Bidimensional model

More recent experiments [62] concerning the viscous sublayer have shown a three-dimensional structure for turbulence near the wall. In a plane normal to the mean flow, counterrotating eddy pairs are involved (Fig. 6c), whereas in the direction of the mean flow, the motion is quasi-periodic (as described earlier). Since the wavelength along the mean flow is much larger than along the perimeter of the tube, a simplified bidimensional model may account only... 

The possible differing mechanisms of action of three mood stabilizers (i.e., lithium, valproate, carbamazepine) are incorporated into a bidimensional model of mood regulation that postulates two gating zones (one for depression and one for mania). These zones are thought to be subserved by different neurochemical abnormalities, leading to a situation in which both could be impacted by certain agents (i.e., mood stabilizers) or, alternatively, could individually be affected by unidirectional compounds (e.g., HCAs). 

A second fundamental aspect to be considered in relation to optical transitions in solids, is that electron states, other than definite energy assignments, are also characterized by a distribution in the momentum space, related to the movement (i.e. to the kinetic energy) of electrons in the soUd. For the sake of pictorial simplicity, bidimensional models of crystals, conceived as a square well potential, are usually employed in this respect, portraying the parabolic valley dependence (in one direction) of energy from the momentum vector k, as schematized in Figure 2.4A. The significance of the downward curvature of the valence band is that if electrons could have a net motion in such a band (i.e. if it were not completely filled), they would be accelerated in the opposite direction with respect to those in the conduction band. 

J. Rajchenbach, E. Clement, and J. Duran. Experimental study of bidimensional models of sand. International Journal of Modern Physics B, 07(09nl0) 1789-1798, 1993. 

Fig. 1.9 Bidimensional representation of the interaction pattern between carnosinase and its substrate carnosine. The model shows how the enzyme recognizes (binds) the ammonium group, the carboxylate group and...

A multicomponent 2D chromatogram is considered as a series of 2D peaks with random position and height. For the sake of simplicity, here we assume that the peaks are modeled with bidimensional Gaussian peaks, thus the signal is expressed as... 

Figure 45.2 illustrates the covering of the two ions bidimensional space range and the seven calibration sequences needed to construct the electronic tongue s response model. 

Furthermore, the models have to be reproducible. The model should give the same result when used by different users in different locations. This fact may lead to a preference toward easier models. Depending on the method for QS AR, some steps may be critical for reproducibility. Indeed, some approaches require manual optimization of the tridimensional structure of the chemical, e.g., in the case of tridimensional descriptors. In other cases, stochastic processes are used. Some more complex models done by skilled operators, such as docking, can be critical. Another source of variability is the software version or brand, even for simple bidimensional descriptors. 

Exciton dispersion As the 0-0 exciton dispersion in anthracene is somewhat complex,101 we assumed a bidimensional parabolic dispersion (effective-mass approximation). This assumption is justified by the absence of interplane coupling for k perpendicular to plane (001) planes2 9—the case of b-polarized exciton under study—and it is aimed to give back the observed stepwise thresholds bound to the bottom of the band. The model most likely fails for the exciton band as a whole, but anyhow, we could not avoid it without lengthening computation times excessively. 

The optical-phonon threshold at low temperature is not as sharp as experimental spectra show. The bidimensional exciton model does not account for the specific dispersions of excitons and phonons in anthracene. 

Calandra et al. [44] adapted Muller s model to potentiodynamic conditions. Mac Donald [45] corrected a typographical error found in the mathematical expressions in the article. Devilliers et al. [46] developed a general model for the formation of low-conductivity films, considering a process controlled by the solution resistance in the pores of the film. The authors simulated the potentiodynamic curves for the following particular cases constant film thickness (bidimensional growth), three-dimensional growth, and a decomposition/dissolution process coupled to the electrochemical reaction. The potentiodynamic curves simulated for constant thickness are identical to those obtained by Calandra et al. [44]. 

Rg.7 Possible packing model for nylon 6 in the mesomorphic form. The chain axes are placed at the nodes of a bidimensional hexagonal lattice. The concomitant formation of H-bonds along lines parallel to [100], [010] and [iTo] lattice direction is indicated. (Reprinted with permission from [163]. Copyright 1997 by the American Chemical Society)... 

The case of constant density of steps modeled by Wakai is equivalent to the diffusion-controlled creep modeled by Raj and Chyung [80], and it is also consistent with terms of the stress, temperature and grain size dependence of the strain rate for interface-reactioncreep predicted by others [80]. However, in the two cases of bidimensional nucleation of step and spiral step, the creep parameters differ from those predicted by the authors cited above. In particular, for 2-D nucleation there is a divergence of the creep parameters which has been recently solved [81], considering in detail the precipitation or solution of the crystalline material at the step, which changes significantly the free enthalpy involved in the process. 

Pseudohomogeneous Model Predictions, The full lines and dotted lines represent the average temperature for the Bidimensional and Unidimensional models, respectively. The broken and broken-dotted lines represent the T -q for the bidimensional and unidimensional models, T -q for the unidimensional model was assessed with eq. (1). 

Figure 2, T(z) functions in a methanol conversion catalytic reactor using Bidimensional and Unidimensional Heterogeneous Models ...

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