Computer simulation Monte Carlo method

This section has illustrated a relatively simple application of the Monte Carlo technique for simulating atmospheric diffusion. With the availability of large-scale computing capacities, Monte Carlo methods can be envi-... 

The same computer revolution that started in the middle of the last century also plays an important, in fact crucial, role in the development of methods and algorithms to study solvation problems. Dealing, for instance, with a liquid system means the inclusion of explicit molecules, in different thermodynamic conditions. The number of possible arrangements of atoms or molecules is enormous, demanding the use of statistical mechanics. Here is where computer simulation, Monte Carlo (MC) or molecular dynamics (MD), makes its entry to treat liquid systems. Computer simulation is now an important, if not central, tool to study solvation phenomena. The last two decades have seen a remarkable development of methods, techniques and algorithms to study solvation problems. Most of the recent developments have focused on combining quantum mechanics and statistical mechanics using MC or... 

Computer simulations, Monte Carlo or molecular dynamics, in fact appear to be the actual most effective way of introducing statistical averages (if one decides not to pass to continuous distributions), in spite of their computational cost. Some concepts, such as the quasi-structure model introduced by Yomosa (1978), have not evolved into algorithms of practical use. The numerous versions of methods based on virial expansion, on integral equation description of correlation functions, on the application of perturbation theory to simple reference systems (the basic aspects of these... 

Liffman, K. 1992 A direct simulation Monte-Carlo method for cluster coagulation. Journal of Computational Physics 100, 116-127. 

B. Monte Carlo simulations. Monte Carlo methods designate simulation procedures whereby certain probabilistic features are introduced into the numerical computations. They contrast sharply with the completely deterministic algebraic expressions that are common in traditional theories of... 

The problem of predicting the thermodynamic properties of such a classical system becomes the problem of evaluation of the configuration integral, the integral over exp(— O). This is still a difficult task. In general, it can be done only through computer simulations (Monte Carlo and molecular dynamics methods). However, there are a few simple approximations which are helpful. 

Agranovich V M, Efremov N A and Kirsanov V V 1980 Computer simulation of kinetics of excitation bimolecular quenching by Monte-Carlo method Fiz. Tverd. Tela 22 2118-27... 

Monte Carlo simulations are commonly used to compute the average thermodynamic properties of a molecule or a system of molecules, and have been employed extensively in the study of the structure and equilibrium properties of liquids and solutions. Monte Carlo methods have also been used to conduct conformational searches under non-equilibrium conditions. 

The study of surface chemical reaction processes using computer simulation techniques is quite an active field of research. Within this context the Monte Carlo method emerges as a powerful tool which contributes to the... 

Force fields split naturally into two main classes all-atom force fields and united atom force fields. In the former, each atom in the system is represented explicitly by potential functions. In the latter, hydrogens attached to heavy atoms (such as carbon) are removed. In their place single united (or extended) atom potentials are used. In this type of force field a CH2 group would appear as a single spherical atom. United atom sites have the advantage of greatly reducing the number of interaction sites in the molecule, but in certain cases can seriously limit the accuracy of the force field. United atom force fields are most usually required for the most computationally expensive tasks, such as the simulation of bulk liquid crystal phases via molecular dynamics or Monte Carlo methods (see Sect. 5.1). 

Since the middle of the 1990s, another computation method, direct simulation Monte Carlo (DSMC), has been employed in analysis of ultra-thin film gas lubrication problems [13-15]. DSMC is a particle-based simulation scheme suitable to treat rarefied gas flow problems. It was introduced by Bird [16] in the 1970s. It has been proven that a DSMC solution is an equivalent solution of the Boltzmann equation, and the method has been effectively used to solve gas flow problems in aerospace engineering. However, a disadvantageous feature of DSMC is heavy time consumption in computing, compared with the approach by solving the slip-flow or F-K models. This limits its application to two- or three-dimensional gas flow problems in microscale. In the... 

The method for estimating parameters from Monte Carlo simulation, described in mathematical detail by Reilly and Duever (in preparation), uses a Bayesian approach to establish the posterior distribution for the parameters based on a Monte Carlo model. The numerical nature of the solution requires that the posterior distribution be handled in discretised form as an array in computer storage using the method of Reilly 2). The stochastic nature of Monte Carlo methods implies that output responses are predicted by the model with some amount of uncertainty for which the term "shimmer" as suggested by Andres (D.B. Chambers, SENES Consultants Limited, personal communication, 1985) has been adopted. The model for the uth of n experiments can be expressed by... 

Molecular dynamics and Monte Carlo simulations have been extensively applied to molten salts since 1968 to study structure, thermodynamic properties, and dynamic properties from a microscopic viewpoint. Several review papers have been published on computer simulation of molten salts. " Since the Monte Carlo method cannot yield dynamic properties, MD methods have been used to calculate dynamic properties. 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

Bouzida, D. Kumar, S. Swendsen, R.H., Efficient Monte Carlo methods for the computer simulation of biological systems, Phys. Rev. A 1992, 45, 8894-8901... 

Sometimes the theoretical or computational approach to description of molecular structure, properties, and reactivity cannot be based on deterministic equations that can be solved by analytical or computational methods. The properties of a molecule or assembly of molecules may be known or describable only in a statistical sense. Molecules and assemblies of molecules exist in distributions of configuration, composition, momentum, and energy. Sometimes, this statistical character is best captured and studied by computer experiments molecular dynamics, Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. Interaction potentials based on quantum mechanics, classical particle mechanics, continuum mechanics, or empiricism are specified and the evolution of the system is then followed in time by simulation of motions resulting from these direct... 

It Is to be remarked that the process described by the Infinite set of kinetic (coagulation) equations can be simulated by Monte-Carlo methods ( ). The Information on the number of molecules of the respective size Is stored In the computer memory and weighting for selection of molecules Is applied given by the number and reactivity of groups In the respective molecule. 

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