A statistical theory of dislocation dynamics. II. Mathematical properties

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