Application of Monte Carlo Method

The total number density is p = 0.9 and the radius of the first coordination sphere was chosen as Rq = 1.3(Tpp. The parameters a and a in (6.119) were chosen after some experimentation with the results obtained from the computations. The arguments underlying the choice of these parameters are discussed in the section following (6.119) and we will not be concerned with them here [for details, see Ben-Naim (1973b)]. 

The second feature of the curves in Fig. 6.25 is the peak at about i = a/ 1.8, which indicates a large probability of finding pairs of 

In Fig. 6.26, the singlet generalized molecular distribution functions Xc K) are plotted for the three cases listed in (6.132). The most prominent feature of these curves is the shift to the left of the most probable coordina- 

For a relatively low HB energy e IkT — —3.0), we find essentially two peaks in Xb(v), one corresponding to singly bonded molecules, and the second to nonbonded molecules. As we increase the HB energy to 

Such a splitting into four quasicomponents can serve as a rigorous basis for a mixture-model approach for this fluid. This has a direct relevance to the theory of real liquid water. Suppose we know the function x v) for water then the validity of various ad hoc models can be assessed according to the form of this function. 

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K. Binder, ed. Applications of Monte Carlo Methods in Statistical Physics. Berlin Springer, 1984. 

Applications of Monte Carlo Methods to Sequence Distributions in Polymers... 

Binder, K., Applications of Monte Carlo methods to statistical physics, Rep. Prog. Phys. 1997, 60, 487-559... 

Up to this point and in the following sections and as long as the contrary is not specified, all the discussion will refer to the study of closed, isothermal systems (N,V,T). Though in the applications of Monte Carlo method to the study of solutions... 

The main drawback with the application of Monte Carlo method in this ensemble lies in the fact that, due to the perturbation [34] that must be applied to the volume, it takes approximately 15% more of computing time than in the canonical (N,V,T) ensemble. Another possible problem is that some interaction potentials may lead to unreasonable densities in the calculation. 

Platowski, K. and Reichert, K. Application of Monte Carlo methods for modelling of polymerisation reactions. Polymer 1999 40 1057. 

Simulated annealing provides a more efficient application of Monte Carlo methods. To apply simulated anneahng to conformation sampling, we implemented the following process [2]. A random walk in the conformation space of a molecule is implemented. 

There is a long history in studies on application of Monte Carlo methods to process engineering. The first serious research paper on a Monte Carlo treatment for systems involving population balances could be credited to Spielman and Levenspiel (42). Since then, a significant number of publications have appeared in the literature on the resolution of population balance equations using Monte Carlo methods (35). Comprehensive Monte Carlo treatments are described in the literature (20,35). Only selected issues on basic techniques are addressed in this section. 

It can be seen that the Monte Carlo methods are applicable to both one-dimensional and multidimensional coalescence processes without any theoretical and algorithmic hurdles. However, most reported results with good agreement with experimental data are limited to one-dimensional systems except that reported by Wauters (52). This is mainly because of the lack of reliable multidimensional kernel models rather than the applicability of Monte Carlo methods. 

The application of Monte Carlo method for the study of hydration of nucleic acids, their components [77-80], and hydration of the DNA-ligand complexes (for example, dCpG with proflavine [81] and DNA with azinomycin B [82] intercalated complexes) was described in literature in detail. Monte Carlo simulations enable to evaluate the low energy conformations of various complexes of DNA fragments. 

With the advent of computers with a reasonable calculation capacity could address the application of Monte Carlo method to study of polyelectrolyte systems. The firsts article appears in the 80s [101], and the amount of papers has growing to become a voluminous literature. A comprehensive review of this literature is beyond the reach of this chapter. However, we have been greatly influenced by the work of enormous number of author, in particular a series of articles of Per Linse et al. [102]. This is possible because the species interact via several types of molecular interactions with different length and time scales. Among those involved are hydrogen bonds, electrostatic, hydrophobic. Van der Waals, hydrogen bonds interactions [103]. In order to theoretically understand the Monte Carlo... 

With the advent of computers with a reasonable calculation capacity could address the application of Monte Carlo method to study of polyelectrolyte systems. The first articles appeared in the 80s [2-8], and the amount of papers has been growing... 

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