Active matter: pattern formation and collective phenomena in biological systems
Abstract:
Pattern formation in out-of-equilibrium systems is one of the most fascinating phenomena in nature. It takes place in a wide variety of physical, chemical and biological systems and on very different spatial and temporal scales, from convection phenomena in geosciences and meteorology down to morphogenesis of organisms and structure formation inside biological cells. While classical systems - like hydrodynamic convection - are typically externally driven, biological systems are locally out-of-equilibrium, due to the energy delivered by metabolism. In particular, biological systems tend to generate forces and to move due to the local energy sources. Recently artificial force-generating/moving objects have been designed from the bottom up. Together these self-propelled objects have been coined 'active matter' and they display new collective phenomena like swarming, formation of bands, non-equilibrium ratcheting, synchronisation, etc.
In the first part of this lecture series, I will give an introduction to the basic phenomena in pattern formation. We will discuss the possible instabilities and the generic nonlinear dynamics of patterns (Ginzburg-Landau equations) and discuss several examples how biological systems make use of these scenarios to structure themselves. In the second part we will discuss simple models for collective motion (Vicsek-type models) and the collective effects emerging in such non-equilibrium systems with self-propulsion.