We investigate dynamical properties of traffic flow using the stochastic car-following model with modified optimal velocity on circular road. The safety distance following the two-second rule and autonomous vehicles, acting as agents, obeying simple requirements are incorporated into the model. The dynamic safety distance increases in a light traffic condition where the average driving velocity is high, while decreases in a dense traffic condition in anticipation of slower traffic motion. The results show that the presence of the agents can enhance overall velocity and traffic current of the system, and postpone the traffic congestion. In a particular phase region, imposing a speed limit enables the system to leave the congested flow phase. The density-dependent speed limit in agent-free condition is obtained to achieve the optimal traffic flow.
Phase transitions and thermodynamics properties of the frustrated antiferromagnetic XY (FAXY) model have been investigated near the two transition temperatures. We found that the Kosterlitz-Thouless (KT) transition corresponding to the rotational U(1) symmetry breaking and the Ising-like (I) transition corresponding to the reflection Z
2 symmetry breaking occur at two-separate transition temperatures, Tkt
< TI
. These temperatures lie close to each other, however in our results the separation is obvious. Our results show the order parameters as a function of temperature and we also estimate the critical exponents, β, α, γ, η and ν. The critical exponent ν indicates that the Ising-like transition is inconsistent with the Ising universality class.
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