A necessary condition that a Stäckel-Killing tensor of valence 2 be the contracted product of a Killing-Yano tensors of valence 2 with itself is re-derived for a Riemannian manifold. This condition is applied to the generalized Euclidean Taub-NUT metrics which admit a Kepler type symmetry. It is shown that in general the Stäckel-Killing tensors involved in the Runge-Lenz vector cannot be expres...

A so-called smart material is a that the seat of one or more multiphysical coupling. One key points in development constitutive laws these materials, either at local global scale, to formulate free energy density (or enthalpy) from vectors, tensors, given order and for class symmetry, depending on symmetry classes crystal constituting representative volume element. This article takes as support...

The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of th...

This article presents an open-source object-oriented C++ library of classes and routines to perform tensor algebra.The primary purpose of the library is to enable post-Hartree–Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and sy...

A geometrical framework is presented for a class of dynamical systems, which are modelled by a mixed system of rst and second-order ordinary diierential equations. The starting point for the model is a bundle : E ! M, where both E and M are bred over IR. We show that there are two connections associated to systems of this kind: the rst one comes from thèconstraint equations' (the rst-order equa...

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...

The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of investigation was initiated for the space of elasticity tensors. Since then, different authors solved this problem for other kinds of physics such as photoelectricity, ...