Duality and phase diagram of one dimensional transport

The observation of duality by Mukherji and Mishra in one dimensional transport problems has been used to develop a general approach to classify and characterize the steady state phase diagrams. The phase diagrams are determined by the zeros of a set of coarse-grained functions without the need of detailed knowledge of microscopic dynamics. In the process, a new class of nonequilibrium multicritical points has been identified.Comment: 6 pages, 2 figures (4 eps files

Cluster size distributions in particle systems with asymmetric dynamics

We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.Comment: 12 pages, 3 figures, RevTe

The totally asymmetric exclusion process with generalized update

We consider the totally asymmetric exclusion process in discrete time with generalized updating rules. We introduce a control parameter into the interaction between particles. Two particular values of the parameter correspond to known parallel and sequential updates. In the whole range of its values the interaction varies from repulsive to attractive. In the latter case the particle flow demonstrates an apparent jamming tendency not typical for the known updates. We solve the master equation for $N$ particles on the infinite lattice by the Bethe ansatz. The non-stationary solution for arbitrary initial conditions is obtained in a closed determinant form.Comment: 11 pages, 3 figure

The Irreducible String and an Infinity of Additional Constants of Motion in a Deposition-Evaporation Model on a Line

We study a model of stochastic deposition-evaporation with recombination, of three species of dimers on a line. This model is a generalization of the model recently introduced by Barma {\it et. al.} (1993 {\it Phys. Rev. Lett.} {\bf 70} 1033) to $q\ge 3$ states per site. It has an infinite number of constants of motion, in addition to the infinity of conservation laws of the original model which are encoded as the conservation of the irreducible string. We determine the number of dynamically disconnected sectors and their sizes in this model exactly. Using the additional symmetry we construct a class of exact eigenvectors of the stochastic matrix. The autocorrelation function decays with different powers of $t$ in different sectors. We find that the spatial correlation function has an algebraic decay with exponent 3/2, in the sector corresponding to the initial state in which all sites are in the same state. The dynamical exponent is nontrivial in this sector, and we estimate it numerically by exact diagonalization of the stochastic matrix for small sizes. We find that in this case $z=2.39\pm0.05$.Comment: Some minor errors in the first version has been correcte

Opinion dynamics model with domain size dependent dynamics: novel features and new universality class

A model for opinion dynamics (Model I) has been recently introduced in which the binary opinions of the individuals are determined according to the size of their neighboring domains (population having the same opinion). The coarsening dynamics of the equivalent Ising model shows power law behavior and has been found to belong to a new universality class with the dynamic exponent $z=1.0 \pm 0.01$ and persistence exponent $\theta \simeq 0.235$ in one dimension. The critical behavior has been found to be robust for a large variety of annealed disorder that has been studied. Further, by mapping Model I to a system of random walkers in one dimension with a tendency to walk towards their nearest neighbour with probability $\epsilon$, we find that for any $\epsilon > 0.5$, the Model I dynamical behaviour is prevalent at long times.Comment: 12 pages, 10 figures. To be published in "Journal of Physics : Conference Series" (2011

Correlation of Positive and Negative Reciprocity Fails to Confer an Evolutionary Advantage: Phase Transitions to Elementary Strategies

Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments

On the Two Species Asymmetric Exclusion Process with Semi-Permeable Boundaries

We investigate the structure of the nonequilibrium stationary state (NESS) of a system of first and second class particles, as well as vacancies (holes), on L sites of a one-dimensional lattice in contact with first class particle reservoirs at the boundary sites; these particles can enter at site 1, when it is vacant, with rate alpha, and exit from site L with rate beta. Second class particles can neither enter nor leave the system, so the boundaries are semi-permeable. The internal dynamics are described by the usual totally asymmetric exclusion process (TASEP) with second class particles. An exact solution of the NESS was found by Arita. Here we describe two consequences of the fact that the flux of second class particles is zero. First, there exist (pinned and unpinned) fat shocks which determine the general structure of the phase diagram and of the local measures; the latter describe the microscopic structure of the system at different macroscopic points (in the limit L going to infinity in terms of superpositions of extremal measures of the infinite system. Second, the distribution of second class particles is given by an equilibrium ensemble in fixed volume, or equivalently but more simply by a pressure ensemble, in which the pair potential between neighboring particles grows logarithmically with distance. We also point out an unexpected feature in the microscopic structure of the NESS for finite L: if there are n second class particles in the system then the distribution of first class particles (respectively holes) on the first (respectively last) n sites is exchangeable.Comment: 28 pages, 4 figures. Changed title and introduction for clarity, added reference

Symmetric Exclusion Process with a Localized Source

We investigate the growth of the total number of particles in a symmetric exclusion process driven by a localized source. The average total number of particles entering an initially empty system grows with time as t^{1/2} in one dimension, t/log(t) in two dimensions, and linearly in higher dimensions. In one and two dimensions, the leading asymptotic behaviors for the average total number of particles are independent on the intensity of the source. We also discuss fluctuations of the total number of particles and determine the asymptotic growth of the variance in one dimension.Comment: 7 pages; small corrections, references added, final versio

Absorbing-state phase transitions with extremal dynamics

Extremal dynamics represents a path to self-organized criticality in which the order parameter is tuned to a value of zero. The order parameter is associated with a phase transition to an absorbing state. Given a process that exhibits a phase transition to an absorbing state, we define an ``extremal absorbing" process, providing the link to the associated extremal (nonabsorbing) process. Stationary properties of the latter correspond to those at the absorbing-state phase transition in the former. Studying the absorbing version of an extremal dynamics model allows to determine certain critical exponents that are not otherwise accessible. In the case of the Bak-Sneppen (BS) model, the absorbing version is closely related to the "$f$-avalanche" introduced by Paczuski, Maslov and Bak [Phys. Rev. E {\bf 53}, 414 (1996)], or, in spreading simulations to the "BS branching process" also studied by these authors. The corresponding nonextremal process belongs to the directed percolation universality class. We revisit the absorbing BS model, obtaining refined estimates for the threshold and critical exponents in one dimension. We also study an extremal version of the usual contact process, using mean-field theory and simulation. The extremal condition slows the spread of activity and modifies the critical behavior radically, defining an ``extremal directed percolation" universality class of absorbing-state phase transitions. Asymmetric updating is a relevant perturbation for this class, even though it is irrelevant for the corresponding nonextremal class.Comment: 24 pages, 11 figure

Dynamical Phase Transition in One Dimensional Traffic Flow Model with Blockage

Effects of a bottleneck in a linear trafficway is investigated using a simple cellular automaton model. Introducing a blockage site which transmit cars at some transmission probability into the rule-184 cellular automaton, we observe three different phases with increasing car concentration: Besides the free phase and the jam phase, which exist already in the pure rule-184 model, the mixed phase of these two appears at intermediate concentration with well-defined phase boundaries. This mixed phase, where cars pile up behind the blockage to form a jam region, is characterized by a constant flow. In the thermodynamic limit, we obtain the exact expressions for several characteristic quantities in terms of the car density and the transmission rate. These quantities depend strongly on the system size at the phase boundaries; We analyse these finite size effects based on the finite-size scaling.Comment: 14 pages, LaTeX 13 postscript figures available upon request,OUCMT-94-