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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.10406 |
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| _version_ | 1866915389102882816 |
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| author | Scheel, Arnd Stevens, Angela |
| author_facet | Scheel, Arnd Stevens, Angela |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing Scheel, Arnd Stevens, Angela Dynamical Systems 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. |
| title | Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2507.10406 |