Monte Carlo simulation methods systems

This method avoids the convergence and accuracy problems of molecular dynamics or Monte Carlo simulations of systems containing explicit solvent molecules, by evaluating the electrostatic free energy of just one solute conformation surrounded by a dielectric continuum, and by adding the surface term and an estimate of the loss of the configurational entropy upon binding.77... 

Figure 11.7 A schematic illustration of the Monte Carlo simulation method for computing the stochastic trajectories of a chemical reaction system following the CME. Two random numbers, r and r2, are sampled from a uniform distribution to simulate each stochastic step r determines when to move, and r2 determines where to move. For a given state of a master equation graph shown in the upper panel, there are four outward reactions, labeled 1-4, each with their corresponding rate constants q, (i = 1, 2, , 4). The upper and lower panels illustrate, respectively, the calculation of the random time T associated with a stochastic move, and the probability pm of moving to state m.

Suter and co-workers presented a novel class of Monte Carlo simulation methods aimed at dense polymer systems.i Properties like the chemical potential and solubilities in polymer systems may be calculated from simulations of this type. The authors presented results on the solubility of long alkanes in polyethylene and for various solutions of long alkanes in near-critical solvents. 

Although Eqs. (26)-(28) and (29)-(31) are quite simple systems, there is an even simpler model that predicts oscillatory behavior. Fichthorn et al. (277) used a Monte Carlo simulation method to model the simplest three-step Langmuir-Hinshelwood mechanism possible ... 

A. Sandvik and J. Kurkijarvi (1991) Quantum Monte Carlo simulation method for spin systems. Phys. Rev. B 43, p. 5950... 

The molecular dynamics and Monte Carlo simulation methods differ in a variety of ways. The most obvious difference is that molecular dynamics provides information about the time dependence of the properties of the system whereas there is no temporal relationship between successive Monte Carlo configurations. In a Monte Carlo simulation the outcome of each trial move depends only upon its immediate predecessor, whereas in molecular dynamics it is possible to predict the configuration of the system at any time in the future - or indeed at any time in the past. Molecular dynamics has a kinetic energy contribution to the total energy whereas in a Monte Carlo simulation the total energy is determined directly from the potential energy function. The two simulation methods also sample from different ensembles. Molecular dynamics is traditionally performed under conditions of constant number of particles (N), volume (V) and energy (E) (the microcanonical or constant NVE ensemble) whereas a traditional Monte Carlo simulation samples from the canonical ensemble (constant N, V and temperature, T). Both the molecular dynamics and Monte Carlo techniques can be modified to sample from other ensembles for example, molecular dynamics can be adapted to simulate from the canonical ensemble. Two other ensembles are common ... 

The properties of the Gibbs ensemble Monte Carlo simulation method have been examined in great detail using simple systems sudi as the Lennard-Jones fluid and simple gases. A... 

Over the last two decades, there has been increasing interest in probabilistic, or stochastic, robust control theory. Monte Carlo simulation methods have been used to synthesize and analyze controllers for uncertain systems [170,255], First- and second-order reliability methods were incorporated to compute the probable performance of linear-quadratic-regulator... 

The thermodynamic properties for a system of N molecules (or N atoms) can be rigorously accounted for using statistical mechanics. Monte Carlo simulation methods provide the foundation for numerically simulating the configurational integral shown in Eq. (B13) that arise from the statistical mechanics treatment. 

A special kind of compartment model is the two-environment model, which divides the tank into micro- and macromixers, the numbers of which depend on the number of impellers. The flow behavior in the macromixer is characterized by the circulation-time distribution (Figure 3.3). Bajpai and Reuss [22] used a Monte Carlo simulation method in which the physical system of the macromixer was divided into a number of discrete elements. In each of these elements, the reaction process was simulated for a short period, at the end of which the system-specific interactions were simulated. The approach has been successfully applied to simulate the growth and metabolic overflow to ethanol at glucose concentrations beyond a threshold value for the yeast S. cerevisiae. 

Analytically solving the PDMP is a difficult task due to the complex behavior of the system (Marseguerra Zio 1996), which contains the sto-chasticities in the components modeled by multistate models and the time-dependent evolutions of the components modeled by physics-based models. On the other hand, Monte Carlo simulation methods are suited for the reliability estimation of the system. 

Zio, E., 2013. The Monte Carlo Simulation Method for System Reliability and Risk Analysis. London, Springer. 

Zio, E. The Monte Carlo Simulation method for system reliability and risk analysis. 2013, Springer series in reliability, London. ISBN 978-1-4417-4587-5. 

ABSTRACT The paper presents analytical and Monte Carlo simulation methods applied to the reliability evaluation of a complex multistate system. A semi-Markov process is applied to construct the multistate model of the system operation process and its main characteristics are determined. Analytical linking of the system operation process model with the system multistate reliability model is proposed to get a general reliability model of the complex system operating at varying in time operation conditions and to find its reliability characteristics. The application of Monte Carlo simulation based on the constructed general reliability model of the complex system is proposed to reliability evaluation of a port grain transportation system and the results of this application are illustrated and compared with the results obtained by analytical method. 

Simulation of adsorption has been performed in various ensembles canonical, grand canonical, isobaric-isothermal, and Gibbs ensemble. The choice of the ensemble depends on the nature of the investigated system and the aim of the simulations. In the case of adsorption on heterogeneous surfaces, usually the grand canonical Monte Carlo simulation method (GCMC) has been used. 

Because of the large size of the systems studied, simple analytical potential energy functions must be used. Thus, almost all of the studies that simulate biological systems at the allatom level do so using molecular mechanics. In order to simulate these systems at a finite temperature, molecular dynamics and Monte Carlo simulation methods must be employed. 

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