Applications of Monte Carlo Methods to the Study of Far-from-Equilibrium Systems

摘要

Computer simulation techniques, such as Monte Carlo methods, molecular dynamics methods, etc., are now recognized as powerful tools in science, complementing both analytical theory and experiments. Due to the lack of a well established framework suitable for the study of far from equilibrium processes, computer simulation plays a particularly important role contributing to the understanding of these systems. The following three examples of the application of Monte Carlo methods, in that field, are presented and discussed: ⅰ) The first case addresses the superconformal filling (SCF) efficiency of nanoscale cavities by a deposited material. Based on extensive numerical simulations and using the dynamic scaling theory of interface growth, it is concluded that the process can be rationalized in terms of relevant physical and geometrical parameters. Both the numerical and theoretical predictions are in excellent agreement with recently reported experimental data for the SCF of electrodeposited copper and chemically deposited silver in confined geometries, thus giving the basis of a new tool to manage nanoengineering-related problems not completely resolved so far.ⅱ) The second example is a system of smart preys and predators that exhibits irreversible phase transitions between prey-predator coexistence and predator extinction. Within the coexistence phase, the system exhibits a transition between a regime where the densities of species remain constant and other with self-sustained oscillations at a certain "natural" frequency, respectively. It is found that in the presence of an external noise the system exhibits Coherent Stochastic Resonance only at the natural frequency. This property allows us to very accurately locate the transition points between the different regimes. ⅲ) Finally, the third case treated here corresponds to the critical behavior of driven-diffusive systems. It is shown that intrinsically anisotropic non-equilibrium systems relaxing by a dynamic process exhibit universal critical behavior during their evolution towards non-equilibrium stationary states. The study of the dynamic behavior of second-order transitions, that occur at half-density of the lattice gas systems, provides a self-consistent method for the evaluation of critical exponents that allow us to solve a longstanding controversy on the universality class and the relevant symmetries of that systems.