Semi-infinite Heterogeneous Media Research Articles

On the sensitivity of surface reflectance to specularity and phase function parameters in MPA modeling of radiative transfer in two-component media

ABSTRACTThe multiphase approach (MPA) is used to analyze the radiation in a semi-infinite heterogeneous medium which is exposed to a normal and collimated laser beam. The directional reflectance, R(θ), has been calculated under various types of boundary condition and scattering phase functions. The main target is to compare the influences of the two limiting cases for boundary conditions, i.e., diffuse and specular, on the normal-directional reflectance of the medium, thermal heat flux, and directional-spatial distribution of the radiation intensity. It is found that the effect of scattering phase functions on the R(θ) depends on the type of boundary condition.

Scale dependent solute dispersion with linear isotherm in heterogeneous medium

This study presents an analytical solution for one-dimensional scale dependent solute dispersion with linear isotherm in semi-infinite heterogeneous medium. The governing advection–dispersion equation includes the terms such as advection, dispersion, zero order production and linear adsorption with respect to the liquid and solid phases. Initially, the medium is assumed to be polluted as the linear combination of source concentration and zero order production term with distance. Time dependent exponentially decreasing input source is assumed at one end of the domain in which initial source concentration is also included i.e., at the origin. The concentration gradient at the other end of the aquifer is assumed zero as there is no mass flux exists at that end. The analytical solution is derived by using the Laplace integral transform technique. Special cases are presented with respect to the different forms of velocity expression which are very much relevant in solute transport analysis. Result shows an excellent agreement between the analytical solutions with the different geological formations and velocity patterns. The impacts of non-dimensional parameters such as Peclet and Courant numbers have also been discussed. The results of analytical solution are compared with numerical solution obtained by explicit finite difference method. The stability condition has also been discussed. The accuracy of the result has been verified with root mean square error analysis. The CPU time has also been calculated for execution of Matlab program.

Disturbances in semi-infinite heterogeneous media generated by torsional sources. I

abstract This paper studies the generation of axially symmetric transient SH waves in semi-infinite heterogeneous media in which μ and ρ vary with depth. The sources generating these waves are taken in the form of time-dependent torsional-body forces of finite dimensions. The solution is obtained using Hankel and Laplace transforms and Green's function. The disturbance from a buried point source of impulsive type is discussed in two cases, (a) μ = μo(1 + ɛz)2, ρ = ρo (1 + ɛz)2, (b) μ = μoe2az, ρ = ρoe2az. It is shown that, in contrast to the results for a homogeneous medium, in case (i), the wave reflected by the free surface generates secondary disturbances which trail behind the wave front and die out as t increases; the incident wave in this medium generates no such disturbance. In case (ii), however, both the incident as well as the reflected waves generate secondary disturbances. Formal solution for the disturbance in a heterogeneous layer of finite depth with stress-free boundaries is discussed in Appendix II.

SH waves from torsional sources in semi-infinite heterogeneous media

The theory of Hankel transforms is used to obtain the displacement field forSH waves generated by time harmonic, buried, torsional sources in semi-infinite heterogenous media in which material properties are functions of the depth coordinate. An application to a heterogeneous medium with exponentially varying properties has been discussed. Surface displacements from a surface source have been evaluated at large distances from the source. The results have been compared with those for the homogeneous medium.

Elastic radiation from buried sources in a semi-infinite heterogeneous medium

The wave equations of elasticity in the presence of body forces for a semi-infinite, isotropic, heterogeneous medium with exponentially varying material properties have been solved. Using double Fourier transform the equations are first transformed to linear second order differential equations. From the solution of these equations the displacements are obtained by the use of inversion theorem for double Fourier transform. The method followed resolves the disturbance into its constitutive parts—incident and reflectedP, SV andSH type waves. Surface displacements due to a single couple, double couple and various other sources have been calculated.