EU Regional School - Stefanelli Seminar
Prof. Dr. Stefanelli - Minimization of Configurational Potentials and Crystallization
University of Vienna
Despite its obvious scientific and technological relevance, the question on why atoms and molecules arrange in crystalline order is still largely eluding a rigorous mathematical treatment. At very low temperature, atomic interactions are expected to be governed solely by the respective positions of particles. One is hence concerned with the minimization of an interaction energy depending on particle positions.The basic crystallization problem consists in characterizing the local and global geometry of ground-state configurations of such an interaction energy. In particular, one says that crystallization occurs when ground states are periodic.
I will present an overview of the available crystallization results in one and two dimensions and comment on the challenges of the many open problems, especially in three-dimensions. The formation and stability of carbon nanostructures such as nanotubes and fullerenes will also be discussed.