Covariant Hysteretic Constitutive Theory for Maxwell's equations: Application to Axially Rotating Media

TL;DR

This paper develops a covariant hysteretic constitutive model for Maxwell's equations, enabling analysis of accelerating magneto-electric materials with memory effects and their electromagnetic responses in rotating media.

Contribution

It introduces a novel covariant hysteretic constitutive framework for Maxwell's equations applicable to accelerating media with memory effects, extending previous models to dynamic, rotating conditions.

Findings

Model accurately describes hysteretic ferroelectric response at rest.

Numerical analysis shows differences in electromagnetic response under rotation.

Framework enables simulation of hysteretic media in non-inertial frames.

Abstract

This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly varying magnetic background fields, generalized models are explored that are applicable to accelerating hysteretic magneto-electric substances coupled self-consistently to Maxwell fields. Using a parameterized model consistent with experimental data for a particular material that exhibits purely ferroelectric hysteresis when at rest in a slowly varying electric field, a constitutive model is constructed that permits a numerical analysis of its response to a driven harmonic electromagnetic field in a rectangular cavity. This response is then contrasted with its predicted response when set in uniform rotary motion in the cavity.