Reversible Switching due to Attraction and Repulsion: Clusters, Gaps, Sorting, and Mixing
Abstract
Abstract. We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence of the transition, infinitesimal parameter variations allow switching between uniform distribution and clusters in single-species models, and between mixed and sorted states in multi-species contexts, without hysteresis. Our main technical contribution is a universal expansion for the size of vacuum bubbles that arise in this phase transition and a quantitative analysis of the effect of noise.
Fields of Study & Subjects
Cellular Automata and Applications
Publication details
- Journal / source
- SIAM Journal on Applied Dynamical Systems
- Volume
- 25
- Issue
- 3
- Pages
- 2022–2043
- Publication date
- 20 August 2026
- Language
- EN