Wave phenomena

The third scenario in Fig. 5.1(c) shows the evolution of a feed pulse in a totally regenerated bed. This can be viewed as a combination of a stepwise increase and a 

The solid lines represent the solute with the higher affinity to the solid phase. 

5 Equilibrium Theory and Nonlinear Waves for Reaction Separation Processes 

The same principles apply to moving-bed chromatographic processes [34]. Important differences between fixed-bed and moving-bed chromatographic processes are the following  

This can be rationalized in the following way. In a moving-bed chromatographic process the solid phase moves in the opposite direction to the fluid phase. Hence, the wave velocity in a moving-bed process is the difference between the wave velocity in a corresponding fixed-bed process and the velocity of the solid flow. Depending on the velocity of the solid flow and the wave velocities, the fronts will either move in the direction of the solid phase or in the direction of the fluid phase toward the inlet of the solid or the fluid phase where they are stopped by the repelling influence of the system boundaries and a steady state is established. If the absolute values of the wave and the solid velocity are equal, a balanced wave is obtained. Because the wave velocities of different wave fronts are different at steady state, at most one concentration front can stand at the middle of the column section whereas the others are at the system boundaries, where they can overlap. 

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The ultrasonic testing of anisotropic austenitic steel welds is a commonly used method in nondestructive testing. Nevertheless, it is often a problem to analyze the received signals in a satisfactory way. Computer simulation of ultrasonics has turned out to be a very helpful tool to gather information and to improve the physical understanding of complicated wave phenomena inside the samples. 

An important ingredient in the analysis has been the positions of zeros of I (x, t) in the complex t plane for a fixed x. Within quantum mechanics the zeros have not been given much attention, but they have been studied in a mathematical context [257] and in some classical wave phenomena ([266] and references cited therein). Their relevance to our study is evident since at its zeros the phase of D(x, t) lacks definition. Euture theoretical work shall focus on a systematic description of the location of zeros. Eurther, practically oriented work will seek out computed or... 

Shock-compression processes are encountered when material bodies are subjected to rapid impulsive loading, whose time of load application is short compared to the time for the body to respond inertially. The inertial responses are stress pulses propagating through the body to communicate the presence of loads to interior points. In our everyday experience, such loadings are the result of impact or explosion. To the untrained observer, such events evoke an image of utter chaos and confusion. Nevertheless, what is experienced by the human senses are the rigid-body effects the time and pressure resolution are not sufficient to sense the wave phenomena. 

Some wave phenomena, familiar to many people from the human senses, include the easy undulation of water waves from a dropped stone or the sharp shock of the sonic boom from high-speed aircraft. The great power and energy of shock events is apparent to the human observer as he stands on the rim of the Meteor Crater of Arizona. Human senses provide little insight into the transition from these directly sensed phenomena to the high-pressure, shock-compression effects in solids. This transition must come from development of the science of shock compression, based on the usual methods of scientific experimentation, theoretical modeling, and numerical simulation. 

P. Lorrain and D. Corson. Electromagnetic Fields andWaves. W. H. Freeman, San Francisco, 1970, p. 518. A general and clear text on electromagnetic wave phenomena at the undergraduate level. 

Chaiken, Hypervelocity Wave Phenomena In Condensed Explosives , JPhChem 33, 760—1... 

Oppenheim, A.K. and Stern, R.A., On the development of gaseous detonation - analysis of wave phenomena. Proc. Combust. Inst., 7, 837, 1959. 

The quantity c = y/rjp is known as the jjjia e velocity, It is the speed a which waves travel along the string. Clearly, the left-hand side of Eq, (4) represents the one-dimensional Laplacian operating on the dependent variable. This expression can be easily generalized to represent wave phenomena in two or more dimensions in space. 

Berggren, K.-F., and A.F. Sadreev. Chaos in quantum billiards and similarities with pure-tone random models in acoustics, microwave cavities and electric networks. Mathematical modelling in physics, engineering and cognitive sciences. Proc. of the conf. Mathematical Modelling of Wave Phenomena , 7 229, 2002. 

The quite loud explosions (either immediate or delayed) which occur when LNG (containing usually high proportions of heavier materials) is spilled onto water are non-combustive and harmless [1]. Superheating and shock-wave phenomena are involved [2], There is a similar effect when LNG of normal composition (90% methane) is spilled on to some CsCghydrocarbons or methanol, acetone or... 

Development of Gaseous Detonations -Analysis of Wave Phenomena , Ibid, pp 837-50 53) F.J. Martin D.R. White,... 

Detonation, Hypervelocity Wave Phenomena in Condensed Explosives. See Detonation, Flash-Across, Heat Pulse and Hypervelocity Phenomena... 

Chaiken, "Comments on Hypervelocity Wave Phenomena in Condensed Explosives , 3rdONRSympDeton (I960), 304-07 10)... 

Electromagnetic wave phenomena and the related photon concept remain somewhat of an enigma in more than one respect. Thus, the latter concept should in principle apply to wavelengths ranging from about... 

The extra degree of freedom introduced into the present theory by the nonzero electric field divergence gives rise to new classes of phenomena such as bound steady electromagnetic equilibria and free dynamic states, including wave phenomena. These possibilities are demonstrated by Fig. 1. 

Here we only summarize those parts of the theory that are of interest in connection with wave phenomena, photon physics, and long-range interaction. We later return to Eqs. (36) when discussing the concepts of... 

The basic equations (l)-(8) also predict the existence of free time-dependent states, in the form of nontransverse wave phenomena in vacuo. Combination of... 

In nearly all natural wave phenomena, losses increase with frequency. Distributed losses due to air drag and internal bulk losses in the string tend to increase with frequency. Similarly, air absorption increases with frequency, adding loss for sound waves in acoustic tubes or open air [Morse and Ingard, 1968],... 

If these super-real visions involve wave phenomena, then the external world takes on a radiance and a revelation that is staggeringly clear. The experienced insight that the world of phenomena exists in the form of waves, electronic images, can produce a sense of illuminated power. Everything is experienced as consciousness. 

Shock-wave phenomena are important in meteorite impacts where high-pressure minerals are often formed. Small diamonds useful for lapping and polishing are made commercially by shocking graphite mixed with iron and copper. The metals cool the diamonds before they can transform back to graphite on pressure release. 

As outlined above, for the regular oscillations on Pt( 100) at high temperatures, spatial coupling will predominantly be mediated through the gas phase, which process is occurring so rapidly that no phase difference between different parts of the surface are to be expected. However, with this system wave phenomena were also observed by means of PEEM under conditions for which the temporal oscillations were less regular... 

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