Site-bond representation and self-duality for totalistic probabilistic cellular automata

We study the one-dimensional two-state totalistic probabilistic cellular automata (TPCA) having an absorbing state with long-range interactions, which can be considered as a natural extension of the Domany-Kinzel model. We establish the conditions for existence of a site-bond representation and self-dual property. Moreover we present an expression of a set-to-set connectedness between two sets, a matrix expression for a condition of the self-duality, and a convergence theorem for the TPCA.Comment: 11 pages, minor corrections, journal reference adde

Noise driven dynamic phase transition in a a one dimensional Ising-like model

The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $\beta$ such that $\beta =0$ corresponds to the Ising model and $\beta \to \infty$ to the original model I. The equilibrium behaviour for any value of $\beta$ is identical: a homogeneous state. We argue, from the behaviour of the dynamical exponent $z$,that for any $\beta \neq 0$, the system belongs to the dynamical class of model I indicating a dynamic phase transition at $\beta = 0$. On the other hand, the persistence probabilities in a system of $L$ spins saturate at a value $P_{sat}(\beta, L) = (\beta/L)^{\alpha}f(\beta)$, where $\alpha$ remains constant for all $\beta \neq 0$ supporting the existence of the dynamic phase transition at $\beta =0$. The scaling function $f(\beta)$ shows a crossover behaviour with $f(\beta) = \rm{constant}$ for $\beta <<1$ and $f(\beta) \propto \beta^{-\alpha}$ for $\beta >>1$.Comment: 4 pages, 5 figures, accepted version in Physical Review

Exact results for one dimensional stochastic cellular automata for different types of updates

We study two common types of time-noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions. We first construct the stationary states using the matrix product formalism. This construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates. Using this connection, we derive explicit relations between the densities and correlation functions for these different stationary states.Comment: 7 pages, Late

The contact process in heterogeneous and weakly-disordered systems

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents $\beta$ (from series expansion) and $\eta$ (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation (DP) universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.Comment: 5 pages, 3 figure

Evolutionary dynamics on degree-heterogeneous graphs

The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process (IP) dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for VM dynamics and to 1/k for IP dynamics.Comment: 4 pages, 4 figures, 2 column revtex4 format. Revisions in response to referee comments for publication in PRL. The version on arxiv.org has one more figure than the published PR

Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics

Cellular automata are widely used to model real-world dynamics. We show using the Domany-Kinzel probabilistic cellular automata that alternating two supercritical dynamics can result in subcritical dynamics in which the population dies out. The analysis of the original and reduced models reveals generality of this paradoxical behavior, which suggests that autonomous or man-made periodic or random environmental changes can cause extinction in otherwise safe population dynamics. Our model also realizes another scenario for the Parrondo's paradox to occur, namely, spatial extensions.Comment: 8 figure

Non-equilibrium mean-field theories on scale-free networks

Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction-diffusion processes. The validity of our non-equilibrium theory is furtherly supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks.Comment: 4 pages, no figures, major changes in the structure of the pape

The contact process in disordered and periodic binary two-dimensional lattices

The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory. Phase-separation lines calculated numerically are found to agree well with analytical predictions around the homogeneous point. For the disordered case, values of static scaling exponents obtained via quasi-stationary simulations are found to change with disorder strength. In particular, the finite-size scaling exponent of the density of infected sites approaches a value consistent with the existence of an infinite-randomness fixed point as conjectured before for the 2d disordered CP. At the same time, both dynamical and static scaling exponents are found to coincide with the values established for the homogeneous case thus confirming that the contact process in a heterogeneous environment belongs to the directed percolation universality class.Comment: submitted to Physical Review

Maintaining Aircraft Orientation Awareness with Audio Displays

This study was conducted to determine an appropriate task with which to test alternative orientation display formats, and to test a preliminary set of audio orientation symbology sets. Participants were required to perform three tasks simultaneously. The first task was a visual search (target designation) task. The second task was a radar monitoring task. Both of these tasks were performed on a head-down display. The third task consisted of monitoring aircraft orientation on a head-up display. The third task employed the study’s one independent variable – orientation symbology sets. When performing the aircraft orientation task, orientation was displayed in three ways: visual only, visual plus discrete audio orientation information, and visual plus continuous audio orientation information. Performance measures on all three tasks were collected. Results showed that participants responded more quickly to changes in aircraft orientation with the presence of discrete audio orientation information. Lessons learned about the tasks chosen for this study and the audio display symbology sets are discussed

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