Propagating waves

The basics of the method are simple. Reflections occur at all layers in the subsurface where an appreciable change in acoustic impedance is seen by the propagating wave. This acoustic impedance is the product of the sonic velocity and density of the formation. There are actually different wave types that propagate in solid rock, but the first arrival (i.e. fastest ray path) is normally the compressional or P wave. The two attributes that are measured are... 

D is basically a succession of 2D or 3D surveys repeated at intervals of time during which it is expected that some production effect has occurred, of sufficient magnitude to effect the acoustic impedance contrast seen by the propagating waves. For example, this oould be changes in the water or gas saturation, or changes in pressure. 

The transducers discussed above were designed to propagate waves in both directions normal to the direction of the fingers. It has been shown [17] that they produce a roughly collimated beam so they can be used to inspect a band of structure whose width is the transducer finger length the maximum distance away from the transducer covered by the beam is dependent on the attenuation of the wave and the signal-noise ratio, but is typically around 1-2 m in a... 

The objective in these gauges is to measure the time-resolved material (particle) velocity in a specimen subjected to shock loading. In many cases, especially at lower impact pressures, the impact shock is unstable and breaks up into two or more shocks, or partially or wholly degrades into a longer risetime stress wave as opposed to a single shock wave. Time-resolved particle velocity gauges are one means by which the actual profile of the propagating wave front can be accurately measured. 

It should be noted that to use the above time-domain formulas for computing rates, one would need an efficient means of propagating wave packets on the neutral and anion surfaces, and one, specifically, that would be valid for longer times than are needed in the optical spectroscopy case. Why Because, in the non-BO situation, the product is multiplied by exp(iEtZh) and then integrated over time. In the spectroscopy case, is multiplied by... 

Random rules giving rise to a propagating wave front. 

FIG. 2. Ca2+ channels can open without activating Ca2+ sparks. Individual sparks are not evoked with very brief depolarizations to activate ICa. With longer depolarizations, delayed Ca2+ sparks (middle panels) or a propagated wave (far right panel) are evoked. X—T linescan image is shown above, voltage and current, below. (From Collier et al 2000.)... 

Brading But do you need a propagated wave using the SR to generate the Ca2+ release ... 

Nelson Were those waves, or oscillations Was the whole cell lighting up, or could you see a propagating wave ... 

When the tube is closed at one end and ignited there, the propagating wave undergoes a transition from subsonic to supersonic speeds. The supersonic wave is called a detonation. In a detonation heat conduction and radical diffusion do not control the velocity rather, the shock wave structure of the developed supersonic wave raises the temperature and pressure substantially to cause explosive reaction and the energy release that sustains the wave propagation. 

The real part of this nnmber is the normal refractive index n = c/v(c and v being the speed of light in vacnnm and in the medium, respectively). The imaginary part of the complex refractive index, k, is called the extinction coefficient. It is necessary to recall here that both magnitndes, n and k, are dependent on the frequency (wavelength) of the propagating wave co,N = N(co). 

For numerical modeling of wave propagation in a structure, it is always advisable to relate the spatial coordinates to the wavelength of the propagating wave. We thus normalize the spatial coordinates as follows ... 

The cross-sections for itinerant electrons, as, e.g., electrons in broad bands, are evaluated by taking into account that the electrons in the initial as well as in the final state may be represented by Bloch-wavefunctions P = u,t(/ ) exp(i R) (see Chap. A). In these wavefunctions atomic information is contained in the amplitude factor Uj (i ), whereas the wave part exp (i R) is characterized by the wavenumber k of the propagating wave (proportional to the momentum of the electron). 

Rivin A.S. Sokolik and briefly described in Ref 7, p 195. The apparatus consisted of a metallic pipe, 40 meters long, closed at one end and folded as indicated in Fig 1. Diameters varied, but it seems that 13 mm pipe was mostly used for such experiments. The great length of the pipe allowed determination without error the existence of a stationary regime for the propagation wave. 

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