The extremum properties of the generalized Rayleigh quotient related to flutter instability are investigated. It is shown that, in addition to the well-known stationary property, under certain circumstances the quotient exhibits maximum-minimum properties which are in contrast to those of the classical Rayleigh quotient. One consequence is that an approximate method of stability analysis using ...

Temperature measurements using vibrational Raman scattering from molecular nitrogen were performed simultaneously with temperature obtained by Rayleigh scattering in the amplitude range between 12 and 30 km. The downward extension of the Rayleigh temperature described in this paper leads to the possibility of obtaining a continuous temperature profile from 12 to nearly 100 km. The temperature p...

The linear governing equations of a transversely isotropic microstretch elastic solid medium are formulated and solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are applied to the required boundary conditions at the free surface of the halfspace of the medium. A frequency equation is obtained for Rayleigh surface wave in the medium. The non-dimens...

The resonance phenomenon observed in Rayleigh wave scattering from surface-breaking cracks has been investigated using Freund's results on reflection of Rayleigh waves from an infinite crack edge. To model the crack as a section of acoustic waveguide, resonances are treated as standing waves in the length and depth directions. The model takes both faces of the crack into consideration, and this...

We discuss variants of the Jacobi–Davidson method for solving the generalized complex-symmetric eigenvalue problem. The Jacobi–Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean inner product xy in C by the bilinear form x y. The Rayleigh quotient based on this bilinear form leads to an asymptotical...

The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modul...