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First we consider a unidirectional flux omega_bar of vehicles each of which is characterized by its `natural velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value omega_bar_c of the control parameter omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density rho_bar rather than the flux omega_bar is the control parameter. Unequal fluxes omega_bar_A and omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.
A two-lane extension of a recently proposed cellular automaton model for traffic flow is discussed. The analysis focuses on the reproduction of the lane usage inversion and the density dependence of the number of lane changes. It is shown that the si
We introduce a class of 1D models mimicking a single-lane bridge with two junctions and two particle species driven in opposite directions. The model exhibits spontaneous symmetry breaking (SSB) for a range of injection/extraction rates. In this phas
We introduce a stochastic lattice gas model including two particle species and two parallel lanes. One lane with exclusion interaction and directed motion and the other lane without exclusion and unbiased diffusion, mimicking a micotubule filament an
A one-way {em street} of width M is modeled as a set of M parallel one-dimensional TASEPs. The intersection of two perpendicular streets is a square lattice of size M times M. We consider hard core particles entering each street with an injection pro
Spontaneous symmetry breaking (SSB) is a key concept in physics that for decades has played a crucial role in the description of many physical phenomena in a large number of different areas, like particle physics, cosmology, and condensed-matter phys