The design of future cooler storage rings for ions and antiprotons at GSI and worldwide, operating far above the beam intensity levels of existing machines, requires a much more detailed understanding of long-time collective phenomena in cooled beams. In cooler storage rings the complex interplay of many processes determines the final equilibrium distribution of the beam particles. The aim of this project is to develop analytical models and simulation tools for the study of the beam distribution function, accounting for all relevant beam cooling and heating processes. The study will include also collective instabilities induced by ring impedances or trapped secondary particles. The physics models will be cast into a modular software library for beam dynamics simulations. Experiments with cooled, low energy ion beams are foreseen at serval storage ring facilities in or to benchmark the physics models and simulation codes that will be developed.