Heuristic models

These, such as the black box that was the receptor at the turn of the century, usually are simple input/output functions with no mechanistic description (i.e., the drug interacts with the receptor and a response ensues). Another type, termed the Parsimonious model, is also simple but has a greater number of estimatable parameters. These do not completely characterize the experimental situation completely but do offer insights into mechanism. Models can be more complex as well. For example, complex models with a large number of estimatable parameters can be used to simulate behavior under a variety of conditions (simulation models). Similarly, complex models for which the number of independently verifiable parameters is low (termed heuristic models) can still be used to describe complex behaviors not apparent by simple inspection of the system. 

Mekenyan OG, Dimitrov SD, Pavlov TS, Veith GD. A systematic approach to simulating metabolism in computational toxicology. I. The TIMES heuristic modelling framework. Curr Pharm Des 2004 10 1273-93. 

The key attribute of flows in micro devices is their laminar character, which stands in contrast to the mostly turbulent flows in macroscopic process equipment. Owing to this feature, micro flows are a priori much more accessible to a model description than macro flows and can be described by first-principle approaches without any further assumptions. In contrast, for the simulation of turbulent flows usually a number of semi-heuristic models are applied, and in many situations it is not clear which description is most adequate for the problem under investigation. As a result, it stands to reason to assume that a rational design of micro reactors... 

On the basis of the presented oscillator-wave model it is also possible to create heuristic models of the interaction of electromagnetic waves with plasma particles in the Earth s ionosphere and magnetosphere, heuristic models of the generation of powerful low-frequency waves in the space around the Earth when a cosmic electromagnetic background is present etc. High-efficient sub-millimeter emitter, built on this basis, could be suitable for radio-physical heating of plasma, e.g. in the experiments aimed the achievement of controlable thermonuclear reaction [ ] ... 

A heuristic model of the CSC internal mechanics has been proposed based on extensive observations. The model provides explanations for qualitative and... 

Thakkar and Pedersen [410] continued this study by computing data for 122 linear molecules at the Hartree-Fock level. The bounds of Eqs. (5.122)-(5.123) were satisfied in all cases. Figure 5.10 shows the ratios Rt = p )lh computed by them [410] for fe = — 1,1,2. It shows that Eq. (5.119) is reasonably accurate with median errors of 2.2% in the = 1 case, but less so with median errors of 9.3 and 12% in the fe = 2 and fc = — 1 cases, respectively. The bounds of Eqs. (5.122) and (5.123) were found to be quite loose for k = —2, 3,4. Thakkar and Pedersen [410] also proposed some simple heuristic models relating (p ) and 4 more closely. The best of these was... 

F. Heslot, T. Baumberger, B. Caroli, and C Caroli, Creep, Stick-slip and Dry Friction Dynamics Experiments and a Heuristic Model, Phys. Rev., E49, 4973 (1994). 

Formulae (1.2) and (1.3) determine the model of a freely-jointed segment chain, which is frequently used in polymer physics as a microscopic heuristic model (Mazars 1996, 1998, 1999). A Kuhn segment in the flexible polymers (polyethylene, polystyrene, for example) usually includes a few monomer units, so that a typical length of the Kuhn segment is about 10 A or 10-7 cm and, at the number of segments 2 = 104, the end-to-end distance (R2)1 2 of a macromolecule is about 10-5 cm. 

One can make use of the heuristic model mentioned previously, in Section 1.1 each macromolecule consists of 2 segments and is surrounded by solvent molecules. It is not essential now to know whether the segments in the chain are connected or independent the results of this section are applicable in both cases. 

The first section of this chapter is devoted to the presentation of some diffusion models constructed on the basis of phenomenological considerations. These so-called heuristic models are often cited in the literature and used for the interpretation of experimental results. A special emphasis is to discuss how the mathematical formulae of these models can correlate with experimetal data and moreover to predict diffusion coefficients beyond the ranges experimentally investigated. This latter aspect is of great interest not only from a fundamental point of view but also in many practical fields where the possibility to predict a diffusion process might be a more economic alternative to its experimental investigation. 

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