# Theoretical particle distributions on curved surfaces

Researchers: Kaisa Kautto, Maria Sammalkorpi ,Kimmo Kaski and Adrian P Sutton

This work has been motivated by the general lack of knowledge concerning the analytic influence of surface curvature on the distribution of particles on the surface. This is relevant for understanding many optimal packing related problems of materials science, for example, biomolecular packings, changes in the vicinity of dislocations and, as in here, nanostructures of carbon. The long term aim of the work is to be able to model deformed carbon nanotubes. This involves understanding uniform distributions of points on curved surfaces and the connection between these distributions and atomic structures. The simplest curved surface is the sphere and therefore we started the analysis by considering the spherical fullerene C60. This carbon structure also known as the buckminsterfullerene corresponds to the uniform distribution of 32 points on a sphere. Studies have also been extended to ellipsoidal surfaces and to the analysis of uniform point distributions of other than 32 points.