Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

We propose the P_N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P_N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.     

Evaluation of solution methods for radiative heat transfer in gaseous oxy-fuel combustion environments

The exact solution to radiative heat transfer in combusting flows is not possible analytically due to the complex nature of the integro-differential radiative transfer equation (RTE). Many different approximate solution methods for the solution of the RTE in multi-dimensional problems are available. In this paper, two of the principal methods, the spherical harmonics (P₁) and the discrete ordinates method (DOM) are used to calculate radiation. The radiative properties of the gases are calculated using a non-gray gas full spectrum k-distribution method and a gray method. Analysis of the effects of numerical quadrature in the DOM and its effect on computation time is performed. Results of different radiative property methods are compared with benchmark statistical narrow band (SNB) data for both cases that simulate air combustion and oxy-fuel combustion. For both cases, results of the non-gray full spectrum k-distribution method are in good agreement with the SNB data. In the case of oxy-fuel simulations with high partial pressures of carbon dioxide, use of gray method for the radiative properties may cause errors and should be avoided.     

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional S_N discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.     

Application of the modified differential approximation for radiative transfer to arbitrary geometry

The first-order spherical harmonics method (or P₁ approximation) has found prolific usage for approximate solution of the radiative transfer equation (RTE) in participating media. However, the accuracy of the P₁ approximation deteriorates as the optical thickness of the medium is decreased. The modified differential approximation (MDA) was originally proposed to remove the shortcomings of the P₁ approximation in optically thin situations. This article presents algorithms to apply the MDA to arbitrary geometry—in particular, geometry with obstructions, and inhomogeneous media. The wall-emitted component of the intensity was computed using a combined view-factor and ray-tracing approach. The Helmholtz equation, arising out of the medium-emitted component, was solved using an unstructured finite-volume procedure. The general procedure was validated for both two-dimensional (2D) and three-dimensional (3D) geometries against benchmark Monte Carlo results. The accuracy of MDA was found to be superior to the P₁ approximation for all optical thicknesses. Its accuracy, when compared with the discrete ordinates method (both S₆ and S₈), was found to be clearly superior in optically thin situations, but problem dependent in optically intermediate and thick situations. For 3D geometries, calculation and storage of the view-factor matrix was found to be a major shortcoming of the MDA. In addition, for inhomogeneous media, calculation of optical distances requires a ray-tracing procedure, which was found to be a bottleneck from a computational efficiency standpoint. Several strategies to reduce both memory and computational time are discussed and demonstrated.     

Numerical solution of radiative and conductive heat transfer in concentric spherical and cylindrical media

A new technique is presented to improve the performance of the discrete ordinates method when solving the coupled conduction-radiation problems in spherical and cylindrical media. In this approach the angular derivative term of the discretized one-dimensional radiative transfer equation is derived from an expansion of the radiative intensity on the basis of Chebyshev polynomials. The set of resulting differential equations, obtained by the application of the S_N method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the Chebyshev transform method compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order S_N calculations.     

On using the FN method for polarization studies in finite plane-parallel atmospheres

The recently established F_N method for solving accurately problems in radiative transfer is used to reduce the azimuth-independent component of a basic polarization problem to a form readily amenable to numerical evaluation.     

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries

The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide means to obtain higher-order approximate solutions to the equation of radiative transfer. Although the assembly of the governing equations for the spherical harmonics method requires tedious algebra, their final form promises great accuracy for any given order, since it is a spectral method (rather than finite difference/finite volume in the case of discrete ordinates). In this study, a new methodology outlined in a previous paper on the spherical harmonics method (P_N) is further developed. The new methodology employs successive elimination of spherical harmonic tensors, thus reducing the number of first-order partial differential equations needed to be solved simultaneously by previous P_N approximations (=(N+1)²). The result is a relatively small set (=N(N+1)/2) of second-order, elliptic partial differential equations, which can be solved with standard PDE solution packages. General boundary conditions and supplementary conditions using rotation of spherical harmonics in terms of local coordinates are formulated for the general P_N approximation for arbitrary three-dimensional geometries. Accuracy of the P_N approximation can be further improved by applying the “modified differential approximation” approach first developed for the P₁-approximation. Numerical computations are carried out with the P₃ approximation for several new two-dimensional problems with emitting, absorbing, and scattering media. Results are compared to Monte Carlo solutions and discrete ordinates simulations and a discussion of ray effects and false scattering is provided.     

