Related papers: Tensorial representations of Reynolds-stress press…
This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…
We propose a method to construct the initial tensor representation of partition functions and observables for the tensor renormalization group (TRG). The TRG is a numerical calculation technique that utilizes a tensor network…
We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square…
We recently developed a tensorial constitutive model for dense, shear-thickening particle suspensions that combines rate-independent microstructural evolution with a stress-dependent jamming threshold. This gives a good qualitative account…
In continuum mechanics, stress concept plays an essential role. For complicated materials, different stress concepts are used with ambiguity or different understanding. Geometrically, a material element is expressed by a closed region with…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
We provide a faithful translation of Hans Richter's important 1949 paper "Verzerrungstensor, Verzerrungsdeviator und Spannungstensor bei endlichen Form\"anderungen" from its original German version into English, complemented by an…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
In this article we propose new discretization-informed expressions for the residual stress tensor (RST) in a finite-volume based large-eddy simulation (LES-FVM). In addition to the classical RST $\overline{u u} - \bar{u} \bar{u}$ resulting…
The quantum many-body problem is an important topic in condensed matter physics. To efficiently solve the problem, several methods have been developped to improve the representation ability of wave-functions. For the Fermi-Hubbard model…
We consider the problem of formulating perturbative expansions of the conformation tensor, which is a positive-definite tensor representing polymer deformation in viscoelastic flows. The classical approach does not explicitly take into…
In a continuum description of materials, the stress tensor field $\bar{% \bar{\sigma}}$ quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that…
Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…
The approximation of the renormalized stress-energy tensor of the quantized massive scalar, spinor, and vector field in the Reissner- Nordstrom spacetime is constructed. It is achieved by functional differentiation of the lowest order of…
We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a "natural" curvature tensor. This tensor either denotes the second fundamental…
The boundary energy - momentum tensors for a static observer in the conformally flat Rindler geometry are considered. We found the surface energy is positive far form the Planck world but the transversal pressures are negative. The…
Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models…
The Taylor-Reynolds and Reynolds number ($Re_\lambda$ and $Re$) dependence of the dimensionless energy dissipation rate $\ceps =\eps L / \u1rms^3$ is derived for statistically stationary isotropic turbulence, employing the results of a…
To study the Reynolds stresses which describe turbulent momentum transport from turbulence affected by large-scale shear and rotation. Three-dimensional numerical simulations are used to study turbulent transport under the influences of…