Problems in modeling

Sparacino, G. and Cobelli, C., Deconvolution of physiological and pharmacokinetic data comparison of algorithms on benchmark problems, in Modeling and Control in Biomedical Systems, Linkens, D.A. and Carson, E., Eds., Elsevier, Oxford, 1997, pp. 151-153. 

Batch processes offer some of the most interesting and challenging problems in modeling and control because of their inherent dynamic nature. Although most... 

One of the main problems in modelling a photochemical process by neural networks is the correct choice of input and output variables to accurately describe the process. In the particular application presented here, the... 

Choice of the mathematical apparatus of macroscopic equilibrium descriptions. Problems in modeling the nonholonomic, nonscleronomous, and nonconservative systems. Possibilities for using differential equations (autonomous and nonautonomous) and MP. 

Another problem in model applications is the adsorption on a nonuniform adsorbent. The immobilization of polyclonal antibodies will lead to different populations of binding sites, and the measurements will only give an apparent adsorption rate constant [22], The properties of the adsorbent surface are also greatly affected by the procedure used for protein immobilization. It may be important to select coupling methods that orient the covalently attached protein... 

Problems in modelling the electrical interfacial layer in metal/oxide aqueous systems... 

Before discussing problems in modelling the electrical interfacial layer (EIL), one should answer two basic questions What is modelling and what is its purpose ... 

A common problem in modeling plasma tools is determining what is coming from walls bounding the plasma. Molecular gases entering the tool... 

As a more definite and concrete substantiation of our claim that a variety of problems in modeling materials are of an inherently multiscale nature, we now turn to a qualitative discussion of the emergence of multiple temporal scales in thinking about diffusion and, similarly, the emergence of multiple spatial scales in considering plasticity. 

Given the examples described in explicit detail above, and by appealing to the examples that have been repeatedly emphasized throughout the book, our present aim is to try to take stock of those features of problems in modeling materials that generically signal the need for some sort of a multiscale approach. In loose terms, it is possible to identify a few different themes that have arisen. 

The insertion of loops is one of the main problems in model building with intermediate homology. If an insertion in the sequence occurs relative to the structure, there is no template to model on, and other techniques have to be applied. The main techniques used to model loops are ... 

Data sets that are not directly comparable are a common problem in model validation because it is assumed that the validation data set is exchangeable with the model development data set, which may not be the case. In this instance, the two concentration time profiles were not superimposable after correcting for differences in dose and hence must have different pharmacokinetic models. And if two data sets have different... 

Coulson s group II is alive and well, although doing much more computing than he would have anticipated. Insofar as ab initio calculations are intractable, Dirac s famous statement notwithstanding, chemistry becomes a problem in model building and subsequent experimental verification. 

Multiple Steady States - Another important problem in modelling monolith reactions for exothermic reactions is the occurrence of multiple steady state solutions (MSSS). It has been shown, by comparing lumped with distributed models, that a one-dimensional model may give false solutions corresponding to higher multiple steady state solutions. 

The basic problem in modelling two-phase flow is the question to what extent equilibrium exists between the phases. In general, there is no equilibrium. Yet, as a rule equilibrium is assumed, since this simplifies the analytical treatment of the problem. Fundamental considerations on two-phase flow can, for example, be encountered in [6]. In what follows the model of Leung [7, 8] is described. The presentation draws upon [8]. 

The proper combination of graphical and statistical analysis will usually provide definitive answers for most problems in model discrimination. Severd specific examples are given below. 

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