Summation of logarithmic interactions in nonrectangular periodic media Original Research Article

We present a set of expressions for practical evaluation of energies, including self-energies, and forces between particles interacting logarithmically in a finite two-dimensional nonrectangular system with periodic boundary conditions. The formalism can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges. The expressions are shown to converge to usual computer accuracy (∼ 10−16) by adding only few terms in a single sum of standard trigonometric functions.