Key reference paper
A New Hierarchy System on the Basis of
a Master Boltzmann Equation for Microscopic Density

by  Shunichi Tsuge and Kenshi Sagara

TARA Center, University of Tsukuba, Japan

Journal of Statistical Physics, Vol.12, No.5, 1975 p.p.403 - 425              | Other Recent Papers |

It is shown that Boltzmann's equation written in terms of microscopic density (namely the unaveraged Boltzmann Function) has a wider range of validity as well as finer resolvability for fluctuations than the conventional Boltzmann equation governing Boltzmann's function. In fact the new Boltzmann equation for ideal gases has implications as a microscopically exact continuity equation like Klimontovich's equation for plasmas, and can be derived without invoking any statistical concepts, e.g., distribution functions, or molecular chaos. The Boltzmann equation in the older formalism is obtained by averaging this equation only under a restricted condition of the molecular chaos. The new Boltzmann equation is seen to contain information comparable with Liouville's equation, and serves as a master kinetic equation. A new hierarchy system is formulated in a certain parallelism to the BBGKY hierarchy.

 

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            Other abstracts available on the Internet - Click to see any of the followings:

  Solitary-wave Solution of Turbulence with Application to Benard Convection
  First principle basis of the direct numerical simulation for turbulence of inert and reactive gases
  A solitary-wave representation of turbulence in the physical-plus-eddy space
  Coherent solitary-wave of mixing layer turbulence in the physical-plus-eddy space
  A New Hierarchy System on the Basis of a Master Boltzmann Equation for Microscopic Density
  Molecular and turbulent transports competing in premixed flames

Or directly obtain the sources by visiting the following URLs:

FOR Title : First principle basis of the direct numerical simulation for turbulence of inert and reactive gases
Location : http://xxx.lanl.gov/abs/chao-dyn/9712020
FOR Title : A solitary-wave representation of turbulence in the physical-plus-eddy space
Location : http://xxx.lanl.gov/abs/chao-dyn/9803013
FOR Title : Coherent solitary-wave of mixing layer turbulence in the physical-plus-eddy space
Location : http://xxx.lanl.gov/abs/chao-dyn/9803035

For further information: STachibana@lbl.gov