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Kinetic Monte Carlo

Kinetic Monte Carlo (KMC) is a method for stochastically modeling "events" in a way that correctly samples the relative probabilities of each event occurring. An event can be a diffusive hop by an atom, the deposition of an atom, a spin flip in a lattice model, a chemical reaction in a biochemical network, or even a person buying a widget in a discrete-event model.

KMC models are typically "coarse-grain" in that an entire event occurs in one iteration/timestep of the simulation code, without the need to track low-level dynamics leading up to the event, e.g. atomic vibrations.

We've written an open-source KMC simulator called SPPARKS which can perform both KMC and Metropolis Monte Carlo updating of various models. The goal of SPPARKS is to provide a framework where basic algorithms for KMC and MMC are provided both in serial and parallel, and which allows new applications to be easily added. Our main focus thus far has been on-lattice KMC for materials phenonmena like grain growth, surface growth and deposition, and void growth. But we have also been working to develop off-lattice KMC applications as well.

SPPARKS can be downloaded here, and the SPPARKS doc pages describes the software in more detail.

Collaborators on SPPARKS:

This paper describes the SPPARKS KMC and MMC code, including its algorithms, code design, and applications:

Parallel simulation via SPPARKS of on-lattice kinetic and Metropolis Monte Carlo models for materials processing, J. A. Mitchell, F. Abdeljawad, C. Battaile, C. Garcia-Cardona, E. A. Holm, E. R. Homer, J. Madison, T. M. Rogers, A. P. Thompson, V. Tikare, E. Webb, S. J. Plimpton, Modelling and Simulation in Materials Science and Engineering, 31, 055001 (2023). (abstract)

This paper describes an efficient kinetic Monte Carlo algorithm, implemented in SPPARKS, which can be used for modeling biochemical reactions, a la the Gillespie Stochastic Simulation Algorithm (SSA):

A Constant-Time Kinetic Monte Carlo Algorithm for Simulation of Large Biochemical Reaction Networks, A. Slepoy, A. P. Thompson, S. J. Plimpton, J Chem Phys, 128, 205101 (2008). (abstract)

This paper describes work in SPPARKS to develop a KMC model of sintering that captures the coupled effects of grain growth, pore migration, and vacancy annihilation to the surface:

Parallel Simulation of 3D Sintering, C. G. Cardona, V. Tikare, S. J. Plimpton, Int J Computational Materials Science and Surface Engineering, 4, 37-54 (2011). (abstract)

This paper describes work to couple KMC and SPPARKS to a continuum-level description of a solid surface via the equation-free methodology:

Equation-Free Accelerated Simulations of the Morphological Relaxation of Crystal Surfaces, G. J. Wagner, X. Zhou, S. J. Plimpton, Int J for Multiscale Computational Engineering, 8, 423-439 (2010). (abstract)

This technical report gives an overall description of SPPARKS and its applications and algorithms. It includes the above J Chem Phys paper as one section:

Crossing the Mesoscale No-Man's Land via Parallel Kinetic Monte Carlo, S. Plimpton, C. Battaile, M. Chandross, L. Holm, A. Thompson, V. Tikare, G. Wagner, E. Webb, X. Zhou, C. Garcia Cardona, A. Slepoy, Sandia Report SAND2009-6226, October 2009. (abstract)

You can download the entire report via this link.