A new efficient method of solution to radiation transfer in absorbing,emitting, isotropically scattering,homogeneous, finite or semi-infinite,plane-parallel media

A new efficient method of analysis, which utilizes the natural eigenfunctions of the problem, is developed for solving radiation transfer in an absorbing, emitting, gray, isotropically scattering, homogeneous, finite or semi-infinite, plane-parallel medium. Expressions for the forward and backward radiation intensities, the incident radiation and forward and backward radiation heat fluxes are included. Since the physical aspects of the problem are well documented, attention is focused on the presentation of the method of analysis and discussion of its convergence and accuracy. For the test case involving uniform incident radiation on the boundary surface at x = 0, it is shown that the solution converges extremely rapidly to the exact results, and that lower-order approximations are highly accurate. For example, the first-order solution predicts values of the incident radiation, reflectivity and transmissivity that are less than 1% in error in almost all cases, for optical thicknesses in the range 0.1 ⩽ L ⩽ 10 and single-scattering albedos in the range 0.1 ⩽ ω ⩽ 0.99. The present method of solution has an excellent potential for generalization to anisotropic scattering and to radiation transfer in spherical and cylindrical geometries.     

Formation of ground and excited hydrogen atoms in proton–potassium inelastic scattering

The inelastic scattering of proton with a potassium atom is treated for the first time as a three-channel problem within the framework of the improved coupled static approximation by assuming that the ground (1s state) and the excited (2s state) hydrogen formation channels are open for seven values of total angular momentum, ? (0≤?≤6) at energies between 50 and 500 keV. The Lipmann–Swinger equation and the Green’s function iterative numerical method are used to calculate iterative partial and total cross-sections. This can be done by calculating the reactance matrix at different values of the considered incident energies to obtain the transition matrix that gives partial and total cross-sections. Present results are in reasonable agreement with previous results.     

Benchmark solutions of radiative transfer equation for three-dimensional rectangular homogeneous media

Three-dimensional steady-state radiative integral transfer equations (RITEs) for a cubic absorbing and isotropically scattering homogeneous medium are solved using the method of “subtraction of singularity”. Surface integrals and volume integrals are carried out analytically to eliminate singularities, to assure highly accurate solutions, and to reduce the computational time. The resulting system of linear equations for the incident energy is solved iteratively. Six benchmark problems for cold participating media subjected to various combinations of externally uniform/non-uniform diffuse radiation loads are considered. The solutions for the incident energy and the net heat flux components are given in tabular form for scattering albedos of ω=0, 0.5 and 1.     

Source function expansion method for radiative transfer in a two-layer slab

Radiative heat transfer in an isotropically scattering, absorbing and emitting two-layer slab with specularly reflecting boundaries is solved by expanding the source function by Legendre polynomials in the space variable in the integral form of the equation of radiative transfer. The reflectivity and the transmissivity of the slab for an externally incident isotropic radiation are determined. The S-1 solution yields results which are sufficiently accurate for most engineering applications.     

Determination of the health hazards due to background radiation sources in the city of Adapazari,Northwestern Turkey

Human body is exposed to ionising radiations both internally and externally by mainly high-energy cosmic ray particles incident on the earth's atmosphere and radioactive nuclides that originated in the earth's crust. The main objective of this study is to assess the health hazards due to environmental radiation sources in the city of Adapazari, one of the most important industrial cities of the country, Northwestern Turkey. For this purpose, natural radiation sources, external terrestrial radiations, cosmic radiations, and inhalation exposures have been investigated. The annual average external terrestrial radiation doses were determined as 0.08 and 0.35 mSv at outdoor and indoor atmospheres, respectively. The annual average cosmic radiation doses were found to be 0.08 and 0.05 mSv for directly ionising photon components and neutron components, respectively. The annual average inhalation exposure doses due to radon and thoron were obtained as 1.42 and 0.19 mSv, respectively, in the region. The annual average effective dose due to natural radiation sources was determined as a total of 2.35 mSv with the predetermined ingestion radiation dose. The lifetime cancer risk due to the background ionising radiations has been determined as 0.9×10^?2 for the residents of the Adapazari city, with the average lifespan of 70 years. The results of the effective doses due to background radiation sources in the region and the worldwide averages were discussed.     

