Equivalence criterion

The RP systems currently in force differ in practice, first in accordance with the size of the market covered. This in turn depends on the equivalence criterion chosen to classify drags, and also on the inclusion or otherwise of patented drags. 

We will take a somewhat different but equivalent criterion in order to describe the crossover. As the crossover time r, we take the Rouse relaxation time of a polymer section, spanning the tube diameter ... 

One delntion of cWraSly is that the molecule be nonstfmrinipgsaUe CO its minor image. An equivalent criterion is (hat it not possess an crnpiupcr axis of eolation (page 52). The absence of a minor plane does not insure optical activity because a molecule may have no mirror plane, yet may possess an improper rotational axis. We can, however, be sure that the molecule with a minor plane will be optically inactive. 

An equivalent diameter of a particle is usually defined in relation to a specific sizing method developed on the basis of a certain equivalency criterion. Several equivalent diameters of a spherical particle commonly employed are discussed in the following sections. 

Again, the above crack kinking and branching criteria are limited to isotropic homogeneous material, which for all practical purposes will include particulate/whisker-filled ceramic matrix composites. No equivalent criterion exists for orthotropic/inhomogeneous material. Limited experimental results show that self-similar crack extension is a rare phenomenon in fracture of fiber-reinforced ceramic matrix composites and thus the kinking and branching criterion, if developed, must necessarily be a three-dimensional one. 

Mixing is considered complete when the standard deviation among rational subgroups, of size n = 4, reaches a certain specified value. Because of the functional relationship between standard deviation and range, an equivalent criterion would require that the range reach a certain value. Since sampling variation is present instead of a single... 

Equation (1,2-15) is a basis for the formulation of phase-equilibrium problems. However, since the chemical potential has some practical and conceptual shortcomings, it is useful to replace it, with a related quantity.i, the fugacity. Equation (1,2-15) is then replaced by the equivalent criterion for phase equilibrium. 

According to Pearson, whether the bonds being broken in the reagents correspond (after symmetrization) to the bonds being formed in the product is an adequate and equivalent criterion for the reaction to be allowed or forbidden in the sense of Woodward-Hoffinann. Apart from simplicity, the efficiency of the rule of bond symmetry is also ensured by the fact that it is equally applicable to it- and cr-bonds. Hence, its predictions are equally applicable to both the full-face ethylene dimerization (Scheme 4a) or to the Diels-Alder reaction (Scheme 4b) and to addition reaction, e.g., the addition of molecular hydrogen to ethylene or butadiene. 

Because of x—y symmetry, the probabilities for choosing cell pairs in the x- and y-directions (with unit vectors <7i and <72 in Fig. 3) are equal, and will be denoted by w. The probability for choosing diagonal pairs (<73 and <74 in Fig. 3) is given hy Wi = - 2w. w and must be chosen so that the hydrodynamic equations are isotropic and do not depend on the orientation of the underlying grid. An equivalent criterion is to guarantee that the relaxation of the velocity distribution is isotropic. These conditions require w = 1/4 and = 1/2. This particular choice also ensures that the kinetic part of the viscous sness tensor is isotropic [45]. 

A slightly more restrictive (but otherwise equivalent) criterion for radiative equilibrium is the requirement that all radiative net fluxes must equal the flux k Fn from the deep interior. This latter flux is a positive constant, and may arise from radioactive decay or from the conversion of gravitational potential energy to internal (heat) energy. We have... 

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