A survey on visualization of tensor field

2019 ◽  
Vol 22 (3) ◽  
pp. 641-660 ◽  
Author(s):  
Chongke Bi ◽  
Lu Yang ◽  
Yulin Duan ◽  
Yun Shi
Keyword(s):  
Tensor Field

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

scholarly journals Erratum to: Hints of unitarity at large N in the O(N)3 tensor field theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Dario Benedetti ◽  
Razvan Gurau ◽  
Sabine Harribey ◽  
Kenta Suzuki
Keyword(s):  
Field Theory ◽  
Tensor Field ◽  
Normalization Factor ◽  
Large N

The measure in equation (2.11) contains a wrong normalization factor, and it should be multiplied by 21−dΓ(d − 1)/Γ(d/2)2.

Can a tensorial analogue of gravitational force explain away the galactic rotation curves without dark matter?

2021 ◽  
Author(s):  
Ram Gopal Vishwakarma
Keyword(s):  
Dark Matter ◽  
Tensor Field ◽  
Gravitational Force ◽  
Direct Detection ◽  
Alternative Theory ◽  
Galactic Rotation ◽  
Rotation Curves ◽  
Modern Physics ◽  
Flat Rotation Curves ◽  
Relativistic Analogue

The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to explain the flat rotation curves of galaxies, and since the whole issue of an alternative theory of gravity remains controversial, it may be worth to reconsider the familiar ground of general relativity (GR) itself for a possible way out. It has recently been discovered that a skew-symmetric rank-three tensor field — the Lanczos tensor field — that generates the Weyl tensor differentially, provides a proper relativistic analogue of the Newtonian gravitational force. By taking account of its conformal invariance, the Lanczos tensor leads to a modified acceleration law which can explain, within the framework of GR itself, the flat rotation curves of galaxies without the need for any dark matter whatsoever.

scholarly journals On a structure satisfyingFK−(−)K+1F=0

1996 ◽  
Vol 19 (1) ◽  
pp. 125-130 ◽  
Author(s):  
Lovejoy S. Das
Keyword(s):  
Tensor Field ◽  
Differentiable Manifold

In this paper we shall obtain certain results on the structure defined byF(K,−(−)K+1)and satisfyingFK−(−)K+1F=0, whereFis a non null tensor field of the type(1,1)Such a structure on ann-dimensional differentiable manifoldMnhas been calledF(K,−(−)K+1)structure of rank “r”, where the rank ofFis constant onMnand is equal to “r” In this caseMnis called anF(K,−(−)K+1)manifold. The case whenKis odd has been considered in this paper

scholarly journals A Note On Umbilics of a Closed Surface

1959 ◽  
Vol 15 ◽  
pp. 219-223
Author(s):  
Minoru Kurita
Keyword(s):  
Riemannian Manifold ◽  
Euclidean Space ◽  
Tensor Field ◽  
Symmetric Tensor ◽  
Closed Surface ◽  
Dimension 2 ◽  
Direction Field

In this paper we investigate indices of umbilics of a closed surface in the euclidean space. Most part of the discussion is concerned with a symmetric tensor field of degree 2, or rather a direction field, on a Riemannian manifold of dimension 2.

scholarly journals DUALITY INVARIANCE OF COSMOLOGICAL SOLUTIONS WITH TORSION

1999 ◽  
Vol 14 (31) ◽  
pp. 4953-4966 ◽  
Author(s):  
DEBASHIS GANGOPADHYAY ◽  
SOUMITRA SENGUPTA
Keyword(s):  
Physical Meaning ◽  
Tensor Field ◽  
Antisymmetric Tensor ◽  
Dilaton Field ◽  
Maximal Symmetry ◽  
Killing Vectors ◽  
Cosmological Solutions ◽  
Antisymmetric Tensor Field ◽  
Vacuum Solutions

We show that for a string moving in a background consisting of maximally symmetric gravity, dilaton field and second rank antisymmetric tensor field, the O(d) ⊗ O(d) transformation on the vacuum solutions gives inequivalent solutions that are not maximally symmetric. We then show that the usual physical meaning of maximal symmetry can be made to remain unaltered even if torsion is present and illustrate this through two toy models by determining the torsion fields, the metric and Killing vectors. Finally we show that under the O(d) ⊗ O(d) transformation this generalized maximal symmetry can be preserved under certain conditions. This is interesting in the context of string related cosmological backgrounds.

scholarly journals Monstars on Glaciers

1983 ◽  
Vol 29 (101) ◽  
pp. 70-77 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Numerical Simulation ◽  
Strain Rate ◽  
Tensor Field ◽  
Pure Shear ◽  
Glacier Surface ◽  
Isotropic Point ◽  
Different Types ◽  
Isolated Points ◽  
Principal Directions ◽  
Structurally Stable

AbstractIsotropic points are structurally stable features of any complicated field of stress or strain-rate, and therefore will almost always be present on the surface of a glacier. A given isotropic point for strain-rate will belong to one of six different classes, depending on the pattern (lemon, star, or monstar) of principal directions and the contours (ellipses or hyperbolas) of constant principal strain-rate values in its neighbourhood. The central isotropic point on a glacier should theoretically have a monstar pattern, but the contours around it may sometimes be elliptic and sometimes hyperbolic. Nearby, but not coincident with it there will be an isotropic point for stress. This will also have a monstar pattern but, in contrast to the strain-rate point, the contours around it must be hyperbolic. Published examples are consistent with these conclusions. In addition to isotropic points for strain-rate a glacier surface will contain isolated points of pure shear; these also can be classified into six different types. Stable features of this kind give information about the essential structure of a tensor field and form useful points of comparison between observation and numerical simulation.

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