Simplifying Concepts

Fluorine to Carbon Ratio (F/C) of Gas Phase Etching Species 

A third simplyfying concept is the utilization factor introduced by Chapman and Minkiewicz which is, in the case of CF etching of Si for example, simply the ratio of the rate at which fluorine is consumed in the etching process to the rate at which fluorine is injected into the system as CF. (Utilization factor = Qo i(SiF )/Q , (CF4) where and are the flow rates out of and into the etching system respectively.) In any etching process, the utilization factor should be substantially less than unity, say of the order of 0.1 or less. 

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Having made the comparison with experiment one may then make an assessment as to whether the simulation agrees sufficiently well to be useful in interpreting the experiment in detail. In cases where the agreement is not good, the detennination of the cause of the discrepancy is often instructive. The errors may arise from the simulation model or from the assumptions used in the experimental data reduction or both. In cases where the quantities examined agree, the simulation can be decomposed so as to isolate the principal components responsible for the observed intensities. Sometimes, then, the dynamics involved can be described by a simplified concept derived from the simulation. 

Develop suitably simplified concept of structural behavior to permit approximate determination of structural response—reactions, stress resultants, stability and stiffness requirements. Make appropriate assumptions within confines of laws of statics... 

Gas-liquid-particle operations are of a comparatively complicated physical nature Three phases are present, the flow patterns are extremely complex, and the number of elementary process steps may be quite large. Exact mathematical models of the fluid flow and the mass and heat transport in these operations probably cannot be developed at the present time. Descriptions of these systems will be based upon simplified concepts. 

The simplified concept of a gas-liquid-particle operation used in the following analysis is illustrated in Fig. 1. By considering a differential volume element of height dz, the following material balances may be formulated for one component in the three phases ... 

Many mixing models which utilize the simplified concepts of micro-mixing and segregation have been introduced. Most notable of these are the two-environment models of Chen and Fan (19), Kearns and Manning (20), and others (21, 22), and the dispersion models of Spielman and Levenspiel (23), and Kattan and Adler (24). 

According to Ashkenazi and Weaver (2007), lecture demonstrations can provide essential experiences that serve as a context for discussion of over-generalized or over-simplified concepts. The design of such demonstrations starts from surveying... 

FIGURE 6.8. A simplified concept for anaerobic transformations of organic matter in wastewater and biofilm of a sewer system. 

In [11] the alpha-particles were included into the EOS, and detailed comparisons of the outcome with respect to the alpha-particle contribution has been made. We will elaborate this item further, first by using a systematic quantum statistical treatment instead of the simplifying concept of excluded volume, second by including also other (two- and three-particle) correlations. 

Stimulated by a variety of commercial applications in fields such as xerography, solar energy conversion, thin-film active devices, and so forth, international interest in this subject area has increased dramatically since these early reports. The absence of long-range order invalidates the use of simplifying concepts such as the Bloch theorem, the counterpart of which has proved elusive for disordered systems. After more than a decade of concentrated research, there remains no example of an amorphous solid for the energy band structure, and the mode of electronic transport is still a subject for continued controversy. 

Additional explanatory material is added throughout the book. Some of the material explains further and simplifies concepts under discussion, while other material adds new information. In Chapter 2 paint pigments and binders are discussed. New information on surprising origins of ancient paint pigments and binders is added. In Chapter 3 supports for paints are described, and information is added about supports used in 50 B.C. that are still used today. In Chapter 6, in which jewelry making and the study of metals and electrochemistry are combined, an electromotive series is added to enhance cell voltage calculations. 

New guidance on traceability presents a simplifying concept of traceability which is appropriate for practical situations. This new paradigm clarifies the relative roles of method development, validation, trace-ability through calibration, and uncertainty estimation and provides a coherent picture of these activities in the context of wider QA management. The principles are... 

In real reactive absorption processes, the thermodynamic equilibrium can seldom be reached. Therefore, some correlation parameters such as tray efficiencies or HETP-values (Height Equivalent to One Theoretical Plate) are introduced to adjust the equilibrium-based theoretical description to the reality. However, reactive absorption always occurs in multicomponent mixtures, for which this simplified concept often fails [16, 23, 24]. 

Though the discovery of electrokinetic phenomena is certainly as old as Reuss s experiments in 1808,2 when he noted the transport of water through a plug of quartz powder, theories of its relation to the double layer began seriously with Helmholtz in 1879.3 He presented a simplified conception of the double layer with a plane layer of positive charges on one side of the phase boundary, and a similar plane layer of negative charges on the other side. 

Landsberg, J. J. Waring, R. H. (1997). A generalised model of forest productivity using simplified concepts of radiation-use efficiency, carbon balance and partitioning. Forest Ecology and Management, 95, 209-28. 

Figure 12-7 Simplified concept of prostaglandin and leukotriene synthesis pathway from eicosapentaenoic acid. Note the enzymes involved in this process (cyclooxygenase and lipoxygenase), which become the target for anti-inflammatory drugs. (From http //www.asthmaworld.org/OMEGA3.htm)...

These simplified concepts tend to exemplify the apparent utility of Prout s hypothesis as an organizing principle. The atomic mass number, often incorrectly truncated to atomic mass, treats protons and neutrons as equals. Taken too literally, the mass of uranium-238 would appear to be roughly equal to that of 238 hydrogens (protium or hydrogen-1 atoms) with some tiny discrepancy understood as arising from the 0.1% difference in mass between protons and neutrons. In fact, if we take the masses of 92 protons, 146 neutrons, and 92 electrons, the total mass is 240.0 amu. 

The overall DOC degradation is a sum of different enzymatic reactions involving different bacterium populations specialized to consume different electron acceptors. Only few models consider these biochemical reactions in detail (cf. Schafer et al., 1998). For simplicity we follow the common simplified concept, in which an overall DOC decay constant including all enzymatic reactions is formulated. For the overall degradation of DOC first order kinetics are assumed. 

The traditional approximation is to consider supersaturation as the driving force behind crystallization and precipitation. In fact, the true driving force is the chemical potential. In reaction crystallization, in particular, this approach is important. However, we will use the simplified concept of supersaturation in the following discussion. Supersaturation is defined as the difference between the actual and equilibrium, and is expressed as follows ... 

Describing the Hamiltonian structure for a constrained system is a little complicated to do formally. The simplifying concept that we exploit is that the symplectic 2-form in the ambient space can be projected to the co-tangent bundle to define an associated symplectic form on the manifold. 

FIGURE 17.16 Illustration showing the simplified concept of a traveling band of depolarization creating a net current dipole in the heart. 

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