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Energy driven pattern formation in thin fluid layers: The good, the bad and the beautiful.

Banff International Research Station for Mathematical Innovation and Discovery

A wide variety of physical and biological systems can be described as continuum limits of inter- acting particles. Their dynamics can often be described in terms of a monotonically decreasing interaction energy that is often non-local in nature. We show how to exploit these energies nu- merically, analytically and asymptotically to characterize the observed behavior. Examples are drawn from the dynamics of thin fluid layers. We show how to use these ideas to derive a simple characterization of the convoluted fingered domains observed experimentally in ferrofluids. Joint work with Jaron Kent-Dobias (HMC 2014), Department of Physics Cornell University

Mathematics; Partial differential equations; Dynamical systems and ergodic theory

video/mp4

Author affiliation: Harvey Mudd College

2017-01-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60058

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/