Variational speed selection for the interface propagation in superconductors

TL;DR

This paper introduces a variational approach to analyze interface propagation speeds in superconductors, including effects of delay and memory through hyperbolic equations, providing bounds for front speed validity.

Contribution

It presents a novel variational method to estimate propagation speed bounds and extends the model with hyperbolic equations to account for delay and memory effects.

Findings

Computed bounds for planar front speed propagation.

Extended the model with hyperbolic equations for delay effects.

Provided conditions for the validity of front speed propagation.

Abstract

We study the interface propagation in superconductors by means of a variational method. We compute the lower and upper bounds for which the planar front speed propagation is valid. To take into account delay or memory effects in the front propagation, an hyperbolic differential equation is introduced as an extension of the model.