Computer Science – Numerical Analysis
Scientific paper
Aug 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982apj...259....1k&link_type=abstract
Astrophysical Journal, Part 1, vol. 259, Aug. 1, 1982, p. 1-8.
Computer Science
Numerical Analysis
15
Correlation Coefficients, Cosmology, Distribution Functions, Hydrodynamics, Liouville Equations, Universe, Maxwell-Boltzmann Density Function, Numerical Analysis
Scientific paper
This paper presents a new, exact equation appropriate for the discussion of correlations and irregularities in an expanding universe. The starting point of the analysis is an N-particle Liouville equation for the evolution of an N-particle distribution function, reformulated in a suitably defined 'average comoving' frame. A projection operator formalism is used to eliminate explicit reference to unwanted details so as to permit the derivation of an exact nonlinear, integro-differential equation for a reduced one-particle distribution. In the limit that detailed fluctuations or correlations may be completely neglected, one recovers Gilbert's collisionless Boltzmann equation. In the weak coupling approximation, one obtains a simple expression which, for the special case of a uniform spatial density, reduces to Fall and Severne's evolution equation.
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