Model quantitative form

If the central atom has different groups or atoms around it, or if one or more of the vertices of the polyhedron is occupied by a lone pair, then variations in bond angles will occur such that distorted polyhedral arrangements are obtained. In its quantitative forms, the VSEPR model parameterizes each individual interaction and makes very accurate predictions of the distortions which are to be expected. 

In summary, the chain dynamics for short times, where entanglement effects do not yet play a role, are excellently described by the picture of Langevin dynamics with entropic restoring forces. The Rouse model quantitatively describes (1) the Q-dependence of the characteristic relaxation rate, (2) the spectral form of both the self- and the pair correlation, and (3) it establishes the correct relation to the macroscopic viscosity. 

The quantitative form of the dead-layer model relates PL intensity to dead-layer thickness, which is assumed to approximate the depletion width W [6,7] ... 

Table I, Quantitative Form of Unified Field Model...

Consider a three-barrier profile in which the middle barrier is high compared with the extreme ones, so that both the inlet pits are in equilibrium with the ambient solutions (Figure 26a). As we will show below, this simple model can form the basis for a quantitative description of the parameters of sodium channels. In this particular case the rate constants are subject to the following condition ... 

This paper investigated the use of BNs expert model to support HRA dependence assessment. Two methods of input ehcitation are proposed (for discrete and continuous variables) to convert the analyst knowledge into the probabilistic input for the model the focus of the discussion and of the examples is on how the uncertainty in the analyst input is handled. Further, an interface is introduced that converts the output of the BN model into a quantitative form for a clear evaluation of the dependence, suitable for PSA application. 

Mr. Webb noted that there are clearly differences between spent fuel and high level r rocessing waste, but there is not any reason for basic safety requirements for either spent fuel or high level waste to be different, whether in store or disposed in a repository. He observed that the principles in the Safety Fundamentals for radioactive waste are very general. Requironents will have to be developed in a quantitative numerical form so that compliance can be demonstrated, for example, through predictive modelling. Quantitative requirements will have to be consistent with the IAEA Basic Safety Standards for radiation protection. For waste storage facilities, the requirements will be closely linked to current safety requirements for any other nuclear facility. 

Jeffreys 1939). Early quantitative forms for a Principle of Model Parsimony utilized a penalty term against using a larger number of uncertain (adjustable) parameters in combination with a quantification of the model data-fit based on the log likelihood of the optimal model in the model class (Akaike 1974) however, the form of this penalty term did not have a very rigorous basis. Subsequent work made it clear that Bayes Theorem at the model class level automatically enforces model parsimony without ad-hoc penalty terms (Gull 1989, Mackay 1991, Beck Yuen 2004). 

Bayesian methods for model updating and model class selection can be used to study systems which are essentially unidentifiable using classical system identification approaches. Additionally, viewing the problem of model class selection in a Bayesian context allows for a quantitative form for a Principle of Model Parsimony with an information-theoretic interpretation of model complexity (it relates to the amount of information extracted from the data by the model class). 

We now introduce a method that provides the simplest possible conceptual framework for analyzing microkinetic models of heterogeneous reactions, the so-called Sabatier analysis. We call it so because it brings out the qualitative reasoning behind the Sabatier principle in a quantitative form. 

Converting this intuition into a more quantitative form requires a more detailed physical model. Two such models are frequently used. In the first, simpler model, both the liquid and vapor are assumed well mixed. In the second model, the liquid is again assumed to be well mixed, but the gas is assumed to move in plug flow. Each is detailed below. 

To search for the forms of potentials we are considering here simple mechanical models. Two of them, namely cluster support algorithm (CSA) and plane support algorithm (PSA), were described in details in [6]. Providing the experiments with simulated and experimental data, it was shown that the iteration procedure yields the sweeping of the structures which are not volumetric-like or surface-like, correspondingly. While the number of required projections for the reconstruction is reduced by 10 -100 times, the quality of reconstruction estimated quantitatively remained quite comparative (sometimes even with less artefacts) with that result obtained by classic Computer Tomography (CT). 

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