Universality in the screening cloud of dislocations surrounding a disclination

A detailed analytical and numerical analysis for the dislocation cloud surrounding a disclination is presented. The analytical results show that the combined system behaves as a single disclination with an effective charge which can be computed from the properties of the grain boundaries forming the dislocation cloud. Expressions are also given when the crystal is subjected to an external two-dimensional pressure. The analytical results are generalized to a scaling form for the energy which up to core energies is given by the Young modulus of the crystal times a universal function. The accuracy of the universality hypothesis is numerically checked to high accuracy. The numerical approach, based on a generalization from previous work by Seung and Nelson [Phys. Rev. A 38, 1005 (1988)], is interesting on its own and allows to compute the energy for an arbitrary distribution of defects, on an arbitrary geometry with an arbitrary elastic energy with very minor additional computational effort. Some implications for recent experimental, computational, and theoretical work are also discussed.