.; Silva, M.B.D.

1995-08-01

We obtain a non-Abelian version of a theory involving vector and tensor and tensor gauge fields interacting via a massive topological coupling, besides the nonminimum one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to compatibilize gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case. (author). 9 refs

Charged black holes in a generalized scalar–tensor gravity model

Directory of Open Access Journals (Sweden)

Yves Brihaye

2017-09-01

Full Text Available We study 4-dimensional charged and static black holes in a generalized scalar–tensor gravity model, in which a shift symmetry for the scalar field exists. For vanishing scalar field the solution corresponds to the Reissner–Nordström (RN solution, while solutions of the full scalar-gravity model have to be constructed numerically. We demonstrate that these black holes support Galilean scalar hair up to a maximal value of the scalar–tensor coupling that depends on the value of the charge and can be up to roughly twice as large as that for uncharged solutions. The Hawking temperature TH of the hairy black holes at maximal scalar–tensor coupling decreases continuously with the increase of the charge and reaches TH=0 for the highest possible charge that these solutions can carry. However, in this limit, the scalar–tensor coupling needs to vanish. The limiting solution hence corresponds to the extremal RN solution, which does not support regular Galilean scalar hair due to its AdS2×S2 near-horizon geometry.

Canonical forms of tensor representations and spontaneous symmetry breaking

International Nuclear Information System (INIS)

Cummins, C.J.

1986-01-01

An algorithm for constructing canonical forms for any tensor representation of the classical compact Lie groups is given. This method is used to find a complete list of the symmetry breaking patterns produced by Higgs fields in the third-rank antisymmetric representations of U(n), SU(n) and SO(n) for n<=7. A simple canonical form is also given for kth-rank symmetric tensor representations. (author)

Fermionic topological quantum states as tensor networks

Science.gov (United States)

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.

Stress field of a dislocating inclined fault

Energy Technology Data Exchange (ETDEWEB)

Huang, F.; Wang, T.

1980-02-01

In this paper, analytical expressions of the stress field given rise by a rectangular dislocating fault of an arbitrary dip in a semi-infinite elastic medium for the case of unequal Lame constants are derived. The results of computations for the stress fields on the ground surface of an inclined strike-slip and an inclined dip-slip fault are represented by contour maps. The effects of the Poisson Ratio of the medium, the dip angle, upper and lower boundaries of the faults on the stress field at the surface have been discussed. As an application, the contour maps for shear stress and hydrostatic stress of near fields of the Tonghai (1970), Haicheng, (1975) and Tangshan (1976) earthquakes have been calculated and compared with the spatial distributions of strong aftershocks of these earthquakes. It is found that most of the strong aftershocks are distributed in the regions of tensional stress where the hydrostatic stress is positive.

Surface impedance tensor in amorphous wires with helical anisotropy: Magnetic hysteresis and asymmetry

International Nuclear Information System (INIS)

Makhnovskiy, D. P.; Panina, L. V.; Mapps, D. J.

2001-01-01

This article concerns the investigation of the magnetic behavior of the surface impedance tensor cflx var-sigma in CoSiB amorphous wires having a residual torsion stress and a helical anisotropy. The full tensor cflx var-sigma involving three different components is found by measuring the S 21 parameter at a required excitation with a Hewlett-Packard network/spectrum analyzer at MHz frequencies. In general, the impedance plots versus axial magnetic field H ex exhibit a hysteresis related to that for the case of static magnetization. The diagonal components of cflx var-sigma (longitudinal var-sigma zz and circular var-sigma v ar-phi v ar-phi) show a sharp peak in a narrow field interval where the domain walls form and contribute to the ac magnetization dynamics. This peak is not seen for the off-diagonal component var-sigma zv ar-phi (var-sigma v ar-phi z ) since the existence of the domain structure suppresses it. Applying a dc bias current results in a gradual transition to a nonhysteretic asymmetrical behavior with an enhanced sensitivity. The portions of the experimental plots associated with the rotational dynamic process are in qualitative agreement with the theory based on a single-domain model. [copyright] 2001 American Institute of Physics

Measuring the stress field around an evolving crack in tensile deformed Mg AZ31 using three-dimensional X-ray diffraction

International Nuclear Information System (INIS)

Oddershede, Jette; Camin, Bettina; Schmidt, Søren; Mikkelsen, Lars P.; Sørensen, Henning Osholm; Lienert, Ulrich; Poulsen, Henning Friis; Reimers, Walter

