The use of the itFN method for radiative transfer problems with reflective boundary conditions

The F_N method is used to compute the net radiative heat flux relevant to radiative transfer in an anisotropically scattering, plane-parallel medium with specularly and diffusely reflecting boundaries.     

Chapman-Enskog-maximum entropy method on time-dependent neutron transport equation

The time-dependent neutron transport equation in semi and infinite medium with linear anisotropic and Rayleigh scattering is proposed. The problem is solved by means of the flux-limited, Chapman-Enskog-maximum entropy for obtaining the solution of the time-dependent neutron transport. The solution gives the neutron distribution density function which is used to compute numerically the radiant energy density E(x,t), net flux F(x,t) and reflectivity R_f. The behaviour of the approximate flux-limited maximum entropy neutron density function are compared with those found by other theories. Numerical calculations for the radiant energy, net flux and reflectivity of the proposed medium are calculated at different time and space.     

Analysis of transport of collimated radiation in a participating media using the lattice Boltzmann method

Application of the lattice Boltzmann method (LBM) recently proposed by Asinari et al. [Asinari P, Mishra SC, Borchiellini R. A lattice Boltzmann formulation to the analysis of radiative heat transfer problems in a participating medium. Numer Heat Transfer B 2010; 57:126–146] is extended to the analysis of transport of collimated radiation in a planar participating medium. To deal with azimuthally symmetric radiation in planar medium, a new lattice structure for the LBM is used. The transport of the collimated component in the medium is analysed by two different, viz., flux splitting and direct approaches. For different angles of incidence of the collimated radiation, the LBM formulation is tested for the effects of the extinction coefficient, the anisotropy factor, and the boundary emissivities on heat flux and emissive power distributions. Results are compared with the benchmark results obtained using the finite volume method. Both the approaches in LBM provide accurate results.     

Interior radiances in optically deep absorbing media—II Rayleigh scattering

The interior radiances are calculated within an optically deep absorbing medium scattering according to the Rayleigh phase function. The accuracy of the matrix operator method is improved by many orders of magnitude through the use of accurate starting values obtained by the Runge-Kutta method rather than from the single scattering approximation. The radiance and flux are given for a range of solar zenith angles and for single scattering albedos of 1, 0.99, 0.9, 0.5 and 0.1. The development of the asymptotic angular distribution of the radiance is illustrated. It is shown that this asymptotic distribution is probably physically unobservable when ω₀ < 0.8, since the flux is less than 10^-8 of its original value at the beginning of the asymptotic region. The ratio of the upward to downward flux is calculated and is shown to be remarkably constant within the medium except very close to the boundaries. The heating rate within the medium is found to be very nearly proportional to the downward flux, except near the boundaries. When the single scattering albedo is small, a number of examples illustrate the significant contribution of the direct solar flux to the total flux even at great optical depths within the medium. The total downward flux decreases exponentially with optical depth away from boundaries when the single scattering albedo is greater than or equal to 0.9; when it is less than or equal to 0.5 only an approximate exponential fit can be obtained within the region accessible to experimental observation.     

Smallest focal hole

We study theoretically routes toward the most confined dark channel that can be obtained using high angular aperture focusing. One possible solution is to use a radially polarized beam combined with an optical singularity. Another possibility is to use an azimuthally polarized light beam combined with an annular aperture or a phase filter. Our results suggest that a focal hole of full-width at half maximum of approximately 0.3λ₀/NA is achievable, where λ₀ is the wavelength in vacuum and NA is the numerical aperture of the focusing system. Finally, we show that by letting a phase-shifted plane wave and a focused scalar wave interfere only one point in the focal plane will exhibit zero intensity. Advantages and disadvantages of the schemes are discussed.     

An extended read model for grain boundaries in GaAs

The space charging properties of grain boundaries in GaAs are discussed using an extended Read dislocation model. Model calculations for medium to high angle grain boundaries show: (1) the core-site occupational probability for a dislocation at the grain boundary is at least an order of magnitude lower than would be expected on the basis of simple Read theory; (2) due to the strong core-core interaction of the dislocations, the depletion width W decreases with an increase in tilt angle θ: and (3) W is approximately independent of θ in highly doped (N_D ? 10₁₇/cm³) material. Comparisons between model predictions and experimentally determined depletion widths of grain boundaries in GaAs are presented.     

