Dynamic Monte Carlo method

About: Dynamic Monte Carlo method is a research topic. Over the lifetime, 13294 publications have been published within this topic receiving 371256 citations.

Monte Carlo simulations of star clusters - I. First Results

Abstract: A revision of Stodoikiewicz's Monte Carlo code is used to simulate evolution of star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The first calculations for isolated, equal-mass N-body systems with three-body energy generation according to Spitzer's formulae show good agreement with direct N-body calculations for N = 2000, 4096 and 10 000 particles. The density, velocity, mass distributions, energy generation, number of binaries, etc., follow the N-body results. Only the number of escapers is slightly too high compared with N-body results, and there is no level-off anisotropy for advanced post-collapse evolution of Monte Carlo models as is seen in N-body simulations for N ≤ 2000. For simulations with N > 10 000 gravothermal oscillations are clearly visible. The calculations of N 2000, 4096, 10 000, 32 000 and 100 000 models take about 2, 6, 20, 130 and 2500 h, respectively. The Monte Carlo code is at least 105 times faster than the N-body one for N = 32 768 with special-purpose hardware. Thus it becomes possible to run several different models to improve statistical quality of the data and run individual models with N as large as 100 000. The Monte Carlo scheme can be regarded as a method which lies in the middle between direct N-body and Fokker–Planck models and combines most advantages of both methods.

Monte Carlo extension of quasi-Monte Carlo

Abstract: The paper surveys recent research on using Monte Carlo techniques to improve quasi-Monte Carlo techniques. Randomized quasi-Monte Carlo methods provide a basis for error estimation. They have, in the special case of scrambled nets, also been observed to improve accuracy. Finally, through Latin supercube sampling it is possible to use Monte Carlo methods to extend quasi-Monte Carlo methods to higher dimensional problems.

Rigorous synchronous relaxation algorithm for parallel kinetic Monte Carlo simulations of thin film growth

Abstract: We investigate the applicability of the synchronous relaxation (SR) algorithm to parallel kinetic Monte Carlo simulations of simple models of thin film growth. A variety of techniques for optimizing the parallel efficiency are also presented. We find that the parallel efficiency is determined by three main factors---the calculation overhead due to relaxation iterations to correct boundary events in neighboring processors, the (extreme) fluctuations in the number of events per cycle in each processor, and the overhead due to interprocessor communications. Due to the existence of fluctuations and the requirement of global synchronization, the SR algorithm does not scale, i.e., the parallel efficiency decreases logarithmically as the number of processors increases. The dependence of the parallel efficiency on simulation parameters such as the processor size, domain decomposition geometry, and the ratio $D∕F$ of the monomer hopping rate $D$ to the deposition rate $F$ is also discussed.