Irreversible processes with nearest-particle rates

The author considers a class of processes on an infinite one-dimensional lattice wherein sites transform irreversibly from vacant to occupied. The transformation rates, beta (l, r), depend only on the distances, l and r, to the nearest occupied sites (or particles) on the left and right, respectively. He shows that the kinetics can be determined exactly, when beta (l, r) is independent of l or r>R, from a truncated set of 2R rate equations. These solvable models can be extended to include simultaneous transformation of strings of N adjacent sites. One can thus generate a general class of continuum cooperative car-parking problems as the N to infinity limit of a class solvable lattice models.