Bases of representations

Reservoir simulation is a technique in which a computer-based mathematical representation of the reservoir is constructed and then used to predict its dynamic behaviour. The reservoir is gridded up into a number of grid blocks. The reservoir rock properties (porosity, saturation, and permeability), and the fluid properties (viscosity and the PVT properties) are specified for each grid block. 

The representation of molecular properties on molecular surfaces is only possible with values based on scalar fields. If vector fields, such as the electric fields of molecules, or potential directions of hydrogen bridge bonding, need to be visualized, other methods of representation must be applied. Generally, directed properties are displayed by spatially oriented cones or by field lines. 

In principle, DSI is the simplest method for sample introduction into a plasma torch since the sample is placed into the base of the flame, which then heats, evaporates, and ionizes the sample, all in one small region. Inherent sensitivity is high because the sample components are already in the flame. A diagrammatic representation of a DSI assembly is shown in Figure 17.4. 

Rules. Rules, first pioneered by early appHcations such as Mycin and Rl, are probably the most common form of representation used in knowledge-based systems. The basic idea of rule-based representation is simple. Pieces of knowledge are represented as IE—THEN rules. IE—THEN rules are essentially association pairs, specifying that IE certain preconditions are met, THEN certain fact(s) can be concluded. The preconditions are referred to as the left-hand side (LHS) of the rule, while the conclusions are referred to as the right-hand side (RHS). In simple rule-based systems, both the... 

Rules are cleady a usehil form of representation for knowledge-based appHcations, with their advantages of representational simplicity, wide apphcabihty, and history of past successes. However, certain important design criteria govern the proper appHcation of rules and there are shortcomings of the rule-based representation. 

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

Representation of GC X GC as a two-dimensional separation, with separation mechanisms based of different chemical properties in each dimension. 

The sub-micro level is real, but is not visible and so it can be difficult to comprehend. As Kozma and Russell (1997) point out, understanding chemistry relies on making sense of the invisible and the untouchable (p. 949). Explaining chemical reactions demands that a mental picture is developed to represent the sub-micro particles in the substances being observed. Chemical diagrams are one form of representation that contributes to a mental model. It is not yet possible to see how the atoms interact, thus the chemist relies on the atomic theory of matter on which the sub-micro level is based. This is presented diagrammatically in Fig. 8.2. The links from the sub-micro level to the theory and representational level is shown with the dotted line. 

Chiu, M. L., Chiu, M. H., Ho, C. Y. (2003). Using cognitive-based dynamie representations to diagnose students conceptions of the characteristics of matter. Proceedings of the National Science Council Part D Mathematics, Science, and Technology Education, 12(3), 91-99. 

How did the pedagogical elements provided in support of the modelhng-based teaching activities contribute to the development of understanding about the levels of representation, thus to the learning of the nature of chemical equilibrium ... 

What capability did the students have both to visualize the three levels of representation and to move between them, during this modelling-based teaching ... 

In order to address this research question, we browsed the original case studies to identify evidence of how the students dealt with the levels of representation and of any possible relationship between such students activities and any of the elements of the modelling-based teaching. In the following discussion, the most relevant elements of this teaching are emphasised. 

What is the relatiorrship between the way stndents nse the three levels of representation and their capability to test their models As testing models (from thought experiments and/or empirical ways) is an essential stage of the modelling process, their expertise in dealing with the three levels of representation seems to be vital for their learning in modelling-based corrtexts. 

Strict requirement and can be theoretically met only if we know the underlying continuous function that provides the values of the derivatives at the time points of a discrete representation. The availability, though, of such a continuous function is based on a series of ad hoc decisions on the character and properties of the functions, and if one prefers to avoid them, then one must accept a series of approximations for the evaluation of first and second derivatives. These approximations provide a sequence of representations with increasing abstraction, leading, ultimately, to qualitative descriptions of the state and trend as follows (Cheung and Stephanopoulos, 1990) ... 

In these frames all specific columns that are relevant for the reasoning process of the expert system can be described in a structured and comprehensive way. The frame-based and rule-based knowledge representation are both required to represent expertise in a natural way. Therefore, in most expert systems a combination of rule-based and frame-based knowledge representation is used. The rule base together with the factual and descriptive knowledge by means, of e.g., frames constitute the knowledge base of the expert system. 

Another group has evaluated self-organizing maps [63] and shape/ pharmacophore models [64]. They developed a new method termed SQUIRREL to compare molecules in terms of both shape and pharmacophore points. Thus from a commercial library of 199,272 compounds, 1926 were selected based on self-organizing maps trained on peroxisome proliferator-activated receptor a (PPARa) "activity islands." The compounds were further evaluated with SQUIRREL and 7 out of 21 molecules selected were found to be active in PPARa. Furthermore, a new virtual screening technique (PhAST) was developed based on representation of molecules as text strings that describe their pharmacophores [65]. 

The eigenvalue equation of the representation of the effective Hamiltonian operators (28) in the base of the number occupation operator of the slow mode is characterized by the equation... 

Now, it may be of interest to look at the connection between the autocorrelation functions appearing in the standard and the adiabatic approaches. Clearly, it is the representation I of the adiabatic approach which is the most narrowing to that of the standard one [see Eqs. (43) and (17)] because both are involving the diagonalization of the matricial representation of Hamiltonians, within the product base built up from the bases of the quantum harmonic oscillators corresponding to the separate slow and fast modes. However, among the... 

---