Hydrodynamic scaling limit of continuum solid-on-solid model

2005/05/31 by Anamaria Savu, Savu, Anamaria
Mathematics · Physics and Astronomy · #60F99 #60G07 #60H30 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:60F99 #msc:60G07 #msc:60H30

paper · pdf · doi:10.48550/arxiv.math/0506001

arxiv created 2005/05/31 · arxiv updated 2009/12/01

Abstract

A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of hydrodynamic scaling limit of nongradient models. What distinguishes our model from other models discussed so far is the presence of two conservation laws for the dynamics in a nonperiodic box and the complex dynamics that is not nearest-neighbor. Along the way, a few steps has to be adapted to our new context. As a byproduct of our main result we also derive the hydrodynamic scaling limit of a perturbation of continuum solid-on-solid model, a model that incorporates both surface diffusion and surface electromigration.

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