Wave front analogy

Finally, we derive an expression for the propagation velocity of the polymerization front analogous to formula (3.58) derived for the gasless combustion wave. We substitute (4.126) into (4.123) to obtain... 

For 4.28 < t < 5.41 (Fig. 15.16), there is a qualitative change once more wave 2 splits, so in addition to the double wave described above, we get a second wave traveling north. In our analogy, since the refraction time is smaller that the delay time the two fire fronts move almost independent in their corridors, except that when fire front 2 passes the center it receives some additional sparks from the wave front 1, which already passed the center. This sets fire to the newly grown grass in die horizontal corridor. 

The diagram of wave-front motions behind the membrane in the duct is known and, by analogy with the classical shock tube [43], is presented in Fig. 11.33. If it is assumed that the membrane is removed instantaneously, then we have the classical case of a membrane rupture and a flat topped shock wave generated in the low-pressure section (air at condition 1) ahead of the membrane. A centered rarefaction wave C travels back to the combustion gas at condition 4. The solution of the problem for parameters of the incident and rarefaction waves is known [43]. As a rule, before the membrane rupture, Tj = 74. The air temperature T2 behind the incident wave at condition 2 and expanding the gas temperature behind the rarefaction wave fan at condition 3 are calculated using the following expressions ... 

In a shock wave, as is known, a change of state occurs on the mean free path of molecules of the gas. The outward analogy between the theory of detonation and the shock wave theory prompted many authors to consider that a detonation front is just as sharp as the front of a shock wave. Jouguet spoke in favor of instantaneous reaction. 

The slower autowave process is similar in some respects to classical combustion, despite the differences in their physical nature. The wave velocity shows the same dependence on thermal conductivity as in the case of flame propagation. Analogously to combustion, the reaction zone is near the maximum temperature Tm [it is near Tm that the critical gradient (dT/dx) switching on the reaction is realized], whereas the greater part of the front... 

For this reason the ASIC concept is based on the modulation of the pressure measurement signal to a carrier frequency fm of approximately 5 kHz by square wave voltage supply of the gauge (H-bridge circuit). The signal is preamplified and then converted into a single-bit data stream with a data rate of fAZ=25G frn (about 1.28 Mbps) by a second-order AS modulator. The analog front-end (preamp and AS) is produced in fully differential SC circuitry. 

The signal band (formerly centered at, ) is thus shifted to dc. The following digital FIR filter with transmission zeros at, 2 fm, and 3 fm cancels out the dc offsets and 1/f noise of the analog front-end (now centered at fm) as well as some overtones of the original square wave abased into the Nyquist band of the signal sampled at 4 fm. 

Figure 3 shows the pressure and temperature variations along the axis ahead of the body. In front of the source the pressure and temperature are seen to increase (a compression wave with x R —5,...,—4) and behind the source, to decrease (flow in the rarefaction wave with xjR —4,..., —3). In the vicinity of the body a difference analog of an SW forms (for Option A the middle of the gradient is shown by an arrow). 

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