The solution of radiation transfer problem for a slab with space-dependent albedo and anisotropic scattering

The transport of thermal radiation has been considered within a finite slab which absorb and scatter anisotropically. The problem involves the space-dependent single-scattering albedow(x). Two approximations are taken forw(x). In the first it is represented in exponential form asw(x)=w ₀ exp(–x/s), wherew ₀ ands are given constants andx is the optical variable. The second approximation assumes the formw(x) = _r=0 ^R d _r ^* p _r (x/a), whered _r ^* are known expansion coefficients anda is the half optical thickness of the slab. Analytic expressions for the forward, backward radiation intensities and fluxes are given in each approximation. The solution of the linear transport equation is performed on the basis of integral Fourier transforms.     

Diffuse reflection and transmission of solar radiation by a finite atmosphere bounded by a reflecting surface

The problem of diffuse reflection and transmission of solar radiation through a planetary atmosphere bounded from below by a reflecting surface is solved. The solution method based on rewriting the solution of the proposed problem in terms of the well known standard problem solution, where the planetary surface does not reflect. The solution of the standard problem can be found elsewhere or as we did by using the maximum entropy method. Numerical results for the angular radiation intensity and for the reflection and transmission coefficients are presented and compared with those obtained by Chandrasekhar's method.     

Padé approximant calculations for the number of scattering during particle diffusion

The mean number of particle scattering in a semi-infinite and finite slab for arbitrary energy sources are calculated by Padé approximants. Uniform source distribution is considered for the finite slab. For the semi-infinite medium we calculatethe number of particles due external radiation and at a particular point in the medium. Numerical calculations and comparisons were performed.     

Discussion of “Interfacing the geographic information system,remote sensing,and the soil conservation service-curve number method to estimate curve number and runoff volume in the ASIR region of Saudi Arabia” by Fawzi S. Mohammad,Jan Adamowski

The soil conservation service curve number (SCS-CN) method is one of the most commonly used methods to compute the direct runoff from a rainfall event. Since the method was established, numerous researches were undertaken to improve the method through accurate estimation of its parameter and especially the curve number (CN). However, the essence of the SCS method, as an event-based Hortonian mechanism method, remained unchanged. The main assumption of the method related to the rainfall input is that the rainfall is continuous in time and uniform over the watershed. Mohammad and Adamowski (2015) paper apparently used the SCS method to estimate the annual runoff using the annual rainfall as one cumulative rainfall input value, which is a violation of the event-based principle of the method and of the assumption of the continuity of the rainfall event.To re-estimate the average annual runoff more realistically for the Asir region, Saudi Arabia, daily rainfall data from 14 rainfall stations are used for calculating the resulting runoff depths, on a daily event-by-event rainfall basis, throughout the whole simulation period. The resulting runoff depths are added for each year, and the total cumulative annual runoff values for each year are averaged to get the average annual runoff. The runoff values based on the previously mentioned procedure are an upper limit of the actual average annual runoff as the underlying SCS equations discard evaporation and similar long-term losses. Nevertheless, the average runoff values obtained in the discussion paper are an order of magnitude (at least five to tenfold) lower than the ones of the original paper. An equation is proposed to obtain a more realistic estimate of the average annual runoff, to be used with the average annual rainfall as an input, if the annual value is the only available rainfall information.     

The Condition of Hydrostatic Equilibrium of Stellar Models Using Optimal Control

The condition of hydrostatic equilibrium of relativistic stellar models is formulated as an optimal control problem. Application of Pontryagin's maximum principle leads directly to the Tolman-Oppenheimer-Volkoff equation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Discrimination of earthquakes and explosions using multi-fractal singularity spectrums properties

A new method of discrimination of seismic records from earthquakes and explosions is proposed which is based on using properties of their multi-fractal singularity spectrums. The efficiency of the method is illustrated by analysing seismic records from the region of Aswan Dam in Egypt. Current pattern of seismicity in the Upper Egypt is composed by three types of records: tectonic earthquakes, reservoir-induced earthquakes and seismic events generated by quarry blasts. To discriminate quarry blasts from earthquakes of both natures, multi-fractal analysis of records were used. Singularity spectrum support width and multi-fractal generalised Hurst exponents were calculated for all seismic events in the selected data set from a given area. The linear Bayesian discriminator using these characteristics of seismic records provides correct classification for 93 % of earthquakes records and for 99 % of quarry blasts records.     

Radiant heat transfer in isotropically-scattering media bounded by diffusely-reflecting plates

The partial heat fluxes of thermal radiation in an emitting, absorbing, and scattering finite medium bounded by diffusely-reflecting plates is studied, assuming the medium to scatter isotropically. Two algebraic equations connecting the partial heat fluxes relevant to this problem and the corresponding one with simple boundary conditions are obtained. The intergral equation is solved in a semi-analytical from by collection method, using Legendre polynomials as basis functions. Numerical results are presented and compared.     

A static axisymmetric anisotropic fluid solution in general relativity

Einstein's interior field equations in general relativity are considered when spacetime is static and axisymmetric and the energy-momentum tensor represents an anisotropic fluid. After imposing a set of simplifying assumptions a two-parameter solution is derived and its properties are discussed. The solution is found to be physically reasonable in a certain range of the parameters in which case the metric could represent a core of anisotropic matter.     

A new class of relativistic stellar models

Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patiño and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patiño and Rago which have been shown by Knutsen to be incorrect. Similar to Tolman solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.     

Bivariational calculations for radiation transfer in an inhomogeneous participating medium

Equations for radiation transfer are obtained for dispersive media with space-dependent albedo. Bivariational bound principle is used to calculate the reflection and transmission coefficients for such media. Numerical results are given and compared.