On normalization of scattering matrices of polarized radiation

The condition of normalization of scattering matrix is derived when the polarized radiation is described by the Stokes parameters I, Q, U, V. The normalization of the matrix is based on energy conservation. It has a probabilistic meaning also. When the scattering particle is nonspherical, scattered radiation may depend not only on the angle between incident and scattered radiation but on orientation of the scattering plane also. In these cases, the known change of the Stokes parameters Q, U of the incident radiation with respect to various scattering planes influences the normalization. The derived normalization includes all elements of the first line of scattering matrix and the characteristics of polarization of the incident radiation. Dependence on this polarization is appeared because the polarization influences intensities of scattered radiation and, therefore, is included in energy conservation. The routine normalization includes the first element of the scattering matrix only. These two normalizations determine the different normalizing constants of the scattering matrix. The simple computational example of scattering by the particle that has the shape of a finite cylinder is considered. This example shows that the values of normalizing constants of the routine normalization may considerably differ from the ones of the obtained normalization. The results of the study may be useful in various investigations of radiation scattering, especially in the cases when the scattering particles are nonspherical.     

Characteristics of Λ andK 0 particles produced in central nucleus nucleus collisions at a 4.5 GeV/c momentum per incident nucleon

Data on Λ's andK ⁰'s, produced in central nucleus-nucleus collisions (C?C, C?Ne, O?Ne, C?Cu, C?Zr, C?Pb, O?Pb) at a 4.5 GeV/c momentum per incident nucleon obtained in the streamer chamber spectrometer SKM-200, are presented. Multiplicities, transverse momenta, rapidities and other characteristics are considered and compared with those for inelastic He?Li interactions. The polarization of Λ's was found to be consistent with zero. The upper limit of \(\bar \Lambda /\Lambda \) production ratio was estimated to be ≤10^?2 with a 90% confidence level. The results are compared with data of other experiments and some model calculations.     

Relationship between cross section and matrix normalization of polarized radiation scattering

A simple relationship between the total scattering cross section and the normalizing constant of the scattering matrix for the general case of an arbitrary scattering particle and elliptically polarized incident radiation is obtained. The polarized radiation is described by the Stokes parameters I, Q, U, V. The obtained relationship is a consequence of two forms of energy conservation. The first one is in terms of the total scattering cross section. The other one involves the normalizing constant of the scattering matrix. The obtained relationship contains dimensionless integrals of the radiation scattered over all directions of scattering. The integrals depend on the elements of the first row of the scattering matrix and on the relative values of the Stokes parameters of the incident radiation. In the case of cross section, the incident radiation is assumed to be a plane wave. In the case of normalization constant, the incident radiation is assumed to be a convergent beam. The possible dependence of the scattering integrals on specificities of the particle illumination is taken into account in the obtained relationship. The relationship may be helpful in the various cases. So, the relationship allows one to determine any of the two characteristics of the scattering process under investigation, cross section or normalizing constant, via the other one. The relationship can be used for obtaining the scattering integrals and for analyzing the influence of the incident radiation polarization on cross section and normalizing constant.     

Longitudinal vibrations in circular rods: A systematic approach

A systematic method is developed for expressing the frequency squared ω² and the corresponding displacement fields of harmonic waves in a long thin rod as an even power series in qa, where q is the wavenumber along the rod and a is a representative transverse dimension. For longitudinal waves in a circular rod, the evaluation is reduced to algebraic recursion, giving coefficients analytically in terms of Poisson's ratio v, to many orders. The second nontrivial coefficient, corresponding to Rayleigh–Love theory in the present longitudinal case and Timoshenko theory in the flexural case, is thus put on a firm footing without reliance on ad hoc physical assumptions. The results are compared to available exact predictions, and shown to be accurate for moderate values of qa (5% accuracy for qa≤1.5) with just two terms. Improvements based on the Rayleigh quotient guarantee positivity and the correct asymptotic power, and the variational principle further ensures that the accuracy improves monotonically with the order of approximation. With these features, accurate results are obtained for larger qa (5% accuracy for qa≤3), so that results are valid for rods that are by no means thin. Application of these methods to the flexural case has been presented separately.     

Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method

The power-Lanczos (PL) method is one kind of Green's function Monte Carlo simulation, which is improved by Lanczos iterations. The ground state energies of strongly-correlated models can be evaluated by this method quite accurately. In this report, the boundary of phase separation (PS) of the two-dimensional t-J model is investigated by the power-Lanczos method and Maxwell construction. The energies are compared with the results evaluated by other methods. Our conclusion is that there is no phase separation for J/t≤0.4.     

Plasma turbulent reactors

Similarity solutions are found for the evolution of the distribution functions of the radiation and relativistic electrons in a plasma turbulent reactor (PTR). These solutions have a “universal” power-law form which is shown to be analogous to the Kolmogorov spectrum for fluid turbulence and stable in the same sense. These results appear to have a minimal model dependence and may have considerable implications for our understanding of nonthermal radiation sources in astrophysics which have power-law spectra. The PTR theory gives two values for the resultant radiation spectrum if the PTR's relativistic electrons are placed in an optically thin environment, namely a spectral falloff of ω^−0.5 and ω⁻¹ in remarkably close agreement with the observed values.     

Response of a two-level system to a sequence of N radiation pulses

A general expression has been obtained for the polarisation of an assembly of two-level systems irradiated by a sequence of N radiation pulses. The times and amplitudes of the echo-polarisation have been obtained. The method is an extension of the T-matrix method for the exact solution of the problem of interaction of radiation with two-level systems. The number of polarisation echoes is 3 ^N?1?N. The echo times are given by $$t' = (1 + a)t_N + (b - a)t_{N - 1} + (c - b)t_{N - 2} + \cdots + (q - p)t_1 $$ wheret _k are the pulse times anda, b, c take on values 1, 0, ? 1. From the general expression the amplitudes of echoes due to sequences of 2, 3 and 4 pulses are obtained as special cases. Distinct echo sequences determined by time relations among the incident pulses are discussed. The echo sequences exhibit interesting features which are of significance in the application of the phenomenon in holophony, etc.     

Non-destructive evaluation of scientific and biological samples by scattering of 145 keV gamma rays

The objective of present experiment is to assign effective atomic number (Z_eff) to samples of scientific interest (oxides of lanthanoids, also called rare earths, and alloys of lead and tin of known composition) and to measure stable iodine content of tissue (biological sample). An HPGe semiconductor detector, placed at 70° to the incident beam, detects gamma photons scattered from the sample under investigation. The experiment is performed on various elements with atomic number satisfying, 6 ≤ Z ≤ 82, for 145 keV incident photons. The intensity ratio of Rayleigh to Compton scattered peaks, corrected for photo-peak efficiency of gamma detector and absorption of photons in the sample and air, is plotted as a function of atomic number and constituted a fit curve. From this fit curve, the respective effective atomic numbers of the scientific samples are determined. The agreement of measured values of Z_eff with theoretical calculations is found to be quite satisfactory. The measured intensity ratio from phantom (KI solutions, simulating thyroid content of stable iodine) varies linearly with KI concentration and provides stable iodine content of tissue.     

Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices

We present an algorithm for polarized radiative transfer in a vertically stratified system consisting of two plane-parallel media with different refractive indices. It is based on the discrete ordinate method and includes multiple elastic scattering, thermal radiation, Fresnel reflection and transmission, incident parallel-beam or isotropic radiation at the top of the upper medium and bidirectional reflection at the bottom of the lower medium. Comparisons with results from Monte Carlo simulations show that the discrete-ordinate code provides accurate results for all four elements of the Stokes vector (I, Q, U, and V) at a speed that is orders of magnitude faster.     

