Monte Carlo simulation INDEX

Pollock et al.(12) have also exploited the fact that poly dispersity index is a function of C2 only in a study utilizing a Monte-Carlo simulation technique to compare error propagation in the method of Balke and Hamielec to a revised method (GPCV2) proposed by Yau et al. (13) which incorporated correction for axial dispersion. 

Powder diffraction techniques have become increasingly useful as tools for crystal structure determination especially in cases where it is sometimes difficult to get a single crystal of sufficient size and quality for traditional single-crystal studies. The solution of a structure can be considered as a three-step process (i) data collection and indexing, (ii) data preparation and Pawley refinement, and (iii) Monte Carlo simulated annealing and rigid-body Rietveld refinement. 

Numerical and Monte Carlo simulations of the peroxidase-catalyzed polymerization of phenols were demonstrated.14 The monomer reactivity, molecular weight, and index were simulated for precise control of the polymerization of bisphenol A. In aqueous 1,4-dioxane, aggregates from p-phenylphenol were detected by difference UV absorption spectroscopy.15 Such aggregate formation might elucidate the specific solvent effects in the enzymatic polymerization of phenols. 

The estimate of the performances of the detector requires detailed Monte-carlo simulations that have to take into account the detector layout and the physical characteristics of the Cerenkov radiator which surrounds the detector tight refraction index, tight absorption and scattering coefficients, in seawater (or ice). These quantities must be accurately measured in situ [38],... 

Monte Carlo Simulations. The epimerization reaction was simulated using the Monte Carlo program we described earlier(17). A 5000 element array was allocated to store information about the configurations of monomer units at various positions in a 5000 unit polymer chain. The positions were indexed in such a way that the polymer could be considered cyclic. This was done to avoid end group effects. The configurations (R or S) at individual sites were indicated by 0 or 1 values. The polymer chain was made isotactic by giving all elements of the array initial values of 0. 

In order to model the asset s cash flow, it uses a Monte Carlo simulation to generate expected default times for each piece of collateral and utilizes Copula functions and equity indexes to estimate correlation in the default times. The default times allow CDOManager to determine the cash flow expected from each asset over the life of a transaction. Summing up the cash flow from all of the assets generates a picture of the expected future cash flow from the CDO collateral pool. 

Of course there are many unsolved problems, and possible directions for further research in this area. The most interesting problem would be to try to extend these exact solutions to some fractals with infinite ramification index. There are some studies of statistical physics models of interacting degrees of freedom on Sierpinski carpets, using Monte Carlo simulations, or approximate renormalization group using bond-moving, or other ad-hoc approximations. An exactly soluble case would be very instructive here. 

Table 3. Mean and standard deviation of the robustness index, obtained theoretically and by Monte-Carlo simulations.

Basically, the idea is to perform a weighted average of the histograms ht E), measured in Monte Carlo simulations for different temperatures, i.e., at (where / = 1,2,..., / indexes the simulation thread), in order to obtain an estimator for the density of states by combining the histograms in an optimal way ... 

The Monte-Carlo simulation of these models reproduces well the charge carrier transport properties in the mesophases, i.e., the mobility independence of both temperature and electric field in the temperature above room temperature, if a small sigma (40 60 meV) is taken for the Gaussian width of the distribution of localized states in Eq. (2.2). In this equation p, is the mobility, a is the Gaussian width of the distributed energy states for hopping sites, E is an index of the positional disorder, k is the Boltzman constant, T is the temperature, E is the electric field and C is a constant. The constants a and n depend on the type of mesophase, e.g., 0.8 and 2 for the SmB phase and 0.78 and 1.5 for the SmE phase, respectively. This value of cr (40-60 meV) is half that for typical amorphous solids [61]. 

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