Population analysis solution to hardness enhancement in TiCxN1−x

We investigated the hardness enhancement in titanium carbonitrides (TiC_xN_1−x) by the population analysis method based on first-principles calculations. Populations for bonds TiC and TiN in TiC_xN_1−x (0.25<x<0.75) are all positive. The enhanced hardness for titanium carbonitrides is well explained by overlap population analysis. Intrinsic hardness of TiC_xN_1−x has been calculated based on the obtained overlap populations. The calculated results are in good agreement with the available experimental data.     

Evaluation of errors from neglecting polarization in the forward modeling of O2A band measurements from space, with relevance to CO2 column retrieval from polarization-sensitive instruments

Sensitivity studies have been performed to evaluate the errors resulting from ignoring polarization in analyzing spectroscopic measurements of the O₂A band from space, using the Orbiting Carbon Observatory (OCO) as a test case. An 11-layer atmosphere, with both gas and aerosol loading, and bounded from below by a lambertian reflecting surface, was used for the study. The numerical computations were performed with a plane-parallel vectorized discrete ordinate radiative transfer code. Beam and viewing geometry, surface reflectance and aerosol loading were varied one at a time to evaluate and understand the individual errors. Different behavior was observed in the line cores and the continuum because of the different paths taken by the photons in the two cases. The errors were largest when the solar zenith angle was high, and the aerosol loading and surface reflectance low. To understand the effect of neglecting polarization on CO₂ column retrievals, a linear error analysis study was performed on simulated measurements from the OCO spectral regions, viz. the 1.61 and 2.06 μm CO₂ bands and the O₂A band. It was seen that neglecting polarization could introduce errors as high as 10 ppm, which is substantially larger than the required retrieval precision of ∼2 ppm. A variety of approaches, including orders of scattering, spectral binning and the use of lookup tables are being explored to reduce the errors.     

Quantitative T(1)(ρ) imaging using phase cycling for B0 and B1 field inhomogeneity compensation

T_1ρ imaging is useful in a number of clinical applications. T_1ρ preparation methods, however, are sensitive to non-uniformities of the B₀ magnetic field and the B₁ RF field. These common system imperfections can result in image artifacts and quantification errors in T_1ρ imaging. We report on a phase-cycling method which can eliminate B₁ RF inhomogeneity effects in T_1ρ imaging. This method does not only correct for image artifacts but also for T_2ρ contamination caused by B₁ RF inhomogeneity. The presence of B₀ magnetic field inhomogeneity can compromise the effectiveness of this method for B₁ RF inhomogeneity correction. We demonstrate that, by combining the spin-locking scheme reported by Dixon et al. (Myocardial suppression in vivo by spin locking with composite pulses. Magn Reson Med 1996; 36:90-94) with phase cycling, we can simultaneously correct B₀ magnetic field inhomogeneity effects and B₁ RF inhomogeneity effects in T_1ρ imaging. Phantom and in vivo data sets are used to demonstrate the proposed methods and to compare them with other existing T_1ρ preparation methods.     

Emission features of Ho ion in Nb2O5, Ta2O5 and La2O3 mixed Li2O-ZrO2-SiO2 glasses

Li₂O-ZrO₂-SiO₂: Ho³⁺ glasses mixed with three interesting d-block elemental oxides, viz., Nb₂O₅, Ta₂O₅ and La₂O₃, were prepared. Optical absorption and photoluminescence spectra of these glasses have been recorded at room temperature. The luminescence spectra of Nb₂O₅ and Ta₂O₅ mixed Li₂O-ZrO₂-SiO₂ glasses (free of Ho³⁺ ions) have also exhibited broad emission band in the blue region. This band is attributed to radiative recombination of self-trapped excitons (STEs) localized on substitutionally positioned octahedral Ta⁵⁺ and Nb⁵⁺ ions in the glass network. The Judd-Ofelt theory was successfully applied to characterize Ho³⁺ spectra of all the three glasses. From this theory various radiative properties, like transition probability A, branching ratio β_r and the radiative lifetime τ_r, for ⁵S₂ emission levels in the spectra of these glasses have been evaluated. The radiative lifetime for ⁵S₂ level of Ho³⁺ ions has also been measured and quantum efficiencies were estimated. Among the three glasses studied the La₂O₃ mixed glass exhibited the highest quantum efficiency. The reasons for such higher value have been discussed based on the relationship between the structural modifications taking place around the Ho³⁺ ions.     