Longitudinal field-induced polarized light transmittance of magnetic fluids

The complete optical transmittance for a polarized light passing through the magnetic fluids is investigated theoretically and experimentally, when the externally magnetic field is applied along the propagation direction of the incident light. Hybrid effects due to the geometric shadowing and Faraday rotation are considered simultaneously. The Langevin-like functions are employed to describe the magnetic-field-dependent volume concentration of the particle-aggregation (φ′) and the approximate number of magnetic nanoparticles in the particle-aggregation (βN₀). Based on the experiments on the geometric shadowing effect of our magnetic fluid sample, the analytical expression for the total transmitted power with externally magnetic field after an analyzer is derived. Theoretical simulations disclose the influence of certain critical parameters of the magnetic fluids on the field-dependent optical transmittance. For the entire polarized light transmittance, qualitative agreement between the calculations and the experiments is achieved. Applications of magnetic fluids to several polarized devices operating in longitudinal field arrangement are proposed and discussed. The results presented in this work may be useful for designing the corresponding magnetic-fluid-based optical devices.     

Anomalous laser energy absorption associated with resonance saturation

Laser energy absorption measurements have been undertaken in an experiment involving the transmission of a pulse of laser radiation through sodium vapour. The wavelength of the laser was tuned to overlap the 589 nm resonance transition of the sodium atoms. Although simple radiation transport appears to account for the attenuation of the laser beam at low values of incident laser irradiance, anomalously large absorption has been observed at high values of incident laser energy. We suggest that this anomalous absorption of laser energy can be regarded as evidence of superlastic electron heating and subsequent ionization.     

Deformed Hartree-Fock calculation of proton-rich nuclei

We perform Hartree-Fock+BCS calculations for even-even nuclei with 2 ≤ Z ≤ 82 and N ranging from outside the proton drip line to the experimental frontier on the neutron-rich side. The ground state solutions are obtained for 737 nuclei, together with shape-coexistence solutions for 480 nuclei. Our method features the Cartesian-mesh representation of single-particle wavefunctions, which is advantageous in treating nucleon skins and exotic shapes. The results are compared with those of the finite-range droplet model of Møller et al. as well as the experimental values.     

Second-order ellipsometric coefficients

We derive analytic expressions for the reflection amplitudes of s and p polarized electromagnetic radiation incident on a planar interface profile of arbitrary form, to second order in the parameter qa, where q is the component of the wavenumber perpendicular to the interface, and a is a length proportional to the interface thickness. New comparison identities, relating the reflection and transmission amplitudes of the p-wave to those for any reference profile, are derived. The second-order results are obtained by using one of these identities, and an integro-differential form of the p-wave equation.     

Polarized radiation transfer in finite binary Markovian random media

The problem of polarized radiation transfer in a finite plane-parallel binary Markovian random medium is studied. Pomraning-Eddington approximation is used for both the total intensity and the difference function of the polarized radiation. The formalism obtained by Levermore et al. and Pomraning is used to average the obtained solution in the deterministic case. The random medium is assumed to have specular-reflecting boundaries with angular-dependent externally incident flux. Numerical results of the average reflectivity and the average transmissivity are calculated for the different degrees of polarization.     

Hybrid nanofluid flow over two different geometries with Cattaneo–Christov heat flux model and heat generation: A model with correlation coefficient and probable error

The authors scrutinize the steady, MHD flow of SiO₂−MoS₂/water hybrid nanofluid towards two different geometries i.e. a wedge and a cone. The Tiwari and Das model is implemented with a generalized–Fourier's model, popularized as Cattaneo-Christov heat flux model. Analysis of heat transfer also incorporates the effects of suction, heat generation and thermal radiation. To showcase the relationship between engineering quantities and pertinent parameters involved in the study, the correlation coefficient for heat transfer coefficient and the skin friction coefficient is computed followed by the computation of probable error and statistical declaration. Similarity transformations are utilized to remodel the constitutive laws of flow in non-dimensional form. Numerical computation of non-linear, coupled O.D.E.’s is performed with the support of the Runge-Kutta-Fehlberg scheme and shooting method. Graphical and tabular illustrations of computed results are provided to report the variation in flow properties with the fluctuation in physical parameters. In both cases, i.e. flow close to a wedge and a cone, the temperature of hybrid nanofluid enhances on intensifying the thermal radiation and experiences a decrement with thermal relaxation parameter and magnetic field. Rising values of the suction parameter, thermal relaxation parameter, and thermal radiation cause increment in heat transfer coefficient. Interestingly, it was spotted that the heat generation parameter has contrary effects on temperature distribution over the two geometries.