Pattern formation in multiscale systems: Homogenization and beyond
Various relevant pattern formation applications are observed in intrinsically heterogeneous reaction-diffusion systems. We derive a simple homogenization scheme and demonstrate that the resulting effective equations are sufficient to qualitatively reproduce the rich pattern dynamics of wave and Turing structures in the BZ-AOT microemulsion system. Furthermore, we validate this effective medium theory by simulations of wave propagation in discrete heterogeneous bistable and excitable media. We find that the approach fails if the heterogeneous medium is near a percolation threshold. For a simple discrete heterogeneous model of cardiac tissue, complex fractionated dynamics and reentrant dynamics appears in such a situation.
Work done with Sergio Alonso, Raymond Kapral and Karin John.