scholarly journals Current Fluctuations in the One-Dimensional Symmetric Exclusion Process with Open Boundaries

2004 ◽  
Vol 115 (3/4) ◽  
pp. 717-748 ◽  
Author(s):  
B. Derrida ◽  
B. Douçot ◽  
P.-E. Roche
Keyword(s):  
Exclusion Process ◽  
Current Fluctuations ◽  
One Dimensional ◽  
Open Boundaries ◽  
The One

scholarly journals Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1028 ◽  
Author(s):  
Alessandro Pelizzola ◽  
Marco Pretti ◽  
Francesco Puccioni
Keyword(s):  
Finite Size ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Pair Approximation ◽  
Fundamental Diagram ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The One

Dynamical transitions, already found in the high- and low-density phases of the Totally Asymmetric Simple Exclusion Process and a couple of its generalizations, are singularities in the rate of relaxation towards the Non-Equilibrium Stationary State (NESS), which do not correspond to any transition in the NESS itself. We investigate dynamical transitions in the one-dimensional Katz–Lebowitz–Spohn model, a further generalization of the Totally Asymmetric Simple Exclusion Process where the hopping rate depends on the occupation state of the 2 nodes adjacent to the nodes affected by the hop. Following previous work, we choose Glauber rates and bulk-adapted boundary conditions. In particular, we consider a value of the repulsion which parameterizes the Glauber rates such that the fundamental diagram of the model exhibits 2 maxima and a minimum, and the NESS phase diagram is especially rich. We provide evidence, based on pair approximation, domain wall theory and exact finite size results, that dynamical transitions also occur in the one-dimensional Katz–Lebowitz–Spohn model, and discuss 2 new phenomena which are peculiar to this model.

scholarly journals THE EFFECT OF OFF-RAMP ON THE ONE-DIMENSIONAL CELLULAR AUTOMATON TRAFFIC FLOW WITH OPEN BOUNDARIES

2004 ◽  
Vol 18 (16) ◽  
pp. 2347-2360 ◽  
Author(s):  
HAMID EZ-ZAHRAOUY ◽  
ZOUBIR BENRIHANE ◽  
ABDELILAH BENYOUSSEF
Keyword(s):  
Cellular Automaton ◽  
Traffic Flow ◽  
Average Density ◽  
Constant Current ◽  
Current Phase ◽  
One Dimensional ◽  
First Order ◽  
Open Boundaries ◽  
Flow Phase ◽  
The One

The effect of the position of the off-ramp (way out), on the traffic flow phase transition is investigated using numerical simulations in the one-dimensional cellular automaton traffic flow model with open boundaries using parallel dynamics. When the off-ramp is located between two critical positions ic1 and ic2 the current increases with the extracting rate β0, for β0<β0c1, and exhibits a plateau (constant current) for β0c1<β0<β0c2 and decreases with β0 for β0>β0c2. However, the density undergoes two successive first order transitions: from high density to plateau current phase at β0=β0c1; and from average density to the low one at β0=β0c2. In the case of two off-ramps located respectively at i1 and i2, these transitions occur only when i2-i1 is smaller than a critical value. Phase diagrams in the (α,β0), (β,β0) and (i1,β0) planes are established. It is found that the transitions between free traffic (FT), congested traffic (CT) and plateau current (PC) phases are of first order. The first order line transition in (i1,β0)-phase diagram terminates by an end point above which the transition disappears.

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