arXiv subjects
Publications and source records attributed to A. Alan Middleton.
A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.
The rounding of the charge density wave depinning transition by thermal noise is examined. Hops by localized modes over small barriers trigger ``avalanches'', resulting in a creep velocity much larger than that expected from comparing thermal energies with typical barriers. For a field equal to the $T=0$ depinning field, the creep velocity is predicted to have a {\em power-law} dependence on the temperature $T$; numerical computations confirm this result. The predicted order of magnitude of the thermal rounding of the depinning transition is consistent with rounding seen in experiment.
We have studied numerically the dynamics of a directed elastic string in a two-dimensional array of quenched random impurities. The string is driven by a constant transverse force and thermal fluctuations are neglected. There is a transition from pinned to unpinned behavior at a critical value $F_T$ of the driving force. At the transition the average string velocity scales with the driving force. The scaling is equally well described by a power law $v_d\sim (F-F_T)^ζ$, with $ζ=0.24\pm0.1$, or by a logarithm, $v_d\sim1/\ln(F-F_T)$. The divergence of the velocity-velocity correlation length at threshold is characterized by an exponent $ν=1.05\pm0.1$.