Modelling Interactions between Channels

While discrete models have the advantage to describe the performance of the separate channels in the monolith matrix, monoliths containing complex geome- 

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In Boyaci (2001), a manufacturer sells through a self-owned distribution channel as well as a competing retail channel This model is distinctive in considering stochastic demand, in which inventory is the basis of interaction between channels. 

Most of the works that model competitive interactions between channel members assume entirely deterministic environments, so that improved information has no value whatsoever. Among models that include uncertainty, the vast majority assumes common knowledge, in which case the channel choice does not affect the manufacturer s state of information. Experience thus far indicates that asymmetric information is difficult to model even in dyadic models with an extremely stylized representation of uncertainty. 

In many practical problems, interactions between the variables appear so that the absolute global optimum can be found heavily. As an example, wavelength selection in NIR determination of blood glucose (see Sect. 6.2.6) is considered. The aim of the selection is to find such combinations of wavelengths with which calibration models are obtained their prediction quality is as near at the global optimum as possible (Danzer et al. [2001], p 174). The number of combinations C for the selection of k wavelengths from n channels of the spectrometer is given by... 

How exactly the molecules are oriented inside the channels depends on their specific shape and on the adsorption interaction between the dyes and the channel walls or charge compensating cations. Because of the dye s oblongness, a double-cone-like distribution in the channels is a reasonable model. This distribution is illustrated in Fig. 19a. The arrows represent the transition moments of the dyes and a describes the half-opening angle of the double cone. The hexagonal structure of the zeolite L crystal hence allows six equivalent positions of the transition moments on this double cone with respect to the channel axis. 

We study the diffusion of the solute particles transported by the Poiseuille velocity profile in a semi-infinite two-dimensional (2D) channel. Solute particles are participants in a chemical reaction with the boundary of the channel. They do not interact between them. The simplest example is described by the following model for the solute concentration c ... 

The ash simulation model (Konstandopoulos et al., 2003 Rodriguez-Perez et al., 2004) consists of ash transport and ash layer evolution equations describing the interaction between ash deposition and re-entrainment in the channels along with the gas mass balance and momentum balance equations in the inlet and outlet channels of the DPF. Ash re-entrainment is initiated by flow... 

Fig. 5.5 A hinged-lid model for Na+-channel inactivation and schematic representation of the interaction between a local anesthetic drug and the amino acid residues in the inactivation gate. (Reprinted from Fig. 2 of ref.

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