2007/07/31 by Darryl D. Holm, D. D. Holm, Vakhtang Putkaradze +3 · 10 citations
Mathematics · Physics and Astronomy · #Anisotropy #Dissipation #Dissipative system #Dust and Plasma Wave Phenomena #Equations of motion #Gas Dynamics and Kinetic Theory #Kinetic energy #Kinetic theory #Smoluchowski coagulation equation #Statistical Mechanics and Entropy #cond-mat.mes-hall #nlin.AO #nlin.PS #physics.chem-ph
paper · pdf · doi:10.1098/rspa.2010.0043
published in Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences 466(2122), 2991-3012 (Royal Society) · 19 pages; no figures. Submitted to Proc. Roy. Soc. A
arxiv created 2010/04/05 · openalex publication_date 2010/04/21 · arxiv updated 2010/04/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double-bracket approach (double-bracket Vlasov, or DBV). The moments of the DBV equation lead to a non-local form of Darcy’s law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double-bracket kinetic equations is expressed as Lie–Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double-bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density-orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.