Nonmonotonic

However, for more complex fluids such as high-polymer solutions and concentrated ionic solutions, where the range of intemiolecular forces is much longer than that for simple fluids and Nq is much smaller, mean-field behaviour is observed much closer to the critical point. Thus the crossover is sharper, and it can also be nonmonotonic. 

J. Putz, R. Holyst, M. Schick. Nonmonotonic behavior of a contact angle on approching critical endpoints. Phys Rev A 46 3369-3312, 1992. Phys Rev E 46 3035, 1993. 

As the large-scale computational fluid dynamics (CFD) simulations often invoke simplifying the kinetics as one-step overall reaction, the extraction of such bulk flame parameter as overall activation energy is especially useful when the CFD calculation with detailed chemistry is not feasible. Based on the experimental results, the deduced overall achvation energies of the three equivalence ratios are shown in Figure 4.1.10a. It can be observed that the variation of with is nonmonotonic and peaks near the stoichiometric condition. 

In Chapter 8.5, B. Veyssiere exposes the state of knowledge in detonations. Particular features of the complex multidimensional structure of detonations are presented in relation with the recent results obtained either by nonintrusive optical diagnostics or numerical simulations from high performance calculations. The role of transverse waves in detonation propagation, the existence of correlations between the characteristic dimension of the cellular structure and the critical conditions for detonation initiation and detonation transmission, and the influence of the nonmonotonous heat release process behind the front are examined. Recent developments in the study of spinning detonations are also discussed. 

NONMONOTONIC REASONING THE SYNTHESIS OF OPERATING PROCEDURES IN CHEMICAL PLANTS... 

Section III introduces the concept of nonmonotonic planning and outlines its basic features. It is shown that the tractability of nonmonotonic planning is directly related to the form of the operators employed simple propositional operators lead to polynomial-time algorithms, whereas conditional and functional operators lead to NP-hard formulations. In addition, three specific subsections establish the theoretical foundation for the conversion of operational constraints on the plans into temporal orderings of primitive operations. The three classes of constraints considered are (1) temporal ordering of abstract operations, (2) avoidable mixtures of chemical species, and (3) quantitative bounding constraints on the state of processing systems. 

In Section IV we provide illustrations of the modeling concepts presented in Section II and how the strategy of nonmonotonic planning has been used to synthesize the switchover operating strategy for a chemical process. 

In summary, nonmonotonic planning of process operations has the following distinguishing features ... 

In this theorem, any proposition p can represent an operator (i.e., an operation step), whereas the situations t and s represent any intermediate state of the process. Although the validity of the theorem is general, its practical utility is confined to monotonic planning with STRIPS-like operators. For example, in nonmonotonic planning the plans are at any point when partially specified and a new mechanism is needed to guarantee that when the partial plan is completed, a given proposition (i.e., a given operation) is still true (i.e., consistent). 

For STRIPS-like operators. Chapman (1985) developed a polynomialtime algorithm, called TWEAK, around five actions that are necessary and sufficient for constructing a correct and complete plan. As soon as we try to extend these ideas to nonmonotonic planning with conditional operators, we realize that no polynomial-time algorithm can be constructed, as the following theorem explicitly prohibits (Chapman, 1985) ... 

Theorem 3 (First Intractability Theorem). The problem of determining whether a proposition is necessarily true in a nonmonotonic plan whose action representation is sufficiently strong to represent conditional actions is NP-hard. 

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