The construction of kinetic models for a practical description of hard sphere dynamics in fluid, amorphous solid, and crystal phases is outlined. The models are constructed to apply for both elastic and dissipative collisions. As an illustration, the Navier-Stokes hydrodynamics and transport...

We study the mean residence time of a random walker on a line segment of a lattice, which randomly switches between two states. In each of the states only motions in a one way direction are allowed. When the particle can leave the line segment through both of its ends, the residence time is a...