Advection of Active Particles in Open Chaotic Flows

We investigate the evolution of active particle ensembles in open chaotic flows. The active processes of the type $A+B\to 2B$ and $A+B\to 2C$ are considered in the limit of weak diffusion. As an illustrative advection dynamics, we choose a model of the von Kármán vortex street, and show that the backbone of the active processes is the fractal structure associated with the passive dynamics' chaotic saddle. This fractal dynamics leads to singularly enhanced concentrations, resulting in a distribution of products that differs entirely from the one in conventional active processes. This may account for the observed filamental intensification of activity in environmental flows.