Model precision

Other aspects such as the quality of the data, the model precision, and the number of possible alternatives presented to the user as possible solutions of the problem or the degree of confidence of the final user on the DSS... 

The stoichiometric model precision was not attained yet. For the next iteration A2, A, and Af, were masked because 2(2), 2(3), and 2(6) were less than 4. In the third iteration the following stoichiometric coefficients were estimated ... 

After this iteration the desired model precision was achieved. Using the estimates of stoichiometric coefficients in chemical reaction equations, the following system is obtained ... 

In numerical studies it turned out that the MILP problem can not only be solved much faster than the MINLP problem, but for most of the model instances it provides solutions of significantly higher solution quality. Certainly, the engineered linearization of the nonlinear problem causes a loss in model precision, but on the other hand it enables a globally optimal solution. Since the MILP solutions are feasible for the MINLP problem, it is clear that the inferior quality of the MINLP solutions originates from the fact that only local minima were found. 

Experience with applying the Reynolds-stress model (RSM) to complex flows has shown that the most critical term in (4.52) to model precisely is the anisotropic rate-of-strain tensor 7 .--1 (Pope 2000). Relatively simple models are thus usually employed for the other unclosed terms. For example, the dissipation term is often assumed to be isotropic ... 

In reaction-rate modeling, precise parameter estimates are nearly as essential as the determination of the adequate functional form of the model. For example, in spite of imprecisely determined parameters, an adequate model will still predict the data well over the range that the data are taken,... 

The cut off parameter a is of order unity. Its value is somewhat arbitrary, reflecting the inability of this continuous spectrum to represent the long time behavior of the Rouse model precisely. Thus, with Eq. (4.33) and Eqs. (3.24) and (3.25) ... 

A management procedure for global model precision was proposed by Kondratyev, Krapivin, and Pshenin (2000). The main idea behind this procedure consists in the use of evolutionary modeling for the synthesis of a combined model whose structure is subject to adaptation against the background of the history of a system of the biosphere and climate components. The form of such a synthesis depends on the spatiotemporal completeness of the global database. 

Although an unstructured and non-segregated model includes simplifications of the cellular complexity, it is often used in culture simulation, because it is an adequate compromise between the available data, the difficulties involved in model formulation, and the desired model precision. 

First of all, it is necessary to continue and improve the monitoring of the principal parameters of the Black Sea and the Sea of Azov environment, which is subjected to a strong variability. In so doing, it is very important to use a combination of different methods of research such as traditional, satellite, drifter, numerical and laboratory modelling. Precisely this kind of approach should allow us to obtain reliable results by comparing the data acquired with different techniques. 

The use of local theories, incorporating parameters such as the eddy viscosity Km and eddy thermal conductivity Ke, has given reasonable descriptions of numerous important flow phenomena, notably large scale atmospheric circulations with small variations in topography and slowly varying surface temperatures. The main reason for this success is that the system dynamics are dominated primarily by inertial effects. In these circumstances it is not necessary that the model precisely describe the role of turbulent momentum and heat transport. By comparison, problems concerned with urban meso-meteorology will be much more sensitive to the assumed mode of the turbulent transport mechanism. The main features of interest for mesoscale calculations involve abrupt... 

Such solvents might be paint thinners, called Varnish Makers and Painters (V.M. P.) naphthas or mineral spirits. There are many other specialty solvent fractions manufactured in petroleum refineries. The product specifications for these solvents as well as for many refinery products are often given in terms of the simple ASTM distillation boiling ranges. However, for best results in modeling, precision distillation analysis is used, with end-product correlation to compare with specifications. Such an approach is often used also for fuel fractions, even to the extent of controlling the operation with gas chromatographic precision distillation analysis. 

The proposed theoretical methodology has been applied here to study and rationalize a 15 elementary reaction microkinetic mechanism for the WGSR on Cu(lll) for illustrative purposes. A reaction network has been constructed that incorporates all of the 26 direct RRs that have been previously generated using the conventional methods. Using the electrical circuit analogy the reaction network was subsequently simplified and reduced to a reaction network involving only 3 dominant RRs. An overall rate equation has been developed that reproduces the complete microkinetic model precisely. 

