Joint dispersion relation

Joint Commission on Biochemical Nomenclature, 17 401 402 Joint dispersion relation, 14 834-835 Joint Expert Committee of Food Additives (JECFA), 24 240... 

Using the requirement that electron and hole momenta are the same, the photon energy can be written as the joint dispersion relation... 

Using the joint dispersion relation, the joint density of states can be calculated and one obtains... 

The model matrix X in least squares modelling describes the variation of the variables included in the model. The matrix X X is symmetric, and hence also the dispersion matrix, (X X). The eigenvalues of the dispersion matrix are related to the precision of the estimated model parameters. The determinant of the dispersion matrix is the product of its eigenvalues. The "Volume" of the joint confidence region of the estimated model parameters is proportional to the square root of the determinant of the dispersion matrix. 

Ceo fullerides exhibit several interesting phenomena related with the presence of strong correlations such as high temperature superconductivity or antiferromagnetism. The existence of non-conventional behaviors can be anticipated from the fact that both the electron-phonon and electron-electron interactions are, respectively, comparable and much larger than the narrow bandwidth predicted by standard electronic structure calculations (a few hundreds of meV). These systems are therefore close to a metal-insula-tor transition of the Mott-Hubbard type and the validity of the adiabatic approximation, assumed in most electronic structure calculations, can be questioned. From the experimental point of view the band derived from the molecular LUMO is usually seen as a quite broad feature, much wider that the theoretical estimates, in photoemission experiments. However, the observation of the band dispersion has proven elusive in ARPES studies until very recently. In a recent joint experimental and theoretical paper, Yang et al. [158] have reported the first photoemission measurement of the band dispersion for a K-doped Qo monolayer deposited on a Ag(lll) substrate. The results have been compared with ab initio calculations performed with SIESTA. In those calculations the Ag substrate was modeled by a slab con-... 

By the addition of non-adsorbing polymers to colloidal suspensions the mixture phase separates into a coUoid-rich and a polymer-rich phase, as discussed above. The understanding of this polymer-induced phase separation is very important, not only for colloid science but also for industrial systems, such as food dispersions [74, 77, 236, 237]) and paint [238]. In these systems colloids and polymers (or surfactants) are jointly present and influence the stability and hence related processing issues. 

A very powerful method to study the electronic structure of solids is electron energy-loss spectroscopy (EELS). Because electrons transfer not only energy to the solid (as do photons) but also momentum, in addition to the energetic position of the electronic states, the dispersion of the bands can also be studied. Figure 1.58 shows the energy-loss spectrum of polypyrrole doped with the sulphonic acid H—(CH2)4—SO3 [126]. The various curves were recorded at different values of momentum transfer q. The dashed lines connect corresponding peaks. Vertical lines are characteristic of transitions into narrow bands (without dispersion), whereas inclined lines indicate broad bands. The maxima in the spectrum with low momentum transfer (bottom curve) are related to the maxima in the electronic joint density of states, but for... 

Relation between the coefficient of variation CV, the dispersion coefficient D, and the allowable defective ratio (1 - R) in strengths of adhesively bonded joints... 

Schon et al. (2005) applied a modular model concept for electrical, hydraulic, and elastic anisotropy studies that allows a joint interpretatiOTi of anisotropic formations. The model crmsideration and analysis of real logging data show that shear wave velocities depend strongly on the shale distribution and that the difference of the velocity of shear waves with different polarization can be related to the shale distributirHi (laminar or dispersed, structural). A shear wave-based method can discriminate between laminated and dispersed shaly zones and provide an estimate of the sand reservoir properties. 

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