Statistical properties of edge dislocation ensembles

Energy of a dislocation ensemble depends on dislocation positions, and, since the details of dislocation configuration are not known, should be viewed as a random number. We study numerically statistical characteristics of energy for periodic ensembles of edge dislocations with a large number of dislocations in a periodic cell. We confirm that there is a limit probability density function of energy for randomly placed dislocations as m -> infinity. The situation with probability density of energy of equilibrium dislocation states is less clear: probability density keeps evolving as increases. We suggest a plausible hypothesis on the limit behaviour of energy distribution. We also study the probability distribution of internal resistance stresses, as well as the derivatives of energy with respect to dislocation polarisation. Internal resistance stress equilibrates the external shear stress in a loaded dislocation structure. We explain why probability distribution of internal resistance stress for randomly placed dislocations does not have a limit for m -> infinity and confirm this by numerical simulations. Surprisingly, numerical simulations show that such limit exists for equilibrium dislocation structures. A preliminary analysis of geometry of equilibrium dislocation structures is also given.