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 algorith
m 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 Greens 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.
We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the diffusing pa
rticles over long distances through a sequence of super-hops, one particle at a time. By partitioning the simulation space into non-overlapping protecting domains each containing only one or two particles, the algorithm factorizes the N-body problem of collisions among multiple Brownian particles into a set of much simpler single-body and two-body problems. Efficient propagation of particles inside their protective domains is enabled through the use of time-dependent Greens functions (propagators) obtained as solutions for the first-passage statistics of random walks. The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock. The algorithm reproduces the statistics of the underlying Monte-Carlo model exactly. Extensive numerical examples demonstrate that for an important class of diffusion-reaction models the new algorithm is efficient at low particle densities, where other existing algorithms slow down severely.
In the paper taking the assumption of the slowness of the change of the parameters of the vertically stratified medium in the horizontal direction and in time, the evolution of the non-harmonic wave packages of the internal gravity waves has been ana
lyzed. The concrete form of the wave packages can be expressed through some model functions and is defined by the local behavior of the dispersive curves of the separate modes near to the corresponding special points. The solution of this problem is possible with the help of the modified variant of the special-time ray method offered by the authors (the method of geometrical optics), the basic difference of which consists that the asymptotic representation of the solution may be found in the form the series of the non-integer degrees of some small parameter. At that the exponent depends on the concrete form of representation of this package. The obvious kind of the representation is determined from the principle of the localness and the asymptotic behavior of the solution in the stationary and the horizontally-homogeneous case. The phases of the wave packages are determined from the corresponding equations of the eikonal, which can be solved numerically on the characteristics (rays). Amplitudes of the wave packages are determined from the laws of conservation of the some invariants along the characteristics (rays).
