Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker–Planck equations

S. Pankavich, Z. Shreif and P. Ortoleva

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 16, 4053-4069

Abstract: Using multiscale analysis and methods of statistical physics, we show that a solution to the N-atom Liouville equation can be decomposed via an expansion in terms of a smallness parameter ϵ, wherein the long scale time behavior depends upon a reduced probability density that is a function of slow-evolving order parameters. This reduced probability density is shown to satisfy the Smoluchowski equation up to O(ϵ2) for a given range of initial conditions. Furthermore, under the additional assumption that the nanoparticle momentum evolves on a slow time scale, we show that this reduced probability density satisfies a Fokker–Planck equation up to O(ϵ2). This approach has applications to a broad range of problems in the nanosciences.

Keywords: Nanosystems; All-atom multiscale analysis (AMA); Gibbs hypothesis; Smoluchowski equations; Fokker–Planck equations (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:16:p:4053-4069

DOI: 10.1016/j.physa.2008.03.008

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