2023/04/17 by Giuseppe Gaeta, Gaeta, Giuseppe, Epifanio G. Virga +1 · 3 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum, superfluid, helium dynamics #Soft Condensed Matter (cond-mat.soft) #Solar and Space Plasma Dynamics #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2304.08311
openalex publication_date 2023/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.