Alignment in a fish school: a mixed Lagrangian–Eulerian approach

摘要: Social organization is one of the fundamental aspects animal behavior, and has received attention both from experimental theoretical perspectives. Examples social groups appear at every size scale microscopic aggregates mammalian cells (such as fibroblasts) to macroscopic herds wildbeast, flocks birds, fish schools. There are two general frameworks when modeling such problems: Lagrangian viewpoint Eulerian one. In this paper, we use approaches in study alignment. An individual-based model (IBM) (Lagrangian) provides a virtual world where forming school try adopt common angular position. Fish assumed lie horizontal planes, an individual position angle made by oriented axis associated with (tail head) fixed direction. Two main forces acting, force alignment, whose strength be given experiment but may modified, dispersion, accounting for all disturbances. A transition dispersion-dominant alignment-dominant can observed IBM experiments. related PDE (Eulerian) used determine sufficient accuracy.