2012-01-01

The stress field around a notch in a coarse grained Mg AZ31 sample has been measured under tensile load using the individual grains as probes in an in situ high energy synchrotron diffraction experiment. The experimental set-up, a variant of three-dimensional X-ray diffraction microscopy, allows the position, orientation and full stress tensor of each illuminated grain to be determined and, hence, enables the study of evolving stress fields in coarse grained materials with a spatial resolution equal to the grain size. Grain resolved information like this is vital for understanding what happens when the traditional continuum mechanics approach breaks down and fracture is governed by local heterogeneities (e.g. phase or stress differences) between grains. As a first approximation the results obtained were averaged through the thickness of the sample and compared with an elastic–plastic continuum finite element simulation. It was found that a full three-dimensional simulation was required to account for the measured transition from the overall plane stress case away from the notch to the essentially plane strain case observed near the notch tip. The measured and simulated stress contours were shown to be in good agreement except at the highest applied load, at which stress relaxation at the notch tip was observed in the experimental data. This stress relaxation is attributed to the initiation and propagation of a crack. Finally, it was demonstrated that the measured lattice rotations could be used as a qualitative measure of the shape and extent of the plastic deformation zone.

Harmonic d-tensors

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.

Boundaries immersed in a scalar quantum field

International Nuclear Information System (INIS)

Actor, A.A.; Bender, I.

1996-01-01

We study the interaction between a scalar quantum field φ(x), and many different boundary configurations constructed from (parallel and orthogonal) thin planar surfaces on which φ(x) is constrained to vanish, or to satisfy Neumann conditions. For most of these boundaries the Casimir problem has not previously been investigated. We calculate the canonical and improved vacuum stress tensors left angle T μv (x) right angle and left angle direct difference μv (x) right angle of φ(x) for each example. From these we obtain the local Casimir forces on all boundary planes. For massless fields, both vacuum stress tensors yield identical attractive local Casimir forces in all Dirichlet examples considered. This desirable outcome is not a priori obvious, given the quite different features of left angle T μv (x) right angle and left angle direct difference μv (x) right angle. For Neumann conditions, left angle T μv (x) right angle and left angle direct difference μv (x) right angle lead to attractive Casimir stresses which are not always the same. We also consider Dirichlet and Neumann boundaries immersed in a common scalar quantum field, and find that these repel. The extensive catalogue of worked examples presented here belongs to a large class of completely solvable Casimir problems. Casimir forces previously unknown are predicted, among them ones which might be measurable. (orig.)

Tensor calculus for engineers and physicists

CERN Document Server

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...

Experimental Measurement of In Situ Stress

Science.gov (United States)

Tibbo, Maria; Milkereit, Bernd; Nasseri, Farzine; Schmitt, Douglas; Young, Paul

2016-04-01

The World Stress Map data is determined by stress indicators including earthquake focal mechanisms, in situ measurement in mining, oil and gas boreholes as well as the borehole cores, and geologic data. Unfortunately, these measurements are not only infrequent but sometimes infeasible, and do not provide nearly enough data points with high accuracy to correctly infer stress fields in deep mines around the world. Improvements in stress measurements of Earth's crust is fundamental to several industries such as oil and gas, mining, nuclear waste management, and enhanced geothermal systems. Quantifying the state of stress and the geophysical properties of different rock types is a major complication in geophysical monitoring of deep mines. Most stress measurement techniques involve either the boreholes or their cores, however these measurements usually only give stress along one axis, not the complete stress tensor. The goal of this project is to investigate a new method of acquiring a complete stress tensor of the in situ stress in the Earth's crust. This project is part of a comprehensive, exploration geophysical study in a deep, highly stressed mine located in Sudbury, Ontario, Canada, and focuses on two boreholes located in this mine. These boreholes are approximately 400 m long with NQ diameters and are located at depths of about 1300 - 1600 m and 1700 - 2000 m. Two borehole logging surveys were performed on both boreholes, October 2013 and July 2015, in order to perform a time-lapse analysis of the geophysical changes in the mine. These multi-parameter surveys include caliper, full waveform sonic, televiewer, chargeability (IP), and resistivity. Laboratory experiments have been performed on borehole core samples of varying geologies from each borehole. These experiments have measured the geophysical properties including elastic modulus, bulk modulus, P- and S-wave velocities, and density. The apparatus' used for this project are geophysical imaging cells capable

Unified cosmology with scalar-tensor theory of gravity

Energy Technology Data Exchange (ETDEWEB)

Tajahmad, Behzad [Faculty of Physics, University of Tabriz, Tabriz (Iran, Islamic Republic of); Sanyal, Abhik Kumar [Jangipur College, Department of Physics, Murshidabad (India)

2017-04-15

Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energy-momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized. (orig.)

