Kinetic logic

Most systems involve several interconnected feedback loops. Such systems cannot be analyzed seriously without a proper formalism, but their detailed description using differential equations is often too heavy. For these reasons we (as many others before) turned to a logical (or Boolean) description, that is, a description in which variables and functions can take only a limited number of values, typically two (1 and 0). Section II is an updated description of a logical method ( kinetic logic ) whose essential aspects were first presented by Thomas and Thomas and Van Ham.2 A less detailed version of this part can be found in Thomas.3 The present paper puts special emphasis on the fact that for each system the Boolean trajectories and final states can be obtained analytically (i.e.,... 

R. Thomas, ed, Kinetic logic A Boolean approach to the analysis of complex regulatory systems, Lecture Notes in Biomathematics, Vol. 29, Springer-Verlag, Berlin, 507 pp. 

Kinetic logic (Thomas, 1979 King, 1986) is also a tool that provides a structural approach to classifying dynamical systems behaviour. As these authors are mainly interested in exotic behaviour we shall say a few words more about this topic in Section 4.3. 

It is interesting to note that several authors were able to provide sufficient conditions for classes of reactions, e.g. Schnakenberg (1979), Csaszar et ai (1981) and experts in kinetic logic (see the papers by Thomas (1979, 1981), King (1980, 1982a,b, 1983, 1986) and Glass (1977)). The problem is that all these statements are mere indications from the strictly mathematical point of view. 

King, R. B. (1986). Kinetic logic as a qualitative approach for the study of oscillating and chaotic systems. In Perspectives in biological dynamics and theoretical medicine, Proc. N. Y. Acad. Sci. Conf. (9-11 April 1986). Abstract No. P-13. 

The proviso all other things being equal in discussing the last point clearly applies to temperature as well, since the kinetic constants are highly sensitive to temperature. To evaluate the effect of temperature variation on the molecular weight of an addition polymer, we follow the same sort of logic as was used in Example 6.3 ... 

It appeared to be a logical consequence to transfer this synthetic principle to more suitable metals like ruthenium and introduce bulky, kinetically stabilizing ligands at the metal. An interesting example for this approach is the complex 78. The latter is synthesized from Cp RuCl(PR3)2 with ClMgCH2SiMe2H through 77 by a thermal Si — H activation reaction. 

A treatise on kinetics is a logical and fitting medium in which to analyze and discuss just such limitations and uncertainties of mechanism. The present chapter will attempt such a treatment for the SN2 mechanism in nucleophilic aromatic substitution. An effort will be made to pinpoint every assumption and highlight every instance where alternate choices are possible. The end result hoped for is a clearer delineation of the known and the probable from the uncertain and the unknown. 

Firstly, there are technical reasons concerning catalyst and reactor requirements. In the chemical industry, catalyst performance is critical. Compared to conventional catalysts, they are relatively expensive and catalyst production and standardization lag behind. In practice, a robust, proven catalyst is needed. For a specific application, an extended catalyst and washcoat development program is unavoidable, and in particular, for the fine chemistry in-house development is a burden. For coated systems, catalyst loading is low, making them unsuited for reactions occurring in the kinetic regime, which is particularly important for bulk chemistry and refineries. In that case, incorporated monolithic catalysts are the logical choice. Catalyst stability is crucial. It determines the amount of catalyst required for a batch process, the number of times the catalyst can be reused, and for a continuous process, the run time. 

The postulation of a reaction mechanism is the result of inductive rather than deductive thinking. Even though the kinetics researcher may present the ideas and experiments that lead to a proposed mechanism in a logical... 

Although pV2/2 represents kinetic energy per unit volume, pV2 is also the flux of momentum carried by the fluid along the conduit. The latter interpretation is more logical in Eq. (5-50), because rw is also a flux of momentum from the fluid to the tube wall. However, the conventional definition includes the (arbitrary) factor i. Other definitions of the pipe friction factor are in use that are some multiple of the Fanning friction factor. For example, the Darcy friction factor, which is equal to 4/, is used frequently by mechanical and civil engineers. Thus, it is important to know which definition is implied when data for friction factors are used. 

The conclusion that the local hardness is given entirely by the variable parts of the kinetic energy is very logical. It is the kinetic energy increase which limits the distribution of electron density in all systems with fixed nuclei. Since the equilibrium state of atoms and molecules is characterized by minimum energy, they will also be marked by maximum kinetic energy because of the virial theorem. This will put them in agreement with the principles of maximum hardness, for which much evidence exists. 

C Several different pieces of kinetic evidence from this writer s laboratory were thought to indicate that for the styrene + perchloric acid system the ester is stabilised by four molecules of styrene (48, 67). This feature seemed so unlikely that it helped to create opposition to the whole idea of the pseudocationic polymerisation by an ester, although that improbable solvation pattern is in no way essential to the theory nor logically connected with it. At this point it is necessary to introduce an important new insight which came to the writer whilst assembling this Prologue (ca. 30 years too late ). 

If the aim of an investigator is to determine equilibrium concentrations in samplers, then the residence time (tm) is a logical parameter to compare among samplers. The tm is the mean length of time that a molecule spends in a passive sampling device, where solute exchange follows first-order kinetics. Residence time is given by... 

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