A Review on Octupolar Tensors
Abstract
In its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank tensor in three space dimensions. So great a body of works have been devoted to this specific class of tensors and their physical applications that a review would perhaps be welcome by a number of students. Here, we endeavour to place octupolar tensors into a broader perspective, considering non-vanishing traces and non-fully symmetric tensors as well. A number of general concepts are recalled and applied to either octupolar and higher-rank tensors. As a tool to navigate the diversity of scenarios we envision, we introduce the octupolar potential, a scalar-valued function which can easily be given an instructive geometrical representation. Physical applications are plenty; those to liquid crystal science play a major role here, as they were the original motivation for our interest in the topic of this review.
Keywords
Cite
@article{arxiv.2304.08311,
title = {A Review on Octupolar Tensors},
author = {Giuseppe Gaeta and Epifanio G. Virga},
journal= {arXiv preprint arXiv:2304.08311},
year = {2023}
}