Critical simplification principle

Principle of critical simplification. In accordance with this principle (Yablonsky et al., 2003), the behavior near critical points, for instance ignition or extinction points in catalytic combustion reactions, is governed by the kinetic parameters of only one reaction—adsorption for ignition and desorption for extinction— which is not necessarily the rate-limiting one. 

The principle of critical simplification was first explained by Yablonsky et al. (Yablonskii and Lazman, 1996 Yablonsky et al., 2003) using the catalytic oxidation reaction as an example. The authors presented a dramatic simplification of the kinetic model for this reaction at critical conditions relating to bifurcation points. In this section, results obtained by GoTdshtein et al. (2015) are also used. 

Boudreau and Cooper showed that adsorptive energy distributions can be computed directly from chromatograms (38)- Their method is similar in principle to the present analysis, except for the use of an adsorption isotherm equation that provides an analytical solution for Equation 15. This simplification, which describes all adsorption isotherms as if they occur below the two-dimensional critical temperature 7 c = 0.60 (6), speeds computation of the histogram. Its practical effect is to broaden the energy scale artificially, however, particularly when light vapors are used to characterize low energy, homogeneous substrates. 

All models are simplifications but some exaggerate in allowing only one cause for a process. Monocausality has a venerable history. The principle first formulated by Occam in 1360 says, in its most radical form, that if one has found one acceptable reason for something, that suffices and the matter should not be made more complicated by looking for a less simple explanation. This version of Occam s razor is often used as a guide for setting up models without a critical appreciation of what is sufficient. Such models are sometimes less than optimal as there is rarely only one determining factor. 

A number of current approaches to software structuring fra safety critical systems aim to simplify the software structure as much as possible, with the structure detomined by the available verification techniques. Whilst simplification of software stincture is to be encouraged, simplification of the safety argument should be a stronger guiding principle. Most current verification methods do not allow this to take place because they do not allow natural software and system structures to be adopted. 

It is obvious that Fig. 2 represents a drastic simplification of reality for complicated molecules The merit of this theory is that it gives a good qualitative picture of real gelation, the first indication for the universality principle that complicated molecular details are not very relevant for the main results. Physicists call Fig. 2 a Bethe lattice, and this gelation process is then called percolation on a Bethe lattice . Hie macromolecules are also designated as Cayley trees since, like trees in a forest, they have no cyclic links between their branches. Many other problems of theoretical physics, besides percolation, have been studied on Bethe lattices. When critical exponents were found they usually agreed with those obtained by using simple approximations for real lattices like mean field (or molecular field) approximation, Landau ansatz for phase transitions, van der Waals equation, etc. We will thus also denote them as mean field approximations. 

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