Quasisteady patterns in interfaces: Folding and Faceting

TL;DR

This paper systematically derives gradient flows for interfacial energies, linking intrinsic and extrinsic variations, and applies them to model systems exhibiting quasi-steady pattern formation such as faceting and membrane interactions.

Contribution

It provides a unified derivation of gradient flows for a broad class of interfacial energies, clarifying the relation between intrinsic and extrinsic interface variations.

Findings

Gradient flows aligned with quasi-steady pattern formation.

Models include coarsening of faceted interfaces.

Incorporates nonlocal interactions like membrane adhesion.

Abstract

We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables formulation brings the gradient flow into alignment with the traditional analysis of quasi-steady dynamical systems defined on a stationary domain. Gradient flows are derived for model systems which exhibit quasi-steady pattern formation including coarsening among faceted interfaces and nonlocal interactions that model membrane self-adhesion and self-avoidance.