Particle simulations, Monte Carlo techniques

Another method of simulating chemical reactions is to separate the reaction and particle displacement steps. This kind of algorithm has been considered in Refs. 90, 153-156. In particular. Smith and Triska [153] have initiated a new route to simulate chemical equilibria in bulk systems. Their method, being in fact a generalization of the Gibbs ensemble Monte Carlo technique [157], has also been used to study chemical reactions at solid surfaces [90]. However, due to space limitations of the chapter, we have decided not to present these results. 

Understanding the dependence of film structure and morphology on system layout and process parameters is a core topic for the further development of ZnO technology. Work is being performed on in situ characterization of deposition processes. Growth processes are simulated using Direct Simulation Monte-Carlo (DSMC) techniques to simulate the gas flow and sputter kinetics simulation and Particle-ln-Cell Monte-Carlo (PICMC) techniques for the plasma simulation [132]. 

Pressure Swing Adsorption (PSA) unit is a dynamic separation process. In order to create a precise model of the process and thus an accurate design, it is necessary to have a good knowledge of the mixture s adsorption behaviour. Consequently, the dilAision rates in the adsorbent particles and the mixture isotherms are extremely vital data. This article intends to present a new approach to study the adsorption behaviour of isomer mixtures on zeolites. In a combined simulation and experimental project we set out to assess the sorption properties of a series of zeolites. The simulations are based on the configurational-bias Monte Carlo technique. The sorption data are measured in a volumetric set-up coupled with an online Near Infra-Red (NIR) spectroscopy, to monitor the bulk composition. Single component isotherms of butane and iso-butane were measured to validate the equipment, and transient volumetric up-take experiments were also performed to access the adsorption kinetics. 

There are two main approaches for the numerical simulation of the gas-solid flow 1) Eulerian framework for the gas phase and Lagrangian framework for the dispersed phase (E-L) and 2) Eulerian framework for all phases (E-E). In the E-L approach, trajectories of dispersed phase particles are calculated by solving Newton s second law of motion for each dispersed particle, and the motion of the continuous phase (gas phase) is modeled using an Eulerian framework with the coupling of the particle-gas interaction force. This approach is also referred to as the distinct element method or discrete particle method when applied to a granular system. The fluid forces acting upon particles would include the drag force, lift force, virtual mass force, and Basset history force.Moreover, particle-wall and particle-particle collision models (such as hard sphere model, soft sphere model, or Monte Carlo techniques) are commonly employed for this approach. In the E-E approach, the particle cloud is treated as a continuum. Local mean... 

Summary. In conclusion, some suggestions are made on how to model the problem of radiative heat transfer in porous media. First, we must choose between a direct simulation and a continuum treatment. Wherever possible, continuum treatment should be used because of the lower cost of computation. However, the volume-averaged radiative properties may not be available in which case continuum treatment cannot be used. Except for the Monte Carlo techniques for large particles, direct simulation techniques have not been developed to solve but the simplest of problems. However, direct simulation techniques should be used in case the number of particles is too small to justify the use of a continuum treatment and as a tool to verify dependent scattering models. 

In the last section we have assumed that we perform our simulation for a fixed number, N, of particles at constant temperature, T, and volume, V, the canonical ensemble. A major advantage of the Monte Carlo technique is that it can be easily adapted to the calculation of averages in other thermodynamic ensembles. Most real experiments are performed in the isobaric-isothermal (constant- ) ensemble, some in the grand-canonical (constant-pFT) ensemble, and even fewer in the canonical ensemble, the standard Monte Carlo ensemble, and near to none in the microcanonical (constant-NFE) ensemble, the standard ensemble for molecular-dynamics simulations. 

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 ... 

Simulations of water in contact with metal surfaces have been performed in a number of ensembles, including the microcanonical (NVE), canonical (NVT), and grand canonical (p-VT) ensembles. The implementation of these ensembles differs for molecular dynamics and for Monte Carlo techniques. The NVT ensemble is convenient because the temperature of the system is maintained along with the number of particles and the volume. However, with the NVE and NVT ensembles care must be exercised to ensure that the density of the water in the system is consistent with the desired equilibrium state. For... 

Molecular simulation techniques, namely Monte Carlo and molecular dynamics methods, in which the liquid is regarded as an assembly of interacting particles, are the most popular... 

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