Longitudinal modes, coupling

Figure 2. A pictorial representation of the mode coupling theory scheme for the calculation of the time-dependent friction (f) on a tagged molecule at time t. The rest of the notation is as follows Fs(q,t), self-scattering function F(q,t), intermediate scattering function D, self-diffusion coefficient t]s(t), time-dependnet shear viscosity Cu(q,t), longitudinal current correlation function C q,t), longitudinal current correlation functioa...

Recently a mode coupling theory study of diffusion and velocity correlation function of a one-dimensional LJ system was carried out [186]. This study reveals that the 1/f3 decay of the velocity correlation function could arise from the coupling of the tagged particle motion to the longitudinal current mode of the surrounding fluid. In this section a brief account of this study is presented. 

Figure 6 Block diagram of the two-color optical parametric amplifier (OPA) and IR-Raman apparatus. CPA = Chirped pulse amplification system Fs OSC = femtosecond Ti sapphire oscillator Stretch = pulse stretcher Regen = regenerative pulse amplifier SHGYAG = intracavity frequency-doubled Q-switched Nd YAG laser YAG = diode-pumped, single longitudinal mode, Q-switched Nd YAG laser KTA = potassium titanyl arsenate crystals BBO = /J-barium borate crystal PMT = photomultiplier tube HNF = holographic notch filter IF = narrow-band interference filter CCD = charge-coupled device optical array detector. (From Ref. 96.)...

The mechanism for ultrasonic emulsification is primarily that of cavitation. A typical sonicator for emulsification consists of a velocity transformer coupled to a transducer, capable of oscillating in a longitudinal mode, where the velocity transformer is immersed in the liquid. Figure 4 illustrates the basic parts of a sonicator with a continuous flow attachment, like the one used in this work. In this case, the flow cell is secured to the velocity transformer by a flange and a Teflon 0-ring. The intensity of cavitation depends on the power delivered to the velocity transformer, which is relayed to the transducer from a variable transformer or some other control device not shown in Fig. 4. 

If a 0, we have the noninertial response. This is treated by Shliomis and Stepanov [9], who were able to factorize the joint distribution of the dipole and easy axis orientations in the Fokker Planck equation into the product of the two separate distributions. Thus as far as the internal relaxation process is concerned, the axially symmetric treatment of Brown [50] applies. Hence no intrinsic coupling between the transverse and longitudinal modes exists that is, the eigenvalues of the longitudinal relaxation process are independent of a. The distribution function of the easy axis orientations n is simply that of a free Brownian rotator excluding inertial effects. 

Figure 20. The scheme of one-dimensional Aharonov-Bohm loop, surrounding the direction of propagation of a longitudinal mode and weakly coupled at points A and B with the external leads L and Li [(a) and (b)]. (d) The model of an ac normal-metal interferometer. R and R2 are the thermal reservoirs held at voltages V/2, respectively.

So far we have employed the exponential model for the memory kernel appearing in the GLE for the density correlation functions. In [60] the model based on the mode-coupling theory described in Sec. 5.2.4is applied to the calculation of the longitudinal current spectra of the same diatomic liquid as discussed here. It is found that the essential features of the results remained the same as far as the collective dynamics is concerned. It is also demonstrated that the results are in fair agreement with those determined from the molecular dynamics simulation. 

In this chapter we have described a theory for dynamics of polyatomic fluids based on the memory-function formalism and on the interaction-site representation of molecular liquids. Approximation schemes for memory functions appearing in the generalized Langevin equation have been developed by assuming an exponential form for memory functions and by employing the mode-coupling approach. Numerical results were presented for longitudinal current spectra of a model diatomic liquid and water, and it has been discussed how the results can be interpreted in... 

Microscopically, an important contribution to the Griineisen parameter coupling in HF Ce compounds comes from a strong volume dependence of the sf-hybridization strength V k) (Allen and Martin 1982, Razafimandimby et al. 1984). Therefore, sound waves of compressional character, e.g., longitudinal modes modulate the mixing term in the Hamiltonian of eq. (107) and consequently couple to electronic states. For smaU displacements one can write... 

Here the transformation to the quasiparticle operators of eq. (Ill) has already been performed. As before only the longitudinal modes have a non-vanishing coupling ... 

The final term in Eq. (1) is the astigmatism factor, K. This accounts for the enhanced coupling of the spontaneous emission to longitudinal modes of the laser. This can be a significant factor in many structures, especially narrow stripe devices in which the gain profile is primarily responsible for the definition of the optical mode, where K = 11 has been observed.However, in single-mode, index-guided SL s, typically, K is very close to unity. 

Another proposed mechanism is the coupling of longitudinal modes. 

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