Modeling hierarchy

Let C, be a temporal constraint, stated between two goals, A, and B at the ith level of the modeling hierarchy (see Section II,B), which indicates that A, must be achieved before B,. Let A(,, and with... 

Figure 2. Multiscale modeling hierarchy. AIMD ab initio molecular dynamics, MD molecular dynamics, KMC kinetic Monte Carlo modeling, and FEA finite element analysis.

It is worth reconsidering the reaction modelling hierarchy of Figure 1 in the light of the foregoing discussion. Clearly, the relevant global models are easily formulated and nicely adaptable to process engineering models. However, they do so at the expense of chemical fundamentals and therefore can only be used as interpretative correlations. At the other extreme, mechanistic models provide detailed chemical analyses of reaction systems. However, they bear the burden of extensive computational requirements and face the reality of the paucity of experimental data. Molecular models provide a convenient compromise between the two. The CPU requirements are reasonable, while at the same time chemical fundamentals are retained because of the implicit connection to reaction mechanisms. 

Obviously, the spectrum of mesoscale, particle-based tools is too vast to be covered in a single paper. Therefore, in this and the subsequent sections, I mainly elaborate on MC methods to illustrate various aspects of multiscale modeling and simulation. Below, the modeling hierarchy for stochastic well-mixed chemically reacting systems is first outlined, followed by a brief introduction to MC methods. 

To account for all representational needs in process engineering, MODEL.LA uses six (6) basic classes of modeling elements, and fairly rich modeling hierarchies of subclasses, emanating from the basic modeling elements. 

MODEL.LA. is a language with infinite extensibility of its vocabulary, enabled by a fixed set of she modeling hierarchies and a fixed set of 13 semantic relationships. In Section IV.C, we discussed the hierarchies of modeling subclasses emanating from the six basic modeling elements. What is far more important for the modeling power of MODEL.LA. is its... 

The modeling hierarchies of constraint and generic-variable (see Section IV.C) have been expanded to a series of subclasses, which... 

Fig. 20. Partial view of the modeling hierarchy of term class, which represent terms in balance equations.

The next level of detail in the model hierarchy of Fig. 6.2 is the so-called dumped rate models" (third from the bottom). They are characterized by a second parameter describing rate limitations apart from axial dispersion. This second parameter subdivides the models into those where either mass transport or kinetic terms are rate limiting. No concentration distribution inside the particles is considered and, formally, the diffusion coefficients inside the adsorbent are assumed to be infinite. 

Specific cross-validation schemes for three-way data are given main emphasis. The choice of models and model hierarchy are explained. It is important to get a good fit and parsimony. The selection of appropriate model rank by the use scree plots, residual analysis and split-half analysis is introduced. Different ways of calculating residual statistics and leverages for three-way arrays are presented. 

Figure 13.2 Multi-scale modelling hierarchy [35], showing the approximate regimes of time and length scales over which atomistic modelling techniques (quantum and molecular mechanics) can usefully be applied and how these link with process methods via mesoscale modelling.

To further demonstrate the concept of model hierarchy and its importance in analysis, let us consider a problem of heat removal from a bath of hot solvent by immersing steel rods into the bath and allowing the heat to dissipate from the hot solvent bath through the rod and thence to the atmosphere (Fig. 1.4). 

Model Hierarchy and Its Importance in Analysis 19 Solving for T from Eq. 1.52 yields... 

To account for effects of temperature gradients in the rod, we must move to the next level in the model hierarchy, which is to say that a differential volume must be considered. 

Levels 1 and 2 solutions have one assumption in common The rod temperature below the solvent surface was taken to be uniform. The validity of this modelling assumption will not be known until we move up one more level in the model hierarchy. 

In summary, we have illustrated how proper model hierarchy sets limits on the lower levels. In particular, one can derive criteria (like Eq. 1.91) to show when the simpler models are valid. Some solutions for the simpler models can be found in Walas (1991). 

Sisti Farr 98 Depends on the model to be abstracted Abstracted Models using boundary, behavior and form abstractions No Objective was to improve accuracy at aggregate level, compared the terms accuracy, complexity and level of detail and showed how to create model hierarchies that can be intercoimected and reused... 

Figure 4.15 Model hierarchy for gas-solid fluidized beds.

First, an overview of various modeling strategies is presented. Then, further details of modeling hierarchy are presented, including governing eqirations, starting from one-dimensional models and extending to fully three-dimensional models. In addition, a simple one dimensional thermal model which computes the temperat-... 

Regarding a hazard log as a tool for Change Safety Management, Configuration Control and Reporting, the anthor analysed the problem domain from the system perspective, identified reqnirements and defined the data model (hierarchy and topology) for the hazard log. 

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