Reverse Monte Carlo procedure

Shick A. and Rajagopalan R., Reverse Monte Carlo procedure for cluster analysis in colloidal systems. Colloids Surf., 66,113-119 (1992). 

In order to extract microscopic quantities such as spatial probabilities and RDFs from collected differential cross scattering data, analysis is typically performed following reverse Monte Carlo (RMC) or empirical potential structure refinement (EPSR) procedures [7]. The latter procedure can be viewed as a Monte Carlo simulation of system utilising a model potential similar to a classical molecular mechanics force field. This model potential is modified in order to bring the total structure factor calculated from the model system as close as possible to the ejq)erimental data. From configurations generated with this refined potential, standard quantities (such as RDFs) may be calculated. 

Reverse Monte Carlo [5] is a reeonstruction method, which is normally used to produce molecular models that match the experimental structure data and some other eonstraints. The constraints are usually based on the knowledge of the material being studied and also can be obtained from experimental evidence. However, no intermolecular potential is used in this methodology, so the stability of the models produced is not guaranteed. In previous works [1,2], a reconstruction procedure based on constrained Reverse Monte Carlo (RMC) was used to generate atomistic models that quantitatively match experimental (diffiaction and small angle) properties of two real porous saccharose cokes CS400 (density ... 

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]. 

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. 

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