Self-organization of charged particles in circular geometry

Thomson problem in the disk

We investigate the classical ground state of a large number of charges confined inside a disk and interacting via the Coulomb potential. By realizing the important role that the peripheral charges play in determining the lowest energy solutions, we have successfully implemented an algorithm that allows us to work with configurations with a desired number of border charges. This feature brings a consistent reduction in the computational complexity of the problem, thus simplifying the search of global minima of the energy. Additionally, we have implemented a divide and conquer approach which has allowed us to study configurations of size never reached before (the largest one corresponding to N=40886 charges). These last configurations, in particular, are seen to display an increasingly rich structure of topological defects as N gets larger.

Stable Configurations of Charged Sedimenting Particles

The qualitative behavior of charged particles in a vacuum is given by Earnshaw's theorem, which states that there is no steady configuration of charged particles in a vacuum that is asymptotically stable to perturbations. In a viscous fluid, examples of stationary configurations of sedimenting uncharged particles are known, but they are unstable or neutrally stable-they are not attractors. In this Letter, it is shown by example that two charged particles settling in a fluid may have a configuration that is asymptotically stable to perturbations for a wide range of charges, radii, and densities. The existence of such "bound states" is essential from a fundamental point of view and it can be significant for dilute charged particulate systems in various biological, medical, and industrial contexts.