Lobe dynamics and front propagation in advection-reaction-diffusion systems

We consider the addition of reaction-diffusion dynamics to systems undergoing chaotic advection. This can be viewed as a simplified model of diverse systems such as combustion dynamics in a chaotic flow, microfluidic chemical reactors, and blooms of phytoplankton and algae. Recently, we have proposed that front propagation in these systems is strongly influenced by burning invariant manifolds (BIMs)---geometric structures analogous to traditional invariant manifolds for passive transport. Additionally, BIMs may be used to define tangle-like structures that support a version of lobe dynamics for front propagation. In this talk, we discuss the theory and structure of BIMs and demonstrate the modified lobe-dynamics. We also present a potential application of the lobe dynamics to the control of reactive flows.