Maximal Current Phase Research Articles

An interacting spin$ndash$flip model for one-dimensional proton conduction

A discrete asymmetric exclusion process (ASEP) is developed to model proton conduction along one-dimensional water wires. Each lattice site represents a water molecule that can be in only one of three states; protonated, left-pointing and right-pointing. Only a right- (left-) pointing water can accept a proton from its left (right). Results of asymptotic mean field analysis and Monte Carlo simulations for the three-species, open boundary exclusion model are presented and compared. The mean field results for the steady-state proton current suggest a number of regimes analogous to the low and maximal current phases found in the single-species ASEP (Derrida B 1998 Phys. Rep. 301 65–83). We find that the mean field results are accurate (compared with lattice Monte Carlo simulations) only in certain regimes. Refinements and extensions including more elaborate forces and pore defects are also discussed.

A study on an improved Nagel-Schreckenberg traffic flow -model with open boundary conditions

Using the improved Nagel-Schreckenberg traffic model with open boundary conditions,we present the fundamental diagrams of traffic flow under different parameters by numerical simulation.It turns out that the traffic flow of the improved Nagel-Schrec-kenberg model is greater than that of the Nagel-Schreckenberg model,then we analyse the characters and critical points of the transition from free flow phase to maximum current phase and the transition from jamming phase to free flow phase.

Minimal current phase and universal boundary layers in driven diffusive systems.

We investigate boundary-driven phase transitions in open driven diffusive systems. The generic phase diagram for systems with short-ranged interactions is governed by a simple extremal principle for the macroscopic current, which results from an interplay of density fluctuations with the motion of shocks. In systems with more than one extremum in the current-density relation, one finds a minimal current phase even though the boundaries support a higher current. The boundary layers of the critical minimal current and maximal current phases are argued to be of a universal form. The predictions of the theory are confirmed by Monte Carlo simulations of the two-parameter family of stochastic particle hopping models of Katz, Lebowitz, and Spohn and by analytical results for a related cellular automaton with deterministic bulk dynamics. The effect of disorder in the particle jump rates on the boundary layer profile is also discussed.

Nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions

We study the phases of the Nagel-Schreckenberg traffic model with open boundary conditions as a function of the randomization probabilities p>0 and the maximum velocity v(max)>1. Due to the existence of "buffer sites" which enhance the free-flow region, the behavior is much richer than that of the related, parallel updated asymmetric exclusion process [(ASEP), v(max)=1]. Such sites exist for v(max)> or =3 and p<p(c) where the phase diagram is qualitatively similar to the p=0 case: there is a free flow and a jamming phase separated by a line of first-order transitions. For p>p(c) an additional maximum current phase separated by second-order transitions occurs like for the ASEP. The density profile decays in the maximum current phase algebraically with an exponent gamma approximately 2 / 3 for all v(max)> or =2 indicating that these models belong to another universality class than the ASEP where gamma=1 / 2.

Relaxation spectrum of the asymmetric exclusion process with open boundaries

We calculate numerically the exact relaxation spectrum of the totally asymmetric simple exclusion process (TASEP) with open boundary conditions on lattices up to 16 sites. In the low- and high-density phases and along the nonequilibrium first-order phase transition between these phases, but sufficiently far away from the second-order phase transition into the maximal-current phase, the low-lying spectrum (corresponding to the longest relaxation times) agrees well with the spectrum of a biased random walker confined to a finite lattice of the same size. The hopping rates of this random walk are given by the hopping rates of a shock (a domain wall separating stationary low- and high-density regions), which are calculated in the framework of a recently developed non-equilibrium version of Zel'dovich's theory of the kinetics of first-order transitions. We conclude that the description of the domain wall motion in the TASEP in terms of this theory of boundary-induced phase transitions is meaningful for very small systems of the order of ten lattice sites.

Exact determination of the phase structure of the p-species asymmetric exclusion process

We consider a multi-species generalization of the Asymmetric Simple Exclusion Process on an open chain, in which particles hop with their characteristic hopping rates and fast particles can overtake slow ones. The number of species is arbitrary and the hopping rates can be selected from a discrete or continuous distribution. We determine exactly the phase structure of this model and show how the phase diagram of the 1-species ASEP is modified. Depending on the distribution of hopping rates, the system can exist in a three-phase regime or a two phase regime. In the three- phase regime the phase structure is almost the same as in the one species case, that is, there are the low density, the high density and the maximal current phases, while in the two-phase regime there is no high density phase.

A simulation study of an asymmetric exclusion model with open boundaries and random rates

Using numerical simulations, we study the asymmetric exclusion model with open boundaries, particlewise disorder and parallel dynamics. At each time step, particles are injected at the left boundary with probability , removed on the right with probability , and jump in the bulk with probability , where is a random rate associated with each injected particle . The parameter interpolates between fully parallel and random sequential dynamics. The phase diagram in the -plane displays high-density, low-density and maximum-current phases, with the first-order transition line between high- and low-density phases shifted away from the line . Within the low-density phase a platoon phase transition occurs, many features of which can be explained using exact results for asymmetric exclusion with particlewise disorder on the ring. In a certain region of parameter space the disorder induces a cusp in the current-density relation at maximum flow. Our simulations indicate that this does not affect the topology of the phase diagram, nor the familiar -decay of the density profile in the maximum-current phase.

Self-organized criticality in 1D stochastic traffic flow model

Results of computer simulations of a 1D particle hopping model of traffic flow are presented. The model is characterized by parallel update and fully asymmetric stochastic hopping dynamics which allows unbounded series of jumps to empty neighbour sites on the right. The considered case of open boundary conditions can be used to model a “bottleneck” situation in traffic. Evidence for self-organized criticality is found in two aspects: the presence of long-range spatial correlations manifested in the shape of density profiles, and long-time temporal correlations showing up in the low-frequency behaviour of the spectral density of the total particle number and flow. A plausible conjecture is to interpret the observed qualitative changes in these features, as a function of the injection rate and the hopping probability, in terms of a nonequilibrium phase transition between a low-density phase and a maximal current phase. This conjecture is supported by the phase diagram obtained in mean-field approximation.

Electron and population temperatures in a non-LTE optically thick plasma

The distribution temperature between excited atomic states in an arc plasma can be determined using self-reversed lines. This technique was applied to a high-pressure mercury arc. The electron temperature was deduced from the distribution temperature between the 63P2,0 metastable levels. The population temperatures of the 63P1, 73S1 and 63D3 levels were also determined as well as the lowering of the population of the 63P1 resonance level caused by resonance radiation. The electron density was deduced from the Saha law, the known electron temperature and the measurement of the density of the 63D2 level. At the arc axis the difference between the electron temperature and the 'equilibrium temperature' deduced from the optically thin line technique assuming local thermodynamic equilibrium (LTE), is of the order of 1000 K and 450 K at the moments of maximum and minimum current phase, respectively. The difference found between the population temperatures of the different levels indicates that collisionally dominated plasma is not a sufficient condition for the presence of LTE in the central region of an inhomogeneous arc where the diffusion of charged particles can disturb the Saha balance.