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Theoretical and numerical comparison of some sampling methods for molecular dynamics. (English) Zbl 1138.82341
Summary: The purpose of the present article is to compare different phase-space sampling methods, such as purely stochastic methods (rejection method, metropolized independence sampler, importance sampling), stochastically perturbed molecular dynamics methods (hybrid Monte Carlo, Langevin dynamics, biased random walk), and purely deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive Multiple Thermostats (RMT) methods). After recalling some theoretical convergence properties for the various methods, we provide some new convergence results for the hybrid Monte Carlo scheme, requiring weaker (and easier to check) conditions than previously known conditions. We then turn to the numerical efficiency of the sampling schemes for a benchmark model of linear alkane molecules. In particular, the numerical distributions that are generated are compared in a systematic way, on the basis of some quantitative convergence indicators.

MSC:
82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
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