Rayleigh’s approach

Rayleigh s approach to the thermal convection problem has been extended to include other boundary conditions, the more important of which are shown in Table III. Such a refinement can be accomplished either by solving a complicated characteristic equation of the type of Eq. (35), or by resorting to a short cut. ... 

The oscillatory behavior of cavities in an acoustic field has been well-described by a variety of mathematical models derived from Rayleigh s original approach with the inclusion of various nonideal liquid properties (28-33). Let us examine, as an example, one such equation of... 

R /f is the numerical aperture (N.A.) and is marked on all objective lenses, together with the magnification. For example, a x25 objective with N.A. = 0.5 is expected to resolve detail of the order of 2X 1 m, ideally. Equation (2.1) has been derived by considering diffraction by a coherently illuminated periodic object. Rayleigh s well-known criterion of resolution, derived for a nonperiodic object incoherently illuminated, gives nearly the same limit of resolution as that determined from the Abbe approach and need not be considered here (see, e.g., Giancoli 1984). 

Alpert et al. (1965) were the first to measure the width of Rayleigh s band in the binary system aniline-fcyclohexane at the critical concentration. They found that the band contracts as the configurative point approaches the critical temperature 7. A direct proportionality of Aw vs vias also found. 

In the above formula, Q is the nuclear coordinate, p, and I/r are the ground state and excited electronic terms. Here Kv is provided through the traditional Rayleigh-Schrodinger perturbation formula and K0 have an electrostatic meaning. This expression will be called traditional approach, which has, in principle, quantum correctness, but requires some amendments when different particular approaches of electronic structure calculation are employed (see the Bersuker s work in this volume). In the traditional formalism the vibronic constants P0 dH/dQ Pr) can be tackled with the electric field integrals at nuclei, while the K0 is ultimately related with electric field gradients. Computationally, these are easy to evaluate but the literally use of equations (1) and (2) definitions does not recover the total curvature computed by the ab initio method at hand. 

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