Application of Synthetic Kernel (SKN) method to participating linearly anisotropically scattering solid spherical medium

The Synthetic Kernel (SK_N) method is applied to a solid spherical absorbing, emitting and linearly anisotropically scattering homogeneous and inhomogeneous medium. The SK_N method relies on approximating the integral transfer kernels by Synthetic Kernels. The radiative integral transfer equation is then reducible to a set of coupled second-order differential equations. The SK_N method, which uses Gauss quadratures, is tested against integral equation and the discrete-ordinates S₈ solutions for various optical radius and scattering albedo variations.     

Resonance-enhanced multiphoton ionization spectroscopy of CH3 and CD3. Two-photon absorption selection rules and rotational line strengths of the ν3- and ν4-active vibronic transitions

To explore the possibility of K-level resolved, 2+1 resonance-enhanced multiphoton ionization (REMPI) processes of the methyl radical, the two-photon absorption selection rules and rotational line strengths of the 3₀¹ and 4₀¹ vibronic bands of the transition (n=3 or 4) were reported. Stringent selection rules, which were imposed upon these two-photon transitions, are the initial K″=3p (p=0,1,2,…), ΔK=±2, ΔU=±3, and ΔN=0,±1,±2 (O, P, Q, R, and S branches). The previously assigned 2₂² vibronic band of the methyl radical should be studied by the REMPI with a better spectral resolution and analyzed by the newly derived two-photon absorption selection rules and rotational line strength formulas.     

Sparse hyperspectral unmixing using an approximate L0 norm

Sparse unmixing aims at finding an optimal subset of spectral signatures in a large spectral library to effectively model each pixel in the hyperspectral image and compute their fractional abundances. In most previous work concerned with the sparse unmixing, L₂ norm is used to measure the error tolerance and the L₁ norm is added as the sparsity regularization. However, in some applications, using L₁ norm to measure the error tolerance has significant robustness advantages over the L₂ norm. Besides, in some cases, using a smooth function to approximate the L₀ norm can obtain more accurate results than the L₁ norm in the field of sparse regression. Thus, in this paper, we consider the two alternative choices for sparse unmixing. A reweighted iteration algorithm is also proposed so that the unconvex regularizer (smoothed L₀ norm) can be efficiently solved through transforming it into a series of weighted L₁ regularizer problems. Experimental results on both synthetic and real hyperspectral data demonstrate the efficacy of the new models.     

Application of the HN method to the critical slab problem for reflecting boundary conditions

The recently developed H_N method is used to solve the critical slab problem for a slab which is surrounded by a reflector. In the special case for R=0 (the reflection coefficient) the problem reduces to the one under vacuum boundary conditions. It is shown that the method is concise and leads to fast converging numerical results. The presented numerical results are compared with the data available in literature.     

Effect of nitrogen content on phase configuration, nanostructure and mechanical behaviors in magnetron sputtered SiCxNy thin films

SiC_xN_y thin films with different nitrogen contents were deposited by way of incorporation of different amounts of nitrogen into SiC_0.70 using unbalanced reactive dc magnetron sputtering method. Their phase configurations, nanostructures and mechanical behaviors were investigated by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), Raman spectroscopy, high-resolution transmission electron microscopy (HRTEM) and microindentation methods. The result indicated SiC_0.70 and all SiC_xN_y thin films exhibited amorphous irrespective of the nitrogen content. The phase configuration and mechanical behaviors of SiC_xN_y thin films strongly depended on nitrogen content. SiC_0.70 exhibited a mixture consisting of SiC, Si and a small amount of C. Incorporated nitrogen, on one hand linked to Si, forming SiN_x, on the other hand produced CN_x and C at the expense of SiC. As a result, an amorphous mixture consisting of SiC, SiN_x, C and CN_x were produced. Such effects were enhanced with increase of nitrogen content. A low hardness of about 16.5 GPa was obtained at nitrogen-free SiC_0.70. Incorporation of nitrogen or increase of nitrogen content increased the film hardness. A microhardness maximum of ∼29 GPa was obtained at a nitrogen content of 15.7 at.%. This value was decreased with further increase of N content, and finally a hardness value of ∼22 GPa was obtained at a N content of ∼25 at.%. The residual compressive stress was consistent with the hardness in the nitrogen content range of 8.6-25.3 at.%.     

