CiteULike: タグ: kmc

INTRODUCTION TO THE KINETIC MONTE CARLO METHOD

Arthur Voter — 2007-10-13T11:41:00-00:00

Radiation Effects in Solids (2007), pp. 1-23.

Monte Carlo refers to a broad class of algorithms that solve problems through the use of random numbers. They .rst emerged in the late 1940’s and 1950’s as electronic computers came into use [1], and the name means just what it sounds like, whimsically referring to the random nature of the gambling at Monte Carlo, Monaco. The most famous of the Monte Carlo methods is the Metropolis algorithm [2], invented just over 50 years ago at Los Alamos National Laboratory. Metropolis Monte Carlo (which is not the subject of this chapter) offers an elegant and powerful way to generate a sampling of geometries appropriate for a desired physical ensemble, such as a thermal ensemble. This is accomplished through surprisingly simple rules, involving almost nothing more than moving one atom at a time by a small random displacement. The Metropolis algorithm and the numerous methods built on it are at the heart of many, if not most, of the simulations studies of equilibrium properties of physical systems.

Net-event kinetic Monte Carlo for overcoming stiffness in spatially homogeneous and distributed systems

MA Snyder — 2008-03-26T17:36:49-00:00

Computers & Chemical Engineering, Vol. 29, No. 4. (15 March 2005), pp. 701-712.

A technique, termed net-event kinetic Monte Carlo (NE-KMC), is presented for overcoming large disparities in time scale that may render conventional KMC inefficient or intractable when fast reversible processes exist. The success of this approach derives from the consolidation of fast reversible processes into single "net events". The resulting self-regulating method appropriately samples rare events even when partial equilibrium (PE) exists between fast reversible microscopic processes. Moreover, we show that computational savings over conventional KMC are proportional to the separation in time scales between the fast reversible process and rare events. We illustrate the capabilities of this new technique for a homogeneous series reaction system, and extend the net-event concept to distributed systems where multiple microscopic processes occur simultaneously. In a culminating example, we combine the time and length scale capabilities of NE-KMC and adaptive coarse-grained MC, respectively, to stochastically model diffusion through a realistically thick membrane.

Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

Tim Schulze — 2008-03-26T18:57:17-00:00

Journal of Computational Physics, Vol. 189, No. 1. (20 July 2003), pp. 197-211.

We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.

A Monte Carlo study of CO oxidation with oscillations induced by site blocking

APJ Jansen — 2008-06-06T18:32:44-00:00

The Journal of Chemical Physics, Vol. 106, No. 5. (1997), pp. 2038-2044.

Theoretical foundations of dynamical Monte Carlo simulations

Kristen Fichthorn — 2008-05-10T02:13:22-00:00

The Journal of Chemical Physics, Vol. 95, No. 2. (1991), pp. 1090-1096.

A Monte Carlo simulation study of lipid bilayer formation on hydrophilic substrates from vesicle solutions

Zheming Zheng — 2008-06-06T19:06:13-00:00

The Journal of Chemical Physics, Vol. 124, No. 6. (2006)

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Monte Carlo studies of vacancy migration in binary ordered alloys: I

WM Young — 2007-03-12T14:22:35-00:00

Proceedings of the Physical Society, Vol. 89, No. 3. (1966), pp. 735-746.

Using a Monte Carlo technique, a simulation study is made of vacancy migration in the binary ordered alloys AB (simple cubic) and B$_3$A (face-centred cubic). The resulting self-diffusion is calculated and in the first case compares very favourably with the existing experimental results of Kuper et al. for a body-centred binary alloy. Quite different results are predicted for an alloy of form B$_3$A and it is hoped that comparison with experiment will establish the importance of the isolated-vacancy mechanism as the means for producing self-diffusion.

Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table

Graeme Henkelman — 2006-01-31T18:10:07-00:00

The Journal of Chemical Physics, Vol. 115, No. 21. (2001), pp. 9657-9666.

We present a method for carrying out long time scale dynamics simulations within the harmonic transition state theory approximation. For each state of the system, characterized by a local minimum on the potential energy surface, multiple searches for saddle points are carried out using random initial directions. The dimer method is used for the saddle point searches and the rate for each transition mechanism is estimated using harmonic transition state theory. Transitions are selected and the clock advanced according to the kinetic Monte Carlo algorithm. Unlike traditional applications of kinetic Monte Carlo, the atoms are not assumed to sit on lattice sites and a list of all possible transitions need not be specified beforehand. Rather, the relevant transitions are found on the fly during the simulation. A multiple time scale simulation of Al(100) crystal growth is presented where the deposition event, occurring on the time scale of picoseconds, is simulated by ordinary classical dynamics, but the time interval in between deposition events, on the order of milliseconds, is simulated by the long time scale algorithm. The Al(100) surface is found to grow remarkably smooth, even at 30 K because of concerted displacements of multiple atoms with significantly lower activation energy than adatom diffusion on the flat terrace. ©2001 American Institute of Physics.