Physics – Condensed Matter – Statistical Mechanics
Scientific paper
May 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975apj...197..667c&link_type=abstract
Astrophysical Journal, vol. 197, May 1, 1975, pt. 1, p. 667-673. Research supported by the City University of New York.
Physics
Condensed Matter
Statistical Mechanics
1
Autocorrelation, Force Distribution, Gravitational Fields, Stellar Motions, Velocity Distribution, Astronomical Models, Gravitational Effects, Normal Density Functions, Root-Mean-Square Errors, Statistical Mechanics, Stellar Gravitation
Scientific paper
The correlation of the force at the same point but at two different times is calculated for bounded gravitational systems. Uniform density and a Gaussian distribution of velocity are assumed. The autocorrelation function decreases as the inverse of the fifth power of t for t approaching infinity. This is in contrast to Chandrasekhar's result for infinite systems, where it decreases only as 1/t. It is shown that for an arbitrary distribution of speeds the decrease with time is generally as the inverse of the fourth power of t and in the case where the distribution is a function of the square of the velocity the decrease is as the inverse of the fifth power of t. The mean-square-velocity change is calculated via the autocorrelation function.
Ahmad Ayesha
Cohen Lawrence
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