Related papers: Cell Escape Probabilities for Markov Processes on …
Particle-in-cell with Monte Carlo collisions (PIC/MCC) is a fully kinetic, particle based numerical simulation method with increasing popularity in the field of low temperature gas discharge physics. Already in its simplest form…
Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…
Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to…
This article reviews the basic computational techniques for carrying out multi-scale simulations using statistical methods, with the focus on simulations of epitaxial growth. First, the statistical-physics background behind Monte Carlo…
We present a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. Formulating the Monte Carlo method from the viewpoint of cells rather than photons allows us to separate local and…
This review article is intended as a practical guide for newcomers to the field of kinetic Monte Carlo (KMC) simulations, and specifically to lattice KMC simulations as prevalently used for surface and interface applications. We will…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
For Cox processes we construct a Markov process with increasing paths to couple the condensations of the Cox process in a monotone way. A similar procedure procedure yields an analogue Markov process for the P\'olya sum process. Moreover,…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In…
Simulations often involve the use of model parameters which are unknown or uncertain. For this reason, simulation experiments are often repeated for multiple combinations of parameter values, often iterating through parameter values lying…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
The escape of particles through a narrow absorbing gate in confined domains is a abundant phenomenon in various systems in physics, chemistry and molecular biophysics. We consider the narrow escape problem in a cellular flow when the two…
Cellular automata lattice gases are useful systems for systematically exploring the connections between non-equilibrium statisitcal mechanics and dynamical systems theory. Here the chaotic properties of a Lorentz lattice gas are studied…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that…
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…
We present the Monte Carlo with Absorbing Markov Chains (MCAMC) method for extremely long kinetic Monte Carlo simulations. The MCAMC algorithm does not modify the system dynamics. It is extremely useful for models with discrete state spaces…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…