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Title: Classical non-Markovian 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 advection-dispersion 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 three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

Authors:
 [1]
  1. Department of Physics and Physical Oceanography, University of North Carolina Wilmington, Wilmington, North Carolina 28403-5606 (United States)
Publication Date:
OSTI Identifier:
22306199
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
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, E-mail: alexanian@uncw.edu. Classical non-Markovian Boltzmann equation. United States: N. p., 2014. Web. doi:10.1063/1.4886475.
Alexanian, Moorad, E-mail: alexanian@uncw.edu. Classical non-Markovian Boltzmann equation. United States. doi:10.1063/1.4886475.
Alexanian, Moorad, E-mail: alexanian@uncw.edu. Fri . "Classical non-Markovian Boltzmann equation". United States. doi:10.1063/1.4886475.
@article{osti_22306199,
title = {Classical non-Markovian Boltzmann equation},
author = {Alexanian, Moorad, E-mail: alexanian@uncw.edu},
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 advection-dispersion 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 three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.},
doi = {10.1063/1.4886475},
journal = {Journal of Mathematical Physics},
number = 8,
volume = 55,
place = {United States},
year = {Fri Aug 01 00:00:00 EDT 2014},
month = {Fri Aug 01 00:00:00 EDT 2014}
}