Compression Behaviour of Chlef Sand and Transition of Fines Content Using Pressure-Dependent Maximum Void Ratios of Sand

Geotechnical and Geological Engineering - This paper presents a study on Chlef sand to examine the effect of fines content (Fc), relative density (RD) and initial conditions on the compressibility...     

Energy-dependent transport problem with generalized boundary conditions

The slowing-down Boltzmann equation for generalized boundary conditions is considered and transformed to one-speed equation in Laplace space. Exact relations between energy reflection and transmission coefficients for a problem with diffuse reflecting boundary conditions and the albedos for the problem with isotropic boundary conditions are obtained. The Galerkin method is used to calculate the energy reflection coefficient for a finite slab for different thicknesses at different mass ratiosA, target to projectile mass, at different synthetic-scattering kernels. The results for partial heat fluxes for isotropic and anisotropic-scattering dispersive medium are given. The results obtained for isotropic boundary conditions are compared well with the exact results.     

Radiation transfer in inhomogeneous dispersive media

Equations for the angular density of radiation, reflected and transmitted intensities associated with radiation scattered by inhomogeneous dispersive media are obtained. The Padé approximant technique is used to calculate these intensities in inhomogeneous and homogeneous media. The results for the [0/1] Padé approximant lead to numerical results that compared with the exact results.     

Padé approximant calculations for dispersive,isotropic scattering,homogeneous media

Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.     

Angular radiation transfer in inhomogeneous dispersive media

The equation of radiative transfer for an inhomogenous dispersive finite medium subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the angular distribution of radiation. Numerical results for the [0/1] Padé approximant lead to numerical results that compared with the exact results.     

Radiation transfer for linearly anisotropic phase functions

Radiative transfer equation in a plane-parallel medium with isotropic boundary conditions for linearly anisotropic scattering phase function is considered. Two coupled integral equations for total density of radiation and total radiation flux are obtained. The Galerkin method is used to solve these equations. Numerical results for the radiative fluxes at the boundaries show that the Galerkin method yields accurate results compared well with other exact methods.     

Angular distribution of radiation in an isotropically scattering slab

The equation of radiative transfer in an isotropically scattering slab subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the reflected and transmitted angular distributions. Numerical results for angular distributions through and at the boundaries of a finite slab are calculated by the Padé approximation technique. The results for a Padé approximation of [0/1] are compared with results obtained by the Galerkin method.