Jamming and asymptotic behavior in competitive random parking of bidisperse cars

Details Jamming and asymptotic behavior in competitive random parking of bidisperse cars Jamming and asymptotic behavior in competitive random parking of bidisperse cars

2002-05-15

arxiv.org/abs/cond-mat/0205315v1

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1016/S0378-4371(02)01236-0

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

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