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Self-propelled agents are ubiquitous, both found naturally in Nature and manufactured artificially in laboratory. Their sizes scale from tens of nanometres (in molecular motor proteins) through tens of microns (active colloids) to tens of millimeters (ensembles of microrobots) to tens of meters (schools of whales). Here we focus on suspensions of active colloid particles interacting purely repulsively by steric repulsion. We model their behavior by generalized lattice gasses in one and two dimensions. The central result we present is the derivation of phenomenological hydrodynamic equations which describe their behavior on a coarse-grained scale. Based on the assumptions of local equilibrium and neglect of long-range correlations they lead to non-linear diffusion equations for the set of local fugacities. We show that this formalism yields analytical solutions in multi-component static case and in single-component piecewise-one-dimensional cases. In general cases, the equations are solved numerically by appropriate PDE solvers. We show how the characteristic emergent phenomena in active matter, including spontaneous ratchet effect and mobility-induced phase separation can be easily calculated in our formalism.
The seminar is organized by Department of condensed matter theory