Interface dynamics for layered structures

TL;DR

This paper derives interface equations for layered structures, capturing their slow deformations and phase dynamics, with distinctions between conserved and non-conserved systems, providing a unified framework for understanding their large-scale behavior.

Contribution

It introduces a coupled set of interface equations for layered structures and clarifies when internal domain motions can be adiabatically eliminated or must be retained.

Findings

Reduced equations for non-conserved systems include only phase variables.

Internal domain motions are slow variables in conserved systems.

The formulation encompasses phase dynamics of layered structures.

Abstract

We investigate dynamics of large scale and slow deformations of layered structures. Starting from the respective model equations for a non-conserved system, a conserved system and a binary fluid, we derive the interface equations which are a coupled set of equations for deformations of the boundaries of each domain. A further reduction of the degrees of freedom is possible for a non-conserved system such that internal motion of each domain is adiabatically eliminated. The resulting equation of motion contains only the displacement of the center of gravity of domains, which is equivalent to the phase variable of a periodic structure. Thus our formulation automatically includes the phase dynamics of layered structures. In a conserved system and a binary fluid, however, the internal motion of domains turns out to be a slow variable in the long wavelength limit because of concentration conservation. Therefore a reduced description only involving the phase variable is not generally justified.