Numerical solution procedure advantage

The linear approach described here is expandable to multienzyme electrodes as well as multilayer electrodes. At least for the stationary case, multilayer models of bienzyme electrodes may be easily treated, too. The whole system is readily adaptable to potentiometric electrodes (Carr and Bowers, 1980). It must be noted, however, that the superiority over purely numerical solution procedures decreases with increasing number of enzyme species and in the multilayer model. The advantage in calculation speed using the sum formulas described (e.g., in Section 2.5.2) amounts to about two orders of magnitude. With multilayer electrodes and formulas containing double and triple sums it is reduced to one order of magnitude. 

Especially for the electrons, the fluid model has the advantage of a lower computational effort than the PIC/MC method. Their low mass (high values of the transport coefficients) and consequent high velocities give rise to small time steps in the numerical simulation (uAf < Aa) if a so-called explicit method is used. This restriction is easily eliminated within the fluid model by use of an implicit method. Also, the electron density is strongly coupled with the electric field, which results in numerical Instabilities. This requires a simultaneous implicit solution of the Poisson equation for the electric field and the transport equation for the electron density. This solution can be deployed within the fluid model and gives a considerable reduction of computational effort as compared to a nonsi-multaneous solution procedure [179]. Within the PIC method, only fully explicit methods can be applied. 

Although chemometrics offers several advantages, complex numerical solutions that are generated by chemometrics approaches could often be misinterpreted unless a proper procedure is implimented. Since problem solving involves multivariate analysis, the interpreter needs to be fairly skilled in terms of analysis and interpretation. This approach also requires a number of experiments to be made, and as such cannot be performed entirely in silico. 

The volatile nature of ethanol makes it eminently suitable for headspace analysis. The principle on which the method is based is that of partition theory, i.e., that the concentration of a volatile species in the headspace above a solution is proportional to the concentration of that species in solution. Procedures based on this principle must therefore be classed as indirect , but nevertheless they have some advantages over direct methods, the most important being that the procedure separates volatile species from the numerous nonvolatile compounds commonly found in alcoholic beverages. As most sensors used in instrumentation for the determination of ethanol are at best semispecific and are usually oxidative in... 

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