Evolution Equation and Transport Coefficients of Swarms in Short Time Development of Initial Relaxation Processes

  • Keiichi Kondo
Conference paper

Abstract

An evolution equation and transport coefficient expressing the short time development of swarms were derived from the space-time dependent Boltzmann equation by introducing the “projection operator” which acts on the velocity distribution function. The evolution equation of the density \( n(\vec r,t) \)\( f(\vec r,\vec v,t = 0) = f0(\vec v)*n(\vec r,t = 0) \) can be generally written as follows: \( \partial _t n(r.t) = \hfill \\ \sum\limits_{k = 1} {\int\limits_o^t {at\Omega ^k } } (t - z)0( - \nabla _r )^k n(r.z) + \sum\limits_{k = 1} {w_o^k } (t)\Theta ( - \nabla _r )^k n(r.t = 0) \hfill \\ \)

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Keiichi Kondo
    • 1
  1. 1.Department of Electrical EngineeringAnan College of TechnologyAnanJapan

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