High-temperature surface oxidation of the decagonal AlCoNi quasicrystal

The interaction of oxygen with the 10-fold-symmetry surface of the decagonal Al_72.9Co_16.7Ni_10.4 quasicrystal at high temperatures was investigated by low-energy-electron diffraction and Auger electron spectroscopy. The results are consistent with a well-ordered aluminum-oxide layer possessing a hexagonal antiphase domain structure with a limited lateral size of about 35 Å. We claim that the separation distances of the domain boundaries, separating domains of equal orientation, are primarily a consequence of the preferential cluster nucleation on decagonal Al-Co-Ni. The domains are azimuthally oriented along one direction of the two sets of five twofold-symmetry axes lying on the decagonal surface in accordance with the local symmetry of the quasicrystal surface, while the size of the domains can be explained in terms of self-size-selecting arguments.     

Magnetoresistance of porous polycrystalline HTSC: Effect of the transport current on magnetic flux compression in intergranular medium

The hysteretic dependences of the magnetoresistance of porous (38% of the theoretical density) granular high-temperature superconductor (HTSC) Bi_1.8Pb_0.3Sr_1.9Ca₂Cu₃O _x have been analyzed in the model of the effective intergranular field. This effective field has been defined by the superposition of the external field and the field induced by magnetic moments of superconducting grains. The magnetic flux compression in an intergranular medium, characterized by the effective field, controls the hysteretic behavior of the magnetoresistance. It has been found that the magnetoresistance hysteresis width for the studied porous HTSC depends on the transport current, in contrast to the superconductor of the same composition with high physical density (more than 90% of the theoretical value). For a porous superconductor, a significant current concentration occurs in the region of the grain boundaries, which is caused by features of its microstructure. A current-induced increase in the effective boundary length results in a decrease in the flux compression, a decrease in the effective field in the intergranular medium, and a magnetoresistance hysteresis narrowing with increasing current.     

Mechanisms of dissipation in a Josephson medium based on a high-temperature superconductor in a magnetic field

This paper reports on the results of an investigation into the influence of magnetic fields (0–60 kOe) on the temperature dependences of the electrical resistance R(T) of the Y_3/4Lu_1/4Ba₂Cu₃O₇ + CuO composites. The structure of these composites is considered to be a network of tunnel-type Josephson junctions in which a nonsuperconducting component (CuO) forms boundaries (barriers) between high-temperature superconducting crystallites. The temperature dependence R(T) of the composites has two steps characteristic of granular superconductors: (i) an abrupt change in the electrical resistance at the critical temperature of high-temperature superconducting crystallites and (ii) a smooth transition to the superconducting state under the influence of the boundaries between the crystallites. The experimental dependences R(T) are analyzed within the Ambegaokar-Halperin model of thermal fluctuations in Josephson junctions and the flux creep model. An increase in the magnetic field leads to a crossover from the Ambegaokar-Halperin mechanism to the flux creep mechanism. The temperature dependences R(T) in the range of weak magnetic fields (from 0 to 10² Oe) are adequately described by the relationship following from the Ambegaokar-Halperin model. In the range of strong magnetic fields (from 10³ to 6 × 10⁴ Oe), the dissipation obeys the Arrhenius law R ～ exp(?U(H)/T)], which is characteristic of the flux creep model with a temperature-independent pinning energy U(H). The effective Josephson coupling energies and the pinning energies corresponding to the Ambegaokar-Halperin and flux creep mechanisms are determined.     

Dominant influence of the compression effect of a magnetic flux in the intergranular medium of a granular high-temperature superconductor on dissipation processes in an external magnetic field

Experiments have been presented that demonstrate the effect of the compression of a magnetic flux in grain boundaries of a granular high-temperature superconductor in an external magnetic field on the dissipation processes. The compression of the magnetic flux is associated with the diamagnetic behavior of superconducting grains and the existence of a Josephson medium in grain boundaries. Under these conditions, grain boundaries are in an effective magnetic field that depends on the magnetic state (magnetization) of the superconducting grains. Based on the analysis of experimental data (dependences of the electrical resistance R and magnetization on the magnetic field H and temperature T, as well as current-voltage characteristics), the conclusion has been drawn that it is the temperature evolution of the effective magnetic field in the intergranular medium which primarily determines the behavior of the dependences R(T) in weak external magnetic fields of no more than ～10³ Oe. This should be taken into account in the interpretation of experiments on the magnetoresistance effect in granular high-temperature superconductors in terms of different theories. The conclusion drawn here also implies a significant correction of the previously obtained results.     

