Direct analogy

It struck me that the bones of the human ear were very massive, indeed, as compared with the delicate membrane that operated them, and the thought occurred that if a membrane so delicate could move bones relatively so massive, why should not a thicker and stouter piece of membrane move my piece of steel. And the telephone was conceived. (Eigure 8.6) 

If an apple is attracted by the earth, why can t any two objects be attracted to each other in the same way (Eigure 8.7) 

Eor engineering applications, Newton s analogy can be generalized and presented as 

If X works in a desired way under given circumstances, why can t Y work in a similar way under the same circumstances  

When a direct analogy is presented in such a general form, it becomes a heuristic and can be used for many engineering and creative purposes. This heuristic helps us to reason that if steel can be used to build a car chassis, aluminum could be also used, as Ford did recently in its 2015 FI 50 light truck. 

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In this section, we concentrate on the relationship between diffraction pattern and surface lattice [5], In direct analogy with the tln-ee-dimensional bulk case, the surface lattice is defined by two vectors a and b parallel to the surface (defined already above), subtended by an angle y a and b together specify one unit cell, as illustrated in figure B1.21.4. Withm that unit cell atoms are arranged according to a basis, which is the list of atomic coordinates within drat unit cell we need not know these positions for the purposes of this discussion. Note that this unit cell can be viewed as being infinitely deep in the third dimension (perpendicular to the surface), so as to include all atoms below the surface to arbitrary depth. 

Cross-Flow Filtration in Porous Pipes. Another way of limiting cake growth is to pump the slurry through porous pipes at high velocities of the order of thousands of times the filtration velocity through the walls of the pipes. This is ia direct analogy with the now weU-estabHshed process of ultrafiltration which itself borders on reverse osmosis at the molecular level. The three processes are closely related yet different ia many respects. 

Hygroscopic (moisture) effects arise for polymer materials such as some epoxies that absorb moisture chemically after curing and therefore expand. These effects are directly analogous to thermal effects and are characterized by coefficients of moisture expansion and p2 in principal material coordinates in direct analogy to a.( and 02 for coefficients of thermal expansion. All calculations for thermal effects with the a can be replaced by or supplemented with analogous terms for moisture expansion. 

For saturated fatty acids, the process of /3-oxidation involves a recurring cycle of four steps, as shown in Figure 24.10. The overall strategy in the first three steps is to create a carbonyl group on the /3-carbon by oxidizing the C, —C bond to form an olefin, with subsequent hydration and oxidation. In essence, this cycle is directly analogous to the sequence of reactions converting succi-... 

Local geometry altering rules are constructed by direct analogy for any two selected sites i and j we restrict attention to site values of vertices contained within a 1-sphere of either site that is, to all kES i,j) = S i) U Si j). Link operators, whose action on the state is represented by —... 

Nine-tnetnbered ir-excessive heterocycles with the general formula 1 are commonly referred to as heteronines. They can be regarded as direct analogs of the cyclononatetraenyl anion and have been extensively studied with regard to the question of their potential 1 On-aroma tic character. Heteronines have been the subject of several reviews.1 4... 

A novel approach to RAFT emulsion polymerization has recently been reported.461529 In a first step, a water-soluble monomer (AA) was polymerized in the aqueous phase to a low degree of polymerization to form a macro RAFT agent. A hydrophobic monomer (BA) was then added under controlled feed to give amphiphilic oligomers that form micelles. These constitute a RAFT-containing seed. Continued controlled feed of hydrophobic monomer may be used to continue the emulsion polymerization. The process appears directly analogous to the self-stabilizing lattices approach previously used in macromonomer RAFT polymerization (Section 9.5.2). Both processes allow emulsion polymerization without added surfactant. 

Chapter 1 treated the simplest type of piston flow reactor, one with constant density and constant reactor cross section. The reactor design equations for this type of piston flow reactor are directly analogous to the design equations for a constant-density batch reactor. What happens in time in the batch reactor happens in space in the piston flow reactor, and the transformation t = z/u converts one design equation to the other. For component A,... 

A marching-ahead solution to a parabolic partial differential equation is conceptually straightforward and directly analogous to the marching-ahead method we have used for solving ordinary differential equations. The difficulties associated with the numerical solution are the familiar ones of accuracy and stability. 

The axial dispersion model is readily extended to nonisothermal reactors. The turbulent mixing that leads to flat concentration profiles will also give flat temperature profiles. An expression for the axial dispersion of heat can be written in direct analogy to Equation (9.14) ... 

In order to give useful information about an enzyme, a conformationally restricted active-site-directed analog inhibitor need not bind to the enzyme irreversibly. In a study of the enzyme fructose 1,6-diphosphatase from rabbit liver, Benkovic et al, have investigated the question of the reactive form of the fructose 1,6-diphosphate in the enzymatic process (104,105). Three likely forms are shown in structures 50, 51 and 52. 

Electric current, which is the flow of electrons, is in many ways directly analogous to the flow of water. Think of a river flowing over a waterfall. The volume of water flowing past a point in the river each second is analogous to electrical current, and the height of the waterfall is analogous to a voltage drop. 

To make the two systems directly analogous, Van Niel<19> suggested that the reaction for photosynthesis in green plants should be written as... 

Photochemical solvolysis reactions are directly analogous to ordinary solvolysis reactions except that the absorption of light energy is necessary for reaction to occur ... 

Carrier-mediated transport is linear with mucosal solute concentration until this concentration exceeds the number of available carriers. At this point the maximal solute flux (7max) is independent of further increases in mucosal solute concentration. In the linear range of solute flux versus mucosal concentration (C), the proportionality constant is the ratio of / to the solute-carrier affinity constant (Km). This description of Michaelis-Menten kinetics is directly analogous to time changes in mass per unit volume (velocity of concentration change) found in enzyme kinetics, while here the appropriate description is the time change in solute mass per unit surface area of membrane supporting the carrier. 

Charge. The small amount of charge distribution data for carbyne complexes (based on Mulliken population analyses) indicates that the metal-carbon bond is generally polarized Ms+—C5- and that the carbyne carbon is always more negative than adjacent carbonyl carbons (28,30). These conclusions are directly analogous to those derived for carbene complexes. 

Although not directly analogous to the coupling of thiols with aryl halides, the reaction of thiourea with an aryl halide in the presence of palladium catalyst, nevertheless, can be used to generate a thiophenol from an aryl halide after hydrolysis (Equation (39)).129 This process occurred in greater than 90% yield with a variety of simple aryl halides ... 

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