Segregation and domain formation in non-local multi-species aggregation equations

• Published in: Physica. D 2023-12, Vol.456, p.133936, Article 133936
• Main Author: Glasner, Karl
• Format: Article
• Language: English
• Subjects: Aggregation equations; Interacting particle systems; Phase segregation
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2023.133936

A system of aggregation equations describing nonlocal interaction of two species is studied. When interspecies repulsive forces dominate intra-species repulsion, phase segregation may occur. This leads to the formation of distinct phase domains, separated by moving interfaces. The one dimensional interface problem is formulated variationally, and conditions for existence and nonexistence are established. The singular limit of large and short-ranged repulsion in two dimensions is then considered, leading to a two-phase free boundary problem describing the evolution of phase interfaces. Long term dynamics are investigated computationally, demonstrating coarsening phenomenon quantitatively different from classical models of phase separation. Finally, the interplay between long-range interspecies attraction and interfacial energy is illustrated, leading to pattern formation. •Multiple species of interacting particles may segregate to form single-species domains.•An asymptotic analysis captures the evolution of domain boundaries.•Evolution in purely repulsive systems is shown to exhibit coarsening and dynamic scaling.•Long range attraction leads to domain pattern formation and equilibration.