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One of the most active areas of physics in the last decades has been that of critical phenomena, and Monte Carlo simulations have played an important role as a guide for the validation and prediction of system properties close to the…
The approach to the ergodic limit in Monte Carlo simulations is studied using both analytic and numerical methods. With the help of a stochastic model, a metric is defined that enables the examination of a simulation in both the ergodic and…
Motivated by the way Japanese tatami mats are placed on the floor, we consider domino tilings with a constraint and estimate the number of such tilings of plane regions. We map the system onto a monomer-dimer model with a novel local…
We study kinetic Monte-Carlo (KMC) descriptions of active particles. By relying on large discrete time steps, KMC algorithms accelerate the relaxational dynamics of active systems towards their steady-state. We show, however, that their…
Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo method with the appealing feature of being amenable to parallel computing. At each iteration, it samples several candidates for the next state of the Markov chain and…
Monte Carlo methods are used to study the phase transition in ammonium chloride from the orientationally ordered $\delta$ phase to the orientationally disordered $\gamma$ phase. An effective pair potential is used to model the interaction…
Successful computer studies of glass-forming materials need to overcome both the natural tendency to structural ordering and the dramatic increase of relaxation times at low temperatures. We present a comprehensive analysis of eleven…
We demonstrate that the multicanonical approach is not restricted to Monte Carlo simulations, but can also be applied to simulation techniques such as molecular dynamics, Langevin, and hybrid Monte Carlo algorithms. The effectiveness of the…
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov…
We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that…
We point out that a newly introduced recursive algorithm for lattice polymers has a much wider range of applicability. In particular, we apply it to the simulation of off-lattice polymers with Lennard-Jones potentials between non-bonded…
We present an enhanced off-lattice kinetic Monte Carlo (OLKMC) model, based on a new method for tolerant classification of atomistic local-environments that is invariant under Euclidean-transformations and permutations of atoms. Our method…
The kinetic Monte Carlo method is used to model the dynamic properties of proton diffusion in anhydrous proton conductors. The results have been discussed with reference to a two-step process called the Grotthuss mechanism. There is a…
For a wide class of applications of the Monte Carlo method, we describe a general sampling methodology that is guaranteed to converge to a specified equilibrium distribution function. The method is distinct from that of Metropolis in that…
In simulations of crystals, unlike liquids or gases, it may happen that the properties of the studied system depend not only on the volume of the simulation cell but also on its shape. For such cases it is desirable to change the shape of…
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…
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…
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…
Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of…
Although histogram methods have been extremely effective for analyzing data from Monte Carlo simulations, they do have certain limitations, including the range over which they are valid and the difficulties of combining data from…