Speaker
Description
In this talk, I present a work in collaboration with V. Calvez. We introduce a two species kinetic model designed to capture congestion effects through a first-order formulation coupled with hard congestion complementarity conditions. We discuss some properties of the model and introduce a numerical method for its resolution.
As an application, we consider the collective motion of the social and predatory soil bacterium Myxococcus xanthus. We focus on the celebrated rippling phenomenon, in which localized back-and-forth movements of bacteria give rise to spatio-temporal wave patterns at the macroscopic scale. We build upon our core model and include biological mechanisms. In this framework, a congestion-induced pressure acts as a nonlocal signal perceived by the bacteria. Combined with a modulation of a refractory period, this mechanism leads to the emergence of periodic patterns. The qualitative behavior of the model is illustrated and analyzed through numerical simulations.