Jamming and asymptotic behavior in competitive random parking of bidisperse cars

TL;DR

This paper studies a generalized car parking problem with bidisperse cars, revealing how mixture composition affects the jamming limit and the approach dynamics, bridging classical and competitive adsorption models.

Contribution

It introduces a generalized model interpolating between classical and competitive parking, analyzing the asymptotic behavior and coverage in bidisperse mixtures.

Findings

Coverage in the jamming limit exceeds the monodisperse case.

Smaller cars approach jamming slowly as t^{-1}.

Larger cars reach asymptotic coverage exponentially fast.

Abstract

We propose a generalized car parking problem where either a car of size $\sigma$ or of size $m\sigma$ ($m>1$) is sequentially parked on a line with probability $q$ and $(1-q)$, respectively. The free parameter $q$ interpolates between the classical car parking problem at either extreme ($q=0$ and $q=1$) and the competitive random sequential adsorption of a binary mixture in between. We find that the coverage in the jamming limit for a mixture always exceeds the value obtained for the uni-sized case. The introduction of a bidisperse mixture results in the slow approach ($\sim t^{-1}$) to the jamming limit by the smaller species while the larger species reach their asymptotic values exponentially fast $\sim t^{-1}e^{-(m-1)qt}$.