Unified cosmology with scalar-tensor theory of gravity

International Nuclear Information System (INIS)

Tajahmad, Behzad; Sanyal, Abhik Kumar

2017-01-01

Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energy-momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized. (orig.)

Holographic duality from random tensor networks

Energy Technology Data Exchange (ETDEWEB)

Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)

2016-11-02

Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main

Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary

International Nuclear Information System (INIS)

Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.

2005-08-01

We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)

Investigations of some rock stress measuring techniques and the stress field in Norway

Energy Technology Data Exchange (ETDEWEB)

Hanssen, Tor Harald

1998-12-31

Rock stresses are important to the safe construction and operation of all man-made structures in rock, whether In mining, civil or petroleum engineering. The crucial issue is their relative magnitude and orientation. This thesis develops equipment and methods for further rock stress assessment and reevaluates existing overcoring rock stress measurements, and relates this information to the present geological setting. Both laboratory work and field work are involved. In the field, rock stresses are measured by the overcoring and the hydraulic fracturing technique. An observation technique for assessing likely high stresses is developed. The field data refer to several hydropower projects and to some offshore hydrocarbon fields. The principal sections are: (1) Tectonic setting in the western Fennoscandia, (2) Triaxial rock stress measurements by overcoring using the NTH cell (a strain gauge cell developed at the Norwegian technical university in Trondheim and based on the CSIR cell of the South African Council for Scientific and Industrial Research), (3) Laboratory testing of the NTH cell, (4) Quality ranking of stresses measured by the NTH cell, (4) Recalculated rock stresses and implications to the regional stress field, (5) Hydraulic fracturing stress measurements. 113 refs., 98 figs., 62 tabs.

Investigations of some rock stress measuring techniques and the stress field in Norway

Energy Technology Data Exchange (ETDEWEB)

Hanssen, Tor Harald

1997-12-31

Rock stresses are important to the safe construction and operation of all man-made structures in rock, whether In mining, civil or petroleum engineering. The crucial issue is their relative magnitude and orientation. This thesis develops equipment and methods for further rock stress assessment and reevaluates existing overcoring rock stress measurements, and relates this information to the present geological setting. Both laboratory work and field work are involved. In the field, rock stresses are measured by the overcoring and the hydraulic fracturing technique. An observation technique for assessing likely high stresses is developed. The field data refer to several hydropower projects and to some offshore hydrocarbon fields. The principal sections are: (1) Tectonic setting in the western Fennoscandia, (2) Triaxial rock stress measurements by overcoring using the NTH cell (a strain gauge cell developed at the Norwegian technical university in Trondheim and based on the CSIR cell of the South African Council for Scientific and Industrial Research), (3) Laboratory testing of the NTH cell, (4) Quality ranking of stresses measured by the NTH cell, (4) Recalculated rock stresses and implications to the regional stress field, (5) Hydraulic fracturing stress measurements. 113 refs., 98 figs., 62 tabs.

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

Science.gov (United States)

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

2012-08-01

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

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.

Vacuum fluctuations of twisted fields in the space time of cosmic strings

International Nuclear Information System (INIS)

Matsas, G.E.A.

1990-01-01

A twisted scalar field conformally coupled to gravitation is used to calculate the vacuum stress-energy tensor in the background spacetime generated by an infinite straight gauge cosmic string. The result has an absolute numerical value close to the one obtained with a non-twisted conformal scalar field but their signals are opposite. (author) [pt

Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

International Nuclear Information System (INIS)

Chernyshenko, Dmitri; Fangohr, Hans

2015-01-01

In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges

A Model of Anisotropic Property of Seepage and Stress for Jointed Rock Mass

Directory of Open Access Journals (Sweden)

Pei-tao Wang

2013-01-01

Full Text Available Joints often have important effects on seepage and elastic properties of jointed rock mass and therefore on the rock slope stability. In the present paper, a model for discrete jointed network is established using contact-free measurement technique and geometrical statistic method. A coupled mathematical model for characterizing anisotropic permeability tensor and stress tensor was presented and finally introduced to a finite element model. A case study of roadway stability at the Heishan Metal Mine in Hebei Province, China, was performed to investigate the influence of joints orientation on the anisotropic properties of seepage and elasticity of the surrounding rock mass around roadways in underground mining. In this work, the influence of the principal direction of the mechanical properties of the rock mass on associated stress field, seepage field, and damage zone of the surrounding rock mass was numerically studied. The numerical simulations indicate that flow velocity, water pressure, and stress field are greatly dependent on the principal direction of joint planes. It is found that the principal direction of joints is the most important factor controlling the failure mode of the surrounding rock mass around roadways.

