Quasi-longitudinal

Like the isotropic wave equation the Christoffel equation has three solutions, although in general there is no degeneracy except along symmetry directions. The motions of the particles are orthogonal for the three solutions, but not necessarily exactly parallel or perpendicular to the propagation direction, and so the waves are described as quasi-longitudinal or quasi-shear. 

For each section, the quantity p(w/k)2 is given for the pure shear wave, which is polarized perpendicular to the plane of the section, and for the quasi-shear and quasi-longitudinal waves, which each have particle motion in the plane of the section. The angle between the wavevector k and the lowest symmetry direction in the plane is denoted by 0. 

Fig. 4 Brillouin spectra recorded at atmospheric pressure at Tc 5 K in right-angle geometry along the direction (101), nearly parallel to the anthracene long axis (left), and the (101) direction almost perpendicular to this long axis (right). The R. T, OT, and QL indicate, respectively, the Rayleigh elastic line, the transverse mode polarized along the b monoclinic axis, and the quasitransverse and quasi longitudinal modes polarized in the (a,c) plane. The tree spectral range is 39.15 GHz. (From Ref. [18].)...

Table 9.1 Raman selection rules for pure and mixed quasi-transverse Q(TO) and quasi-longitudinal Q(LO) phonon modes ofwurtzite group III nitrides. The z direction is parallel to...

Depending on the system used, the excitation of a beam can result in quasi-longitudinal, torsional and bending waves. Surface waves are obtained only at high frequencies. In practice, only bending waves are used for the determination of moduli and loss factors, because of the relative simplicity with which this wave type can be achieved. 

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

Significant simplification of the governing equations may be achieved by using a quasi-one-dimensional model for the flow. Assume that (1) the ratio of meniscus depth to its radius is sufficiently small, (2) the velocity, temperature and pressure distributions in the cross-section are close to uniform, and (3) all parameters depend on the longitudinal coordinate. Differentiating Eqs. (8.32-8.35) and (8.37) we reduce the problem to the following dimensionless equations ... 

The nonlinear part of the susceptibility was introduced into the quasi-linear finite-difference scheme via iterations, so that at any longitudinal point, the magnitude of E calculated at the previous longitudinal point was used as a zero approximation. This approach is better than the split-step method since it allows one to jointly simulate both the mode field diffraction on irregular sections of the waveguide and the self-action effect by introducing the nonlinear permittivity into the implicit finite-difference scheme which describes the propagation of the total field. 

Figure 28. Longitudinal variation of power of the light beam calculated over the computational window in nonlinear waveguide of the stmcture A, To(0)=20fs (dashed line), To(0)= lOfs (dotted line), solid line corresponds to the quasi-static approximation.

Figure 29. Longitudinal dependence of the relative variation of the pulse duration at the waveguide axis for some values of L2 ( 2=0.001,-0.001,0.004,-0.004), in fsVpm. ppeak 2 (solid lines), 4 (dashed lines), tq = 16 fs, = 3.0 pm qsa - quasi-static...

These are quantized vibrations of conduction electrons in a metal or semiconductor 4°). The quantized energy levels of the collective longitudinal vibrations of the electron gas are quasi-particles in the sense of the definition given above and are called plasmons. The frequency of this longitudinal vibration, the plasma frequency u>P, is given by 40>... 

We focus on the polymer film. Since heat diffusion is propagated by segmental thermal excitations, it corresponds to the propagation of longitudinal phonons from the hot substrate-polymer interface to the colder polymer-air surface. Associated with the heat flux is a momentum flux (or rather, a flux in quasi-momentum [36])... 

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