A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that preserve the dynamics of the model are described. These include the $n$-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC) algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use of these algorithms, they are applied to some simplified models of dynamic physical systems. The models studied include a model for ion motion through a pore such as a biological ion channel and the metastable decay of the ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic algorithms, which are in the class of parallel discrete event simulations, are discussed. Efforts are made to keep the article at an elementary level by concentrating on a simple model in each case that illustrates the use of the advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure

Determination of the basic timescale in kinetic Monte Carlo simulations by comparison with cyclic-voltammetry experiments

While kinetic Monte Carlo simulations can provide long-time simulations of the dynamics of physical and chemical systems, it is not yet possible in general to identify the inverse Monte Carlo attempt frequency with a physical timescale. Here we demonstrate such an identification by comparing simulations with experimental data. Using a dynamic lattice-gas model for the electrosorption of Br on Ag(100), we measure the scan-rate dependence of the separation between positive-and negative-going peaks in cyclic-voltammetry (CV) and compare simulated and experimental peak separations. By adjusting the Monte Carlo attempt frequency, good agreement between simulated and experimental peak separations is achieved. It is also found that the uniqueness of such a determination is dependent on the relative values of the adsorption/desorption and diffusion free-energy barriers.Comment: Accepted for publication in Surface Science Letters,8 pages, 4 figure

Transient behavior in Single-File Systems

We have used Monte-Carlo methods and analytical techniques to investigate the influence of the characteristics, such as pipe length, diffusion, adsorption, desorption and reaction rates on the transient properties of Single-File Systems. The transient or the relaxation regime is the period in which the system is evolving to equilibrium. We have studied the system when all the sites are reactive and when only some of them are reactive. Comparisons between Mean-Field predictions, Cluster Approximation predictions, and Monte Carlo simulations for the relaxation time of the system are shown. We outline the cases where Mean-Field analysis gives good results compared to Dynamic Monte-Carlo results. For some specific cases we can analytically derive the relaxation time. Occupancy profiles for different distribution of the sites both for Mean-Field and simulations are compared. Different results for slow and fast reaction systems and different distribution of reactive sites are discussed.Comment: 18 pages, 19 figure

Monte Carlo-based Reliability Estimation Methods for Power Devices in Power Electronics Systems

Monte Carlo simulation has been widely used for reliability assessment of power electronic systems. In this approach, multiple simulations are carried out during the lifetime estimation of the components in power converter, e.g., power devices, where the parameter variations are considered. In the previous mission-profile based reliability assessment methods, the dynamic thermal stress profiles are usually converted into a set of static parameters. However, this simplification may introduce a certain uncertainty during the reliability assessment, since the static parameters may not be able to accurately represent the thermal stress under highly dynamic conditions. Moreover, the previous research did not take into account the correlation between the method of introducing the parameter variation and the required number of Monte Carlo simulations. This can significantly affect both the accuracy and computation burden of the Monte Carlo simulation. To address this issue, an in-depth analysis of Monte Carlo simulation applied to reliability assessment of power devices in power electronic systems is provided in this paper. Two additional Monte Carlo simulation approaches based on semi-dynamic and dynamic parameters are proposed, and their reliability evaluation results are compared with the traditional static parameter method. It is demonstrated in a case study of photovoltaic (PV) inverter application that the reliability of power converter can be overestimated up to 30% when using the static parameters

An Algorithm for Dynamic Load Balancing of Synchronous Monte Carlo Simulations on Multiprocessor Systems

We describe an algorithm for dynamic load balancing of geometrically parallelized synchronous Monte Carlo simulations of physical models. This algorithm is designed for a (heterogeneous) multiprocessor system of the MIMD type with distributed memory. The algorithm is based on a dynamic partitioning of the domain of the algorithm, taking into account the actual processor resources of the various processors of the multiprocessor system.Comment: 12 pages, uuencoded figures included, 75.93.0

Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field

It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is on the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures