Title: Active matter invasion of a viscous fluid and a no-flow theorem
Abstract: Suspensions of swimmers or active particles in fluids exhibit incredibly rich behavior, from organization on length scales much longer than the individual particle size to mixing flows and negative viscosities. We will discuss the dynamics of hydrodynamically interacting motile and non-motile stress-generating particles as they invade a surrounding viscous fluid, modeled by equations which couple particle motions and viscous fluid flow. Depending on the nature of their self-propulsion, colonies of swimmers can either exhibit a dramatic splay, or instead a cascade of transverse concentration instabilities, governed at small times by an equation which also describes the Saffman-Taylor instability in a Hele-Shaw cell, or Rayleigh-Taylor instability in two-dimensional flow through a porous medium. Analysis of concentrated distributions of particles matches the results of full numerical simulations. Along the way we will prove a very surprising “no-flow theorem”: particle distributions initially isotropic in orientation lose isotropy immediately but in such a way that results in no fluid flow anywhere and at any time.
Title: Introduction to right-angled Artin groups
Speaker: Michael Yampolsky (U. Toronto)
Title: Renormalization of rotation domains
Abstract: Renormalization has emerged as a key theme in low-dimensional dynamics. I will start with a review of renormalization of maps of the circle, and will then discuss applications of renormalization theory to the study of Siegel disks in one and two complex variables.