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- W2019078907 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 epsilon, 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 order epsilon squared 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 the same order in epsilon. This approach applies to a broad range of problems in the nanosciences." @default.
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- W2019078907 date "2008-07-01" @default.
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- W2019078907 title "Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker–Planck equations" @default.
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- W2019078907 doi "https://doi.org/10.1016/j.physa.2008.03.008" @default.
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