Boolean kinetic equations

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.,... 

ABSTRACT. A fundamental approach is outlined for the kinetic modeling of complex processes like thermal cracking or catalytic hydrocracking of mixtures of hydrocarbons. The reaction networks are written in terms of radical mechanisms in the first case and of carbenium ion mechanisms in the second case. Since the elementary steps of the networks pertain to a relatively small number of classes, the number of rate coefficients is kept within tractable limits. The reaction networks are generated by computer through Boolean relation matrices. The number of continuity equations is limited by the elimination of radicals or carbenium ions through the pseudo-steady-state approximation. 

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