Related papers: The Approach to Ergodicity in Monte Carlo Simulati…
To better understand the capture process by a nanopore, we introduce an efficient Kinetic Monte Carlo (KMC) algorithm that can simulate long times and large system sizes by mapping the dynamic of a point-like particle in a 3D spherically…
We report microcanonical Monte Carlo simulations of melting and superheating of a generic, Lennard-Jones system starting from the crystalline phase. The isochoric curve, the melting temperature $T_m$ and the critical superheating…
The finite-size scaling method in the equilibrium Monte Carlo(MC) simulations and the finite-time scaling method in the nonequilibrium-relaxation simulations are compromised. MC time data of various physical quantities are scaled by the MC…
A quantitative measure of convergence to effective ergodicity, the Thirumalai-Mountain (TM) metric, is applied to Metropolis and Glauber single-spin-flip dynamics. In computing this measure, finite lattice ensemble averages are obtained…
We experiment with a massively parallel implementation of an algorithm for simulating the dynamics of metastable decay in kinetic Ising models. The parallel scheme is directly applicable to a wide range of stochastic cellular automata where…
A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations,…
The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…
We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution of the quantity of interest, the computation cost across…
The Monte Carlo (MC) method is the most common technique used for uncertainty quantification, due to its simplicity and good statistical results. However, its computational cost is extremely high, and, in many cases, prohibitive.…
We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid…
We present and analyze a micro/macro acceleration technique for the Monte Carlo simulation of stochastic differential equations (SDEs) in which there is a separation between the (fast) time-scale on which individual trajectories of the SDE…
An intercomparison of microdosimetric and nanodosimetric quantities simulated Monte Carlo codes is in progress with the goal of assessing the uncertainty contribution to simulated results due to the uncertainties of the electron interaction…
We develop a biased Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels. Given a trajectory with a fixed number of collisions, the algorithm modifies both the waiting…
We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three colour model, appears to have a dynamic exponent close to zero, making it…
The advances in materials and biological sciences have necessitated the use of molecular simulations to study polymers. The Markov chain Monte Carlo simulations enable the sampling of relevant microstates of polymeric systems by traversing…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
Taking the two-dimensional Ising model for example, short-time behavior of critical dynamics with a conserved order parameter is investigated by Monte Carlo simulations. Scaling behavior is observed, but the dynamic exponent $z$ is updating…
The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic non-stationary statistical properties of its fluctuations. Here, we study…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…