Instability of hysteretic phase interfaces in a mean-field model with inhomogeneities

TL;DR

This paper investigates the stability and dynamics of phase interfaces in a mean-field model with inhomogeneities, revealing two regimes of interface behavior and their relation to hysteresis and relaxation effects.

Contribution

It proves the existence and stability of traveling wave solutions in a non-local mean-field model with inhomogeneities, and connects these to observed dynamical regimes.

Findings

Identification of two dynamical regimes for phase interfaces.

Existence and stability of traveling wave solutions.

Convergence to a rate-independent hysteresis model.

Abstract

We study a system of non-identical bistable particles that is driven by a dynamical constraint and coupled through a non-local mean-field. Assuming piecewise affine constitutive laws we prove the existence of traveling wave solutions and characterize their dynamical stability. Our findings explain the two dynamical regimes for phase interface that can be observed in numerical simulations with different parameters. We further discuss the convergence to a rate-independent model with strong hysteresis in the limit of vanishing relaxation time.