Leading order asymptotics for non-local energies and the Read-Shockley law

Peter J. Grabner, Florian Theil

We study an energy minimization problem ${\sum }_{i\ne j}W(z_i-z_j)$ for $N$ points $\left\{z_1,\dots ,z_N\right\}$ with applications in dislocation theory. The $N$ points lie i…