Craig model

The Lorenz-Craig model Appetitive behavior - releasing stimulus situation - consummatory act was later modified by N. Tinbergens hierarchy model of appetite behaviors (for details see I. Eibl-Eibesfeldt 1975, 1987). 

Finally, by inserting the value of R in Eq. 6.17b, we obtain the number of stages in the Craig model corresponding to a Gaussian distribution of the solute in a column, given by... 

The difference between the two plate models has been discussed by Klinkenberg and Sjenitzer [16]. In both models, we have a series of identical mixers, each containing the same amoimt of mobile and stationary phases. In the Martin and Synge model, by contrast with the Craig model, the mobile phase flows continuously. The result is that we have two different distributions, but both of them tends toward the same limit (Eq. 6.5) when the number of stages increases indefinitely. 

Comparison of Eqs. 6.6b and 6.18 shows that the peak dispersion in the Craig model is less than in the Martin-Synge model if we use the same number of stages. In order for the two results to become equal, the number of stages used in the Craig model should be smaller than in the Martin-Synge model. We should have... 

Seshadri and Deming [44] have used the Craig model to calculate band profiles in chromatographic systems. However, they selected an unrealistic isotherm, (Ji = ( j + biCj)Ci, i.e., an isotherm which, for each component i, is linear in respect to its concentration, but with a retention factor that is a linear function of the other component concentration. There is little physical basis for this model, and this prevented them from deriving any useful conclusions. More recently, Eble et al. [45] have used the Craig model to calculate band profiles in isocratic elution and to develop general correlations between the sample size on the one hand and the apparent retention factor and the column efficiency on the other. Experimental data confirm the approximate validity of the relationships obtained [24,25] (Eig-ure 10.3). The use of such empirical relationships allowed an estimation of the band shape on a personal computer for column efficiencies not exceeding a few hxmdred theoretical plates. 

The backward-forward finite difference scheme is identical to the Craig model if we choose the time and space increments such that = H. The Craig model has been used by many authors, including Eble et ah [45], Czok and Guiochon [49,50], and El Fallah and Guiochon [55]. This model affords a good numerical solution of the gradient elution problem, which is very difficult to solve numerically with the forward-backward finite difference scheme [55,56]. 

R. W. Doerge, Bruce A. Craig, Model selection for quantitative trait locus analysis in polypolids. Proceedings of the Na tional Academy of Sciences USA, 97 (2000), 7951-7956. 

HENRY CRAIG Modeling of Molecular Shape, Similarity, and Mechanism 71... 

HENRY CRAIG Modeling of Makadar Shape, Sinularity, and Mechanism 79... 

These models assume that the chromatographic column can be divided into a series of a finite number of identical plates. Each plate contains volumes and of the mobile and stationary phases, respectively. The sample is introduced as a solution of known concentration in the mobile phase used to fill the required number of plates. Plate models are essentially empirical, and cannot be related to first principles. Depending upon whether one assumes continuous or batch operation. two plate models can be considered The Craig model and the Martin and Synge model. 

As the plate number N increases, just as in the case of the Craig model the profile tends rapidly toward a Gaussian profile ... 

Note that, although both models lead to the same profile, the resulting relationships between number of plates in the column and standard deviation differ. The conventional plate number as defined in chromatography is equal to N for the Martin and Synge model, and to N (l+ k o)lk o for the Craig model. In any discussion of column efficiency it is convenient to consider the height equivalent to a theoretical plate (or HETP). 

A much simpler model in concept is the Craig model of chromatography. This is more a phenomenological model in that it tries to mimic the physical processes occurring in the column. As we will see, it uses most of the same assumptions as are necessary for the solution of the mass balance model and it also gives closely similar results. 

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