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...

Abstract A generally anisotropic elasticity tensor, which might be obtained from physical measurements, can be approximated by a tensor belonging to a particular material-symmetry class; we refer to such a tensor as the effective tensor. The effective tensor is the closest to the generally anisotropic tensor among the tensors of that symmetry class. The concept of closeness is formalized in the...

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 piezoelectricity law is a constitutive model that describes how mechanical andelectric fields are coupled within material. In its linear formulation this comprises threeconstitutive tensors of increasing order: the second order permittivity tensor S, third orderpiezoelectricity P and fourth-order elasticity C. first part paper,the symmetry classes alone investigated. Using new approachbased...

If all space is occupied by a linear bianisotropic material — whether homogeneous or not — then the concurrent replacements of the permittivity and the impermeability tensors by the negatives of their respective complex conjugates and of the magnetoelectric tensors by their respective complex conjugates (in the Boys–Post representation) imply the conjugation of both E and H, in the absence of e...

in order to study the effect of elevation on quantitative and qualitative characteristics of the humid forests of guilan shafaroud, series 17, 16 and 7 were selected that fall in to three height classes; class 1 (‏less than 500 m), class 2 (‏500 – 1000 m) and class 3 (‏1000 – 1600 m). in height class 1, 2 and 3 sample plots were determined as 4, 15 and 20 respectively and each sample plot was 0...