Computer modeling input data problem with

The oxidative deterioration of most commercial polymers when exposed to sunlight has restricted their use in outdoor applications. A novel approach to the problem of predicting 20-year performance for such materials in solar photovoltaic devices has been developed in our laboratories. The process of photooxidation has been described by a qualitative model, in terms of elementary reactions with corresponding rates. A numerical integration procedure on the computer provides the predicted values of all species concentration terms over time, without any further assumptions. In principle, once the model has been verified with experimental data from accelerated and/or outdoor exposures of appropriate materials, we can have some confidence in the necessary numerical extrapolation of the solutions to very extended time periods. Moreover, manipulation of this computer model affords a novel and relatively simple means of testing common theories related to photooxidation and stabilization. The computations are derived from a chosen input block based on the literature where data are available and on experience gained from other studies of polymer photochemical reactions. Despite the problems associated with a somewhat arbitrary choice of rate constants for certain reactions, it is hoped that the study can unravel some of the complexity of the process, resolve some of the contentious issues and point the way for further experimentation. 

The advent of perturbation theory for altered systems (see Section V,F) opens a new field for the application of perturbation theory—the field of perturbation sensitivity studies. This is the study of changes in effects of perturbations, or system alterations, caused by uncertainties or variations in input parameters. Examples are (1) the uncertainty of the change in an integral parameter (such as the breeding ratio) resulting from design variations due to uncertainties in cross sections, (2) nonlinear effects of cross-section uncertainties, and (3) the effects of data uncertainties, approximations in computational models, or design variations on the detector response in a deep-penetration problem that is solved with a flux-difference or an adjoint-difference method (see Section V,E). 

We see that the models which best reproduce the location of all the six data points are the tracks which do not fit the solar location. The models whose convection is calibrated on the 2D simulation make a poor job, as the FST models and other models with efficient convection do therefore this result can not be inputed to the fact that we employ local convection models. A possibility is that we are in front of an opacity problem, more that in front of a convection problem. Actually we would be inclined to say that opacities are not a problem (we have shown this in Montalban et al. (2004), by comparing models computed with Heiter et al (2002) or with AH97 model atmospheres), but something can still be badly wrong, as implied by the recent redetermination of solar metallicity (Asplund et al., 2004). A further possibility is that the inefficient convection in PMS requires the introduction of a second parameter -linked to the stellar rotation and magnetic field, as we have suggested in the past (Ventura et al., 1998 D Antona et al., 2000), but this remains to be worked out. 

The key methods that are the focus of this section are categorized as analytical versus numerical methods. Analytical methods can be solved using explicit equations. In some cases, the methods can be conveniently applied using pencil and paper, although for most practical problems, such methods are more commonly coded into a spreadsheet or other software. Analytical methods can provide exact solutions for some specific situations. Unfortunately, such situations are not often encountered in practice. Numerical methods require the use of a computer simulation package. They offer the advantage of broader applicability and flexibility to deal with a wide range of input distribution types and model functional forms and can produce a wide variety of output data. 

Figure 1 shows a computational framework, representing many years of Braun s research and development efforts in pyrolysis technology. Input to the system is a data base including pilot, commercial and literature sources. The data form the basis of a pyrolysis reactor model consistent with both theoretical and practical considerations. Modern computational techniques are used in the identification of model parameters. The model is then incorporated into a computer system capable of handling a wide range of industrial problems. Some of the applications are reactor design, economic and flexibility studies and process optimization and control. 

The computing problem is concerned with calculating the maximum number of unknown parameters of a proposed reaction system from available experimental data. This data can be any combination of values for constant parameters (rate and equilibrium constants) and variable parameters (concentration versus time data). Moreover, data for different variable parameters need not have the same time scale. When the unknown parameters are calculated, it is important that the mathematical validity of the proposed model be determined in terms of the experimental accuracy of the data. Also, if it is impossible to solve for all unknown parameters, then the model must be automatically reduced to a form that contains only solvable parameters. Thus, the input to CRAMS consists of 1) a description of a proposed reaction system model and, 2) experimental data for those parameters that were measured or previously determined. The output of CRAMS is 1) information concerning the mathematical validity of the model and 2) values for the maximum number of computable unknown parameters and, if possible, the associated reliabilities. The system checks for model validity only in those reactions with unknown rate constants. Thus a simulation-only problem does not invoke any model validation procedures. 

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