Coarse-graining the Dynamics of a Driven Interface in the Presence of Mobile Impurities: Effective Description via Diffusion Maps - Condensed Matter > Statistical MechanicsReport as inadecuate




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Abstract: Developing effective descriptions of the microscopic dynamics of manyphysical phenomena can both dramatically enhance their computationalexploration and lead to a more fundamental understanding of the underlyingphysics. Previously, an effective description of a driven interface in thepresence of mobile impurities, based on an Ising variant model and a singleempirical coarse variable, was partially successful; yet it underlined thenecessity of selecting additional coarse variables in certain parameterregimes. In this paper we use a data mining approach to help identify thecoarse variables required. We discuss the implementation of this diffusion mapapproach, the selection of a similarity measure between system snapshotsrequired in the approach, and the correspondence between empirically selectedand automatically detected coarse variables. We conclude by illustrating theuse of the diffusion map variables in assisting the atomistic simulations, andwe discuss the translation of information between fine and coarse descriptionsusing lifting and restriction operators.



Author: Benjamin E. Sonday, Mikko Haataja, Ioannis G. Kevrekidis

Source: https://arxiv.org/







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