We formulate effective necessary and sufficient conditions to identify the symmetry class of an elasticity tensor, a fourth-order tensor which is cornerstone theory toy model for linear constitutive laws in physics. The novelty that these are written using polynomial covariants. As corollary, we deduce classes affine algebraic sets, result seems be new. Meanwhile, have been lead produce minimal...

<p style='text-indent:20px;'>C-eigenvalues of piezoelectric-type tensors play an crucial role in piezoelectric effect and converse effect. In this paper, by the partial symmetry property tensors, we present three intervals to locate all C-eigenvalues a given tensor. Numerical examples show that our results are better than existing ones.</p>

Citation Chen, Xie et al. " Tensor product representation of a topological ordered phase: Necessary symmetry conditions. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story mat...

Polycyclic aromatic hydrocarbons (PAHs) are a class of compounds consisting of more than twobenzene rings fused in a linear, angular, or clustered arrangement and do not contain hetero atomsor carry subsistent. PAHs originate from various sources. They are primarily formed byincomplete combustion of carbon-containing fuels such as wood, coal, diesel, fat, or tobacco. Thepresent study reports an...

It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating matrix is derived for the rotation matrix of tensors of order n. The Euler-Rodrigues formula for rigid body rotation is recovered by n = 1. A Cayley form of the n...

Tensor field visualization is a challenging task due in part to the multi-variate nature of individual tensor samples. Glyphs convey tensor variables by mapping the tensor eigenvectors and eigenvalues to the orientation and shape of a geometric primitive, such as a cuboid or ellipsoid. Though widespread, cuboids and ellipsoids have problems of asymmetry and visual ambiguity. Cuboids can display...