# gst: reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing.

AA << ️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. >>

Their << 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. >>

Arnd Scheel, Angela Stevens. Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing. arXiv: 2507.10406v1 [math.DS]. Jul 14, 2025.

https://arxiv.org/abs/2507.10406

Also: particle, bubble, noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, bubbles, noise, short-range repulsion, long-range attraction, phase transitions.