3rd year computational Physics assignment concerning localization of equilibrium points of electric field for complex multi-charges system on a 2-dimensional disc.

This problem is intractable and hence needs to be solved with the use of Monte Carlo sampling techniques. These were implemented, alongside with e.g. a range of convergence enhancements of the form of e.g. cooling techniques.

Equilibrium state for a disc with 13 charges:

Equilibrium state for a disc with 28 charges:

Equilibrium energy increases with an addition of a new charge. Blue dots signify states that were computed analytically. Beyond 12 charges, analytic solutions become intractable. Orange equilibrium states were found with the use of Monte Carlo algorithms. One can see that energy increase is roughly following linear trendline.