Quasi-homogeneous

A piezo-composite consists of a piezoelectric active phase and a passive plastic phase [2]. In the 1-3-configuration adopted in our case, piezoelectric rods parallely aligned in thickness direction are imbedded in a three-dimensional plastic matrix (Fig. 1). The distance between the rods has to be chosen inferior to the half wave length of the shear wave in the matrix material ensuring that the whole compound is vibrating as a quasi-homogeneous material. 

Solutions of Moiseev s giant Pd colloids [49,161-166] were shown to catalyze a number of reactions in the quasi homogeneous phase, namely oxidative ace-toxylation reactions [162], the oxidative carbonylation of phenol to diphenyl carbonate [166], the hydrogen-transfer reduction of multiple bonds by formic acid [387], the... 

A quasi homogeneous form for the reaction term is assumed. 

This monomer concentration Ma in the formalism of the quasi-homogeneous approximation, unlike M a, refers to the whole volume of the two-phase system. The aforementioned quantities are connected by the simple relationship Ma = flM a where y01 stands for the volume fraction of the a-th phase in miniemulsion. An analogous relation, Ra = sdaR a, exists between the concentrations Ra of the a-th type active centers in the entire system and those R a in the surface layer of the a-th phase. This layer thickness da has the scale of average spatial size of the a-th type block, which hereafter is presumed to be small as compared to the average radius of miniemulsion drops. Apparently, in this case, the curvature of the interphase surface can be neg-... 

Under the quasi-homogeneous approach the monomer mixture composition is characterized by vector x with components xi = Mj/M and x2 = M2/M, whose drift with conversion is described by equations [84]... 

A quasi-homogeneous form for the reaction term is assumed. The boundary conditions are given by... 

In order to evaluate the catalytic characteristics of colloidal platinum, a comparison of the efficiency of Pt nanoparticles in the quasi-homogeneous reaction shown in Equation 3.7, with that of supported colloids of the same charge and of a conventional heterogeneous platinum catalyst was performed. The quasi-homogeneous colloidal system surpassed the conventional catalyst in turnover frequency by a factor of 3 [157], Enantioselectivity of the reaction (Equation 3.7) in the presence of polyvinyl-pyrrolidone as stabilizer has been studied by Bradley et al. [158,159], who observed that the presence of HC1 in as-prepared cinchona alkaloids modified Pt sols had a marked effect on the rate and reproducibility [158], Removal of HC1 by dialysis improved the performance of the catalysts in both rate and reproducibility. These purified colloidal catalysts can serve as reliable... 

Clusters, as possible catalytic reactors, are perfectly dispersed in solutions. They are thus suitable systems for observing, under quasi-homogeneous conditions by time-resolved techniques, the kinetics of catalyzed electron transfer, which would be inaccessible on a solid catalyst. It was demonstrated that the reaction of radiation-induced free radicals COT and (CH3)2COH catalyzed by metal clusters started by the storage of electrons on clusters as charge pools and that electrons were then transferred pairwise to water-producing molecular hydrogen [22,75]. 

Negligible transport resistance exists in the internal phase (I) because the phase I droplets are very small (ri< 5 pm) a quasi-homogeneous state. 

Shear yielding in the form of a quasi-homogeneous,bulk process can contribute substantially to the crack resistance of a polymeric solid. On the other hand, however, localized shear yielding in the form of shear micro-bands is befleved to be a precursor of brittle fracture in many semicrystalline and glassy thermoplas-... 

Mathematical models of packed bed reactors can be classified into two broad categories (1) one-phase, or pseudohomogeneous, models in which the reactor bed is approximated as a quasi-homogeneous medium and (2) two-phase, or heterogeneous, models in which the catalyst and fluid phases and the heat and mass transfer between phases are treated explicitly. Although the... 

The contradiction in Equation (1) concerning the homogeneity and heterogeneity of the surface is eliminated by accepting the theory of quasi-homogeneous surfaces developed in some detail by the author (22). A quasi-homogeneous surface is one, the two different active centers of which are characterized by a constant ratio... 

At the same time the zr are constant over the entire quasi-homogeneous surface ... 

The two-film model representation can serve as a basis for more complicated models used to describe heterogeneously catalyzed RSPs or systems containing suspended solids. In these processes a third solid phase is present, and thus the two-film model is combined with the description of this third phase. This can be done using different levels of model complexity, from quasi-homogeneous description up to the four-film presentations that provide a very detailed description of both vapor/gas/liquid-liquid and solid/liquid interfaces (see, e.g., Refs. 62, 68 and 91). A comparative study of the modeling complexity is given in Ref. 64 for fuel ether synthesis of MTBE and TAME by CD. 

Yuxiang Z, Xien X. Study on catalytic distillation processes. Part B. Simulation of catalytic distillation processes—quasi-homogenous and rate-based model. Trans IChemE 1992 70 465 470. 

Ocean basin variability. Therefore, formation of the scheme of spatial distribution of soil-vegetation formations and quasi-homogeneous World Ocean basins will make it possible to overcome such shortcomings in other models. A system of balance equations for this scheme is as follows ... 

Figure 3.10. Distribution of the depth of the upper quasi-homogeneous layer of the World Ocean at latitudinal zones 0°-10°N (solid curve) and 60°N-70°N (dashed curve).

A switching electrode having nanometer dimensions leads to profound difference in poling of fe thin films and fe bulk crystals. In the case of fe thin films with a thickness of about 100 nm, a voltage application between the bottom electrode and an afm tip of 50-100 nm radius forms a quasi-homogeneous electric field. Such a distribution implies a conventional polarization reversal setup as in the case of uniform switching electrodes applied to polar faces of a fe sample. 

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