Global behaviour

It is a recent discovery, presented in Chapter 6, that behind the apparent chaos of Table 4.2 there are some simple regularities which enable one to predict the r vs local and global behaviour on the basis of the open-circuit... 

If an additional hint is needed the reader may jump to Table 6.1 in Section 6.2. Table 6.1 is the same with Table 4.3, except that the reactions are there listed on the basis of their r vs global behaviour. 

Table 4.2 lists the same catalytic systems but now grouped in terms of different reaction types (oxidations, hydrogenations, reductions and others). In this table and in subsequent chapters the subscript D denotes and electron donor reactant while the subscript A denotes an electron acceptor reactant. The table also lists the temperature and gas composition range of each investigation in terms of the parameter Pa/Pd which as subsequently shown plays an important role on the observed r vs O global behaviour. Table 4.3 is the same as Table 4.2 but also provides additional information regarding the open-circuit catalytic kinetics, whenever available. Table 4.3 is useful for extracting the promotional rules discussed Chapter 6. 

This again can be confirmed from Table 6.1 and all Figures 6.3 to 6.8 as well as from the more complex ones Figures 6.9 to 6.12 which show the transition from one global behaviour to another as pA and Pd are varied. Note, for example in Figure 6.12 that when a reaction exhibits a maximum in the r vs pD (=Pco) behaviour, it also exhibits a maximum (volcano) in the r vs 0 behaviour. 

Figure 6.18 shows how the model predicts the four main types of r vs O global behaviour (electrophobic, electrophilic, volcano, inverted volcano) for fixed XD and IA, Pd and pA, by just varying the adsorption equilibrium constants kD and kA. Note that in Figure 6.18 and till the end of this chapter we omit the units of Pd and pA (e.g. kPa) and kD,kA (e.g. kPa 1), unless we refer to experimental data. This is because one is free to use any consistent set of units, since only the dimensionless products kApA and kDpD enter the calculations. 

As shown in Figure 6.24a and b (top) the model predicts the shift in global behaviour in a truly impressive semiquantitative manner and in fact with very reasonable XD and XA values (XD > 0, XA <0). 

The roots of eq. (39) with v and y considered as parameters determine branches of candidates for butterfly singularity points, which advance to that status if certain conditions are not violated. We have already seen how the conditions A 0, e 0, w —y arise naturally in the derivation of eq. (39) as guarantees that solutions of the latter equation are valid solutions of (28a)-(28e). A separate class of conditions arise from the theory of Golubitsky and Schaeffer, allowing one to relate the quasi-global behaviour of the system of interest to that of simple polynomial functions. For example, the minimum conditions from the theory for a butterfly point are that eqs (28a)-(28e) be satisfied and also... 

In the last 23 years remote sensing of atmospheric constituents has established itself as an important research field. Global remote sensing observations are essential to understand the natural processes which determine the global behaviour of the atmosphere and to assess the impact of human activity on the atmosphere. In addition, remote sensing of the atmosphere provides data needed to assess die impact of international agreements designed to limit the environmental impact of industrial activity. 

The techniques described in the present chapter follow on logically from Chapters 1 to 3 which described the tools needed for the generation of comprehensive mechanisms. In the future, they are intended to provide a link between these mechanisms and the sort of tools introduced in Chapter 5 for the analysis of the global behaviour and the rich dynamics found in combustion systems. The beauty of the methods described in Chapter 5 is... 

Global Behaviour in the Oxidation of Hydrogen, Carbon Monoxide and Simple Hydrocarbons... 

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