Fisher effect interaction

Short-range order interaction [40] (sometimes called configurational interaction or Fisher effect) can also occur. If, for example, the binding energy... 

Historically, factorial designs were introduced by Sir R. A. Fisher to counter the then prevalent idea that if one were to discover the effect of a factor, all other factors must be held constant and only the factor of interest could be varied. Fisher showed that all factors of interest could be varied simultaneously, and the individual factor effects and their interactions could be estimated by proper mathematical treatment. The Yates algorithm and its variations are often used to obtain these estimates, but the use of least squares fitting of linear models gives essentially identical results. 

Bednorz-Muller theory Beer-Lambert law Bose-Einstein statistics Debye-Huckel theory Diels-Alder reaction Fermi-Dirac statistics Fischer-Tropsch effect Fisher-lohns hypothesis Flory-Huggins interaction Franck-Condon factor Friedel-Crafts reaction Geiger-Miiller effect... 

All isothermal calculations discussed here employ Lennard-Jones potential functions and, unless otherwise stated, simulate free-boundary conditions. The neglect of three-particle interactions for a similar (Barker-Fisher-Watts) isolated pair potential has been shown to produce effects that are quite small for Ar systems. For clusters of more than three particles, the third-order potential energy terms 3 increase as the number of three-particle interactions increases. In the limit of zero temperature, where the third-order effects are most prevalent, 3 of the 13-particle Ar cluster (although already 60% of its bulk value) is less than 4.5% of the cluster s total potential energy. For a five-particle Ar cluster, 3 is less than 3% of the total potential energy. 

Crosswhite (23) has used the correlated multiconfiguration Hartree-Fock scheme of Froese-Fisher and Saxena (24) with the approximate relativistic corrections of Cowan and Griffin (25) to calculate the Slater, spin-orbit, and Marvin radial integrals for all of the actinide ions. A comparison of the calculated and effective parameters is shown in Table II. The relatively large differences between calculation and experiment are due to the fact that configuration interaction effects have not been properly included in the calculation. In spite of this fact, the differences vary smoothly and often monotonically across the series. Because the Marvin radial integral M agrees with the experimental value, the calculated ratios M3(HRF)/M (HRF) =0.56 and M4 (HRF)/M° (HRF) =0.38 for all tripositive actinide ions, are used to fix M and M4 in the experimental scheme. 

Bednorz—Muller theory Beer—Lambert law Bose—Einstein statistics Debye-Hiickel theory Diels—Alder reaction Fermi—Dirac statistics Fischer—Tropsch effect Fisher—Johns hypothesis Flory—Huggins interaction Franck—Condon factor Friedel—Crafts reaction Geiger-Miiller effect... 

Bildea, C. S., S. Cruz, Dimian, A. C., ledema, P., 2002, Design of tubular reactors in recycle systems. Proceedings ESCAPE-12, Elsevier, 439-444 Dimian, A. C., A. J. Groenendijk, P. ledema, 2001, Recycle interaction effects on the ontrol of impurities in a complex plant, 2001, Ind. Eng. Chem. Res., 40,5784-5794 Downs, J., 1992, Distillation control in a plantwide control environment, in W. Luyben (ed), Practical Distillation Control, van Nostrand Reinhold, New York Fisher, W. R., M. F. Doherty, J. M. Douglas, 1988, The Interface between design and control, Ind. Eng. Chem. Res., 27, 597-611... 

The stochastic approach to reaction-diffusion systems is not mathematically well-established. Though spatio-temporal stochastic phenomena ought to be associated with random fields, and not with stochastic processes, the usual investigation of such kinds of physicochemical problems starts from the master equation, and then it is extended by some heuristic procedure. From the physical point of view the role of spatial fluctuations is obviously important. It is well known that the density fluctuations are spatially correlated, and according to the modern theory of critical phenomena (e.g. Fisher, 1974 Wilson Kogut, 1974) small fluctuations are amplified owing to spatial interactions causing drastic macroscopic effects. 

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