Model parallel

The load sharing between fiber and matrix can be viewed as a simple springs-in-parallel model as in Figure 3-7. There, if all springs deform the same amount (the equal-strains assumption) and kf > > k, then the fiber spring takes most of the applied load. 

The three layers can be treated as an iso-strain parallel model in the flow direction. The total cross-section Atotai and the total tensile modulus totai E,) of a composite sample can be determined as follows ... 

This function is intermediate between the parallel model and the series model and referred to as the logarithmic law of mixture shown in curve 3. The law of mixture is valid for a composite system when there is no interaction in the interface. However, it is natural to consider that interaction will occur in the interface due to contact between A and B. Then considering the creation of interfacial phase C, different from A and B, the following equation can be presented ... 

Fig. 9. Upper (parallel model) and lower (series model) bounds for the microhardness of a two-component composite as function of crystalline volume function. Hardness expressed as H/Hc for Hc/H = 120...

Pake spectrum 26, 38, 44 Paraffin crystals 129 Parallel model 130 Partially ordered systems 27... 

On concluding this chapter, it is worthwhile to address a few issues that associate in particular with the boundary friction, i.e., the friction originated from the shear of surface films. The emphasis is given to the discussion of the shear strength and two parallel models that describe the boundary friction in terms of different mechanisms. 

Figure 12.4. Galactitol (left) and sorbitol (right) concentrations versus lactose conversion comparison of consecutive model (1-3, 4b upper figures) and parallel model (1-3, 4a, lower figmes). Reaction conditions 120°C, 50 bar (left) and 60 bar (right), Ru/C catalyst.

Two likely causes of these under-abundances are suggested by the Be nature of B 12 (i) veiling of the continuum due to a disk, and (ii) departures from standard non-rotating plane parallel models caused by rapid rotation. 

Mench et al. developed a technique to embed microthermocouples in a multilayered membrane of an operating PEM fuel cell so that the membrane temperature can be measured in situ. These microthermocouples can be embedded inside two thin layers of the membrane without causing delamination or leakage. An array of up to 10 thermocouples can be instrumented into a single membrane for temperature distribution measurements. Figure 32 shows the deviation of the membrane temperature in an operating fuel cell from its open-circuit state as a function of the current density. This new data in conjunction with a parallel modeling effort of Ju et al. helped to probe the thermal environment of PEM fuel cells. 

As the above results show, the gross features of the cellulose I crystal structure predicted by various methods do not differ appreciably, but the accompanying deviations in the R -factors are significant. When these predictions are used to assess, for example, whether the cellulose I crystal structure is based on parallel- or antmarallel-chains, the range in the R"-factors seen for the parallel models (cf. Table II) is comparable to that between the two different polarity models. As shown in Fig. 5, the most probable parallel- and antiparallel-chain structures of cellulose I, refined by minimizing the function O, differ in R -factors by approximately the same extent as the three predictions for the parallel model shown in Fig. 4 and Table II. 

Only with less efficient catalysts and at low temperature, have p-chelate intermediates been intercepted by P H HP NMR spectroscopy in the course of copolymerisations in MeOH-d4 [5g]. The unambiguous detection of p-chelates has been observed in a reaction catalysed by the l,r-bis(diphenylphosphino)ferro-cene complex [Pd(H20)2(dppf)](0Ts)2 (3) at room temperature (Scheme 7.7) [5g]. As shown in the sequence of P H NMR spectra reported in Figure 7.8, the P-chelate intermediates 4- disappeared already at 50 °C. A parallel model study confirmed the formation and the structure of the dppf P-chelates and also provided information of more elusive intermediates (see Section 7.2.1.8) [19]. 

Loeb, N. G., and R. Davies, Observational Evidence of Plane Parallel Model Biases Apparent Dependence of Cloud Optical Depth on Solar Zenith Angle, J. Geophys. Res., 101, 1621-1634 (1996). 

Figure 5.61 (a) Kelvin-Voigt spring and dashpot in parallel model of viscoelasticity and... 

We now consider some models of polymer structure and ascertain their usefulness as representative volume elements. The Takayanagi48) series and parallel models are widely used as descriptive devices for viscoelastic behaviour but it is not correct to use them as RVE s for the following reasons. First, they assume homogeneous stress and displacement throughout each phase. Second, they are one-dimensional only, which means that the modulus derived from them depends upon the directions of the surface tractions. If we want to make up models such as the Takayanagi ones in three dimensions then we shall have a composite brick wall with two or more elements in each of which the stress is non-uniform. 

