Non-uniform distribution

This is illustrated in Eig. 2.30 [2.167]. The surface was that of a fractured compact of SiC to which horon and carhon had been added to aid the sintering process. The aim of the analysis was to establish the uniformity of distribution of the additives and the presence or absence of impurities. The Auger maps show not only very non-uniform distribution of boron (Eig. 2.30a) but also strong correlation of boron with sodium (Eig. 2.30c), and weaker correlation of boron with potassium (Eig. 2.30b). Point analyses for points A and B marked on the images reveal the presence of sulfur and cal-... 

Intermittent (I) - In this flow pattern the liquid inventory in the pipe is non-uniformly distributed axially. Plugs or slugs of liquid that fill the pipe are separated by gas zones that contain a stratified liquid layer flowing along the bottom of the... 

For distributors of any design, including the PAN, it is important to filter the feed or reflux liquid entering tlie distributor to reduce the possibilities of plugging of tlic orifice holes. Otherwise, the landom plugging will cause non-uniform distribution onto the packing below. It is important to avoid leakage around the risers because this can destroy the liquid distiibution pattern [131]. 

Since it is often difficult to visualise the extent of attack in terms of depth from such mass-loss units as mdd, it is common practice to convert these mdd figures into others to indicate depth of penetration, i.e. inches per year (ipy), mils or mm y" . Such calculations suffer from the same defects as the mdd figures in that they take into account neither changes in corrosion rates with time nor non-uniform distribution of corrosion. However, since such conversions are often made it is desirable for the initial reporter of the test results to make the calculations accurately and to report corrosion rates in both mdd and mm y or similar units. 

Weights will be unconsciously applied if operating conditions are non-uniformly distributed in the experimental space. Estimated model parameters will then better reproduce the experimental data from that part of the space where the density of experimentation is greater. Therefore, statistical methods of planning of kinetic experiments, possibly modified by appropriate transformation of variables, are strongly recommended. 

Uneven distributions of residuals. The MaxEnt calculations in presence of an overall chi-square constraint suffer from highly non-uniform distributions of residuals, first reported and discussed by Jauch and Palmer [29, 30] the error accumulates on a few strong reflexions at low-resolution. The phenomenon is only partially cured by devising an ad hoc weighting scheme [20,31, 32]. Carvalho et al. have discussed this topic, and suggested that the recourse to as many constraints as degrees of freedom would cure the problem [33]. 

Finally, recent work of Iversen et al. has carefully examined the bias associated to the accumulation of the error on low-order reflexions, and attempted a correction of the MaxEnt density [39]. The study, based on a number of noisy data sets generated with Monte Carlo simulations, has produced less non-uniform distribution of residuals, and has given quantitative estimate of the bias introduced by the uniform prior prejudice. For more details on this work, we refer the reader to the chapter by Iversen that appears in this same book. 

Anisotropy Non-uniform distribution of electrons about a group which can lead to non-uniform localised magnetic fields within a molecule. The phenomenon leads to unexpected chemical shifts -particularly in 1H NMR - in molecules where steric constraints are present. 

Owing to the chain orientation distribution the fracture mechanism of oriented polymer fibres is different from that of isotropic fibres. The presence of this distribution leads to a non-uniform distribution of the strain energy between the domains. The strain energy is defined by... 

The rate of uptake from blood and by different organs varies widely, and so does the rate of elimination from different organs. Inorganic mercury is characterized by a markedly non-uniform distribution in the body. Compartmentali-zation of mercury within different parts of the organ or in subcellular structures, the binding of mercury to various chemical compounds within the cell, and the metabolic transformation of mercury, complicate the evaluation of distribution. 

For multi-dimensional flows, the mean velocity field may be a function of x. For this case, deterministic errors can be introduced through (V )(A-I" t), resulting in a non-uniform distribution for Xin, (t). This is an important source of numerical error in transported PDF codes, and we will look at this problem in more detail in Chapter 7. 

Pore diameters of the PS layer formed under a given set of conditions have a distinct distribution. Normal, log-normal, bimodal, fractal, and non-uniform distributions have been found for PS formed under different conditions.26,29,60,88,89,90,91... 

Statistics plays a crucial role in any data analysis, and accordingly, the statistical aspects are mentioned and appropriate equations/code are supplied. E.g. examples are given for the least-squares analysis of data with white noise as well as y2-analyses for data with non-uniformly distributed noise. However, the statistical background for the appropriate choice of the two methods and more importantly, the effects of wrong assumptions about the noise structure are not included. 

Inhaled nicotine is efficiently delivered to the brain (see chapter by Benowitz, this volume) where it selectively interacts with its central targets, the neuronal nicotinic acetylcholine receptors (nAChRs). The multiple subtypes of uAChR (see chapter by Collins et al, this volume) all bind nicotine but with different affinities, depending on the subunit composition of the uAChR. Binding may result in activation or desensitisation of uAChRs, reflecting the temporal characteristics of nicotine dehvery and local concentration of nicotine. Another level of complexity of the actions of nicotine reflects the widespread and non-uniform distribution of uAChR subtypes within the brain, such that nicotine can influence many centrally regulated functions in addition to the reward systems. In this chapter, we address the consequences of nicotine interactions with nAChRs at the molecular, cellular and anatomical levels. We critically evaluate experimental approaches, with respect to their relevance to human smoking, and contrast the acute and chronic effects of nicotine. 

While adsorption equiUbrium considerations do justify the possibility to regenerate an adsorbent bed completely and to uniform levels, this is rarely achieved in practice in either thermal swing adsorption and is almost never the case in pressure swing adsorption. Some residual sorbate is always left on the sorbent and in general, except for TSA with only one or two sorbates, the residual loadings are almost always found as a non-uniformly distributed profile across the length of the bed. 

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