A First-Passage Kinetic Monte Carlo Algorithm for Complex Diffusion-Reaction Systems
arXiv:0905.3576 · doi:10.1016/j.jcp.2009.12.038
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 [Phys. Rev. Lett., 97:230602, 2006] 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.
See also arXiv:0905.3575
References in corpus (2)
Cited by in corpus (25)
- Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
- A Convergent Reaction-Diffusion Master Equation
- Minimal coarse-grained models for molecular self-organisation in biology
- Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach
- MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
- A Comparison of Bimolecular Reaction Models for Stochastic Reaction Diffusion Systems
- Event Driven Langevin simulations of Hard Spheres
- Efficient Reactive Brownian Dynamics
- An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions
- A Minimally-Resolved Immersed Boundary Model for Reaction-Diffusion Problems
- Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics
- A First-Passage Kinetic Monte Carlo Method for Reaction-Drift-Diffusion Processes
- Grand canonical diffusion-influenced reactions: a stochastic theory with applications to multiscale reaction-diffusion simulations
- An efficient multi-scale Green's Functions Reaction Dynamics scheme
- Analysis and design of jump coefficients in discrete stochastic diffusion models
- Efficient kinetic Monte Carlo method for reaction-diffusion processes with spatially varying annihilation rates
- Numerical analysis of homogeneous and inhomogeneous intermittent search strategies
- Detailed Balance for Particle Models of Reversible Reactions in Bounded Domains
- Point-particle method to compute diffusion-limited cellular uptake
- Single molecule simulations in complex geometries with embedded dynamic one-dimensional structures
- Simulating Stochastic Reaction-Diffusion Systems on and within Moving Boundaries
- Absorption kinetics of vacancies by cavities in Aluminum: numerical characterization of sink strengths and first-passage statistics through Krylov subspace projection and eigenvalue deflation
- Reaction-drift-diffusion models from master equations: application to material defects
- On the formalization of Asynchronous First Passage Algorithms
- Emergence of sector and spiral patterns from a two-species mutualistic cross-feeding model