Abstract:In this paper we derive the continuum limit of a multiple-species, interacting particle system by proving a Γ-convergence result on the interaction energy as the number of particles tends to infinity. As the leading application, we consider n edge dislocations in multiple slip systems. Since the interaction potential of dislocations has a logarithmic singularity at zero with a sign that depends on the orientation of the slip systems, the interaction energy is unbounded from below. To make the minimization pr… Show more
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