Pattern formation in self-propelled particles with density-dependent motility
We study the behavior of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained by explicitly coarse graining the model, we show that interactions lead generically to the formation of a host of patterns, including moving clumps, active lanes, and asters. This general mechanism could explain many of the patterns seen in recent experiments and simulations.
We present a novel numerical method based on finite differences to solve the problem of impurities' migration from a hollow core multilayer cylinder filled with a known liquid medium. We expose the numerical method and the developed application. The validation is performed by calculating the migration in a configuration which allows an analytic solution. Applications are foreseen in modeling impurities' migration from modern multilayer water pipes into drinking water.