Model dependency

The number and shape of the grid blocks in the model depend upon the objectives of the simulation. A 100 grid block model may be sufficient to confirm rate dependent processes described in the previous section, but a full field simulation to be used to optimise well locations and perforation intervals for a large field may contain up to 100,000 grid blocks. The larger the model, the more time consuming to build, and slower to run on the computer. 

The amount of detail input, and the type of simulation model depend upon the issues to be investigated, and the amount of data available. At the exploration and appraisal stage it would be unusual to create a simulation model, since the lack of data make simpler methods cheaper and as reliable. Simulation models are typically constructed at the field development planning stage of a field life, and are continually updated and increased in detail as more information becomes available. 

The quality of the results that can be obtained with point charge or dipole models depends critically on the input solvation shell structure. In view of the computer power available today, taking the most rigorous route... 

As reactants transfonn to products in a chemical reaction, reactant bonds are broken and refomied for the products. Different theoretical models are used to describe this process ranging from time-dependent classical or quantum dynamics [1,2], in which the motions of individual atoms are propagated, to models based on the postidates of statistical mechanics [3], The validity of the latter models depends on whether statistical mechanical treatments represent the actual nature of the atomic motions during the chemical reaction. Such a statistical mechanical description has been widely used in imimolecular kinetics [4] and appears to be an accurate model for many reactions. It is particularly instructive to discuss statistical models for unimolecular reactions, since the model may be fomuilated at the elementary microcanonical level and then averaged to obtain the canonical model. 

The utility of a protein model depends upon the use to which it is put. In some cases, on< only interested in the general fold that the protein adopts and so a relatively low-resoluti structure is acceptable. For other applications, such as drug design, the model must be me more accurate, including the loops and side chains. In such cases, a poor model may often fa r worse than no model at all, as it can be seriously misleading. 

Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Computations have shown that in the quantum region it is possible to have various most probable transition paths (ranging from the classical minimum energy path (MEP) to the straight-line one-dimensional tunneling of early models), depending on the PES geometry. 

The model-dependent aspect of ellipsometric analysis makes it a difficult technique. Several different models fit to one set of data may produce equivalendy low MSEs. The user must integrate and evaluate all available information about the sample to develop a physically realistic model. Another problem in applying ellip-sometry is determining when the parameters of the model are mathematically correlated for example, a thicker film but lower index of refraaion might give the same MSE as some other combinations of index and thickness. That is, the answer is not always unique. 

The effectiveness of a fluidized bed as a ehemical reactor depends to a large extent on the amount of convective and diffusive transfer between bubble gas and emulsion phase, since reaction usually occurs only when gas and solids are in contact. Often gas in the bubble cloud complex passes through the reactor in plug flow with little back mixing, while the solids are assumed to be well mixed. Actual reactor models depend greatly on kinetics and fluidization characteristics and become too complex to treat here. 

Markov modeling is a technique for calculating system reliability as exponential transitions between various states of operability, much like atomic transitions. In addition to the use of constant transition rates, the model depends only on the initial and final states (no memory). 

Use of the term mean-bulk temperature is to define the model from which temperatures are computed. In shock-compression modeling, especially in porous solids, temperatures computed are model dependent and are without definition unless specification of assumptions used in the calculations is given. The term mean-bulk temperature describes a model calculation in which the compressional energy is uniformly distributed throughout the sample without an attempt to specify local effects. In the energy localization case, it is well known that the computed temperatures can vary by an order of magnitude depending on the assumptions used in the calculation. 

Modify the value obtained from the previous stage to reflect possible dependencies among error probabilities assigned to individual steps in the task being evaluated. A dependence model is provided which allows for levels of dependence from complete dependence to independence to be modeled. Dependence could occur if one error affected the probability of subsequent errors, for example if the total time available to perform the task was reduced. 

In Section 8.4 we will encounter many empirical measures of solvent polarity. These are empirical in the sense that they are model dependent that is, they are defined in terms of a particular standard reaction or process. Thus, these empirical measures play a role in the study of solvent effects exactly analogous to that of the substituent constants in Chapter 7.)... 

We have seen that physical properties fail to correlate rate data in any general way, although some limited relationships can be found. Many workers have, therefore, sought alternative measures of solvent behavior as means for correlating and understanding reactivity data. These alternative quantities are the empirical measures described in this section. The adjective empirical in this usage is synonymous with model dependent this is. therefore, an extrathermodynamic approach, entirely analogous to the LFER methods of Chapter 7 with which structure-reactivity relationships can be studied. 

Some of these model-dependent quantities were formulated as measures of a particular phenomenon, such as electron-pair donor ability but many of them have been proposed as empirical measures of solvent polarity, with the goal, or hope, that they may embody a useful blend of solvent properties that quantitatively accounts for the solvent effect on reactivity. This section describes many, although not all, of these empirical measures. Reichardt has reviewed this subject. 

Casing must be designed to resist expected burst pressure at any depth. In burst pressure consideration, it is suggested to consider different design models depending upon the type of casing string. 

The margin of error of a final structural model depends on the sequence or fold similarity to the starting structural template. 

The action of a muscle is a consequence of electrochemically stimulated conformational relaxation processes that occur along every electroactive chain inside a polymeric film. A free-volume model dependent on the... 

Another model, first introduced by Moore, et al. (2i), was used to examine the role of terrestrial vegetation and the global carbon cycle, but did not include an ocean component. This model depended on estimates of carbon pool size and rates of CO2 uptake and release. This model has been used to project the effect of forest clearing and land-use change on the global carbon cycle (22, 23, 24). 

The dynamics of these models depend strictly on carbon fluxes, but the fluxes are poorly measured or are calculated from carbon reservoir size and assumptions about the residence time of the carbon in the reservoir. In addition, model fluxes are linear functions while in reality few, if any, probably are linear. 

The results reproduced from Ref. [28] and presented in Figure 7.1.9 show that the internal structure of the "flamelets" within the studied flames displays strong departures from both unstretched laminar flamelet and stretched counterflow flamelets. Figure 7.1.9 supports the picture of the perturbed flamelet model recently introduced in Ref. [29]. In this model, depending on the local value of the ratio of laminar flame thickness and... 

We observe that, in addition to the strain rate a, the computational model depends on the equivalence ratio (j) which is a measure of the relative proportion... 

For ionizable molecules, the membrane permeability, P (Pc in cellular models), depends on pH of the bulk aqueous solution. The maximum possible Pm is designated Pq, the intrinsic permeabiUty of the uncharged species. For monoprotic weak acids and bases, the relationship between P and Pq may be stated in terms of the fraction of the uncharged species,, as Pm= Pofo, i-e. ... 

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