A First-Passage Kinetic Monte Carlo Algorithm for Complex Diffusion-Reaction Systems

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.Comment: See also arXiv:0905.357

Perturbative Forward Walking in the Context of the Mirror Potential Approach to the Fermion Problem

We introduce and discuss a perturbative variant of "forward walking" in Quantum Monte Carlo and develop the theory as applied to many-fermion problems

Model Fermion Monte Carlo with Correlated Pairs

The issues that prevent the development of efficient and stable algorithms for fermion Monte Carlo in continuum systems are reexamined with special reference to the implications of the "plus/minus" symmetry. This is a property of many algorithms that use signed walkers, namely that the dynamics are unchanged when the signs of the walkers are interchanged. Algorithms that obey this symmetry cannot exhibit the necessary stability. Specifically, estimates of the overlap with any antisymmetric test function cannot be bounded away from zero in the limit of many iterations. Within the framework of a diffusion Monte Carlo treatment of the Schroedinger equation, it is shown that this symmetry is easily broken for pairs of walkers while at the same time preserving the correct marginal dynamics for each member of the pair. The key is to create different classes of correlations between members of pairs and to use (at least) two distinct correlations for a pair and for the same pair withthe signs exchanged. The ideas are applied successfully for a class of simplemodel problems in two dimensions

Monte Carlo methods

This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matte