ABSTRACT
This chapter presents simulations of a system of increasing thickness in order to assess the transition, so to say, between a flat two-dimensional system and a three-dimensional nanoparticle. In two dimensions, although relatively complex from a dynamical point of view, the configurations roughly boil down to uniform, one central vortex, and an array of vortices on a surface. Langevin-style simulations are well adapted to such interests as they allow to observe the full history of a sample, starting from some adequately chosen initial conditions, and both extensive structural and dynamical information is naturally obtained. If reasonable attention is devoted to computational speed and accuracy, this can be performed at relatively moderate cost in terms of human and computer resources. Langevin simulations generally have a reputation for being unreliable for dynamic properties as one must introduce a characteristic relaxation time that is connected with the damping coefficient.
