Francisco Jiménez-Morales

Periodical forcing for the control of chaos in a chemical reaction.

Control of the chaotic behavior of a chemical system can be achieved perturbing periodically some control parameters of the system. This procedure based on external forcing, which is based on the phenomenon of resonance, can change a chaotic behavior into a periodical one by means of the application of a sinusoidal perturbation. In this paper, the influence of a periodical modulation added to the parameter controlling the oxygen adsorption rate in a cellular automaton (CA) model studying CO oxidation is analyzed. This CA model considers the oxidation reaction of CO on a catalytic surface, taking into account the catalyst temperature variation in order to analyze the reaction time oscillatory behavior. Simulations of the CA model exhibit chaotic and quasiperiodical behaviors, and it can be shown that the periodical forcing strategy can suppress the chaotic dynamics by means of the stabilization of periodical solutions.

Application of shannon's entropy to classify emergent behaviors in a simulation of laser dynamics

Laser dynamics simulations have been carried out using a cellular automata model. The Shannons entropy has been used to study the different emergent behaviors exhibited by the system, mainly the laser spiking and the laser constant operation. It is also shown that the Shannons entropy of the distribution of the populations of photons and electrons reproduces the laser stability curve, in agreement with the theoretical predictions from the laser rate equations and with the experimental results.

Monte Carlo simulation of a surface reaction model with local interaction

Influence of the interaction between nearest‐neighbor adatoms in a reaction of catalyzed oxidation of carbon monoxide has been studied by Monte Carlo simulation. The transition probabilities are chosen in the Arrhenius form, and the activation energy is divided into two additive terms, corresponding to the action of the substrate and to the interaction between nearest adatoms, respectively. When the interaction makes desorption easier or hinders adsorption the behavior is similar: Three steady state regimes or phases were observed; in the first phase, the surface is poisoned by oxygen; in the second phase there is a reactive steady state in which carbon dioxide is continuously produced, and in the third phase, the surface is poisoned by carbon monoxide. The transition from the O‐poisoned phase to the reactive phase is continuous, or second order, and the transition from the reaction to the CO‐poisoned phase is first order. The same occurs when the interaction is not considered. The interaction makes the s...

Parallel implementation of a cellular automaton model for the simulation of laser dynamics

The classical modeling approach for laser study relies on the differential equations. In this paper, a cellular automaton model is proposed as an alternative for the simulation of population dynamics. Even though the model is simplified it captures the essence of laser phenomenology: (i) there is a threshold pumping rate that depends inversely on the decaying lifetime of the atoms and the photons; and (ii) depending on these lifetimes and on the pumping rate, a constant or an oscillatory behavior can be observed. More complex behaviors such as spiking and pattern formation can also be studied with the cellular automaton model.

Influence of the interaction on oscillatory behavior in a surface reaction model

Bistability and oscillations of temperature and concentrations are observed in a kinetic model, based on the oxidation of carbon monoxide on a solid surface. The macroscopic kinetic equations, which govern the reaction, are obtained by applying a closure approximation of mean-field type. With the aim of studying how the interaction affects the oscillatory behavior in the reaction, we have explicitly considered the interaction between nearest-neighbor adsorbed species, CO–CO, CO–O, and O–O. Interactions favoring CO2 production are analyzed.

Simulation of the Dynamics of Pulsed Pumped Lasers Based on Cellular Automata

Laser dynamics is traditionally modeled using differential equations. Recently, a new approach has been introduced in which laser dynamics is modeled using two-dimensional Cellular Automata (CA). In this work, we study a modified version of this model in order to simulate the dynamics of pulsed pumped lasers. The results of the CA approach are in qualitative agreement with the outcome of the numerical integration of the laser rate equations.

CELLULAR AUTOMATA AND CLUSTER COMPUTING: AN APPLICATION TO THE SIMULATION OF LASER DYNAMICS

Firstly, the application of a cellular automata (CA) model to simulate the dynamics of lasers is reviewed. With this kind of model, the macroscopic properties of the laser system emerge as a cooperative phenomenon from elementary components locally interacting under simple rules. Secondly, a parallel implementation of this kind of model for distributed-memory parallel computers is presented. Performance and scalability of this parallel implementation running on a computer cluster are analyzed, giving very satisfactory results. This confirms the feasibility of running large 3D simulations — unaffordable on an individual machine — on computer clusters, in order to simulate specific real laser systems.

A cellular automaton for the modeling of oscillations in a surface reaction

The reaction of CO and O over a catalytic surface is studied with a cellular automata (CA) model. We extend the CA model proposed by Mai and von Niessen [Phys. Rev. A 44 R6165 (1991)] taking into account the variation of the temperature of the catalyst with the aim of analyzing the existence of oscillations in this reaction. The rate constants for different processes which govern the reaction are chosen in the Arrhenius form. Quasiperiodic, aperiodic, O-poisoned, and CO-poisoned regimes are observed depending on the temperature relaxation parameter. The results from the CA model presented are in agreement with several oscillatory behaviors which the catalyzed oxidation of CO exhibits.

Application of Shannon's entropy to classify emergent behaviors in a simulation of laser dynamics

Laser dynamics simulations have been carried out using a cellular automata model. The Shannons entropy has been used to study the different emergent behaviors exhibited by the system, mainly the laser spiking and the laser constant operation. It is also shown that the Shannons entropy of the distribution of the populations of photons and electrons reproduces the laser stability curve, in agreement with the theoretical predictions from the laser rate equations and with the experimental results.

Evolving One Dimensional Cellular Automata to Perform Non-trivial Collective Behavior Task: One Case Study

Here we present preliminary results in which a genetic algorithm (GA) is used to evolve one-dimensional binary-state cellular automata (CA) to perform a non-trivial task requiring collective behavior. Using a fitness function that is an average area in the iterative map,the GA discovers rules that produce a period-3 oscillation in the concentration of 1s in the lattice. We study one run in which the final state reached by the best evolved rule consists of a regular pattern plus some defects. The structural organization of the CA dynamics is uncovered using the tools of computational mechanics.