INDEX OF SUBJECTS

Index of Subjects as Alternate Names of Items A677... 

Examples of the reduction of the number of equations abound. With adiabatic reactors in the steady state, the temperature is a function of the composition (see [A, D, F] and the introductions to papers under Adiabatic in the Index of Subjects in Publications.) This is the case also with the catalyst particle (see I, Ch. 2, and [81, 122] and Example 9). Examples of reduction in the number of equations because one or more can be solved immediately are given in Example 12 see also [280] and [310]. 

The parametric approach, which is not strictly needed for a single Gray-Scott reaction, works very well for an arbitrary number of parallel reactions and for continuous mixtures. Figure 16 shows a case of two parallel reactions for which an isola and a mushroom coexist. Because the notions of continuous mixtures and reactions will be treated in Chapter 8, G H and in the group of papers listed in the Index of Subjects in Publications under the heading Continuous mixtures, we can be very brief and start with the nondimensional equations. Let x be the index of the mixture whose species are /4(x). The steady-state concentration of the material with index in (x, x + dx) is V(x)dx, the feed concentration a(x)dx and the conversion U(x) = 1 - V/(x)/a(x), the last being defined only for values of x for which a(x) is not zero. B, the autocatalytic agent, forms itself as an undifferentiated product whose concentration is W. The rate of the first reaction, and hence p,(x), depends on the... 

I am sorry that there is not space for the paper [62], which was based on Gavalas dissertation, for it laid the foundations of continuous mixture kinetics of the first order. When Astarita and Ocone revived the subject again in the late 1980s, the emphasis was on underlying kinetics other than first order. Reprint G is a paper from the second period, the first being represented only by the last section of Reprint E. Papers on continuous mixtures may be traced through the Index of Subjects in Publications. 

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