Periodic patterns for a model involving short-range and long-range interactions

TL;DR

This paper investigates a physical model with surface tension and screened Coulomb interactions, revealing how periodic equilibrium patterns bifurcate from simple structures like lamellae, cylinders, and spheres under volume constraints.

Contribution

It introduces a mathematical analysis of pattern bifurcations in a 3D model with competing short-range and long-range forces, identifying new equilibrium configurations.

Findings

Periodic patterns bifurcate smoothly from basic structures.

Lattices of cylinders and balls are identified as equilibrium solutions.

The study provides a framework for understanding pattern formation in similar physical systems.

Abstract

We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy, under some volume constraints. The patterns bifurcate smoothly from straight lamellae, lattices of round solid cylinders and lattices of round balls.