Thomson’s problem, Coulombic interaction, charge distribution, numericaloptimization.

We have investigated configurational and energetical features of classical identicalpoint charges confined to a one-dimensional (1D) rod and two-dimensional (2D)plate-like geometrical structures. The charges are under the eect of a Coulombic 1=rfield. After an introductory brief chapter dealing with the physics of the problem athand, we have presented a highly detailed literature review about the main subject.What follow are then the numerical and analytical approaches towards the solution ofthe problem. Then we have presented our outcomes in great detail about the globalminimum-energy configurations of charges on a square, on a disk, on an ellipse, andon a 2D ellipsoid. The numerical results reported here are obtained from computationalsimulations which are generally based on force minimization method, with ahighly basic application of Monte-Carlo approach.