Stochastic mode reduction for particle-based simulation methods for complex microfluid systems

Peter R. Kramer, Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

We illustrate the stochastic mode reduction procedure as formulated recently by Majda, Timofeyev, and Vanden-Eijnden [Comm. Pure Appl. Math., 54 (2001), pp. 891-974] (MTV) on the equations of motion underlying various particle-based simulation approaches (such as Stokesian dynamics and Brownian dynamics) and the conceptually distinct dissipative particle dynamics (DPD) simulation approaches for complex microfluid systems. The resulting coarse-grained dynamics are compared and contrasted with each other. We show that the stochastic mode reduction procedure provides a way to recover the Smoluchowski dynamics for a standard model of multiple interacting particles in a fluid. The DPD, however, has some subtle aspects which obstruct the application of the stochastic mode reduction procedure. We discuss the mathematical and physical properties of the DPD method that underlie this difficulty.

Original languageEnglish (US)
Pages (from-to)401-422
Number of pages22
JournalSIAM Journal on Applied Mathematics
Volume64
Issue number2
DOIs
StatePublished - 2004

Keywords

  • Brownian dynamics
  • Brownian motion
  • Dissipative particle dynamics
  • Smoluchowski reduction

ASJC Scopus subject areas

  • Applied Mathematics

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