Monte Carlo prediction

Bayesian methods are very amenable to applying diverse types of information. An example provided during the workshop involved Monte Carlo predictions of pesticide disappearance from a water body based on laboratory-derived rate constants. Field data for a particular time after application was used to adjust or update the priors of the Monte Carlo simulation results for that day. The field data and laboratory data were included in the analysis to produce a posterior estimate of predicted concentrations through time. Bayesian methods also allow subjective weight of evidence and objective evidence to be combined in producing an informed statement of risk. 

Perlstein, J. (1992). Molecular self-assemblies Monte Carlo predictions for the structure of the one-dimensional translation aggregate. J. Am. Chem. Soc., 114, 1955-63. [183]... 

Hale and Bohn [252] measured the scattered radiation from a finite sample of reticulated alumina from an incident laser beam at 488 nm. They then matched Monte Carlo predictions of the scattered radiation calculated from various values of extinction coefficient and scattering albedo and chose the values that best matched the experimental data for reticulated alumina samples of 10, 20, 30, and 65 ppi. A scattering albedo of 0.999 and an assumed isotropic scattering phase function reproduced the measured data for all pore sizes. The large reported albedo value indicates that alumina is very highly scattering and that radiative absorption is extremely small for this material. 

J. T. Farmer and J. R. Howell, Monte Carlo Prediction of Radiative Heat Transfer in Inhomogeneous, Anisotropic, Non-gray Media, AIAA Journal of Thermophysics and Heat Transfer, 8(1), pp. 133-139,1994. 

Calculation Results WIMSE 69Croup Monte Carlo Predictions... 

Detailed Monte Carlo studies were needed to prepare for the data analysis, with particular attention being given to a reliable Monte Carlo prediction of the p f variable. Appropriate techniques to validate the analysis method using a data-driven approach had to be developed, which also illustrates the challenges one faces at the LHC to perform this analysis. 

An important difference between the wave treatment and the SCA is that energy conservation is retained exactly and when the energy of the projectile is less than the energy required to excite the state under consideration the cross section is zero. This is called a threshold. In fig. 5.8 is plotted the measured ratio for ionization produced by equal-velocity positron and proton projectiles incident on helium. Just above the threshold, 24eV, Uie electron cross section falls below that due to the heavier proton. The ratio is compared to a CTMC (classical trajectory Monte Carlo) prediction and also to the ratio of the PWBA to the SCA cross sections showing the importance of the mass of the projectile to the result. The CTMC method will be discussed in more detail shortly. 

Consequently, there has been a concerted effort to apply Weibull statistics to the laboratory and field data to assess [16,20] the future development of damage, its dispersion, and the benefit of various mitigation actions. An example of this development is shown via the Monte Carlo predictions in Figure 18.9 for the cumulative percentage of cracked vessel head... 

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

Gdanitz, R J 1992. Prediction of Molecular Crystal Stluctures by Monte Carlo Simulated Annealing Without Reference to Diffraction Data. Chemical Physics Letters 190 391-396. 

Surface tension is usually predicted using group additivity methods for neat liquids. It is much more difficult to predict the surface tension of a mixture, especially when surfactants are involved. Very large molecular dynamics or Monte Carlo simulations can also be used. Often, it is easier to measure surface tension in the laboratory than to compute it. 

Monte Carlo simulations are an efficient way of predicting liquid structure, including the preferred orientation of liquid molecules near a surface. This is an efficient method because it is not necessary to compute energy derivatives, thus reducing the time required for each iteration. The statistical nature of these simulations ensures that both enthalpic and entropic effects are included. 

Figure 6 shows the field dependence of hole mobiUty for TAPC-doped bisphenol A polycarbonate at various temperatures (37). The mobilities decrease with increasing field at low fields. At high fields, a log oc relationship is observed. The experimental results can be reproduced by Monte Carlo simulation, shown by soHd lines in Figure 6. The model predicts that the high field mobiUty follows the following equation (37) where d = a/kT (p is the width of the Gaussian distribution density of states), Z is a parameter that characterizes the degree of positional disorder, E is the electric field, is a prefactor mobihty, and Cis an empirical constant given as 2.9 X lO " (cm/V). ...

RH Smith Jr, WL Jorgensen, J Tirado-Rives, ML Lamb, PAJ Janssen, CJ Michejda, MBK Smith. Prediction of binding affinities for TIBO inhibitors of HIV-1 reverse transcriptase using Monte Carlo simulations m a linear response method. J Med Chem 41 5272-5286, 1998. 

Figure 8.27 Comparing Monte Carlo model predictions with MSMPR experimental data for calcium carbonate due to Hostomsky and Jones, 1991 (Faiope etal., 2001)...

Phase transitions in two-dimensional layers often have very interesting and surprising features. The phase diagram of the multicomponent Widom-Rowhnson model with purely repulsive interactions contains a nontrivial phase where only one of the sublattices is preferentially occupied. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are molecular layers of H2, D2, N2 and CO molecules on graphite substrates. We review the path integral Monte Carlo (PIMC) approach to such phenomena, clarify certain experimentally observed anomalies in H2 and D2 layers, and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are analyzed via PIMC as well. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions where quantum effects play a role. 

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