Variational Monte Carlo characteristics

Allowing for rotation about the Ca—C bond (/.e., variation of ijr) and for some degree of freedom about the peptide bond [i.e., small variation of ro), the characteristic ratios of the form / (crs) and form II [trans) poly(L-proline) chain are calculated by a Monte Carlo method in which the conformational energies are used as weighting factors. The Monte Carlo method enabled short-range interactions (beyond those involved in a single residue) to be taken into account. 

Box and Meyer (1986, 1993) provided Bayesian methods for obtaining posterior probabilities that effects are active see Chapter 11, Section 2, for more details. There followed a flurry of papers proposing new frequentist methods, giving refinements of the methods, and making empirical comparisons of the many variations. Hamada and Balakrishnan (1998) provided an extensive review of these methods, including a Monte Carlo-based comparison of the operating characteristics of the methods that is, a comparison of the power of the methods for a variety of combinations of effect values (parameter configurations). They found that comparison of methods is difficult for various reasons. For example, some... 

Vn.30. In general, all of these sonrces of uncertainty should be integrally observed in the variability of the calculated results obtained for the critical experiments. The variability should include the Monte Carlo standard deviation in each calculated critical experiment value as well as any change in the calculated value caused by the consideration of experimental uncertainties. Thus these uncertainties will be intrinsically included in the bias and uncertainty in the bias. This variation or nncertainty in the bias should be established by a valid statistical treatment of the calculated k y values for the critical experiments. Methods exist [VII. 10] that enable the bias and uncertainty in the bias to be evaluated as a function of changes in a selected characteristic parameter. 

The effect of. these variations On a number of characteristics of the diva f critical assembly have been calculate by a Monte Carlo code and are summarized in Table n. The effect of a 30% decrease in the, nuclear temperature used in the evaporation model also investigated. The results are eiqiressed as differences, in percent, between the values obtained from using the evaporation model at all energies at the Ugber temperature and the values bbtained by each of the other variations. 

A third distinct type of electrode model developed in response to the need for modelling the composite structure of SOFC electrodes more accurately is the Monte Carlo, or stochastic structure, model. This model is based on a random number-generated 2- or 3-D structure of electrode particles, electrolyte particles, and holes (for gas pores). It has been shown to represent the composite conductivity quite well and may be able to model polarisation behaviour adequately [56-58]. This is of Interest because microstructure, and in particular hard-to-control variations in local microstructure, may have an important effect on overall polarisation, perhaps more so than the intrinsic kinetic characteristics measured at an ideal interface. 

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