Changes in pnrity and yield of anserine-carnosine, concentrations of each component, and permeate flnx valne with processing time calculated with the mathematical model are shown in Fignre 22.11 together with experimental resnlts. The lines show calcnlated valnes, and the plots show experimental values. The calculated values are in good agreement with experimental valnes, and it was confirmed that the efficiency of the membrane pnrification process conld be predicted with this model precisely. 

Erman, B. The Gaussian network model precise prediction of residue fluctuations and application to binding problems, Biophys. J. 2006, 91,3589. 

We can increase model precision by performing replicates of the runs with the pure components. Then we will have =y and =J2, where and 3 2 are the averages of the rephcate responses. The standard errors of the and 63 values can be obtained directly from the expression we derived for the standard error of an average (Section 2.6) ... 

Experimental data never fit the model precisely. Often a variety of parameter estimates may give similarly good fits to the model and some of the predicted characteristics may be inconsistent with the physiological observations (Cobum et al., 1985). In the two-pool model used by Johansson et al., the urinary excretion of isotope after a single bolus will follow an equation of the general form... 

These three theoretical distributions describe only a very small portion of the diversity of polymer microstructures that are produced every day in academia and industry. Even for the polymerization systems they describe, they are only strictly valid as instantaneous distributions. If conditions in the polymerization reactor fluctuate as a function of time or spatial location, the distributions for the polymer product may be considerably more complex. In this case, it is very difficult to And a mathematical model precise enough to describe the complete polymer microstructure, and we must rely solely on experimental fractionation for its determination. In fact, the comparison of experimentally-measured mi-crostructural distributions with the ones predicted by theory is a powerful tool to investigate pol5mierization mechanisms and imderstand polymer reactor nonidealities. Nonetheless, these distributions are essential to realize the complexity of polymer microstructure and the interdependency of the distributions of molecular weight, chemical composition (or tacticity), and long-chain branching. This interdependency should always be kept in mind when interpreting the firactionation data from any experimental technique. 

The averaging procedure as discussed above for the isolated system is of limited value for several reasons. In the first place there is difficulty in calculating the value of Cl for such systems. Secondly, we are usually much more interested in the properties of a thermostated system than of an isolated one. Finally, as shown in Chapter 1, the second law is bound up with conditions relating to an energy transfer, and this involves at least two bodies. The case discussed above is thus of limited value as a statistical model precisely because the system in question is of fixed energy. 

Fluid effects are also very non-linear and it is often hard to model precisely interactions between tens of different air jets. Applying coherent control laws for hundreds of independent air jets is thus a complex problem. 

However, besides the simple ranking there is quite often even a quantitative prediction of the proeess attrition requested. This requires both an attrition model with a precise description of the process stress and as an input parameter to the model precise information on the material s attritability under this specific type of stress. This calls for attrition/friability tests that duplicate the process stress entirely. As will be elucidated in Sec. 5, the stress in a given fluidized bed system will be generated from at least three sources, i.e., the grid jets, the bubbling bed, and the cyclones. For each there is a corresponding friability test procedure. 

In the vicinity of the wall the tracers are submitted to a Taylor dispersion, that is, their diffusion combined with shear enhances the migration speed in the flow direction. This phenomenon seriously complicates all velocimetry methods since to extract the velocity of fluid this effect should be modeled precisely. As shown by analysis of DF-FCS data, large observed values of the apparent slip at the hydrophilic wall are normally fully attributed to a Taylor dispersion of nanotracers (see Fig. 2.6). The data obtained with other velocimetry technique still awaits clarification. We suggest, however, that some very large values of a hydrophobic slip might reflect a Taylor dispersion too. 

Before stating the model precisely, it should be pointed out although elementary, it is similar to the Arsenious acide-Iodate reaction and thus can provide useful results. 

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