Abstract:
We investigate both static and dynamic properties of systems described by hard spheres. They comprise glassy state of colloids, random packing of granular matter and dynamic critical phenomena, like dynamical arrest and self-organized critical state. We use sophisticated versions of mean-field approximation, using 1) large-dimensionality limit 2) branching processes 3) back-reaction mechanism for Langevin equation. In static approach we are able to find analytically the equation of state for hard spheres, while dynamics describes well the observed approach to critical state and ergodicity breaking in colloidal glass.