Analytic model for a ballistic deposition process

We study a continuous ballistic deposition process in which disks are incident vertically on an infinite line in random positions. If an incoming disk 1 falls on top of an already adsorbed disk 2, it will, unless prevented by a neighboring disk, roll over the surface of disk 2 until it contacts the line. The kinetics of formation of the first layer, when formulated in terms of a gap distribution function, may be solved exactly. We find in particular that the saturation density is {ρ}({∞})=0.808 65 . . . . The results are compared with the simpler random sequential adsorption process.