  We present a method to model the interaction and the dynamics of atoms
excited to Rydberg states. We show a way to solve the optical Bloch equations
for laser excitation of the frozen gas in good agreement with the experiment. A
second method, the Kinetic Monte Carlo method gives an exact solution of rate
equations. Using a simple N-body integrator (Verlet), we are able to describe
dynamical processes in space and time. Unlike more sophisticated methods, the
Kinetic Monte Carlo simulation offers the possibility of numerically following
the evolution of tens of thousands of atoms within a reasonable computation
time. The Kinetic Monte Carlo simulation gives good agreement with
dipole-blockade type of experiment. The role of ions and the individual
particle effects are investigated.
