Kinetic Description of Multiscale Phenomena

The Annual Kinetic FRG Meeting
May 23-26, 2011

Van Vleck Hall
Department of Mathematics
University of Wisconsin -Madison
Madison, WI 53706

A new model for self-organized dynamics

Prof. Eitan Tadmor

University of Maryland

Abstract:  We introduce a new particle-based model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The new model does not involve any explicit dependence on the number of agents: only their self-driven geometry in phase space enters the model. It lacks, however, the symmetry property, which is the key y for the various studies of C-S flocking behavior. To this end, we introduce here a new unifying framework to analyze the phenomenon of flocking for a general class of dynamical systems in the presence of non-symmetric influence matrices. In particular, we prove the emerging behavior of flocking in the proposed model, when the pairwise long-range interactions between its agents decays sufficiently slow. The methodology presented in this paper is based on the notion of active sets, which carries over from the particle to the kinetic and hydrodynamic descriptions. In particular, we discuss the hydrodynamic description of our new model for self-organized dynamics, and we prove its unconditional flocking for sufficiently slowly decaying influence functions.