Model decoupling

Let s look at two issues that arise with the use of encapsulation in packages model decoupling with auxiliary definitions and the use of encapsulation in specifications. 

Model Decoupling with Encapsulated Auxiliary Definitions... 

The multicomputer model decouples node-local activities from communication. This simplification decouples the performance critical aspects of parallel hardware calculations and communications. In practice it treats a multi-... 

SMART is applicable if integral information on contaminant behaviour in groundwater is sufficient. If point information is needed a conventional FD or FE model has to be used. Although it is obvious that the streamtube approach is not as flexible as real 3D models , decoupling of conservative transport and physico-chemical processes allow to model three-dimensional contaminant transport in a convenient and computationally efficient way, especially if only one representative streamtube must be modelled. Computation times, as observed by Peter et al. (chapter 14) are much lower compared to MT3D simulations. It should also be mentioned, that the streamtube approach possesses some advantages compared to real 3D models even if each and every streamtube has to be modelled by means of a numerical model in order to evaluate F. Since only one dimensional advective-reactive transport must be modelled, numerical solutions based on discrete or mechanistical approaches, free of numerical dispersion, can be applied. In SMART this is done by a so-called parceltracking approach where contaminant transport is described by means of a continuous series of water volumes ( parcels ) as described in Finkel et al. (1998). 

The MHM and the water balance model decouple when the liquid saturation is constant with this assumption, effective parameters of transport and reaction will be constant as well. This is the situation normally evaluated in CCL modeling. It will be considered next. Specific effects due to the complex coupling between porous morphology, liquid water formation, oxygen transport, and reaction rate distributions will be discussed in the section Water in Catalyst Layers The Watershed. ... 

For model A, the interfaces decouple from the bulk dynamics and their motion is driven entirely by the local curvature, and the surface tension plays only a background, but still an important, role. From this model A... 

Outline of a decoupled scheme for the differential constitutive models... 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

MODELS BASED ON DECOUPLED FLOW EQUATIONS -SIMULATION OF THE FLOW INSIDE A CONE-AND-PLATE RHEOMETER... 

In Chapter 4 the development of axisymmetric models in which the radial and axial components of flow field variables remain constant in the circumferential direction is discussed. In situations where deviation from such a perfect symmetry is small it may still be possible to decouple components of the equation of motion and analyse the flow regime as a combination of one- and two-dimensional systems. To provide an illustrative example for this type of approximation, in this section we consider the modelling of the flow field inside a cone-and-plate viscometer. 

MODELS BASED ON DECOUPLED FLOW EQUATIONS 163 Componeot of the equation of motion in the predominant, i.e. 6 direction... 

In principle, ideal decouphng eliminates control loop interactions and allows the closed-loop system to behave as a set of independent control loops. But in practice, this ideal behavior is not attained for a variety of reasons, including imperfect process models and the presence of saturation constraints on controller outputs and manipulated variables. Furthermore, the ideal decoupler design equations in (8-52) and (8-53) may not be physically realizable andthus would have to be approximated. 

Having demonstrated that our simulation reproduces the neutron data reasonably well, we may critically evaluate the models used to interpret the data. For the models to be analytically tractable, it is generally assumed that the center-of-mass and internal motions are decoupled so that the total intermediate scattering function can be written as a product of the expression for the center-of-mass motion and that for the internal motions. We have confirmed the validity of the decoupling assumption over a wide range of Q (data not shown). In the next two sections we take a closer look at our simulation to see to what extent the dynamics is consistent with models used to describe the dynamics. We discuss the motion of the center of mass in the next section and the internal dynamics of the hydrocarbon chains in Section IV.F. 

For either experiment we can consider that irradiated protons to flip back and forth between their two spin-states so rapidly that they no longer couple with other protons in the same molecule. An alternative rationale can be couched in terms of the decoupling field equalizing the populations of the two energy levels of the irradiated protons, which is qualitatively equivalent to saturating that resonance. (Although neither of these two models is strictly correct, they do at least provide a simple rationale for the N.M.D.R. experiment.)... 

In summary the results of our 2H NMR investigation illustrate the spacer model for liquid crystalline polymers, indicating, however, that the decoupling of the mesogenic groups from the main chain, while effective, is not complete. 

Thus it is important to obtain reliable models for catalyst deactivation and to investigate, whether it is possible to decouple the deactivation model from the kinetic model or if it is necessary to treat the catalyst deactivation as one of the surface reactions on the catalyst [45]. 

In conclusion, the inclined U-Pa and U-Th arrays appear to have some time significance because their interpretation as simply the result of recent mixing with a fluid containing Th and Pa as well as U requires fluid partition coefficients for Th and Pa well in excess of those observed experimentally. The corollary is that that there must be a decoupling between Ra-Th and Th-U disequilibria. A further possibility is a combination of the two end-member models discussed above into one in which some Th and Pa addition by fluids is followed by some in-growth due to ageing. In this case (discussed further below) the age inferred from the U-Th and U-Pa arrays is necessarily less straight forward to interpret. 

Therefore, efficient computation schemes of the state and sensitivity equations are of paramount importance. One such scheme can be developed based on the sequential integration of the sensitivity coefficients. The idea of decoupling the direct calculation of the sensitivity coefficients from the solution of the model equations was first introduced by Dunker (1984) for stiff chemical mechanisms... 

The physical significance of Eq. (53) is clear. At an isolated resonance the excitation and dissociation processes decouple, all memory of the two excitation pathways is lost by the time the molecule falls apart, and the associated phase vanishes. The structure described by Eq. (53) was observed in the channel phase for the dissociation of HI in the vicinity of the (isolated) 5sg resonance. The simplest model depicting this class of problems is shown schematically in Fig. 5d, corresponding to an isolated predissociation resonance. Figures 5e and 5f extend the sketches of Figs. 5c and 5d, respectively, to account qualitatively for overlapping resonances. 

Fig. 2.—A Portion of the Proton-decoupled, Natural-abundance, 13C-N.m.r. Spectra of Model Compound 6 and Bovine Ribonuclease B at 67.9 MHz. [(A) Compound 8 in HzO (25 mM, pH 6.5) after 8192 scans (2-s recycle-time) (B) spectrum of ribonuclease B after digital subtraction of the spectrum of ribonuclease A. (This enzyme has the same amino acid composition as ribonuclease B, but contains no carbohydrate.) Spectra were taken from Ref. 27.1...

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