Effect of surface segregation on the sharpness of heteroboundaries in multilayered Si(Ge)/Si1−x Gex structures grown from atomic beams in vacuum

The main reasons for composition intermixing in the vicinity of heteroboundaries in an Si(Ge)/Si_1?x Ge_x heterosystem grown by the molecular beam epitaxy method are considered. The proposed model explains all the experimentally observed peculiarities, such as the clearly manifested asymmetry of the solid solution profile in layers, and demonstrates the noticeable erosion of the composition profile at the boundaries even in the absence of the surface segregation effect. It is shown that the surface segregation in the Ge/Si_1?x Ge_x system may play a positive role, leading to an increase in the profile steepness of the Si_1?x Ge_x layer near the boundaries.     

Numerical results for the thermal scattering functions

A recent formulation in radiative transfer defined the thermal scattering functions that characterize radiative transfer from a general, plane-parallel, finite medium driven solely by an internal distribution of thermal sources. Exiting diffuse intensities are expressed as space convolutions of the thermal scattering functions with any thermal source distribution. A parametric study is presented to obtain the basic structure of these scattering functions. The independent variables of these azimuthally independent functions are the direction consine μ and source location t, while the parameters are the single scattering albedo ω, total optical depth t₀, and the asymmetry factor g in the Henyey-Greenstein phase function. The basic functional trends are discussed using various parametric plots, and selected tabular results are given to allow numerical checks. The computational method is invariant imbedding. As a particular application, these functions are used in the following companion paper to obtain exiting intensities from inhomogeneous and nonisothermal media.     

Radiation-induced phase transition in a film of niobium-tin solid solution

A 5-μm-thick film of a niobium-tin solid solution (18.3 at % Sn) grown by ion-plasma sputtering with subsequent codeposition of ultrafine metal particles is irradiated by a fast proton flux with a fluence of 10¹⁹ p ⁺/cm². X-ray diffraction analysis carried out using CuK _α (λ = 0.154178 nm), CoK _α (λ = 0.179021 nm), and MoK _α (λ = 0.071069 nm) radiations shows the presence of a radiation-induced stannide niobium (Nb₃Sn) phase in the region of proton energy dissipation (at a depth of 2.5 μm from the surface of the solid solution film). It is found that at the end of the particle range, nonlocal interaction between the protons and the concentrated matrix solid solution takes place. When interacting with the supersaturated solid solution, a bombarding particle covers a tangible area of the solution, so that an intermetallic phase greater than critical in size nucleates. The feasibility is demonstrated of using a fast particle flux to produce an intermetallic (superconducting) phase inside a solid solution layer with a composition close to the stoichiometric composition of the intermetallic.     

Effect of self-fields on the electron cyclotron maser instability in a dielectric loaded waveguide

The influence of self-fields on the cyclotron maser instability in a hollow electron beam propagating parallel to a uniform axial magnetic field B ₀ ê _z in a dielectric loaded waveguide is investigated. The theoretical analysis is carried out within the framework of linearized Vlasov-Maxwell equations. It is assumed that the beam is thin with the radial thickness much smaller than the beam radius. A new dispersion relation for azimuthally symmetric electromagnetic perturbation is derived and analyzed numerically. The influence of self-fields on the cyclotron maser instability in a dielectric loaded waveguide for different dielectric medium is studied. It is found that unlike the hollow waveguide the growth rate is increased by increasing self-fields. The instability band width decreases due to the increasing self-fields. The maximum growth rate increases gradually as self-fields increase as regards a different dielectric medium.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

Abstract

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Photon path length analysis of radiative heat transfer in planar layers with arbitrary temperature distributions

