A multiscale variational approach to the kinetics of viscous classical liquids: The coarsegrained mean field approximation
A closed kinetic equation for the singleparticle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarsegrained meanfield (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 Nparticle 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 nearestneighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is massconserving and closed in the singleparticle 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 GrossPitaevskii equation in the weakgradient shortrange force limit.
 Authors:

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 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; BOLTZMANNVLASOV EQUATION; DENSITY; INTERACTIONS; KINETIC EQUATIONS; KINETICS; LIQUIDS; MEANFIELD THEORY; PARTICLES; PERTURBATION THEORY; PROBABILITY; VARIATIONAL METHODS