An exploding glass ?

TL;DR

This paper explores the analogy between self-similar focusing dynamics in nonlinear PDEs and the glass transition, particularly the divergence of relaxation times near random close packing.

Contribution

It introduces a 'normal form' to describe the onset of dynamic self-similarity in both nonlinear PDEs and glass transition phenomena.

Findings

Illustrates the analogy in the critical case

Proposes a normal form for dynamic self-similarity

Links PDE dynamics to glass transition features

Abstract

We propose a connection between self-similar, focusing dynamics in nonlinear partial differential equations (PDEs) and macroscopic dynamic features of the glass transition. In particular, we explore the divergence of the appropriate relaxation times in the case of hard spheres as the limit of random close packing is approached. We illustrate the analogy in the critical case, and suggest a ``normal form'' that can capture the onset of dynamic self-similarity in both phenomena.