Analytic model for the ballistic adsorption of polydisperse mixtures.
We study the ballistic adsorption of a polydisperse mixture of spheres onto a line. Within a mean-field approximation, the problem can be analytically solved by means of a kinetic equation for the gap distribution. In the mean-field approach, the adsorbed substrate is replaced by a set of effective particles having the same size, equal to the average diameter of the spheres in the original mixture. The analytic solution in the case of binary mixtures agrees quantitatively with direct Monte Carlo simulations of the model, and qualitatively with previous simulations of a related model in d=2.
Pastor-Satorras
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Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. romu@ictp.trieste.it