The Thirteenth Israeli Mini-Workshop in Applied
and Computational Mathematics
Amy Novick-Cohen (Mathematics, Technion)
Coarsening and the deep quench obstacle problem
Phase separation occurs in a wide spectrum of contexts, from galaxy formation to biofilm formation,
and many models have been proposed to describe the dynamics. Common to these processes is a linear regime
dominated by a "most unstable mode" and a later coarsening regime during which larger components grow at
the expense of the smaller components. We explore some of the features of the dynamics within the relatively
simple context of the deep quench (low temperature) obstacle problem. We obtain new analytical bounds on the
rate of coarsening, and present results of numerical simulations based on a number of benchmarks. By
following the dynamics using a number of different benchmarks, we find that partial scaling can be verified,
and that the transition between linear and coarsening behavior is in fact characterized by a number of
sequential transitions requiring further analysis.
Joint work with A. Shishkov, L.Banas, and R. Nurnberg
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