Critical DSRs and CSTRs

In the previous sections, we described how the boundary of the AR consists of, at most, two distinct surfaces  

Ruled surfaces that are obtained from mixing lines (lin-eations). 

Protrusions (a surface of exposed points) that are derived specifically from the union of PFR trajectories. 

We also discussed how specialized CSTRs and DSRs— termed connectors, or critical reactors—are used in connecting to PFR points on the AR boundary. The underlying stmcture of the AR boundary is, in fact, fairly simple as a result. Yet we still have not explained how to determine whether a given CSTR or DSR point is critical, or how these specialized reactors are calculated. It will be the goal of this section to understand these topics. 

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Other points that might exist on the AR boundary are critical DSR and CSTR connector points. Tliese will be described by theorem 2. 

We also described how concrete equations for critical DSR and CSTRs may be computed. These expressions are complicated to compute analytically, which are derived from geometric controllability arguments developed by Feinberg (2000a, 2000b). These conditions are intricate, and thus it is often not possible to compute analytic solutions to the equations that describe critical reactors. For three-dimensional systems, a shortcut method involving the vDelR condition may be used to find critical a policies. Irrespective of the method used, the conditions for critical reactors are well defined, irrespective of the legitimacy of the kinetics studied, and thus these conditions must be enforced if we wish to attain points on the true AR boundary. 

Although Chapter 6 discusses how precise conditions exist for computing critical DSRs and CSTRs, the complex nature of the resulting equations not only provides a rigid set of constraints but also brings about uncertainty related... 

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