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Kinetic Monte Carlo Algorithms

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An Introduction to Kinetic Monte Carlo Simulations of Surface Reactions

Part of the book series: Lecture Notes in Physics ((LNP,volume 856))

Abstract

Kinetic Monte Carlo generates a sequence of configurations and times when the transitions between these configurations occur. This solves the master equation in the sense that a configuration α is obtained at time t with a probability P α (t) that is a solution of the master equation. There are many algorithms that yield such a sequence of configurations and which are statistically equivalent. They all need to determine repeatedly the time that the next process will occur, the type of process that will occur, and the position on the surface where the process will occur. Each of these can be determined in a number of ways, which can be combined in even more ways. This results in many algorithms. Few of them are however efficient. We discuss in detail the Variable Step Size Method, the Random Selection Method, and the First Reaction Method. We use the Variable Step Size Method to show how to handle lists of processes, different ways to make selections of processes and process types, and how computer time and memory scales with system size. Time-dependent rate constants are discusses separately as the determination of when processes take place pose special problems. Parallelization is discussed as well as some older algorithms. Some guidelines are given of how to choose an algorithm for a simulation.

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  1. ST/SKA, Eindhoven University of Technology, Eindhoven, Netherlands

    A. P. J. Jansen

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Jansen, A.P.J. (2012). Kinetic Monte Carlo Algorithms. In: An Introduction to Kinetic Monte Carlo Simulations of Surface Reactions. Lecture Notes in Physics, vol 856. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29488-4_3

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