标题： 吸引力和排斥力引起的可逆切换：团簇、间隙、分选和混合 显示英文标题

标题： Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing

摘要： 我们描述了相互作用粒子系统在连续极限中的相变，该相变表现出垂直分岔图。 这种转变是由短程排斥和长程吸引之间的竞争所介导的。 作为这种转变的结果，微小的参数变化允许在单种群模型中在均匀分布和簇之间切换，在多物种情况下允许在混合态和有序态之间切换，而不会产生滞后效应。 我们的主要技术贡献是针对这种相变中出现的真空泡大小的通用展开式，以及对噪声影响的定量分析。 显示英文摘要

摘要： 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.