Stacking probability models

An improved modelling of the average structure of ice Ic includes linear combination of stacking-probability driven structure models and anisotropic size broadening. It allows for a quantitative modelling of neutron diffraction data of different ice Ic samples. It will serve as well for the description of ice Ih samples with stacking faults. 

Because of extreme venting conditions assumed, effective stack heights and resultant plumes from both 3- and 5-minute discharge conditions attain heights beyond the micro-meteorological conditions assumed in accepted computation models. It is therefore highly probable there will be considerably further atmospheric dispersion and diffusion of the VCM than predicted in the results shown. That is, the ground level concentration can be expected to be considerably lower than the values shown in Table 6. 

The General Series Expansion for Stacks. In practice, ID scattering intensities can always be modeled by programming the obvious series expansion of such a structural entity every correlated distance along the stack axis is producing an attenuated oscillation according to Hk (5) that is weighted by the probability of its occurrence under consideration of the zero-sum rule and the related correlation-construction principle (p. 158, Fig. 8.30)... 

On the basis of the model (Case-1), diffraction intensity from an infinite 2-dimensional crystal was mathematically formulated by incorporating the probability, p, of occurrence of a stacking fault (-AA- or -BB- ) in the crystal [30-32], The result clearly showed that the SAED pattern is well reproduced by this formulation with p<0.5. 

Most chemists would probably guess the former. Afterall, benzene is flat and flat things stack . However, graphical models lead one to the correct conclusion that a perpendicular arrangement is favored. 

Metal Emission Limits. Limits for metals, both carcinogenic and noncarcinogenic, are based on an adjusted stack height. Failure to meet these limits requires risk assessments using site specific factors and modeling to establish limits for each metal. The assessments are based on the probability of developing adverse health effects or cancer, based on an inhalation exposure pathway to maximum exposed individuals located near the incinerator (see Hazard ANALYSIS AND RISKASSESSL nt). 

In order to estimate the probability of impact of the moistened part of a particle by surrounded particles in the fluidized bed, a simple model was developed [69], As an assumption that the fluidized bed is in an homogeneous condition, a certain portion of the relative porosity is assigned to each particle, and the shape of air covering the particle is taken to be a cube (Fig. 16.16). The entire bed consists of stacked cubes containing a particle at their center. The amount of air - and in consequence the distance between the particles - becomes larger for example, with the same fluidization mass flow the Archimedes number is decreased. The bed will then expand with a greater fluidization throughput and with a constant Archimedes number hence, the distance between the surrounded particles will increase. 

Tuncel et al. tabulated S/Se ratios for particles from many locations (4). The ratio is about 3000 at rural sites downwind, but outside of coal-burning areas. In the midst of the ORV, it is depressed to about 1700, in agreement with the model. In the midst of cities in which substantial coal is burned, the ratio is depressed to 1000 or less. Except for a few samples at Allegheny Mt. collected downwind from three power plants, Tuncel et al. did not see sudden drops in the S/Se ratio that one would expect to see occasionally in fresh plumes from coal-fired plants. A major flaw in the Gor-don/Olmez model is the assumption of uniform vertical concentration profiles, which is surely a poor assumption just beyond a source. Most power plants have tall stacks, whereas, measurements are at ground level. The S/Se ratio will surely be depressed near the plume centerline, but the effect will usually be washed out before the plume hits ground level. However, around cities, there are probably some ground level sources. 

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