Reverse Monte Carlo method

Instead of calculations, practical work can be done with scale models (33). In any case, calculations should be checked wherever possible by experimental methods. Using a Monte Carlo method, for example, on a shape that was not measured experimentaUy, the sample size in the computation was aUowed to degrade in such a way that the results of the computation were inaccurate (see Fig. 8) (30,31). Reversing the computation or augmenting the sample size as the calculation proceeds can reveal or eliminate this source of error. 

Random structure methods have proved useful in solving structures from X-ray powder diffraction patterns. The unit cell can usually be found from these patterns, but the normal single-crystal techniques for solving the structure cannot be used. A variation on this technique, the reverse Monte Carlo method, includes in the cost function the difference between the observed powder diffraction pattern and the powder pattern calculated from the model (McGreevy 1997). It is, however, always necessary to include some chemical information if the correct structure is to be found. Various constraints can be added to the cost function, such as target coordination numbers or the deviation between the bond valence sum and atomic valence (Adams and Swenson 2000b Swenson and Adams 2001). 

McGreevy, R. L. (1997). Reverse Monte Carlo methods for structure modelling. In C. R. A. Catlow (ed.), Computer Modelling in Inorganic Crystallography. San Diego and New York Academic Press, pp. 151-84. 

Tucker MG, Dove MT, Keen DA (2000) Application of the Reverse Monte Carlo method to ciystalhne materials. Journal of Applied Crystallography (submitted)... 

Proffen T, Welbeny TR (1997) Analysis of diffuse scattering via the reverse Monte Carlo technique A systematic investigation. Acta Crystallogr Sect A 53 202-216 Proffen T, Welbeny TR (1998) Analysis of diffuse scattering of single ciystals using Monte Carlo methods. Phase Transit 67 373-397... 

REVERSE ENGINEERING USING MONTE CARLO METHODS... 

Monte Carlo and Reverse Monte Carlo methods... 

Pikunic, J., Clinard, C., Cohaut, N., et al. (2003). Structural modehng of porous carbons constrained reverse Monte Carlo method. Langmuir, 19, 8565—82. 

Reverse Monte Carlo Methods for Structural Modelling... 

One example of the NMR reconstraction problem employs the reversible-jump Markov chain Monte-Carlo method [16]. It assumes that the model spectram S Fi,F2) is made up of a limited number m of two-dimensional Gaussian resonance lines. Then m, the linewidths, intensities, and frequency co-ordinates are varied until the Markov chain reaches convergence. The allowed transitions between the current map M and the new map M comprise movement, merging or splitting of resonance lines, and birth or death of component responses. Compatibility with the experimental traces is checked by projecting M at the appropriate angles. The procedure has been found to be stable and reproducible [16]. 

The Monte Carlo method, however, is prone to model risk. If the stochastic process chosen for the underlying variable is unrealistic, so will be the estimate of VaR. This is why the choice of the underlying model is particularly important. The geometric Brownian motion model described above adequately describes the behavior of some financial variables, but certainly not that of short-term fixed-income securities. In the Brownian motion, shocks on prices are never reversed. This does not represent the price process for default-free bonds, which must converge to their face value at expiration. 

In this paper, the results of a Monte Carlo method for the simulation of the stochastic time evolution of the micellization process are presented. The computational algorithm [1] used represents an optimization of a general procedure introduced by Gillespie some years ago [2]. It was applied to the case of surfactant reversible association according to the general mechanism reported in Fig. 1 that allows associations and dissociations among -mers of whatever aggregation number. 

Dove, M.T., Pryde, A.K.A., and Keen, D.A. (2000b) Phase transitions in tridymite studied using Rigid Unit Mode theory. Reverse Monte Carlo methods and molecular dynamics simulations. Mineral. Mag., 64, 257-283. 

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