This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic non-equilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.

Non-equilibrium critical phenomena and phase transitions into absorbing states

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate $(C)$ or to defect $(D)$ unconditionally. The players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques, we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect. In the limits $\stackrel{\ensuremath{\rightarrow}}{c}0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.

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Evolutionary prisoner's dilemma game on a square lattice

Preface 1. Introduction 2. Cellular automata modeling 3. Statistical mechanics of lattice gas 4. Diffusion phenomena 5. Reaction-diffusion processes 6. Non-equilibrium phase transitions 7. Other models and applications Bibliography Glossary Index.

Cellular automata modeling of physical systems

This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic nonequilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.

Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States

Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1405&context=physastro_pubs

Random and cooperative sequential adsorption

An irreversible kinetic surface-reaction model, based upon the reaction of carbon monoxide and oxygen on a catalyst surface, is presented. It is found by computer simulation that the adsorbed molecules on the surface undergo both first- and second-order kinetic phase transitions. These transitions correspond to the "poisoning" phenomenon seen on catalysts. Interesting transient and periodic behavior is also seen.

Kinetic phase transitions in an irreversible surface-reaction model.

Carbon monoxide oxidation under transient conditions: A fourier-transform infrared transmission spectroscopy study

Catalytic oxidation of CO on alumina-supported platinum was studied in a tubular isothermal reactor with applied concentration transients. A completely automated reactor system capable of switching frequencies as high as 0.2 Hz was constructed.

Concentration cycling resulted in reaction rates that were much higher than the maximum rate achievable at steady-state operation. Mapping of the time-averaged carbon dioxide production rate in the time-period duty-fraction plane, resulted in a unique global maximum. We find that the maximum in rate occurs when the switching times are comparable to the characteristic time of the surface reaction. Results of our experiments also rule out significant contribution from the Eley-Rideal mechanism at the temperature range of this work (below 120°C).

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A dynamic study of CO oxidation on supported platinum

Co oxidation on Pd/Al2O3. Transient response and rate enhancement through forced concentration cycling

Forced concentration cycling was used to study the feasibility of rate and selectivity enhancement in FT synthesis. Our results indicate that it is possible to increase the time averaged rate of reaction by as much as 210% over the equivalent steady state rate. The improvements in selectivity are more complex. In general concentration cycling leads to increased rates of methane production. Under certain operating conditions it is possible to enhance the selectivity to propane by as much as 400% over the equivalent steady state rate. Selectivity enhancements for ethane and butane were also observed Analysis of the transient response data indicates that perhaps there are separate sites for methane and higher hydrocarbon synthesis. Transient response experiments showed that higher hydrocarbons are always produced before methane. During transient response and periodic operation methane production was found to be in phase with water production

Yoav Barshad

Papers

Kinetic phase transitions in an irreversible surface-reaction model.

Carbon monoxide oxidation under transient conditions: A fourier-transform infrared transmission spectroscopy study

A dynamic study of CO oxidation on supported platinum

Co oxidation on Pd/Al2O3. Transient response and rate enhancement through forced concentration cycling

MODIFICATION OF PRODUCT DISTRIBUTION THROUGH PERIODIC OPERATION: FISCHER TROPSCH SYNTHESIS OVER Ru/A12O3