Dispersion diagram

The nonlinear modes are usually referred to as solutions to the nonlinear Helmholtz equation in the waveguide cross-section. For their investigation, power-dispersion diagrams are commonly used that give values of critical powers and are helpful in stability analysis of the fundamental mode. ... 

For the analysis of a nonlinear mode stability which is important for a problem of nonlinear waveguide excitation, consider the power dispersion diagrams (Fig.5). 

Figure 5. Power dispersion diagrams of symmetric mode (solid lines) and anti-symmetric mode (dashed lines) for some values of a (a= 1.5 m, 2.0 m, 4.0 m).

Figure 3.5 Phonon dispersion diagram for a complete unit cell with degrees of freedom. From Kieffer (1985). Reprinted with permission of The Mineralogical Society of America.

A typical vibrational spectrum of a crystalline phase appears as a section of the dispersion diagram along the ordinate axis. Figure 3.7 shows a generaUzed... 

A Dispersion Diagram is made by superimposing the dispersion ladder (qv) for direction on the dispersion ladder for range and indicating in each rectangLe the percentage of shots expected to fall therein... 

Figure 2.5. Dispersion diagram of the system of vibron-multiparticle states. The vibrons coupled to two-particle states become unstable (broken curves).

The above results may be interpreted as follows Figure 3.10 shows the dispersion diagrams co(/0 for the uncoupled and the coupled matter-radiation systems. Thus, the coupling induces, for cK < oj0, a splitting off of the lower state of the effective continuum, repelled to lower energies by its interaction with the matter state K>.126... 

Figure 5.1. The band dispersion diagram for a one-dimensionai Bioch sum of cr-bonded p atomic orbitais.

For the d y orbitals, there are no axial contributions. However, for the and dy orbitals, there are two axial contributions per metal atom at all three of the k points of Figure 5.8, which are not shown in that figure. Thus, the band dispersion diagram for... 

The bidimensional methods of representation most used by multivariate techniques are direct methods, such as matricial dispersion diagrams, and icon plots based on histograms, profiles or stars projection approach techniques, that represent observations in the new variables obtained, and which fulfil a specific objective (principal components, canonical variables, etc.) and dendrograms that inform about the similarity of observations or variables (Krzanowski 1988). 

For Nal, the large group of points in the center of the bulk band in FX near the F point are probably due to phonon-assisted bound state resonances which were also found for NaCl and for LiF [58, 61, 63]. In the case of NaCl, the bound state energies had been determined by other scattering experiments [75, 76] so that the peaks in the TOF spectra due to bulk phonon resonances could be reliably removed from the phonon dispersion diagram in Fig. 24. For Nal the values of the bound states still need to be established. 

Figure 15.12 Dispersion diagrams for the (a) metallic, (b) ferromagnetic, and (c) antiferromagnetic states of K4P3 as obtained with a value of U = 4.0eV. In the ferromagnetic case, bands in blue correspond to spin up, those in red to spin down. The...

For each value of k, I there are now three different values of frequency a, all real, which correspond to the three time derivatives in the shallow-water equations. Figure 3 gives the dispersion diagram for some representative parameters the frequency a, nondimensionalized by /o, is the ordinate wavenumber k nondimensionalized by is the abscissa where Zr = (The length scale... 

FIGURE 3 Dispersion diagram for the midlatitude )0-plane (a) inertia-gravity waves, (b) Rossby waves. (Note different scales along the ordinates.) The frequency a and zonal wavenumber k are nondimensionalized by fo and the Rossby radius Lr, respectively. Curves are labeled by the index n corresponding to meridional wavenumbers In = for n = 0, 1, 2, 3. See text for additional details. 

From the dispersion diagram, note that the wave solutions separate clearly into two distinct classes ... 

This cubic equation for is conspicuously similar to the midlatitude dispersion relation. Indeed, the dispersion diagram, shown in Fig. 4, has distinct similarities. Inertia-gravity waves are present in the high-frequency region and are approximately described by observing that if k /cyA < crl Eq. (97) yields... 

Figure 20.11 shows the energy band dispersion diagram and DOS for Srln204 [20]. The lowest band consisted of the Sr 4s atomic orbital (AO). The second, third, and fourth bands from the bottom were formed by the O 2s, Sr 4p, and In 4d AOs, respectively. The valence band consisted of 48 orbitals, which was the number that all the O 2p AOs for 16 0 atoms were fully occupied ( 73 through 120 in this numbering as shown in Figure 20.11). 

Figure 20.24 Band dispersion diagram and projected density of states for Zn2Ge04...

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