捆绑SM社区

Abstract:Unsteady flows typically contain clumps of particles moving coherently, in addition to regions in which extensive mixing occurs. The boundaries of each of these regions might be considered as "unsteady flow barriers," since they move about in time. Exactly defining what these are is, however, problematic. Such flow barriers may be thought to demarcate geophysical features such as the Antarctic Circumpolar Vortex (ozone hole), or the interface between two fluids that one desires to mix together for DNA synthesis in a microfluidic device. This talk will examine several theoretical issues and applications arising from attempting to understand, and use, unsteady flow barriers. The relationship to stable and unstable manifolds of hyperbolic trajectories in nonautonomous dynamical systems will be established. Using the solution to the energy-constrained optimization problem of maximizing mixing between two fluids across their mutual interface, an optimum design for a cross-channel micromixer is proposed. Ongoing work on manipulating flow barriers according to a user-defined unsteady prescription is presented; this offers an exciting new tool for flow control. Additionally, some emerging work on how these ideas can be used to correct errors in oceanic velocity data obtained from satellite observations will be briefly discussed.