Inverse iteration, if applied to a symmetric positive definite matrix, is shown to generate a sequence of iterates with monotonously decreasing Rayleigh quotients. We present sharp bounds from above and from below which highlight inverse iteration as a descent scheme for the Rayleigh quotient. Such estimates provide the background for the analysis of the behavior of the Rayleigh quotient in cer...

In this paper a transient free convection flow around a sphere with variable surface temperature and embedded in a porous medium has been considered. The temperature of the sphere is suddenly raised and subsequently maintained at values that varies with position on surface. The method of asymptotic expansions is applied for small Rayleigh numbers and then a finite-difference scheme is used to s...

Laminar natural convection from an array of horizontal isothermal cylinders confined between two vertical walls, at low Rayleigh numbers, is investigated by theoretical and numerical methods. The height of the walls is kept constant, however, number of the cylinders and their spacing, the distance between the walls and Rayleigh number have been varied. The optimal spacing (confining walls) and ...

In this investigation Rayleigh-Ritz variational method has been applied to determine the least natural frequency coefficient for the title problem. Classical plate theory assumptions have been used to calculate strain energy and kinetic energy. Coordinate functions are combination of polynomials which satisfy boundary conditions at the outer boundary and trigonometric terms. In the second part ...

During the last few years, a number of numerical boundary condition schemes have been used to study various aspects of the no-slip wall condition using the lattice Boltzmann method. In this paper, a modified boundary condition method is employed to simulate the no-slip wall condition in the presence of the body force term near the wall. These conditions are based on the idea of the bounce-back ...

Temperature detection remains challenging in the low stratosphere, where the Rayleigh integration lidar is perturbed by aerosol contamination and ozone absorption while the rotational Raman lidar is suffered from its low scattering cross section. To correct the impacts of temperature on the Rayleigh Doppler lidar, a high spectral resolution lidar (HSRL) based on cavity scanning Fabry-Perot Inte...

In the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully use...

The table of source phase differences between Rayle igh and Love waves which was described in Pa r t I and used in Pa r t 2 is presented in a concise form for the case of a surface focus.

Thrust fault earthquakes are studied in a laboratory earthquake setup previously used to investigate analog strike-slip seismic events. Dynamic mode II ruptures are generated along preexisting faults in an analog material, Homalite H-100, and their interaction with the free surface is studied for both sub-Rayleigh and supershear rupture speeds. High-speed digital photography and laser velocimet...

A criterion for predicting the formation of freckles for Pb-Sn and Ni-base superalloys is evaluated using available experimental data. The criterion is based on a maximum value of the Rayleigh number, which indicates that the magnitude of buoyancy forces is largest with respect to the retarding frictional forces. The definition of the Rayleigh number involves a characteristic length scale. The ...