INTERACTING MANY-PARTICLE SYSTEMS OF DIFFERENT PARTICLE TYPES CONVERGE TO A SORTED STATE

Simon Lyngby Kokkendorff, Jens Starke, N. Hummel

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We consider a model class of interacting many-particle systems consisting of different types of particles defined by a gradient flow. The corresponding potential expresses attractive and repulsive interactions between particles of the same type and different types, respectively. The introduced system converges by self-organized pattern formation to a sorted state where particles of the same type share a common position and those of different types are separated from each other. This is proved in the sense that we show that the property of being sorted is asymptotically stable and all other states are unstable. The models are motivated from physics, chemistry, and biology, and the principal investigations can be useful for many systems with interacting particles or agents. The models match particularly well a system in neuroscience, namely the axonal pathfinding and sorting in the olfactory system of vertebrates.
    Original languageEnglish
    JournalS I A M Journal on Applied Mathematics
    Volume70
    Issue number7
    Pages (from-to)2534-2555
    ISSN0036-1399
    DOIs
    Publication statusPublished - 2010

    Keywords

    • neuroscience
    • self-organization
    • gradient flows
    • stability
    • pattern formation
    • many-particle systems
    • olfactory system

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