Generic equations for pattern formation in evolving interfaces

TL;DR

This paper introduces a comprehensive formalism for deriving evolution equations of pattern formation in interfaces, applicable across scales and validated through experiments on ion plasma erosion.

Contribution

The authors develop a general, symmetry-based approach to classify nonlinear terms in interface evolution equations, unifying diverse pattern formation phenomena.

Findings

Validates the formalism with ion plasma erosion experiments.

Classifies key nonlinear terms in interface evolution.

Applicable to nanostructures and macroscopic patterns.

Abstract

We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits the relevance of coarsening dynamics. Our approach becomes especially significant in the presence of surface morphological instabilities and allows us to classify the most relevant nonlinear terms in the continuum description of these systems. The formalism applies to systems ranging from eroded nanostructures to macroscopic pattern formation. In particular, we show the validity of the theory for novel experiments on ion plasma erosion.