Coarse-grained stochastic processes for microscopic lattice systems.
Diverse scientific disciplines ranging from materials science to catalysis to biomolecular dynamics to climate modeling involve nonlinear interactions across a large range of physically significant length scales. Here a class of coarse-grained stochastic processes and corresponding Monte Carlo simulation methods, describing computationally feasible mesoscopic length scales, are derived directly from microscopic lattice systems. It is demonstrated below that the coarse-grained stochastic models can capture large-scale structures while retaining significant microscopic information. The requirement of detailed balance is used as a systematic design principle to guarantee correct noise fluctuations for the coarse-grained model. The coarse-grained stochastic algorithms provide large computational savings without increasing programming complexity or computer time per executive event compared to microscopic Monte Carlo simulations.
Katsoulakis
Markos A
MA
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA.
Majda
Andrew J
AJ
Vlachos
Dionisios G
DG
D000465:Algorithms; D055592:Biophysical Phenomena; D001703:Biophysics; D007700:Kinetics; D008853:Microscopy / Q000379:methods*; D009010:Monte Carlo Method; D013997:Time Factors