| 1. |
- Donev, Aleksandar, et al.
(författare)
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A First-Passage Kinetic Monte Carlo algorithm for complex diffusion-reaction systems
- 2010
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 229:9, s. 3214-3236
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Tidskriftsartikel (refereegranskat)abstract
- We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The FPKMC algorithm presented here is based on the method introduced in Oppelstrup et al. [10] and is implemented in a robust and flexible framework. Unlike standard KMC algorithms such as the n-fold algorithm, FPKMC is most efficient at low densities where it replaces the many small hops needed for reactants to find each other with large first-passage hops sampled from exact time-dependent Green's functions, without sacrificing accuracy. We describe in detail the key components of the algorithm, including the event-loop and the sampling of first-passage probability distributions, and demonstrate the accuracy of the new method. We apply the FPKMC algorithm to the challenging problem of simulation of long-term irradiation of metals, relevant to the performance and aging of nuclear materials in current and future nuclear power plants. The problem of radiation damage spans many decades of time-scales, from picosecond spikes caused by primary cascades, to years of slow damage annealing and microstructure evolution. Our implementation of the FPKMC algorithm has been able to simulate the irradiation of a metal sample for durations that are orders of magnitude longer than any previous simulations using the standard Object KMC or more recent asynchronous algorithms. (C) 2010 Elsevier Inc. All rights reserved.
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| 2. |
- Oppelstrup, Tomas, 1977-, et al.
(författare)
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First-Passage Kinetic Monte Carlo method
- 2009
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 80:6, s. 066701-
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Tidskriftsartikel (refereegranskat)abstract
- We present a new effcient method for Monte Carlo simulations of diusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditionalsmall diusion hops and propagates the diusing particles over long distances through asequence of super-hops, one particle at a time. By partitioning the simulation space into nonoverlappingprotecting domains each containing only one or two particles, the algorithm factorizesthe N-body problem of collisions among multiple Brownian particles into a set of much simplersingle-body and two-body problems. Ecient propagation of particles inside their protective domainsis enabled through the use of time-dependent Green's functions (propagators) obtained assolutions for the rst-passage statistics of random walks. The resulting Monte Carlo algorithmis event-driven and asynchronous; each Brownian particle propagates inside its own protectivedomain and on its own time clock. The algorithm reproduces the statistics of the underlyingMonte-Carlo model exactly. Extensive numerical examples demonstrate that for an importantclass of diusion-reaction models the new algorithm is effcient at low particle densities, whereother existing algorithms slow down severely.
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| 3. |
- Oppelstrup, Tomas, 1977-, et al.
(författare)
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First-Passage Monte Carlo Algorithm: Diffusion without All the Hops
- 2006
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 97, s. 230602-
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Tidskriftsartikel (refereegranskat)abstract
- We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green’s functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hopsused in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicablet o many important physical situations in arbitrary integer dimensions.
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