Time evolution of one dimensional gases with long and short range potentials
Abstract
An exact equation for the time evolution of the one-dimensional gravitational gas which demonstrates the natural formation of a hierarchy of structures was introduced by Muriel and Esguerra. The gas is assumed to be exploded from an initial Gaussian space distribution and a smooth symmetric momentum distribution. In this paper, we computationally investigate the behavior of one-dimensional gases by comparing the time evolution of this one-dimensional gravitational gas to that of another one-dimensional gas with a short range potential. The relevant formulas are derived, qualitatively analyzed, and graphically rendered.
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