Second sound

It is easy to check that sometimes k can exceed the Cu conductivity. The very high thermal conductivity of 4He n allows for the propagation of temperature waves (second sound) [42-48]. 

VC is made by cracking EDC in a pyrolysis furnace much like that in an ethylene plant. Thats one of the three reactions, shown in Figure 9—1, involved in the process. The other two have formidable names—chlorination and oxychlorination—but simple enough reactions—the addition of chlorine and the addition of oxygen and chlorine. What is a little complicated is the fact that the hydrogen chloride used to make the EDC in the first reaction comes from cracking EDC in the second. Sounds like a closed circle until you peel it back and examine it. 

Alternatively, a more realistic music attack or speech plosive may be obtained by splicing into die synthesized deterministic component using the method described in section 3.6. Splicing of the actual attack has been shown to significantly improve the sound quality for a number of musical sounds including the piano and marimba [Serra, 1989]. Hybrid sounds can also be created by matching the sine-wave phases of the attack of one sound with the phases of the deterministic component of a second sound at a splice point. 

Mandelstam LI, Leontovich MA (1937) To the theory of the second sound. Zh Exper Theor Fiziki 7 438-449 (in Russian)... 

The velocity of sound in liquid helium-I and -II has been measured. Second sound i a peculiar type of wave motion in liquid helium-II ( 8.VIII E) its velocity is about 1900 m./sec. at 1-74 K. the velocity is zero at the /I-point... 

This is referred to as the Maxwell-Cattanero equation, because it was postulated first by Maxwell [15] and later on by Cattaneo [16], Note that the relaxation time r defined as t=o/c2 is assumed to be constant, where C is the speed of "second sound" (diermal shock wave). 

SECOND Sound a warning so that others may take cover. 

Therefore, when the wavevector of second sound is normal to the layers, it becomes a purely dissipative mode with a relaxation rate... 

Furthermore, second sound is a critical mode, i.e., its velocity goes to zero... 

This surprising result prompted Mazenko, Ramaswamy and Toner to examine the anharmonic fluctuation effects in the hydrodynamics of smectics. We have already shown that the undulation modes are purely dissipative with a relaxation rate given by (5.3.39). To calculate the effect of these slow, thermally excited modes on the viscosities, we recall that a distortion u results in a force normal to the layers given by (5.3.32). This is the divergence of a stress, which, from (5.3.53), contains the non-linear term 0,(Vj uf. Thus, there is a non-linear contribution (Vj uf to the stress. Now the viscosity at frequency co is the Fourier transform of a stress autocorrelation function, so that At (co), the contribution of the undulations to the viscosity, can be evaluated. It was shown by Mazenko et that Atj(co) 1 /co. In other words, the damping of first and second sounds in smectics, which should go as >/(oo)oo , will now vary linearly as co at low frequencies. 

If we consider the words span, stan and scan, we see that we have a three way contrast, in which the second sound differs in terms of place of articulation. There is however no voieing contrast possible at these points, so there are only three possible phonemes, unlike in word initial position where we have three place of articulation contrasts in addition to a voicing contrast, giving us six phonemes in all. The question then is, should span be transcribed as /s p ae n/ or /s b ae n/ The phonetic evidence tends to favour /p/, but this is not conclusive, and will vary from speaker to speaker and accent to accent. Clearly though there is a systematic effect going on. There is probably no objective answer to this, so we obey the normal convention (which may have been infiuenced by the spelling) and represent these words with the unvoiced phonemes /p/, 1x1 and Dd. 

It has also been used to study the second sound resonance in smectic A liquid crystals and measure the compression modulus. For measuring the flexocoefficients (ei — 63) and (ei + 63), hybrid-aligned nematic cells have been used extensively. AC techniques avoid problems associated with ionic impurities, but require elaborate numerical fitting of the data. Some observations on the pnblished measurements of flexo-coefHcients are made in Section 2.4, which ends with a few concluding remarks. 

Fig. 4a shows several kinetic temperature profiles as a function of time "measured at a fixed station in the lattice. Curve C is the average kinetic temperature of planes 71 to 75 taken from Fig. 3. Other curves are explained in the figure caption. The general rise of these curves beyond was due to thermal diffusion (curve D), as discussed above. These results may be compared with the experimental measurements of McNelly et al. [14]. The similarities between our results and McNelly s are striking, especially our profile A and McNelly s at 14.3 K in their Fig. lb our first sound pulses and corresponded to their "ballistic" phonon pulses L and T, and our heat pulse H H> to their "new pulse. Our second sound velocities, viz., Ci/JZ, etc., were also in agreement with...

The arrival times of L, etc., at the measuring station may be obtained by constructing a wave diagram as in Fig. 4b. Because of the finite duration of the heat pulse, the second sound signals Hi, and... 

As a further check, we also calculated the heat pulse propagation in a two-dimensional model. We again obtained three second sounds, with velocities equal to 1/72, instead of 1/73, times Q, and Cg. 

Thermal relaxation occurs behind the shock front to restore thermal equilibrium. In a condensed system, this involves the reestablishment of the equilibrium distribution of both the frequencies and the velocities of the particles, i.e., their potential and kinetic energy distributions. In the simplest case without structural relaxation and the accompanying stress relaxation, we expect this process to occur at the appropriate second sound velocity. In the fully relaxed region the kinetic and potential energy distributions are in equilibrium. In the relaxing region these distributions are not steady. The shock profile as a whole is therefore unsteady. 

The solution to the diffusion equation (2.30) implies that the temperature decreases monotonically with z at all times. It is interesting that this uniform behavior is not a property of ultrapure materials. Instead, heat is propagated as a wave, in a fashion similar to the propagation of sound. This phenomenon, known as second sound, was first discovered in liquid helium at very low temperatures. It has since been observed in solid helium and has been reported to occur as well in the isotopically and chemically pure materials NaF and Bi at very low temperatures. For a discussion of the effect see B. Bertram and D. J. Sandiford, Scientific American 222(5), 92 (1970). 

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