Dual phase model

Dar-El, E., Ayas, K., and GUad, I. (1995a), A Dual-Phase Model for the Individual Learning Process in Industrial Tasks, HE Transactions, Vol. 27, pp. 265-271. 

Structure and properties of nanocrystalline alloys 2.1 Dual phase model... 

This simple mixing rule demonstrates satisfactory agreement with experimental evidence from experiments with binary fluid blends [. l Furthermore, it is similar in form with the result from a continuum theory approach by Davis [ ], applicable for IPN with dual phase continuity but which are not mixed on a molecular level. This last model involves an exponent equal to 1/5 instead of 1/2 and is quite successful in predicting the experimental evidence [1 ] from permanent networks. 

The oscillatory structure just mentioned has been clearly demonstrated to result from quantum-mechanical phase-interference phenomena. The necessary condition264,265 for the occurrence of oscillatory structure in the total cross section is the existence in the internuclear potentials of an inner pseudocrossing, at short internuclear distance, as well as an outer pseudo-crossing, at long internuclear distance. A schematic illustration of this dual-interaction model, proposed by Rosenthal and Foley,264 is shown in Fig. 37. The interaction can be considered to involve three separate phases, as discussed by Tolk and et al. 279 (1) the primary excitation mechanism, in which, as the collision partners approach, a transition is made from the ground UQ state to at least two inelastic channels U, and U2 (the transition occurs at the internuclear separation 7 , the inner pseudocrossing, in Fig. 37), (2) development of a phase difference between the inelastic channels,... 

The pressure dependence of the concentration of sorbed gas was consistent with the dual mode model while the relaxation data addressed itself to the validity of the assumptions made by the model. The assumption of rapid interchange was found to be valid for this system while the assumption of an immobile adsorbed phase could introduce a small error in the analysis It should be possible to reduce this error by more exact measurements of the concentration of sorbed gas as classical pressure experiments could... 

As is clear solid oxide electrolytes are not useful for applications as oxygen separation membrane, unless operated with external circuitry (oxygen pump) or as a constituent phase of a dual-phase membrane. Both modes of operation, classified in this paper as electrochemical oxygen separation, are briefly discussed in Section 10.4.3. But we first start with a discussion of the models that have been developed to describe the oxygen semi-permeability of solid oxide... 

Hydrogenations of MAA were carried out both in gas-phase and liquid phase with flowing hydrogen. Optical 5delds were 8-15% in the former and 30-32% in the latter cases, and no significant structure sensivities were observed. In the range of 4-10 mn no influence of particle size was seen in the ee s of the methyl 3-hydroxybutyrate product The results were considered confirmation of the dual site model" (Sachtler which states that one sort... 

Unfortunately, this type of model has the drawback that re-yielding and hardening stagnation after re-yielding cannot be fitted to modem steels like dual phase or complex phase steels, which gives the motivation for the short introduction of the following second model. 

The well-known dual-phase-lag heat conduction model introduces time delays to account for the responses among the heat flux vector, the temperature gradient and the energy transport. The dual-phase-lag heat conduction model has been used to interpret the non-Fourier heat conduction phenomena. The onedimensional dual-phase-lag constitutive equation relating heat flux to temperature gradient is expressed as (Xu, 2011 Zhou et al., 2009)... 

Al-Nimr et al. (2000) investigated the effect of the phase-lags in temperature and in heat flux on the nonequilibrium entropy production. As the difference between xj-and Xq increases, the propagation of the entropy production shifts from the diffusive type to the wavy type. For most practical applications involving the dual-phase-lag model, the nonequilibrium temperature may be replaced by the equilibrium temperature. 

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