The most simple version of our model considers the two-phase nature of the fluidized beds in the reactor and in the regenerator in a simplified way. The kinetic model that we use considers three pseudocomponents in modeling type IV FCC units. This model is a consecutive-parallel model formed of three lumped components and coke as follows ... 

The tilted configuration of butane was not considered in the analysis of the monolayer vibrational spectrum in Sec. II.C.2. Normal mode calculations are now being performed (20) with this orientation to see if the fit to the observed spectrum can be improved. The tilting of the molecule may be related to the inconsistency encountered in the plane-parallel model in which different atom-substrate force constants had to be introduced for the co-planar CH- and CH, hydrogens. In the tilted configuration this bottom layer of hydrogens is split into two separate levels of atoms. This difference in height above the surface may provide a physical basis for two different force constants. 

Rpl =0.179, Rp2 = 0.202, Ral =0.207, and Ra2 = 0.249. Statistical tests show that model a2 can be rejected in favor of aj. The choice between the parallel models pj and p2 is more difficult but examination of model p2 shows that this model cannot be fully hydrogen bonded, and hence p2 is rejected in favor of pj, which also gives better x-ray agreement. Thus models pj and aj were taken as the most likely parallel and antiparallel models for further refinement. At this point the unobserved data were included, calculating weighted R and R" where w = l for observed and w=l/2 for unobserved reflections. F(hkl) for an unobserved reflection was set at two thirds an assigned threshold and was included only if the calculated structure amplitude exceeded the threshold. The final residuals for the two models were Rpi = 0.233, R = 0.299, and Rj = 0.215, R j = 0.270. Application of the Hamilton statistical test (13) to these data indicates that the a model can be rejected at the 99.5% level. 

Both models, the one given by Judd and the model of Richards and Parks, are psychophysical models of color perception. No explanation is given on how or why the results would depend on either the average apparent reflectance or the average luminance. They are phenomenological descriptions of color vision and not computational theories of color vision (Marr 1982). In this respect, the parallel model described in Chapter 10 in combination with local color shifts described in Section 11.2 is much more satisfying. 

The thermal conductivity of the composite may be calculated by combining the thermal conductivities of the matrix, kTm, and fibers, kTf, using the parallel model at the corresponding volume fraction of fibers, Vf ... 

Hinton, G.E. and Anderson, J.A. (1989) Parallel Models of Associative Memory Lawrence Erlbaum Assoc Publ, Hillsdale, N.J... 

The conflicting serial/parallel models for IVR/VP are not readily distinguished until time resolved experiments can be performed on the systems of interest. Both models can relate the relative intensities of the emission features to the various model parameters, but the serial process seems more in line with a simple, conventional [Fermi s Golden Rule for IVR (Avouris et al. 1977 Beswick and Jortner 1981 Jortner et al. 1988 Lin 1980 Mukamel 1985 Mukamel and Jortner 1977) and RRKM theory for VP (Forst 1973 Gilbert and Smith 1990 Kelley and Bernstein 1986 Levine and Bernstein 1987 Pritchard 1984 Robinson and Holbrook 1972 Steinfeld et al. 1989)], few parameter approach. Time resolved measurements do distinguish the models because in a serial model the rises and decays of various vibronic states should be linked, whereas in a parallel one they are, in general, unrelated. Moreover, the time dependent studies allow one to determine how the rates of the IVR and VP processes vary with excitation energy, density of states, mode properties, and isotropic substitution. 

Figure 5- Models, a, general case. Fluid flows from left to right at constant velocity and is transferred from the E.E. (unshaded tubes, Min. Mix.) to the L.E. (shaded area, Max. Mix.). In the s(, a) space, a particle having a given residence time tg describes a trajectory between the plane a = 0 and the plane X = 0 b, a model of Spencer et stl. (68). Each particle stays in the E.E. for a duration proportional to its residence time c,r p model of Spencer et al. (68), which is also the series model of Weinstein and Adler (69) Each particle stays for a constant time in the E.E., provided tg> d, parallel model of Weinstein and Adler...

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