Seminar: A coalescing particle approach to simulating blow-up in the Keller-Segel system
Event Description:
Abstract: The Patlak-Keller-Segel PDEs describe the chemotaxis of slime mold, and exhibit finite-time blow-up when the system mass is above a certain threshold--a mathematical manifestation of the biological observation that mold aggregates when its quantity is sufficiently high. In this talk, we associate a colliding stochastic particle system with these PDEs. By relating the squared Bessel process to the evolution of localized clusters of particles, we develop a numerical method capable of detecting collisions of many point particles without the use of pairwise computations, or very refined adaptive timestepping; and apply this method to the numerical solution of the Patlak-Keller-Segel system and its variants. We show that the presented numerical method is well-suited for the simulation of the formation of finite-time singularities in the PKS, as well as PKS pre- and post-blow-up dynamics. (Joint with Ibrahim Fatkullin.)
How to attend: Please join via Zoom link: https://unm.zoom.us/j/91046392437