Wave propagation phenomena

If the dominating process is much faster than the typical time scale of the oscillations, Eq. (2) reduces to Eq. (1) and the whole surface is in fact oscillating in phase. Otherwise, spatial self-organization will be associated with wave propagation phenomena. Again these general conclusions will be illustrated by detailed observations. 

The general solutions of the fundamental systems of nonlinear equations [Eq. (2)] will be of the type wherein the state variables are dependent both on time and space, which will manifest in the form of wave propagation. Coupling between several parts of the system will be transmitted through the generalized diffusion coefficient D. If the associated transport process proceeds on a time scale comparable to or slower than the period of the temporal oscillation, macroscopic wave propagation phenomena are to be expected, as, for example, realized with the Belousov-Zhabotinsky... 

D.B. Bogy and F.E. Talke, Experimental and theoretical study of wave propagation phenomena in drop-on-demand ink jet devices. IBM Journal of Research Development, 29 (1984)314-321. 

In the equilibrium regime, the dynamic behavior of an RD column in transformed concentration variables is essentially the same like the dynamic behavior of a non-RD column. Hence it is not surprising that under these conditions we can observe all kinds of multiplicity, oscillations, and wave propagation phenomena like in non-RD. Any novel feature, such as reactive azeotropy, is introduced by the static transformation between physical and transformed concentrations. 

Ray TtiacU.ng. An electromagnetic wave propagating perpendicular to the gradient of the refractive index of the medium will bend in the direction of this gradient. The bending phenomenon is completely described by the ray equation ... 

Following is a resume of paper by Fickett (Ref 2) If a cylinder of explosive is suddenly heated or struck at one end, a detonation wave propagates down the length of the charge with approximately constant velocity. This phenomenon is often treated by the model of von Neumann-Zel dovich. Transport properties are neglected, and the wave consists of a plane shock followed by a short reaction zone of constant length in which the explosive material is rapidly transformed into decomposition or detonation products. 

The propagation of pressure waves such as acoustic wave, shock wave, and Prandtl-Meyer expansion through a gas-solid suspension is a phenomenon associated primarily with the transfer of momentum although certain processes of energy transfer such as kinetic energy dissipation and heat transfer between gas and solids almost always occur. Typical applications of the pressure wave propagation include the measurements of the solids concentration and flow rate by use of acoustic devices as well as detonation combustion such as in a rocket propellant combustor or in the barrel of a gun. 

Figure 4.23 Schematic of the phenomenon of the isothermal "chemical" wave propagation. The profiles exhibit the concentrations of catalytic intermediates in the successive moments of time tt < T2 < T3.

The first contribution to the polarization induces a modification of the wave propagation in the material, for both its amplitude and phase, but without any frequency change. This phenomenon is known as the optical Kerr effect, by analogy with the magneto-optic and electro-optic Kerr effects where the medium refractive index varies proportionally with the square of the applied magnetic or electric static field. The second contribution corresponds to the third harmonics generation (THG). 

A recent review of detonation theory is given elsewhere [12]. Models of the phenomenon envisage a detonation wave propagating into unreacted material with a sharp discontinuity in temperature and pressure at the detonation front. A reaction zone of a millimeter or smaller dimensions and yielding the equilibrium quantities of reaction products at high temperature and pressure abuts the up-stream side of the front. Using macroscopic hydrodynamic-thermodynamic theory, the energy released, and an equation of state for the assumed products, detonation velocities, pressures, and temperatures may be calculated in certain cases. 

The propagation of concentric and spiral waves of Ca in Xenopus oocytes has also been studied (Lechleiter et al., 1991) by means of simulations based on cellular automata (Gerhard, Schuster Tyson, 1990 Markus Hess, 1990) such a mathematical representation of excitable systems in terms of a set of rules simulated on a computer considers the existence of a finite number of cell states (excitable, excited, refractory). The comparison of numerical simulations with experiments suggested (Lechleiter et al, 1991) that the species responsible for the spatial propagation of the wave is cytosolic rather than IP3. Moreover, the characteristics of the phenomenon fit with the view (Berridge Irvine, 1989) that CICR is the primary mechanism imderlying Ca " wave propagation. 

Light travels from place to place as though it were a wave phenomenon (i.e., as though it were a continuous propagating phenomenon). 

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