2018/10/07 by Paolo Amore, Amore, Paolo, Martin Jacobo +1
Mathematics · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Soft Condensed Matter (cond-mat.soft) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1810.03230
openalex publication_date 2018/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We have studied the configurations of minimal energy of N charges on a curve on the plane, interacting with a repulsive potential Vij = 1/rijs, with s ≥ 1 and i,j=1,…, N. Among the examples considered are ellipses of different eccentricity, a straight wire and a cardioid. We have found that, for some geometries, multiple minima are present, as well as points of unstable equilibrium. For the case of the cardioid, we observe that the presence of the cusp has a dramatic effect on the distribution of the charges, in the limit N ≫ 1.