Statistical screening effect

Despite the fact that formalism of the standard chemical kinetics (Chapter 2) was widely and successfully used in interpreting actual experimental data [70], it is not well justified theoretically in fact, in its derivation the solution of a pair problem with non-screened potential U (r) = — e2/(er) is used. However, in the statistical physics of a system of charged particles the so-called Coulomb catastrophes [75] have been known for a long time and they have arisen just because of the neglect of the essentially many-particle charge screening effects. An attempt [76] to use the screened Coulomb interaction characterized by the phenomenological parameter - the Debye radius Rd [75] does not solve the problem since K(oo) has been still traditionally calculated in the same pair approximation. 

The ruggedization of the analytical procedure was performed by applying statistical screening techniques to minimize the effort required and, therefore, reduce the time and the cost substantially. The statistical approaches used in this study were those first introduced by Plackett-Burman (3.) and Youden-Steiner (4). Both techniques reduce the required effort since they use balanced incomplete block design experiments which can clearly indicate the non-affecting parameters from those that may have an effect. In this study the important variables of the analytical method were identified by using the Plackett-Burman technique. 

In addition to these screening effects, the actual evolution of matrix cracks at stresses above amc is governed by statistics that relate to the size and spatial distribution of matrix flaws. If this distribution is known, the evolution can be predicted. Such statistical effects arise when the matrix flaws are smaller than the transition size, a at which steady state commences (Eqn. (36)). In this case, a flaw size distribution must be combined with the short crack solution for K,ip (Eqn. (37)) in order to predict crack evolution. At the simplest level, this... 

The state of a statistical fractal in which the excluded volume effect is compensated by the screening effect is referred to as the compensated state. For this state. Family has found that ... 

Screening effects from the inner shell have been examined also in the work devoted to double X-vacancy sharing. For the system S + Ar McDonald et alP have detected a 20% difference in the one-electron probability for transitions into the 2o- MO with one and two vacancies. However, for most heavier systems such effects have not been observed. The experimental results for double X-vacancy sharing have been shown to be in accordance with statistical rules for nonrelaxed orbitals such as those given in Eq. (28). Hence, as expected, the screening effects from inner shells diminish for heavier collision partners. 

The screening effect of other ions is neglected, as g is considered to be small. Let I be that part of the statistical mechanical phase integral which corresponds to the region close to the line charge ... 

Because of the complexities involved in understanding cause-effect relationships, an alternative approach to control the thin film microstructure has been pursued by some investigators—the use of statistically designed experiments to identify key processing parameters.114115 In these approaches, as illustrated in Table 2.6 for a Plackett-Burman screening study,114 limiting values for various experimental parameters are chosen. Films are then prepared from solutions synthesized under these conditions, and resulting film... 

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