Related papers: Symmetry classes for even-order tensors
In this paper, we propose two new classes of tensors: double B-tensors and quasi-double B-tensors, give some properties of double B-tensors and quasi-double B-tensors, discuss their relationships with B-tensors and positive definite tensors…
This article is the second in a series devoted to the study of spacetimes sourced by a stationary cylinder of fluid rigidly rotating around its symmetry axis and exhibiting an anisotropic pressure by using new exact interior solutions of…
In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a…
Functional bases, synonymous with separating sets, are usually formulated for an entire vector space, such as the space Ela of elasticity tensors. We propose here to define functional bases limited to symmetry strata, i.e. sets of tensors…
An anisotropic elasticity tensor can be approximated by the closest tensor belonging to a higher symmetry class. The closeness of tensors depends on the choice of a criterion. We compare the closest isotropic tensors obtained using four…
We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an $n-$manifold of…
Identifying locally optimal solutions is an important issue given an optimization model. In this paper, we focus on a special class of symmetric tensors termed regular simplex tensors, which is a newly-emerging concept, and investigate its…
We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger--Reissner mixed…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple axisymmetric…
This article extends the author's past work [Inv. Probl. Imaging, 10:2 (2016), 433--459] to attenuated X-ray transforms, where the attenuation is complex-valued and only depends on position. We give a positive and constructive answer to the…
For two-dimensional polycrystals the effective elasticity tensor $C_*$ as a function $C_*(C_0)$ of the elasticity tensor $C_0$ of the constituent crystal is considered. It is shown that this function can be approximated by one with a…
Tensegrity mechanisms are composed of rigid and tensile parts that are in equilibrium. They are interesting alternative designs for some applications, such as modelling musculo-skeleton systems. Tensegrity mechanisms are more difficult to…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
The symmetry-constrained response tensors on transport, optical, and electromagnetic effects are of central importance in condensed matter physics because they can guide experimental detections and verify theoretical calculations. These…
We show that there is the same number of (n,l)-alternating sign trapezoids as there is of column strict shifted plane partitions of class l-1 with at most n parts in the top row, thereby proving a result that was conjectured independently…
Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently…
Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the…
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
We consider an infinitesimal volume where there are many rigid molecules of the same kind, and discuss the description and classification of the local anisotropy in this volume by tensors. First, we examine the symmetry of a rigid molecule,…