Abstract

I will address the spontaneous formation of structure, including layers, in diffusive active particles without alignment interactions. These can described in terms of a scalar density field with diffusive dynamics, and also in some cases, birth/death dynamics. Such density fields are governed by stochastic PDEs where the noise stems from the underlying microscopic motion. For active systems this motion need not obey detailed balance conditions, so that that the noiseless evolution is not in general a gradient flow, allowing a wider variety of behaviour than in passive systems close to thermal equilibrium, for which it is. In neither case is linear diffusive instability of the uniform state (aka antidiffusion) a prerequisite for structure formation; the alternative is noise-induced nucleation of the structured state.