Jamming and asymptotic behavior in competitive random parking of bidisperse cars

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 $\sim t^{-1}{e}^{-(m-1)qt}$.

6 pages (in Revtex4), 4 eps figures; To appear in Physica A (2002)

References in corpus (3)

• Jamming coverage in competitive random sequential adsorption of binary mixture
• Competitive random sequential adsorption of point and fixed-sized particles: analytical results
• Model of correlated sequential adsorption of colloidal particles

Cited by in corpus (2)

• Relaxation of saturated random sequential adsorption packings of discorectangles aligned on a line
• Adsorption of a binary mixture of monomers with nearest-neighbour cooperative effects