Mathematical modeling drawback

Remark 1 The main motivation behind the development of the simplified superstructure was to end up with a mathematical model that features only linear constraints while the nonlinearities appear only in the objective function. Yee et al. (1990a) identified the assumption of isothermal mixing which eliminates the need for the energy balances, which are the nonconvex, nonlinear equality constraints, and which at the same time reduces the size of the mathematical model. These benefits of the isothermal mixing assumption are, however, accompanied by the drawback of eliminating from consideration a number of HEN structures. Nevertheless, as has been illustrated by Yee and Grossmann (1990), despite this simplification, good HEN structures can be obtained. 

Some authors consider diffusion (a), (b) as consecutive processes, and assume the existence of colliding pairs [7-9]. Other models stress the importance of segmental diffusion of the active ends in a common volume of the two colliding macro molecules [10-12]. A common drawback of the mathematical models is the lack of a generally formulated expression for the effective diffusion coefficient of the active end in a coiling chain. Most models try to solve this difficulty by introducing suitable parameters with some physical meaning. 

The advantage of feedback control is that corrective action is taken regardless of the source of the disturbance. Its chief drawback is that no corrective action is taken until after the controlled variable deviates from the set point. Feedback control may also result in undesirable oscillations in the controlled variable if the controller is not tuned properly that is, if the adjustable controller parameters are not set at appropriate values. Although trial-and-error tuning can achieve satisfactory performance in some cases, the tuning of the controller can be aided by using a mathematical model of the dynamic process. 

Although adsorptive processes have been extensively studied for gas separation, catalysis, it is only recently that they have been proposed for heat management. M. Tather et al. [51] developed a mathematical model for a novel arrangement proposed in order to cope with the drawbacks originating from the inefficient heat and mass transfer in adsorption heating pumps with Zeolite 4A used as the adsorbent. L. Bonaccorsi et al. [52] have successfully synthesized zeolite coatings on metal supports with thickness ranging from few to several tens of microns, which had important technical applications in adsorption heat pumps. 

Neural networks are versatile and flexible tools for modelling complex relationships between variables. However, there are some drawbacks to their use, which are related to the fact that they make no assumptions about the underlying model. This means that a larger training set is required than for the other techniques described in this chapter. Also there is no direct way to extract information about a suitable mathematical model for the relationship between the variahies or to estimate confidence intervals mathematically. 

This mathematical model has some drawbacks, however. First, infinite stresses cannot exist in a material they cannot exceed the theoretical strength of the bond or, for an elas-toplastic material, the yield stress (Jq. Second, it is not easy to see by which mechanism the crack recedes when G < w and by which mechanism a reduction of w by adsorption or segregation increases the crack velocity when G > w. The difficulty arises from the fact that cohesion or adhesion forces g z) are only taken into accounty by their integral... 

Over the last decades, the application of computational fluid dynamics (CFD) to study the velocity and temperature profiles in packed column has been frequently reported [1-5]. However, for the prediction of concentration profile, the method commonly employed is by guessing an empirical turbulent Schmidt number Sc, or by using experimentally determined turbulent mass diffusivity D, obtained by using the inert tracer technique under the condition of no mass transfer [6, 7]. Nevertheless, the use of such empirical methods of computation, as pointed out in Chap. 3, is unreliable and not always possible. To overcome these drawbacks, the development of rigorous mathematical model is the best choice. 

PCR takes no account of the concentration of the samples in the calibration set when finding the principal components and this has been considered a drawback. PLS was developed to use the concentration data when developing the mathematical model. PLS is thus claimed to be superior to PCR. 

The fascination of geochemistry rests primarily on its intermediate position between exact sciences (chemistry, physics, mathematics) and natural sciences. The molding of the quantitative approach taken in physical chemistry, thermodynamics, mathematics, and analytical chemistry to natural observation offers enormous advantages. These are counterbalanced, however, by the inevitable drawbacks that have to be faced when writing a textbook on geochemistry 1) the need to summarize and apply, very often in a superficial and incomplete fashion, concepts that would require an entire volume if they were to be described with sufficient accuracy and completeness 2) the difficulty of overcoming the diffidence of nature-oriented scientists who consider the application of exact sciences to natural observations no more than models (in the worst sense of that term). 

A recently developed metapopulation model to extrapolate responses of aquatic invertebrates as observed in mesocosms to assess their recovery potential in the field is provided by Van den Brink et al. (2007). When the primary interest is in the recovery of processes and functional groups, food-web models are the required mathematical tools (for an example, see Traas et al. 2004). Two drawbacks of these models are that they require detailed information on the species and functional groups of concern and that they are very specific to the species and functional groups and sites for which they are developed. 

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