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...

We demonstrate that the rotating black holes in an arbitrary number of dimensions and without any restrictions on their rotation parameters possess the same hidden symmetry as the four-dimensional Kerr metric. Namely, besides the spacetime symmetries generated by the Killing vectors they also admit the (antisymmetric) Killing-Yano and symmetric Killing tensors.

The character table of the fully nonrigid water cluster (cyclic forms), (H_{2}O){_i}, with C{_ih} symmetry derived for the first time, for 2<=i <=6. The group of all feasible permutations is the wreath product of groups S{_i}[S{_2}] which consists of i!2i operations for i = 2, ..., 6 divided into ( w.r.t) 5, 10, 20, 36, 65 conjugacy classes and 5, 10, 20, 36, 65 irreducible representations resp...

We introduce a new type of object characterization, which is capable accurately describing small isolated inclusions for potential field inverse problems such as in electrostatics, magnetostatics, and related low frequency Maxwell problems. Relevant applications include characterizing ferrous unexploded ordnance from magnetostatic measurements magnetometry, conducting medical imaging using elec...