- 8:55 AM

Temporal Coarse-Graining of Lattice Kinetic Monte Carlo Simulations

Dionisios G. Vlachos, Department of Chemical Engineering, University of Delaware, 150 Academy Street, Newark, DE 19716

Kinetic Monte Carlo (KMC) simulation on lattices has been widely used in diverse areas such as crystal growth, surface reactions, isotherms, diffusion on surfaces and in microporous materials, defects in materials, and biology to name a few 1-6. KMC simulation is fairly slow for three reasons, namely (i) calculation of all microscopic rates (hereafter also termed transition probabilities per unit time) at each MC trial, (ii) execution of one event (at best) at a time, and (iii) separation of time scales, usually arising from a disparity in activation energies of various processes. Recent work attempts to overcome these issues, but the majority of research has focused on well-mixed systems with limited exceptions that focus on spatial KMC 7-12. In this paper we describe a temporal coarse-graining method for lattice KMC simulation. The new method combines the recently introduced t-leap method for well-mixed systems 13 with microscopic lattices without violating the basic premises of the coarse method. As a result, one can execute simultaneously all processes several times resulting in large time steps advancements of the time clock. An example from crystal growth with the simple solid-on-solid approximation illustrates the implementation of the technique. The new technique can provide substantial acceleration. More importantly, it enables much easier implementation than currently one-at-a time continuous time spatial KMC methods.

[1] G. H. Gilmer and P. Bennema, "Simulation of crystal growth with surface diffusion", J. Appl. Phys. 43, 1347-1360 (1972). [2] G. Gilmer, "Computer models of crystal growth", Science 208, 355-363 (1980). [3] R. M. Ziff, E. Gulari, and Y. Barshad, "Kinetic phase transitions in an irreversible surface-reaction model", Phys. Rev. Letters 56, 2553-2556 (1986). [4] S. M. Auerbach, "Theory and simulation of jump dynamics, diffusion and phase equilibrium in nanopores", Int. Rev. Phys. Chem. 19, 155-198 (2000). [5] P. J. Woolf and J. J. Linderman, "Self organization of membrane proteins via dimerization", Biophys. Chem. 104, 217227 (2003). [6] T. A. J. Duke, N. Le Novere, and D. Bray, "Conformational spread in a ring of proteins: A stochastic approach to allostery", J. Mol. Bio. 308, 541-553 (2001). [7] M. Katsoulakis, A. J. Majda, and D. G. Vlachos, "Coarse-grained stochastic processes for microscopic lattice systems", Proc. Natl. Acad. Sci. 100, 782-787 (2003). [8] M. A. Katsoulakis, A. J. Majda, and D. G. Vlachos, "Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems", J. Comp. Phys. 186, 250-278 (2003). [9] M. A. Katsoulakis and D. G. Vlachos, "Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles", J. Chem. Phys. 119, 9412-9428 (2003). [10] M. A. Katsoulakis and J. Trashorras, "Information loss in coarse-graining of stochastic particle dynamics", J. Stat. Phys. accepted (2005). [11] A. Chatterjee, D. G. Vlachos, and M. Katsoulakis, "Numerical assessment of theoretical error estimates in coarse-grained kinetic Monte Carlo simulations: Application to surface diffusion", Int. J. Multiscale Comp. Eng. 3, 59-70 (2005). [12] A. Chatterjee, M. A. Katsoulakis, and D. G. Vlachos, "Spatially adaptive grand canonical ensemble Monte Carlo simulations", Phys. Rev. E 71, 0267021-0267026 (2005). [13] D. T. Gillespie, "Approximate accelerated stochastic simulation of chemically reacting systems", J. Chem. Phys. 115, 1716-1733 (2001).