Vacuum bubble and fissure formation in collective motion with competing attractive and repulsive forces
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912991391252480 |
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| author | Clifton, Olivia Chavez, Angel Madrigal, Antonio Warren, Annie Yeung, Paige Scheel, Arnd |
| author_facet | Clifton, Olivia Chavez, Angel Madrigal, Antonio Warren, Annie Yeung, Paige Scheel, Arnd |
| contents | We study the continuum limit of the motion of agents in the plane driven by competing short-range repulsion and long-range attractive forces. At a critical parameter value, we find destabilization of a trivial branch of uniformly distributed solutions and analyze bifurcating solutions. Curiously, the bifurcating branch is vertical, leading to a reversible, non-hysteretic phase transition. Near the bifurcation point, we demonstrate scaling laws for the size of vacuum regions, which can form fissures or bubbles. We also study the effect of small noise and the eventual topological transition from vacuum bubbles to isolated particle clusters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vacuum bubble and fissure formation in collective motion with competing attractive and repulsive forces Clifton, Olivia Chavez, Angel Madrigal, Antonio Warren, Annie Yeung, Paige Scheel, Arnd Pattern Formation and Solitons We study the continuum limit of the motion of agents in the plane driven by competing short-range repulsion and long-range attractive forces. At a critical parameter value, we find destabilization of a trivial branch of uniformly distributed solutions and analyze bifurcating solutions. Curiously, the bifurcating branch is vertical, leading to a reversible, non-hysteretic phase transition. Near the bifurcation point, we demonstrate scaling laws for the size of vacuum regions, which can form fissures or bubbles. We also study the effect of small noise and the eventual topological transition from vacuum bubbles to isolated particle clusters. |
| title | Vacuum bubble and fissure formation in collective motion with competing attractive and repulsive forces |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2508.14827 |