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| We take a low-dimensional dynamical systems approach to understanding the propagation of fronts in flows. In particular, we are motivated to connect with experiments involving chemical reaction fronts in fluid flows. An interesting feature of these systems is that with an appropriate balance between fluid flow and propagation, there can exist stable front configurations - much like a bunsen burner flame. We examine a simple model of fronts in flows, and find a variety of new results: The stable fronts are precisely the "burning invariant manifolds" recently discussed as one-way barriers in these systems. Certain flow conditions may lead to stable fronts composed of multiple interleaved manifolds. The set of stable states has a nontrivial poset structure. More can be said about elementary canonical flows such as single and double vortex flows and their bifurcations. We also attempt to extend this thinking to more statistical contexts, beginning to bridge the gap between theory and "natural" flow systems. |
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