Modeling friction on a mesoscale: Master equation for the   earthquake-like model
  The earthquake-like model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach naturally describes stick-slip and smooth sliding regimes of tribological systems within a framework which separates the calculation of the friction force from the studies of the properties of the contacts. 
Oleg Braun, Michel Peyrard (Phys-ENS)