Analysis of pattern formation in systems with competing range interactions

We analyzed pattern formation and identified various morphologies in a system of particles interacting through a non-monotonic potential with a competing range interaction characterized by a repulsive core (r < r(c)) and an attractive tail (r > r(c)), using molecular-dynamics simulations. Depending on parameters, the interaction potential models the inter-particle interaction in various physical systems ranging from atoms, molecules and colloids to vortices in low kappa type-II superconductors and in recently discovered 'type-1.5' superconductors. We constructed a 'morphology diagram' in the plane 'critical radius r(c)-density n' and proposed a new approach to characterizing the different types of patterns. Namely, we elaborated a set of quantitative criteria in order to identify the different pattern types, using the radial distribution function (RDF), the local density function and the occupation factor.