Generalized motion by mean curvature as a macroscopic limit of stochastic ising models with long range interactions and Glauber dynamics |
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| Authors: | Markos A. Katsoulakis Panagiotis E. Souganidis |
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| Affiliation: | (1) Center for Mathematical Sciences, University of Wisconsin-Madison, 53706 Madison, WI, USA;(2) Present address: Department of Mathematics, Michigan State University, 48824 E. Lansing, MI, USA;(3) Department of Mathematics, University of Wisconsin-Madison, 53706 Madison, WI, USA |
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| Abstract: | We study themacroscopic limit of an appropriately rescaledstochastic Ising model withlong range interactions evolving withGlauber dynamics as well as the correspondingmean field equation, which is nonlinear and nonlocal. In the limit we obtain an interface evolving with normal velocity  k, wherek isthe mean curvature and thetransport coefficient is identified by aneffective Green-Kubo type formula. The above assertions are valid for all positive times, the motion of the interface being interpreted in theviscosity sense after the onset of the geometric singularities.Supported by ONRPartially supported by NSF, ARO, ONR and the Alfred P. Sloan Foundation |
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