Coarse-grained lattice kinetic Monte Carlo simulation of systems of strongly interacting particles

Abstract

A general approach is presented for spatially coarse-graining lattice kinetic Monte Carlo (LKMC) simulations of systems containing strongly interacting particles. While previous work has relied on approximations that are valid in the limit of weak interactions, here we show that it is possible to compute coarse-grained transition rates for strongly interacting systems without a large computational burden. A two-dimensional square lattice is employed on which a collection of (supersaturated) strongly interacting particles is allowed to reversibly evolve into clusters. A detailed analysis is presented of the various approximations applied in LKMC coarse graining, and a number of numerical closure rules are contrasted and compared. In each case, the overall cluster size distribution and individual cluster structures are used to assess the accuracy of the coarse-graining approach. The resulting closure approach is shown to provide an excellent coarse-grained representation of the systems considered in this study. A general approach is presented for spatially coarse-graining lattice kinetic Monte Carlo ͑LKMC͒ simulations of systems containing strongly interacting particles. While previous work has relied on approximations that are valid in the limit of weak interactions, here we show that it is possible to compute coarse-grained transition rates for strongly interacting systems without a large computational burden. A two-dimensional square lattice is employed on which a collection of ͑supersaturated͒ strongly interacting particles is allowed to reversibly evolve into clusters. A detailed analysis is presented of the various approximations applied in LKMC coarse graining, and a number of numerical closure rules are contrasted and compared. In each case, the overall cluster size distribution and individual cluster structures are used to assess the accuracy of the coarse-graining approach. The resulting closure approach is shown to provide an excellent coarse-grained representation of the systems considered in this study.

Modeling and control of ibuprofen crystal growth and size distribution

“…On the other hand, kMC simulations allow for more realistic length and time scales by using rate equations that describe different microscopic phenomena. To this end, kMC simulation methods have been widely used to simulate molecular-level phenomena like crystal nucleation, growth, and aggregation (Bortz et al, 1975;Dai et al, 2005Dai et al, , 2008Gillespie, 1976Gillespie, , 2007Rathinam et al, 2003;Reese et al, 2001;Snyder et al, 2005;Gilmer and Bennema, 1972;Kwon et al 2013aKwon et al , b, 2014Jolliffe and Gerogiorgis, 2015). Furthermore, kMC simulation methods have been successfully applied to compute the net crystal steady-state growth rate accounting for the dependence of the desorption and migration rates on the local surface microconfiguration.…”

Information-theoretic tools for parametrized coarse-graining of non-equilibrium extended systems

“…In the case of continuous time processes such as Kinetic Monte Carlo, the coarse-grained stochastic process is defined in terms of coarse transition ratesc(η, η ′ ) which captures macroscopic information from the fine scale rates c(σ, σ ′ ). For example, for stochastic lattice systems, approximate coarse rate functions are explicitly known from coarse graining (CG) techniques of 10,21,25 , see (36). Similarly, when we consider temporally discretized stochastic processes such as Langevin Dynamics, the coarsegrained process is given in terms of transition probabilitiesp(η, η ′ ) which capture macroscopic information from the fine scale transition probabilities p(σ, σ ′ ).…”

Improving the acceptance in Monte Carlo simulations: Sampling through intermediate states

“…[3][4][5][6] and the references therein) as well as for the coarse-graining from the atomistic to the mesoscopic scale [7][8][9][10][11][12][13][14][15][16][17][18]. Ranging from properly tailored biases [5,[19][20][21][22][23][24][25][26] and the sampling of 'rejectable' states [27,28] to the combination of Nonequilibrium Candidate Monte Carlo with Configurational Freezing [29][30][31], up to now a large number of strategies and alternative algorithms aimed to improve the acceptance of random moves constitute the vast realm of MC methods for the simulation of physical systems.…”