Attenuation Models

Until now, we have discussed the use of additivity schemes to estimate global properties of a molecule such as its mean molecular polarizability, its heat of formation, or its average binding energy to a protein receptor. 

Many phenomena ask for local, site-specific properties of a molecule such as the partial charge on a specific atom in a molecule or the hydrogen bond donor ability of a certain OH group. It would be highly desirable to have methods as simple as an additivity model to estimate such site-specific molecular properties. 

328 I 7,1 Empirical Approaches to the Calculation of Properties normal binders 

Clearly, simple additivity of atom properties will no longer suffice, as the contribution of an atom will diminish the hirther it is away from the atom whose property has to be estimated. In the following, we present two methods of accounting for the influence of one atom on another, attenuated over the distance between the two atoms. 

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The polarizability effect can be calculated by a simple attenuation model. 

Aziz CE, Newell CJ, Gonzales JR, Haas PE, Clement TP, Sun Y (1999) Biochlor natural attenuation model for chlorinated solvent sites. Natural attenuation of chlorinated solvents,petroleum,hydrocarbons, and other organic compounds. Battelle Press, Columbus, OH... 

Keywords contaminated land natural attenuation model 1. Introduction... 

BIOSCREEN A natural attenuation model for hydrocarbon plumes ... 

BIOPLUME IV A new natural attenuation model for evaluating emerging degradation pathways. 

Fig. 14.17 A. Diagram illustrating the double BSR observed in seismic data in the vicinity of Site 1247. B. Chloride concentration in pore waters from site 1247, compared with expected values derived from a diffusive attenuation model following gas hydrate dissociation. The assumed hydrate content at time zero has a width of 10 m and a magnitude comparable to the anomaly observed just above the present BSR (BSRp). The data suggest that the hydrate dissociation occurred 5000 yrs ago. The authors postulate that pressure and temperature changes in the period of 8000 to 4000 years ago, led to a shift in the depth of the hydrate stability zone, creating the double BSR (modified from Bangs et al. 2005).

The rates of photochemical production that were input into the model are taken from laboratory quantum yield measurements, discussed earlier (see section In situ formation"). These are Incorporated Into a light attenuation model that employs the extinction coefficient of light In water with the clarity of the Gulf of Mexico. The dark decay lifetime of 2 2 chosen to be 4 days, and constant with depth. The dark decay lifetime varies from hours In coastal environments to over a week In ollgotrophlc waters, but 4 days Is commonly observed for offshore surface water (7). It is clear from Figure 7 that. In the absence of any mixing processes, builds up to high concentrations with little dlel... 

The coupling of photochemistry and physical mixing in a model is a challenging task for three reasons. First, the photochemical production and decomposition rates, as well as the dark decay rates of Interest, are often poor estimates. This Is both because of the lack of good laboratory kinetic measurements and because the light attenuation models Into which such measurements are Incorporated are subject to additional uncertainties. Second, the one-dlmenslonal mixing models make certain assumptions and... 

In the literature Shi and Shen [235], Wang et al. [270], Wong et al. [273] and Zheng and Wong [302], the Crouse-McGuire model [65] was used for the attenuation model with the strong-motion records from different areas of China and this model has essentially a different functional form from Equation (6.75) ... 

The BIOCHLOR Natural Attenuation Model simulates ehlorinated solvent natural attenuation using an Exeel based interfaee. BIOCHLOR simulates the following reduetive deehlorination proeess ... 

Table 3.2 Residual analysis for each sugar attenuation modelled using the modified Gompertz, IBF and 5P logistic models...

Another significant change was the attenuation model for fluence through the vessel wall. In Revision 1, the attenuation model used a fast neutron exposure (n/cm, E > 1 MeV) as the attenuated fluence, whereas Revision 2 used a displacements per atom (dpa) model for attenuation through the vessel wall. The attenuation using dpa is less than for fast neutron, which means that the projected embrittlement at 14-thickness and %-thickness is higher using the dpa model. 

Fig. 8 Response spectra for an event Mw = 7 and R = 10 km) scaled to the median SJJo) = 0.12 g of a set of 98 records and the median spectrum for the set. The median is compared with the average of the four NGA attenuation models (Bozorgnia et al. 2014).

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