A statistical theory of dislocation dynamics. II. Mathematical properties

Abstract

For pt.I see ibid., vol.14, no.4, p.699 (1981). Investigates the mathematical properties of the statistical model for dislocation dynamics introduced in the context of creep. The situation corresponds to a nonstationary process in which all the cumulants depend on the density. Based on expressions derived for the first four cumulants via a series expansion derived in the authors' earlier work, they derive an approximate form for the characteristic function. The solution is shown to be a good approximation. The distribution function is platykurtic in nature. The velocity autocorrelation function is also calculated.