Barry Cox School of Mathematics & Applied Statistics, University of Wollongong Mechanics and geometry of carbon nanostructures Wednesday 16th April 14:05-14:55pm, Eastern Avenue Lecture Theatre. Carbon nanostructures occur in many familiar forms such as cylinders, spheres and spheroids, and therefore mathematical modeling can be a useful tool for solving problems in nanotechnology. There are many diverse applications for modeling, such as nano-oscillating devices, drug delivery and memory devices, to name just a few. Two different approaches to modeling carbon nanostructures are presented in this seminar. Firstly, the conventional theory for carbon nanotubes is introduced and while it is readily applicable in many cases, there are short-comings in the case of very small radius nanotubes which exhibit curvature effects which are not captured by the conventional theory. A new model is then described that is based on only geometric considerations, but which captures the effects of curvature and can also be justified with an energy minimization argument. The new model provides considerable insight into discrete nanotube structure, and the results are shown to be entirely in agreement with computational studies. Essentially, the new model provides the correct polyhedral structure for a cylinder, which surprisingly enough seems not to have been previously given in the mathematical literature. The second modeling approach is a continuous formulation of the van der Waals interaction energy between nanostructures. This approach is used to model molecules as a surface distribution of atoms and then calculate the interaction between molecules by formal integration over the two surfaces in question. In this area a number of integrals are evaluated in closed analytical forms, and which have not previously appeared in the literature. The analytical evaluation is particularly important when it is necessary to obtain a large numerical landscape in situations when it would be prohibitive to use a purely computational approach. Finally, the notions of suction and acceptance energies are introduced which give a framework for evaluating different oscillating systems.