Perturbation local

The chemistry of interest is often not merely the inhnite crystal, but rather how some other species will interact with that crystal. As such, it is necessary to model a system that is an inhnite crystal except for a particular site where something is diherent. The same techniques for doing this can be used, regardless of whether it refers to a defect within the crystal or something binding to the surface. The most common technique is a Mott-Littleton defect calculation. This technique embeds a defect in an inhnite crystal, which can be considered a local perturbation to the band structure. 

Conventional physical descriptions of materials in the solid state are concerned with solids in which properties are controlled or substantially influenced by the crystal lattice. When defects are treated in typical solid state studies, they are considered to modify and cause local perturbations to bonding controlled by lattice properties. In these cases, defect concentrations are typically low and usually characterized as either point, linear, or higher-order defects, which are seldom encountered together. 

The operation involved in the definition of the EPI is an exchange of atoms on sites i and j and it is a kind of localized perturbation. So the orbital peeling method provides an efficient means for obtaining the generalized phase shifts. 

Friedel used the local perturbation f/—as a model for the scattering potential, reduced it even to one spherically symmetric scatterer and calculated the scattering by free electrons. By that, for the scatterer at the origin labeled by j = 0,... 

Kirtman B (1999) Local Space Approximation Methods for Correlated Electronic Structure Calculations in Large Delocalized Systems that are Locally Perturbed. 203 147-166 Kita Y, see Tohma H (2003) 224 209-248 KleiJ AW, see Kreiter R (2001) 217 163-199 Klein Gebbink RJM, see Kreiter R (2001) 217 163-199... 

Apart from inversions, there is another way to determine whether or not there is mixing in the Sun. Any spherically symmetric, localized sharp feature or discontinuity in the Sun s internal structure leaves a definite signature on the solar p-mode frequencies. Gough (1990) showed that changes of this type contribute a characteristic oscillatory component to the frequencies z/ / of those modes which penetrate below the localized perturbation. The amplitude of the oscillations increases with increasing severity of the discontinuity, and the wavelength of the oscillation is essentially the acoustic depth of the sharp-feature. Solar modes... 

The ENDOR data demonstrate that intermolecular interactions dominate the potential function for the ring rotation. The fast exchange limit of V(bz)2 is reached at lower temperatures in Fe(cp)2 than in Cr(bz)2. This is in qualitative agreement with the NMR relaxation results of Campbell et al.280) on the pure host materials. Since a transition temperature of Tc = 79 K is predicted for Fe(cp)2 from the NMR data, one can conclude that the dynamic behavior of the guest molecules is not entirely determined by the host properties alone, but that the guest V(bz)2 introduces a significant local perturbation into the host lattice by its larger size. 

A criticism often aimed at the use of extrinsic fluorescent probes is the possible local perturbation induced by the probe itself on the microenvironment to be probed. There are indeed several cases of systems perturbed by fluorescent probes. However, it should be emphasized that many examples of results consistent with those obtained by other techniques can be found in the literature (transition temperature in lipid bilayer, flexibility of polymer chains, etc.). To minimize the perturbation, attention must be paid to the size and shape of the probe with respect to the probed region. 

Flow along a particle surface can be affected either by cavitations or by protrusions. In both cases, the flow pattern on the particle surface is changed and the dissolution rate may be altered due to local perturbations. 

Besides the remarkable directionality of the motion, the images also demonstrate a periodic variation of the cluster from an elongated to a circular shape (Fig. 39). The diagrams in Fig. 39 depict the time dependence of the displacement and the cluster size. Until the cluster was finally trapped, the speed remained fairly constant as can be seen from the constant slope in Fig. 39 a. The oscillatory variation of the cluster shape is shown in Fig. 39b. Although a coarse model for the motion has been presented in Fig. 39, the actual cause of the motion remains unknown. The ratchet model proposed by J. Frost requires a non-equiUb-rium variation in the energetic potential to bias the Brownian motion of a molecule or particle under anisotropic boundary conditions [177]. Such local perturbations of the molecular structure are believed to be caused by the mechanical contact with the scaiming tip. A detailed and systematic study of this question is still in progress. 

For the purpose of illustration, in this paper we use a viscosity-capillarity model (Truskinovsky, 1982 Slemrod, 1983) as an artificial "micromodel",and investigate how the information about the behavior of solutions at the microscale can be used to narrow the nonuniqueness at the macroscale. The viscosity-capillarity model contains a parameter -Je with a scale of length, and the nonlinear wave equation is viewed as a limit of this "micromodel" obtained when this parameter tends to zero. As we show, the localized perturbations of the form x /-4I) can influence the choice of attractor for this type of perturbation, support (but not amplitude) vanishes as the small parameter goes to zero. Another manifestation of this effect is the essential dependence of the limiting solution on the... 

Bachelot, R., Gleyzes, R, and Boccara, A. C. 1995. Near-field optical microscope based on local perturbation of a diffraction spot. Opt. Lett. 20 1924-26. 

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