Modeling strategy

A practical consideration in reaction modeling is choosing the extent to which reaction kinetics should be integrated into the calculations. On the one hand, kinetic 

We might take a purist s approach and attempt to use kinetic theory to describe the dissolution and precipitation of each mineral that might appear in the calculation. Such an approach, although appealing and conceptually correct, is seldom practical. The database required to support the calculation would have to include rate laws for every possible reaction mechanism for each of perhaps hundreds of minerals. Even unstable minerals that can be neglected in equilibrium models would have to be included in the database, since they might well form in a kinetic model (see Section 26.4, Ostwald s Step Rule). If we are to allow new minerals to form, furthermore, it will be necessary to describe how quickly each mineral can nucleate on each possible substrate. 

The modeling software would have to trace a number of reactions occurring at broadly different rates. Although certainly feasible, such a calculation can present practical difficulties, especially at the onset of a reaction path, if the software must take very small steps to accurately trace the progress of the faster reactions. For each calculation, furthermore, we would need to be able to set initial conditions, 

A practical consideration in reaction modeling is choosing the extent to which reaction kinetics should be integrated into the calculations. On the one hand, kinetic theory is an important generalization of the equilibrium model that lets us account for the fact that fluids and minerals do not necessarily coexist at equilibrium. On the other hand, the theory can add considerable complexity to developing and evaluating a reaction model. 

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The merits and demerits of the many computer-simulation approaches to grain growth are critically analysed in a book chapter by Humphreys and Hatherly (1995), and the reader is referred to this to gain an appreciation of how alternative modelling strategies can be compared and evaluated. A still more recent and very clear critical comparison of the various modelling approaches is by Miodownik (2001). 

Pais L. S., Loureiro J. M., Rodrigues A. E. (1998a) Modeling Strategies for Enantiomers Separation by SMB Chromatography, AIChEJ 44 561-569. 

In fact, we have already used a modeling strategy when Po(AU) was approximated as a Gaussian. This led to the second-order perturbation theory, which is only of limited accuracy. A simple extension of this approach is to represent Pq(AU) as a linear combination of n Gaussian functions, p, (AU), with different mean values and variances [40]... 

Teutschbein C, Seibert J (2010) Regional climate models for hydrological impact studies at the catchment scale a review of recent model strategies. Geogr Compass 4(7) 834—860... 

A general modeling strategy that has been successfully employed to model the joint velocity PDF in a wide class of turbulent flows30 is to develop stochastic models which... 

For an overview on this modeling strategy, see Pope (2000). For an alternative view based on statistical physics, see Minier and Pozorski (1997). 

For an ea HRh(CO)(alkene)(diphosphine), in which the hydride is assumed, as in Figure 3, to be in axial position, alkene have two coordination sites available, four conformations for each site, two rotation sides, N ligand conformations, and therefore 16xN TS s. Computation of the full catalytic cycle, all intermediates and TS s, from the entry of the substrate to the departure and regeneration of the catalyst, complemented with IRC calculations to confirm the connection between TS s and intermediates is out of reach for current computational resources. However, suitable modeling strategies can reduce of the problem, and still provide useful insight. 

Most of the modeling procedures commonly used require that the model first be reduced to a form which is linear in the unknown parameters. This procedure represents very good tactics the technique will be exploited frequently in this review, particularly in Section V. If the scope of the models to be used or the range of experimental variables to be explored is not limited when applying this philosophy, the procedure also represents good modeling strategy. 

For these reasons, a proper balance must be achieved between the linearization tactics and the overall modeling strategy. Both linear and nonlinear methods will be illustrated in the review, along with the problems encountered when relying too heavily on either single approach. First, however, some of the more common linear procedures will be discussed. 

Further development of statistical closures, especially in the algebraic form, is strongly recommended for description of two-phase flows. Of interest is inclusion of evaporation in the modeling strategies. It is expected that optimum closures will remain at the level of single-point, one-time, second-order moment. Consideration of differential transport equations for such moments appears to be computationally excessive so algebraic closures are expected to be more widely utilized. These closures portray the simplicity of zero-order schemes, yet preserve (some of) the capabilities of second-order closures. In more complicated flows, it... 

Jeanmougin M et al (2010) Should we abandon the r-test in the analysis of gene expression microarray data a comparison of variance modeling strategies. PLoS One 5 el2336. doi 10.1371/journal.pone.0012336... 

So, while there is growing interest in hybrid models of all sorts (as discussed in more detail in the next chapter), the choice of a mixed solvent model is not necessarily intrinsically better than a pure explicit or pure implicit model. In general, unless there is a strong suspicion that first-solvation-shell effects are drastically different from those more typically encountered, there is no particularly compelling reason to pursue a mixed modeling strategy. An example... 

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