Spring 2016
Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.
Date: April 1, 2016
Speaker: Kevin Mitchell
School of Natural Sciences,
University of California, Merced
Title: "Dynamical Barriers to Front Propagation in Active Fluid Flows"
Abstract:
The passive advection of inert particles in fluid flows is important both for its direct relevance to fluid mixing and for its broader connection to Hamiltonian dynamics and chaos. This talk considers the generalization of advective transport to "active" media, specifically to media that support some kind of front propagation: for example, the expansion of chemical reaction fronts in microfluidic mixers, plankton blooms in large-scale oceanic flows, phase transitions in liquid crystals, or even the spread of disease within a mixing population. A low-dimensional nonlinear dynamics model is used to predict the existence--and to explain the properties--of robust, one-sided barriers to front propagation. We call these barriers Burning Invariant Manifolds (BIMs). BIMs play a central role in guiding the propagating fronts through the medium, determining the patterns formed by the fronts, and in determining the average propagation speeds. We compare our theory to table-top experiments in magneto-hydrodynamically driven flows, and we highlight the role of BIMs for experimental phenomena, such as the mode-locking and pinning of reaction fronts. Finally, we introduce a theory of burning Lagrangian Coherent Structures (bLCSs), which are generalizations of BIMs to the more challenging problem of front propagation in unsteady, aperiodic fluid flow.