کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
977931 | 1480188 | 2008 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker-Planck equations
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker-Planck equations Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker-Planck equations](/preview/png/977931.png)
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 387, Issues 16â17, 1 July 2008, Pages 4053-4069
Journal: Physica A: Statistical Mechanics and its Applications - Volume 387, Issues 16â17, 1 July 2008, Pages 4053-4069
نویسندگان
S. Pankavich, Z. Shreif, P. Ortoleva,