In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

The energy equation for turbulent flow of fiber suspensions was derived in terms of second order correlation tensors. Fiber motion of turbulent energy including the correlation between pressure fluctuations and velocity fluctuations was discussed at two points of flow field, at which the correlation tensors were the functions of space coordinates, distance between two points, and time.

Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we propose Blocked Compact Symmetric Storage wherein we consider the tensor by blocks and store only the unique blocks of a symmetric tensor. We propose an algo...

We generalize the Perron–Frobenius Theorem for nonnegative matrices to the class of nonnegative tensors.

Abstract Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of metric can be considered subclass more general type transformation, so-called disformal transformation. Here, we investigate implications pure symmetry ...

Visualization of fourth-order tensors from solid mechanics has not been explored in depth previously. Challenges include the large number of components (3x3x3x3 for 3D), loss of major symmetry and loss of positive definiteness (with possibly zero or negative eigenvalues). This paper presents a decomposition of fourth-order tensors that facilitates their visualization and understanding. Fourth-o...

Herein we study the following problem: Suppose we are given a supply of grains, which are of the same material and have equal volume. Given a finite set of material tensors (i), can we find an arrangement of grains in an aggregate so that all the tensors (i) pertaining to this aggregate are isotropic? In this paper we examine the preceding problem within the special context of physical theories...

Fabric tensor has proved to be an effective tool statistically characterizing directional data in a smooth and frame-indifferent form. Directional data arising from microscopic physics and mechanics can be summed up as tensor-valued orientation distribution functions ODFs . Two characterizations of the tensor-valued ODFs are proposed, using the asymmetric and symmetric fabric tensors respective...