The internal source analytical technique is extended to predict the radiative heat transfer for a layer having an arbitrary temperature distribution. By combining a number of internal sources distributed at various optical depths in the layer and weighting them appropriately, a nonisothermal layer is modeled. Heat flux and intensity distributions within layers having a single internal source are presented. The distributions are found to present trends unique to the internal source problem. Isothermal layers are modeled and compare very well with published results. Increased accuracy is attained for all cases and particularly for larger optical depths and smaller albedos by increasing the number of internal sources. The technique is applied to a nonisothermal layer having a temperature distribution similar to that for a hot medium with a cold boundary region. The effect of the boundary region on the normalized heat flux leaving the layer is seen to collapse to a single line for small layer optical thicknesses and large albedos, the slope of which is governed by the temperature ratio T_max/T_min.     

Families of solutions to the generalized Ginzburg-Landau equation and structural transitions between them

Solutions to the generalized Ginzburg-Landau equations for superconductors are obtained for a Ginzburg-Landau parameter κ close to unity. The families of solutions with arbitrary number n of flux quanta in a unit cell are analyzed. It is shown that under certain conditions, a cascade of phase transitions between different structures in a magnetic field appears near T _c . Algebraic equations are derived for determining the boundaries of coexistence of different phases on the {T, H ₀} plane.     

Effect of the microstructure of epitaxial YBa2Cu3O7 − x films on their electrophysical and nonlinear microwave properties

The local nonlinear microwave response of YBa₂Cu₃O_{7 ? x} films was measured by near-zone field microscopy with a spatial resolution of 50 μm, and YBa₂Cu₃O_{7 ? x} film microbridges were locally studied by low-temperature scanning microscopy with a spatial resolution of 4 μm. The microstructure of epitaxial YBa₂Cu₃O_{7 ? x} films was examined using x-ray diffraction and electron microscopy. A correlation is detected between the average crystallite size and the half-widths of the temperature dependences of the third-harmonic power (W _TH) and the electron-beam-induced voltage (W _EBIV). The experimental results are described in terms of a model of a two-phase medium taking into account the nonlinear I-V characteristic of the superconductor. For large crystallites, the nonlinear microwave response is shown to be caused by intracrystallite vortex pinning. As the average crystallite size decreases, an additional contribution to the nonlinear response appears due to the pinning of a magnetic flux by the Josephson network of crystallite boundaries. Calculations show that a three-fold increase in the crystallite size decreases the nonlinearity coefficient of YBa₂Cu₃O_{7 ? x} films by two orders of magnitude.     

Line vortex pinning and spacing in a three-dimensional ordered Josephson medium

A method of calculating the configuration of two line vortices interacting in a three-dimensional ordered Josephson medium and a minimal distance between them at a given pinning parameter is proposed. The axes of the vortices lie in the middle row of an infinite slab 9 or 13 cells thick with different conditions at the boundaries of the slab. Away from the centers of the vortices, the system of finite-difference equations becomes linear. Fluxoid quantization conditions in cells near the centers of the vortices serve as boundary conditions. An exact solution is approached by iterations in those phase discontinuities which cannot be considered small. This technique provides a much higher calculation accuracy and offers a wider domain of applicability than the earlier methods. Critical values I _d of the pinning parameter at which two initial vortices keep given spacing d between them are calculated. For various vortex configurations, maximal pinning forces are calculated as functions of the pinning parameter and the distance to the nearest vortices. It is shown that the pinning force decreases near parallel vortices and increases near antiparallel ones.     

Two-dimensional radiative equilibrium: Boundary emissive powers for a finite medium subjected to cosine varying radiation

Exact expressions are presented for the emissive power at the boundaries of a two- dimensional, finite, planar, absorbing-emitting, gray medium exposed on one side to cosine varying radiation and on the other side to no radiation. The emissive powers at the boundaries of a medium illuminated by cosine varying collimated radiation are the generalized X- and Y-functions which are analogous to Chandrasekhar's X- and Y-functions. Integro-differential equations for the generalized X- and Y-functions are formulated and reduced to a system of ordinary differential equations and are solved numerically. The emissive powers at the boundaries for cosine varying diffuse radiation are moments of the generalized X- and Y-functions.