It was recalled that 2 different approaches were applied to the description of dislocation pattern formation. In one, the collective behavior of many individual dislocations was investigated by using analytical or numerical methods. In the other, the dislocation system was described by means of continuous functions of the space coordinates. A method was proposed here for establishing a link between the 2 length-scales. Beginning with the exact equation for the N-dislocation distribution function, a hierarchy of equations was derived for 1-, 2-, 3- … particle-distribution functions. By assuming that the 3-particle correlation function was negligible, a closed set of equations could be obtained for the dislocation density and the 2-particle correlation functions.

Link between the Microscopic and Mesoscopic Length-Scale Description of the Collective Behavior of Dislocations I.Groma: Physical Review B, 1997, 56[10], 5807-13