EXACT SOLUTION OF A GENERALIZED BALLISTIC-DEPOSITION MODEL

We study a monolayer deposition model which generalizes both random sequential adsorption and ballistic deposition: hard disks are dropped vertically and randomly onto a line; they can adsorb on the line either by direct deposition or after rolling over preadsorbed disks. An exact solution is given for the gap distribution function and for the density of adsorbed disks. Properties of the system at or close to the jamming limit are discussed. This generalized ballistic-deposition process leads to formation of connected clusters of all sizes: the time evolution of the cluster distribution is obtained analytically.