Wave fronts

The geometry of Fig. 10.3 leads to a result known as Snell s law, which relates the refractive index of the medium to the angles formed by two wave fronts with the interface. Defining 6q and 6, respectively, as the angles between the phase boundary and the wave front under vacuum and in the medium of refractive index n, show that Snell s law requires n = sin Oo/sind. 

If the turn-to-turn voltage, ef, and the front time, so achieved falls within the design parameters, no additional measures would be necessary to further reduce the TRV. However, if It is felt that the dampened voltage, ef, may exceed the required value of r.r.r.v. during operation, a surge capacitor may also be introduced in the circuit as illustrated in Figure 17.23 to reduce the wave front a2 to b2, so that the front time is enhanced to a permissible... 

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. 

Figure 4.16. Free-surface velocity profiles measured on 1400° C molybdenum. The free-surface velocity profile is characterized by an 0.05 km/s amplitude elastic precursor, a plastic wave front, and a spall signal (characteristic dip) upon unloading. The dashed lines represent the expected free surface velocity based on impedance-match calculation [Duffy and Ahrens, unpublished].

In the following development we consider a plane wave of infinite lateral extent traveling in the positive Xj direction (the wave front itself lies in the Xj, Xj plane). When discussing anisotropic materials we restrict discussion to those propagation directions which produce longitudinal particle motion only i.e., if u is the particle velocity, then Uj = Uj = 0. The <100>, <110>, and <111 > direction in cubic crystals have this property, for example. The derivations presented here are heuristic with emphasis on the essential qualitative features of plastic flow. References are provided for those interested in proper quantitative features of crystal anisotropy and nonlinear thermoelasticity. 

If we accept the assumption that the elastic wave can be treated to good aproximation as a mathematical discontinuity, then the stress decay at the elastic wave front is given by (A. 15) and (A. 16) in terms of the material-dependent and amplitude-dependent wave speeds c, (the isentropic longitudinal elastic sound speed), U (the finite-amplitude elastic shock velocity), and Cfi [(A.9)]. In general, all three wave velocities are different. We know, for example, that... 

Figure 8.7. Propagation of wave profile in an elastic-plastic material from the spall plane to the monitoring interface. The wave front propagates at a plastic wave speed whereas the wave release propagates at an elastic wave speed and complicates the analysis of the material spall strength.

In a GAC column, dynamic adsorption occurs along an adsorption wave front where the impurity concentration changes. 

Based on the preceding local history, the boundaries at the elastic and plastic wave fronts are characterized by bound surface charges of equal magnitude and opposite sign to the initial piezoelectric states. The polarization in the region behind the plastic wave E3, has magnitude equal to the change... 

A detonation shock wave is an abrupt gas dynamic discontinuity across which properties such as gas pressure, density, temperature, and local flow velocities change discontinnonsly. Shockwaves are always characterized by the observation that the wave travels with a velocity that is faster than the local speed of sound in the undisturbed mixtnre ahead of the wave front. The ratio of the wave velocity to the speed of sound is called the Mach number. 

A radial force on the pipe wall ahead of the deflagration wave. There is a varying pressnre between the aconstic wave and the flame front where the pressnre bnilds from near atmospheric pressnre, Pi (step change at the wave front) to eight times Pi (or higher) at the flame front. The pressnre ratios depend on the flame acceleration. There is no snch effect with a detonation. 

Wellen-front, /. wave front, wave head, -ppfel,... 

Fig, 9.9 Wave propagation in the HPP lattice geis, starting from a localized disturbance. Notice the appearance of a circular wave front on the macro-scale despite the discrete anisotropy at the microscopic (i.e. dynamical) level. 

This concept has been known for over a century. Expressed as Brewster s Constant law, it states that the index of refraction in a strained material becomes directional, and the change of the index is proportional to the magnitude of the stress (or strain) present. Therefore, a polarized beam in the clear plastic splits into two wave fronts in the X and Y directions that contain vibrations oriented along the directions of principal stresses. An analyzing filter passes only vibrations parallel to its own transmitting plane (Chapter 4, TRANSPARENT AND OPTICAL PRODUCT, Polarized Lighting). 

Furthermore, under certain conditions (e.g. local unidirectional block) it is possible that the activation wavefront is delayed and encounters areas already repolarized. This may result in a circulating wave-front (= reentrant circuit reentrant arrhythmia), from which centrifugal activation waves originate and elicit life-threatening ventricular fibrillation. 

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