Dislocation group dynamics V. Equilibrium revisited

Abstract

The equilibrium of a dislocation distribution is considered for the case where the applied stress field is a rational function. A function of a complex variable is introduced and it is shown that for equilibrium this function satisfies a quadratic equation. The stress field of the distribution and the distribution itself are different aspects of this complex function and are determined together. The known prevalence of square roots in distributions is a consequence of finding the roots of the quadratic equation. The connection between this complex representation of equilibrium and that used in Part IV for dislocation dynamics is discussed.