Consistent Hydrodynamics for Phase Field Crystals

TL;DR

This paper develops a hydrodynamic phase field crystal model using amplitude expansion, linking microscopic structure to fluid flow, and demonstrates its consistency with macroscopic theories and phonon dynamics.

Contribution

It introduces a coupled hydrodynamic phase field crystal model that captures elastic and phonon phenomena, bridging microscopic and macroscopic descriptions.

Findings

Model reduces to Navier-Stokes and wave equations in limits

Captures long wavelength phonon modes

Numerical simulations show elastic excitations relax via phonon emission

Abstract

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.