Acceleration waves

The simplest arrangement for a linear accelerator is shown in Fig. 5. Here a single source, either a self-oscillating magnetron or klystron amplifier with appropriate drive stages, feeds power into a single length of accelerator wave-... 

The most distinctive aspect of the shock work is the determination of higher-order piezoelectric constants. The values determined for the constants are, by far, the most accurate available for quartz and lithium niobate, again due to the direct nature of the measurements. Unfortunately it has not been possible to determine the full set of constants. Given the expense and destructive nature of the shock experiment, it is unlikely that a full set of higher-order piezoelectric constants can be determined. A less expensive investigation of higher-order constants could be conducted with the ramp wave or acceleration wave loading experiment described in the chapter. 

By the wave equation, curvature waves, y" = y/c2, are simply a scaling of acceleration waves. 

H)N-NDR systems DL activator accelerated waves, inhomogeneous (BF unstable) oscillations stationary domains, standing waves, anti-phase oscillations with n = 1 pulses, target patterns, clusters enhanced acceleration of potential fronts, mainly homogenizing effect cluster formation in the oscillatory region... 

The normal experimental technique is to scan rapidly through the velocity range and repeat this scan many times imtil data of the required accuracy has been accumulated. The Doppler motion is provided by an electromechanical drive system controlled by a servo -amplifier. Usually, the source is attached to the drive shaft and driven either in a saw-tooth or a triangular constant acceleration wave form. The transducer is coupled to a multichannel analyser operating in the multiscaler mode, and the servo-amplifier is controlled by the channel advance frequency. The dwell time in each channel, corresponding to a specific velocity increment, is 100 ps, and while the channel gate is open it accepts pulses from the detector. 

Bowen, R.M., Chen, P.J. Acceleration waves in a mixture of chemically reacting materials with memory. Acta Mech. 19(3 ), 201-214 (1974)... 

Bowen, R.M., Rankin, R.L. Acceleration waves in ideal fluid mixtures with several temperatures. Arch. Ration. Mech. Anal. 51(4), 261-277 (1973)... 

Ingebo, R. D., Capillary and Acceleration Wave Breakup of Liquid Jets in Axial Flow Air-Streams, NASA Technical Paper, 1981, p. 1791. 

Generally, from physical point of view, field rp suffer discontinuity at the interface. Then such interface is called as surface of discontinuity. More precisely, a disturbance in the continuity of a phenomenon or physical field is termed as singularity. The singularity will present as discontinuous functions or their derivatives. The examples of the first type are shock and acceleration waves. (A surface that is singular with respect to some quantity and that has a nonzero speed of propagation is said to be a propagating singular surface or wave.)... 

On a singular surface of order 2, the deformation gradients and the velocity of the medium will be continuous, while the second gradients of motion and the acceleration of material particles may suffer jumps. Such a propagating singular surface will be called an acceleration wave. 

These formulae show that a singular surface of order 2 is completely determined by a vector b and the speed of propagation, U. In particular, material discontinuities of second order affect only the derivatives x, while discontinuities in the acceleration and in the velocity gradient are necessarily propagated, and conversely, every wave of second order carries jumps in the velocity gradient and the acceleration. Waves of second order are therefore called acceleration waves. 

Equation (5.92) shows that Q(z/) 1/jj l/t °. Thus, by increasing the air flow velocity one can decrease the instability increment at the cost of accelerated wave propagation (cf. Eq. (5.96)). Note that appears in (5.92) as a factor l/ ) rather than as a separate term. This means that... 

Hill, R. (1962), Acceleration waves in solids. Journal of the Mechanics and Physics of Solids 10, 1-16. 

Physical quantity area volume speed, velocity acceleration wave number density, mass density specific volume current density magnetic field strength concentration (of amount of substance) luminance refiuctive index... 

Consider now an isotropic micropolar elastic medium traversed by a second-order singular surface S, that is, a surface across which the acceleration vector and also the second-order gradients of the displacement vector suffer jumps. Such a singular surface is called an acceleration wave. We further assume that the... 

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