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Title: A multiscale variational approach to the kinetics of viscous classical liquids: The coarse-grained mean field approximation

A closed kinetic equation for the single-particle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarse-grained mean-field (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the N-particle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearest-neighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is mass-conserving and closed in the single-particle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the Gross-Pitaevskii equation in the weak-gradient short-range force limit.
Authors:
;  [1]
  1. Department of Chemistry, Indiana University, 800 E. Kirkwood Ave., Bloomington, Indiana 47405 (United States)
Publication Date:
OSTI Identifier:
22253314
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 13; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; APPROXIMATIONS; BOLTZMANN-VLASOV EQUATION; DENSITY; INTERACTIONS; KINETIC EQUATIONS; KINETICS; LIQUIDS; MEAN-FIELD THEORY; PARTICLES; PERTURBATION THEORY; PROBABILITY; VARIATIONAL METHODS