Analytical model for a cooperative ballistic deposition in one dimension

We formulate a model for a cooperative ballistic deposition (CBD) process whereby the incoming particles are correlated with those already adsorbed via attractive force. The strength of the correlation is controlled by a tunable parameter a that interpolates the classical car parking problem at a=0, the ballistic deposition at a=1, and the CBD model at a>1. The effects of the correlation in the CBD model are as follows. The jamming coverage q(a) increases with the strength of attraction a due to an ever-increasing tendency of cluster formation. The system almost reaches the closest packing structure as a-->infinity but never forms a percolating cluster, which is typical of one-dimensional systems. In the large a regime, the mean cluster size k increases as a(1/2). Furthermore, the asymptotic approach towards the closest packing is purely algebraic both with a as q(infinity)-q(a) approximately a(-1/2) and with k as q(infinity)-q(k) approximately k(-1), where q(infinity) approximately 1.