Classical nonMarkovian Boltzmann equation
Abstract
The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advectiondispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the threeparticle distribution function are neglected. We show that the inclusion of higherorder distribution functions give rise to an exact, nonMarkovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two and the threeparticle distribution functions are considered under the assumption that the two and the threeparticle correlation functions are translationally invariant that allows us to obtain advectiondispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.
 Authors:

 Department of Physics and Physical Oceanography, University of North Carolina Wilmington, Wilmington, North Carolina 284035606 (United States)
 Publication Date:
 OSTI Identifier:
 22306199
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Mathematical Physics
 Additional Journal Information:
 Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00222488
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ADVECTION; BOLTZMANN EQUATION; CORRELATION FUNCTIONS; DIFFUSION; DISTRIBUTION FUNCTIONS; MARKOV PROCESS; TRANSPORT THEORY
Citation Formats
Alexanian, Moorad. Classical nonMarkovian Boltzmann equation. United States: N. p., 2014.
Web. doi:10.1063/1.4886475.
Alexanian, Moorad. Classical nonMarkovian Boltzmann equation. United States. doi:10.1063/1.4886475.
Alexanian, Moorad. Fri .
"Classical nonMarkovian Boltzmann equation". United States. doi:10.1063/1.4886475.
@article{osti_22306199,
title = {Classical nonMarkovian Boltzmann equation},
author = {Alexanian, Moorad},
abstractNote = {The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advectiondispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the threeparticle distribution function are neglected. We show that the inclusion of higherorder distribution functions give rise to an exact, nonMarkovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two and the threeparticle distribution functions are considered under the assumption that the two and the threeparticle correlation functions are translationally invariant that allows us to obtain advectiondispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.},
doi = {10.1063/1.4886475},
journal = {Journal of Mathematical Physics},
issn = {00222488},
number = 8,
volume = 55,
place = {United States},
year = {2014},
month = {8}
}