Sines, Law

The amplitude modulation of the antiphase proton magnetization 2/,-5 2, generated prior to the generation of zero and double quantum coherences by the first Sn 90° pulse, obeys a sine law of the type sin[/7cA] with j=V( Sn, H). This amplitude modulation as a function of the coupling constant varying from 0 to 200 Hz is presented in Figure S for two fixed delays, A = 3.8 and 62 ms. 

I had come from Australia, where I had been studying the mechanical properties of wool (and where there are about 10 times as many sheep as there are humans) to Utah (where there are about 10 times as many humans as there are sheep) to learn something about the theory of rate processes and its application to viscoelastic problems. Eyring and co-workers had developed the hyberbolic sine law of flow and applied it to many systems—both solid and liquid—and I had expected to find this kind of work going on full pace. 

Shear Forming, Fig. 3 Deviation from sine law in shear forming... 

The polycrystalline microstructure is the microstructure we observe after sintering a powder compact to full density. In homogeneous polycrystalline materials, this microstructure is determined, in general, by the interfacial tension. Figure 3.1 illustrates an equilibrium state between three interfacial tensions. For this geometry, the sine law is satisfied so that... 

Shear spinning is a variation on the basic metal spinning technique that allows conical and dished shapes to be spun in one spinning pass. The technique follows the sine law which simply means that the thickness of the spun part is equal to the thickness of the blank multiplied by the sine of half the angle between the... 

Several years ago, our group at The University of Chicago set out to demonstrate the ability of nonimaging optics to concentrate sunlight at or near the theoretical limit implied by the sine law. Actually, we chose to immerse the hot zone in a refractive medium to further boost the limit by the square of the index of refraction. These have been small-scale roof-top experiments carried out by talented and dedicated graduate students. In the first round of experiments we attained 56,000 suns. This was a fairly conservative design where the nonimaging optical element was a hollow silver funnel filled with... 

Using the sine law power distribution the axial enthalpy can be written as... 

The exponential relationship is also vahd under natural conditions, i.e., for unilateral irradiation of vertical or incHned organisms. The gravitropic stimulus, S, and the ehcited response depend (in darkness) on the sine of the initial inclination angle (sine law of JuHus Sachs ) ... 

Galland, R, Tropisms in Avena coleoptiles sine law for gravitropism, exponential law for photogravitropic equiHbrium, Planta, 215, 779-784, 2002. 

Galland, R, WaUacher, Y., Finger, H., Hannappel, M., Troster, S., Bold, E., and GroHg, E, Tropisms in Phycomyces sine law for gravitropism, exponential law for photogravitropic equiHbrium, Planta, 214, 931, 2002. 

To describe the seeondary creep behavior of solder joints, two steady-state ereep constitutive laws are used in this study. The Garofalo-Arrhenius hyperbolic sine law, shown in Equation (5), is chosen to describe the behavior of dominant secondary creep. 

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