Power-law Function Of Radius Research Articles

Multiphysical time-dependent creep response of FGMEE hollow cylinder in thermal and humid environment

In this paper, we investigate the history of radial displacement, stresses, electric potential, and magnetic potential of a functionally graded magneto-electro-elastic (FGMEE) hollow cylinder subjected to an axisymmetric hygro-thermo-magneto-electro-mechanical loading for the plane strain condition. The material properties are taken as a power-law function of radius. Using stress-displacement relations, equations of equilibrium, electrostatic and magnetostatic equations, we find a differential equation including creep strains. Initially, eliminating creep strains, we obtain an analytical solution for the primitive stresses and electric and magnetic potential. In the next step, considering creep strains, we find the creep stress rates by applying the Norton law and Prandtl–Reuss equations for steady-state hygrothermal boundary condition. Finally, using an iterative method, we find the time-dependent creep stresses, radial displacement, and magnetic and potential field redistributions at any time. In numerical section, are comprehensively investigate the effects of grading index, hygrothermal environmental conditions, rotating speed, and temperature- and moisture-dependency of elastic constant of FGMEE.

A self-similar solution for thermal disc winds

We derive a self-similar description for the 2D streamline topology and flow structure of an axi-symmetric, thermally driven wind originating from a disc in which the density is a power law function of radius. Our scale-free solution is strictly only valid in the absence of gravity or centrifugal support; comparison with 2D hydrodynamic simulations of winds from Keplerian discs however demonstrates that the scale-free solution is a good approximation also in the outer regions of such discs, and can provide a reasonable description even for launch radii well within the gravitational radius of the flow. Although other authors have considered the flow properties along streamlines whose geometry has been specified in advance, this is the first isothermal calculation in which the flow geometry and variation of flow variables along streamlines is determined self-consistently. It is found that the flow trajectory is very sensitive to the power-law index of radial density variation in the disc: the steeper the density gradient, the stronger is the curvature of streamlines close to the flow base that is required in order to maintain momentum balance perpendicular to the flow. Steeper disc density profiles are also associated with more rapid acceleration, and a faster fall-off of density, with height above the disc plane. The derivation of a set of simple governing equations for the flow structure of thermal winds from the outer regions of power law discs offers the possibility of deriving flow observables without having to resort to hydrodynamical simulation.

Retrieving Properties of Thin Clouds from Solar Aureole Measurements

Abstract This paper describes a newly designed Sun and Aureole Measurement (SAM) aureolegraph and the first results obtained with this instrument. SAM measurements of solar aureoles produced by cirrus and cumulus clouds were taken at the Atmospheric Radiation Measurement Program (ARM) Central Facility in Oklahoma during field experiments conducted in June 2007 and compared with simultaneous measurements from a variety of other ground-based instruments. A theoretical relationship between the slope of the aureole profile and the size distribution of spherical cloud particles is based on approximating scattering as due solely to diffraction, which in turn is approximated using a rectangle function. When the particle size distribution is expressed as a power-law function of radius, the aureole radiance as a function of angle from the center of the solar disk also follows a power law, with the sum of the two powers being −5. This result also holds if diffraction is modeled with an Airy function. The diffraction approximation is applied to SAM measurements with optical depths ≲2 to derive the effective radii of cloud particles and particle size distributions between ∼2.5 and ∼25 μm. The SAM results yielded information on cloud properties complementary to that obtained with ARM Central Facility instrumentation. A network of automated SAM units [similar to the Aerosol Robotic Network (AERONET) system] would provide a practical means to gain fundamental new information on the global statistical properties of thin (optical depth ≲ 10) clouds, thereby providing unique information on the effects of such clouds upon the earth’s energy budget.

Coupled thermoelasticity and second sound in finite length functionally graded thick hollow cylinders (without energy dissipation)

In this article, the coupled thermoelasticity behavior of functionally graded thick hollow cylinders is studied. The governing coupled thermoelasticity and the energy equations are solved for a finite length functionally graded cylinder subjected to thermal shock load. The coupled thermoelastic equations are considered based on Green–Naghdi theory. The mechanical properties of cylinder are graded across the thickness as a power law function of radius. The cylinder is assumed to be made of many isotropic sub-cylinders (layers) across the thickness. Functionally graded properties are created by suitable arrangement of layers and governing equations are expanded in longitudinal direction by means of trigonometric function expansion. The Galerkin Finite Element and Newmark Methods are used to analyze the cylinder. The dynamic behavior of temperature distribution, mechanical displacement and thermal stresses is obtained and discussed. The second sound and elastic wave propagation are determined for various kinds of variation in the mechanical properties. The comparison of present results with published data shows the excellent agreement.

Model atmospheres for SN 1987A and the distance to the Large Magellanic Cloud

A code which simultaneously solves the non-LTE equations of statistical equilibrium and the time-independent equation of radiation transport in an expanding atmosphere is applied to analyze the spectrum of SN 1987A. The behavior of a model atmosphere in which the density structure is a power-law function of radius has been studied and compared closely with SN 1987A data. This model atmosphere is used to derive corrections to the expanding photosphere method for determining distances to supernovae. The distance to the Large Magellanic Cloud derived from SN 1987A observations by this 'custom yardstick' is 49 + or - 6 kpc in excellent accord with results for RR Lyrae stars and for Cepheids. This empirical test of the expanding photosphere method provides the basis for hope that it may make a significant contribution to the extragalactic distance scale at cosmologically interesting distances.