Spatially uniform compression

Figure 10.59(b) indicates that as few as three e = 1, spatially uniform compressions of PS are capable of heating it past its Tg. Thus, there is good agreement between the... 

FIGURE 5.7 Comparison of spatially uniform compression to propagative compression. 

In fluidized bed reactors and regenerators, the magnitude of compressed gas pressure varies whether the compression is made slowly or rapidly. A gas that is compressed slowly such that the pressure rises uniformly in a control volume is known as slow, or spatially uniform, compression. A rapidly compressed gas, such as by a rapid piston motion, is known as propagative compression. Figure 5.7 shows the schematics of both spatially uniform and propagative compression. 

For spatially uniform compression, the amount of work done is... 

Thus, you can see that the propagative compression results in a final pressure are 2.3 times that produced by spatially uniform compression. There is the added effect of shock with propagative compression that can enhance forces exerted on internal vessel components. 

The last term of Vpp in Eq. (3.90) is introduced so that the driving potential satisfies AVpp = 0. The term proportional to in Eq. (3.88) was omitted because it affects only the spatially uniform phase of the wave function. Thus, the wave function of the intermediate state has a spin-dependent phase factor exy)[iARmcngsJ qK)] added to the phase displayed in Eq. (3.17), and this property can be used to control relative phase between different spin states. It is possible to design the time dependence of R so that the last term of Vpp in Eq. (3.90) does not cause unwanted excitation after the rotation. Although the last term of Vpp compresses the wave function in the z-direction during the rotation around the z-axis, at the final time the wave function Ppp becomes that of the desired rotated state without compression or oscillation in the z-direction. 

At the other extreme, after an infinite time, the load is supported wholly by the elastic host, the fluid stops flowing and the fluid pressure is not only hydrostatic at each local point but spatially uniform as well. This means that at all fluid-solid interfaces, the stress in the solid has a component normal to the interface of some magnitude P (see Figure 10.1) it is only in the solid s interior, away from any flat-lying fluid interface, that vertical compressive stresses with magnitude greater than P can exist and support the load. 

The flat fielding procedure described above essentially removes all spatial variation in what is assumed to be a uniform imaging field. Nonuniformities in signal that are not due to the detector, but are caused by such phenomena as heel effect of the X-ray tube, variation in X-ray path length through air (inverse square law), the beam filter, compression plate, and... 

Especially, for monolayers consisting of more than one substance, there is an immense amonnt of information contained in the pressure-area isotherm. For example, a mixed behenic acid/cholesterol film gives what seems at first sight to be a very noisy isotherm, bnt in fact it contains characteristic oscillation freqnencies, as can readily be seen from the Fourier transform of the derivative (with respect to time the monolayer was compressed at a uniform rate, hence in effect making area and time equivalent) of the isotherm (Figure 5). The origin of these oscillations has been traced to spatial structming. ... 

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