Zusammenfassung für den Vortrag am 15.06.2006 (11:15 Uhr)Seminar MATHEMATISCHE MODELLIERUNG BIOLOGISCHER SYSTEME
Wolfgang Alt (Universität Bonn, Germany)
Dynamics of neighbor interaction and pattern formation in bird swarms and cell tissues
Swarms of birds (as cranes or starlets) as well as confluent layers of tissue cells (as keratinocytes) show characteristic patterns of cohort formation and movement, which resemble the dynamics of compressible fluids with quite smooth free boundaries. Derivation and simulation of neighbor interaction models implemented into standard stochastic ODE systems for multi-particle motion reproduce a wide spectrum of observed phenomena and dynamic behavior as, for example, nonlinear waves and phase transitions between different types of swarm formation. Moreover, for such nonlinear local interaction systems we consider, at least in the 1-dimensional case, suitable continuum limits yielding hyperbolic equations of generalized Navier-Stokes type.