Monte Carlo methods structure simulation models

Despite such restrictions, real space crystallographic methods based on genetic algorithms, Monte-Carlo methods, or simulated annealing techniques have proved to be powerful means for structure solutions from X-ray powder patterns. Provided with the unit cell, the composition and configuration of the asymmetric unit, and sufficiently texture-free diffraction data, refinable structure models can be obtained within minutes on a personal computer, even for molecules with multiple internal degrees of freedom. The resulting structure models are then refined by Rietveld techniques, which use the whole profile of the X-ray diffraction pattern for refinement . ... 

Monte Carlo methods, direct tracking methods, and vertex models, where the evolution of the two-dimensional grain structure is described in terms of the motion of the vertices. After initial transients, all of these simulations exhibit statistical self-similarity during growth and an average grain area that increases linearly with time according to Eq. 15.35. 

All the statistical characteristics of copolymer chain structure and composition inhomogeneity, (including the ones reported in the above papers) can be easily calculated by means of the Markov chain formalism for any of kinetic models presented in Sect. 2. Then it does not seem advisable for the solution of such problems to apply the Monte-Carlo method with which the simulation of the copolymer chain growth was carried out [83-93]. 

A novel approach to protein conformation is the entropy-sampling Monte Carlo method (ESMC), which is described in detail in another contribution to this volume. The method provides a complete thermodynamic description of protein models, but it is computationally quite expensive. However, because of the underlying data-parallel structure of ESMC algorithms, computations could be done on massively parallel computers essentially without the communication overhead typical for the majority of other simulation techniques. This technique will undoubtedly be applied to numerous systems in the near future. 

The problem could have been resolved only by the theories based on the first principle. One of the theoretical approaches based on the Hamiltonian model is the molecular simulations, or the molecular dynamics and Monte-Carlo methods. The methods have made great contribution for heuristic understanding of structural, dynamical as well as some thermodynamic properties of water. Since so many review articles have already been published concerning the simulation of water [53], here we will not take a trouble of reiterating them. 

Monte Carlo methods of sampling combined with energy calculation and minimization for structural models, template-framework configurations, adsorption simulation, slow diffusion, etc. 

Such methods of analysing and describing adsorption data have considerable merit in describing microporosity in porous carbons, which are not crystalline, or for microporous solids of unknown structure, but for zeolites of known structure they add little to our understanding. In such cases, the form of the adsorption isotherms can be modelled by computer simulation using Grand Canonical Monte Carlo methods. In this approach all the parameters are known or can be measured or calculated (see Section 4.5.1) so that the adsorption isotherm can be simulated using a physically well-characterised model. 

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