Related papers: On Plastic Dislocation Density Tensor
This paper develops a geometrical model of dislocations and disclinations in single crystals at the mesoscopic scale. In the continuation of previous work the distribution theory is used to represent concentrated effects in the defect lines…
We develop deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors, in a spirit similar to classical results for matrices such as those due to Weyl, Davis, Kahan and Wedin. Our bounds…
It has recently become popular to analyze the behavior of excess dislocations in plastic deformation under the assumption that such dislocations are arranged into walls with periodic dislocation spacing along the wall direction. This…
In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a…
In its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank tensor in three space dimensions. So great a body of works have been devoted to this specific class of tensors and their physical applications…
A recent suggested definition of a relativistically correct three dimensional charge density of an extended hadron is shown to be physically and intuitively connected to an earlier relativistically correct two dimensional charge density…
As an extension to strain-gradient models of size-dependent plastic behaviour, this work proposes a model for a stress-gradient theory. The model is distinguished from earlier works on the topic by its being embedded in a thermodynamically…
Inspired by the definition of tense operators on distributive lattices presented by Chajda and Paseka in 2015, in this paper, we introduce and study the variety of tense distributive lattices with implication and we prove that these are…
This paper studies the issues about tensors. Three typical kinds of tensor decomposition are mentioned. Among these decompositions, the t-SVD is proposed in this decade. Different definitions of rank derive from tensor decompositions. Based…
Smectic materials represent a unique state between fluids and solids, characterized by orientational and partial positional order, making them notoriously difficult to model, particularly in confining geometries. We propose a complex order…
Laser hardening of metals occurs under the influence of a shock wave, which changes the distribution and density of one-dimensional defects - dislocations. There is a relationship between the density of dislocations, the grain size and the…
Continuum dislocation dynamics (CDD) has become the state-of-the-art theoretical approach for mesoscale dislocation plasticity of metals. Within this approach, there are multiple CDD theories that can all be derived from the principles of…
We lay the geometric foundations for the study of the characteristic polynomial of tensors. For symmetric tensors of order $d \geq 3$ and dimension $2$ and symmetric tensors of order $3$ and dimension $3$, we prove that only finitely many…
A new mathematical formulation for the constitutive laws governing elastic perfectly plastic materials is proposed here. In particular, it is shown that the elastic strain rate and the plastic strain rate form an orthogonal decomposition…
The rich order parameter of Spin Density Waves allows for unusual object of a complex topological nature: a half-integer dislocation combined with a semi-vortex of a staggered magnetization. It becomes energetically preferable to ordinary…
We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization…
Recent data on neutron resonance widths indicate disagreement with the Porter-Thomas distribution (PTD). I discuss the theoretical arguments for the PTD, possible theoretical modifications, and I summarize the experimantal evidence.
The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the…
We compare different approximation schemes for investigating ferromagnetism in the periodic Anderson model. The use of several approximations allows for a detailed analysis of the implications of the respective methods, and also of the…
It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…