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In this work, we revisited the Ziff-Gulari-Barshad (ZGB) model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We used a method proposed recently to locate the non-equilibrium…
We present a method for computing stationary distributions for activated processes in equilibrium and non-equilibrium systems using Forward Flux Sampling (FFS). In this method, the stationary distributions are obtained directly from the…
We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform…
Rare events such as nucleation processes are of ubiquitous importance in real systems. The most popular method for nonequilibrium systems, forward flux sampling (FFS), samples rare events by using interfaces to partition the whole…
Rare events are ubiquitous in many different fields, yet they are notoriously difficult to simulate because few, if any, events are observed in a conventiona l simulation run. Over the past several decades, specialised simulation methods…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and away from both stationary and…
We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the…
Forward-flux sampling (FFS) is a path sampling technique that has gained increased popularity in recent years, and has been used to compute rates of rare event phenomena such as crystallization, condensation, hydrophobic evaporation, DNA…
An approach was developed to describe the first passage time (FPT) in multistep stochastic processes with discrete states governed by a master equation (ME). The approach is an extension of the totally absorbing boundary approach given for…
I give an overview of rare event simulation techniques to generate dynamical pathways across high free energy barriers. The methods on which I will concentrate are the reactive flux approach, transition path sampling, (replica-exchange)…
In many dynamical systems there is a large separation of time scales between typical events and "rare" events which can be the cases of interest. Rare-event rates are quite difficult to compute numerically, but they are of considerable…
Equilibrium rate theories play a crucial role in understanding rare, reactive events. However, they are inapplicable to a range of irreversible processes in systems driven far from thermodynamic equilibrium like active and biological…
In this paper we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white…
The first passage time (FPT) is a generic measure that quantifies when a random quantity reaches a specific state. We consider the FTP distribution in nonlinear stochastic biochemical networks, where obtaining exact solutions of the…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
We present the statistical method as a direct extension of the mean first-passage time concept to the analysis of molecular dynamics simulation data of a phase transformation. According to the method, the mean first-passage time…
A random distribution of inert sites is introduced in the Ziff-Gulari-Barshad model to study the phase transitions between active and poisoned states. The adsorption of ${\rm CO}$ and ${\rm O_2}$ molecules is not possible at the position of…
Fastest arrival events, where the first among many diffusing particles reaches a target, are central in triggering signal initiation in molecular stochastic systems. Classical approaches to simulate such events rely on full trajectory…