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

International Nuclear Information System (INIS)

Sitenko, Yu A; Vlasii, N D

2012-01-01

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

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

Science.gov (United States)

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

2012-05-01

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

Nonperturbative loop quantization of scalar-tensor theories of gravity

International Nuclear Information System (INIS)

Zhang Xiangdong; Ma Yongge

2011-01-01

The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter ω(φ). In the sector of ω(φ)=-(3/2), the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of ω(φ)≠-(3/2), the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. By canonical transformations, we further obtain the connection-dynamical formalism of the scalar-tensor theories with real su(2) connections as configuration variables in both sectors. This formalism enables us to extend the scheme of nonperturbative loop quantum gravity to the scalar-tensor theories. The quantum kinematical framework for the scalar-tensor theories is rigorously constructed. Both the Hamiltonian constraint operator and master constraint operator are well defined and proposed to represent quantum dynamics. Thus the loop quantum gravity method is also valid for general scalar-tensor theories.

Cylindrically symmetric solutions of a scalar--tensor theory of gravitation

International Nuclear Information System (INIS)

Singh, T.

1975-01-01

The cylindrically symmetric solutions for the Einstein--Rosen metric of a scalar--tensor theory proposed by Dunn have been obtained. A method has been given by which one can obtain, under certain conditions, solutions of this scalar--tensor theory from known solutions of the empty space field equations of Einstein's theory of gravitation. It is also found that one of the solutions of the scalar--tensor theory is nonsingular in the sense of Bonnor. Further some special solutions are obtained which reduce to the well-known solution of Levi-Civita and a time dependent solution obtained by Misra and Radhakrishna

Seismic moment tensor for anisotropic media: implication for Non-double-couple earthquakes

Science.gov (United States)

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

Susceptibility Tensor Imaging (STI) of the Brain

Science.gov (United States)

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

TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

OpenAIRE

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...

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

Science.gov (United States)

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

2017-11-01

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

A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

OpenAIRE

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...

Spin dynamics of paramagnetic centers with anisotropic g tensor and spin of 1/2

Science.gov (United States)

Maryasov, Alexander G.; Bowman, Michael K.

2012-08-01

The influence of g tensor anisotropy on spin dynamics of paramagnetic centers having real or effective spin of 1/2 is studied. The g anisotropy affects both the excitation and the detection of EPR signals, producing noticeable differences between conventional continuous-wave (cw) EPR and pulsed EPR spectra. The magnitudes and directions of the spin and magnetic moment vectors are generally not proportional to each other, but are related to each other through the g tensor. The equilibrium magnetic moment direction is generally parallel to neither the magnetic field nor the spin quantization axis due to the g anisotropy. After excitation with short microwave pulses, the spin vector precesses around its quantization axis, in a plane that is generally not perpendicular to the applied magnetic field. Paradoxically, the magnetic moment vector precesses around its equilibrium direction in a plane exactly perpendicular to the external magnetic field. In the general case, the oscillating part of the magnetic moment is elliptically polarized and the direction of precession is determined by the sign of the g tensor determinant (g tensor signature). Conventional pulsed and cw EPR spectrometers do not allow determination of the g tensor signature or the ellipticity of the magnetic moment trajectory. It is generally impossible to set a uniform spin turning angle for simple pulses in an unoriented or 'powder' sample when g tensor anisotropy is significant.

Convergence of scalar-tensor theories towards general relativity and primordial nucleosynthesis

International Nuclear Information System (INIS)

Serna, A; Alimi, J-M; Navarro, A

2002-01-01

In this paper, we analyse the conditions for convergence towards general relativity of scalar-tensor gravity theories defined by an arbitrary coupling function α (in the Einstein frame). We show that, in general, the evolution of the scalar field (φ) is governed by two opposite mechanisms: an attraction mechanism which tends to drive scalar-tensor models towards Einstein's theory, and a repulsion mechanism which has the contrary effect. The attraction mechanism dominates the recent epochs of the universe evolution if, and only if, the scalar field and its derivative satisfy certain boundary conditions. Since these conditions for convergence towards general relativity depend on the particular scalar-tensor theory used to describe the universe evolution, the nucleosynthesis bounds on the present value of the coupling function, α 0 , strongly differ from some theories to others. For example, in theories defined by α ∝ |φ| analytical estimates lead to very stringent nucleosynthesis bounds on α 0 (∼ -19 ). By contrast, in scalar-tensor theories defined by α ∝ φ much larger limits on α 0 (∼ -7 ) are found

Time integration of tensor trains

OpenAIRE

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...

Tensor spaces and exterior algebra

CERN Document Server

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.