Magnetic properties and room-temperature magnetocaloric effect in the doped antipervoskite compounds Ga1−xAlxCMn3 (0≤x≤0.15)

We report the effects of Al doping on the structure, magnetic properties, and magnetocaloric effect of antiperovskite compounds Ga_1−xAl_xCMn₃ (0≤x≤0.15). Partial substitutions of Al for Ga enhance the Curie temperature (from 250 K for x=0.0 to 312 K for x=0.15) and the saturation magnetization. On increasing the doping level x, the maximum values of the magnetic entropy change (−ΔS_M) decreases while the temperature span of −ΔS_M vs. T plot broadens. Furthermore, the relative cooling power (RCP) is also studied. For 20 kOe, the RCP value tends to saturate at a high doping level (for x=0.12, 119 J/kg at 296 K). However, at 45 kOe, the RCP value increases quickly with increasing x (for x=0.15, 293 J/kg at 312 K). Considering the relatively large RCP and inexpensive raw materials, Ga_1−xAl_xCMn₃ may be alternative candidates for room-temperature magnetic refrigeration.     

Characterization and properties of ZnO1−xSx alloy films fabricated by radio-frequency magnetron sputtering

A series of ZnO_1−xS_x alloy films (0 ≤ x ≤ 1) were grown on quartz substrates by radio-frequency (rf) magnetron sputtering of ZnS ceramic target, using oxygen and argon as working gas. X-ray diffraction measurement shows that the ZnO_1−xS_x films have wurtzite structure with (0 0 2) preferential orientation in O-rich side (0 ≤ x ≤ 0.23) and zinc blende structure with (1 1 1) preferential orientation in S-rich side (0.77 ≤ x ≤ 1). However, when the S content is in the range of 0.23 < x < 0.77, the ZnO_1−xS_x film consists of two phases of wurtzite and zinc blende or amorphous ZnO_1−xS_x phase. The band gap energy of the films shows non-linear dependence on the S content, with an optical bowing parameter of about 2.9 eV. The photoluminescence (PL) measurement reveals that the PL spectrum of the wurtzite ZnO_1−xS_x is dominated by visible band and its PL intensity and intensity ratio of UV to visible band decrease greatly compared with undoped ZnO. All as-grown ZnO_1−xS_x films behave insulating, but show n-type conductivity for w-ZnO_1−xS_x and maintain insulating properties for β-ZnO_1−xS_x after annealed. Mechanisms of effects of S on optical and electrical properties of the ZnO_1−xS_x alloy are discussed in the present work.     

Comparison of radiative transfer approximations for a highly forward scattering planar medium

We examine critically the accuracy of the two-flux, spherical harmonics and discrete ordinates methods for predicting radiative transfer in a planar, highly-forward scattering and absorbing medium. Numerical results for the radiative fluxes show that the two-flux and P₃-approximations yield accurate results compared to solutions based on the F_N-method. Indeed, these approximate methods are relatively simple and have potential for generalization to predict radiative transfer in multidimensional systems, as long as an appropriate simplification of the phase function is utilized.     

The 2003 edition of the GEISA/IASI spectroscopic database

The content of the current (2003) version, GEISA/IASI-03, of the computer-accessible spectroscopic database, GEISA/IASI, is described. This “system” or database is comprised of three independent spectroscopic archives, which are (a) a database of individual spectral line parameters on 14 molecules, H₂O, CO₂, O₃, N₂O, CO, CH₄, O₂, NO, SO₂, NO₂, HNO₃, OCS, C₂H₂, N₂, and the related 51 isotopomers and isotopologues, representing 702,550 entries, in the spectral range 599-, (b) a database of spectral absorption cross-sections (6,572,329 entries related to six molecules, CFC-11, CFC-12, CFC-14, HCFC-22, N₂O₅, CCl₄), and a catalogue of microphysical and optical properties (mainly, the refractive indices) of atmospheric aerosols. The modifications and improvements, which have been implemented since the earlier editions of this database, in terms of content and management, have been explained in detail. GEISA/IASI has been created with the specific purpose of assessing the capability of measurement by the IASI instrument within the designated goals of ISSWG in the frame of the CNES/EUMETSAT European Polar System preparation.All the archived data can be handled through a user-friendly associated management software, which is posted on the ARA/LMD group web site at http://ara.lmd.polytechnique.fr.