Macroscopic Car Condensation in a Parking Garage

Abstract

An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes macroscopically occupied. The total car density ${\rho }_o$ and the exit probability $\alpha$ are the two control parameters. At the transition, the number of parked cars $N_p$ diverges in both cases, with the length of the road $N_s$, as $N_p\sim N_s^{y_p}$ with $y_p=1/2$. Towards the transition, the number of parked cars vanishes as $N_p\sim {\epsilon }^{\beta }$ with $\beta =1$, $\epsilon =|\alpha -{\alpha }^{\ast }|$ or $\epsilon =|{\rho }_o^{\ast }-{\rho }_o|$ being the distance from the transition. The transition into the normal phase represents also the onset of transmission of information through the garage. This gives rise to unusual parked car autocorrelations and car density profiles near the garage, which depend strongly on the group velocity of the fluctuations along the road.

12 pages including 15 figures; published version in PRE

References in corpus (3)

• Electronic Transport in Metal Nanocrystal Arrays: The Effect of Structural Disorder on Scaling Behavior
• Steady-state selection in driven diffusive systems with open boundaries
• Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition

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