[en] A discontinuous spectral element method (DSEM) is presented to solve radiative heat transfer in multidimensional semitransparent media. This method is based on the general discontinuous Galerkin formulation. Chebyshev polynomial is used to build basis function on each element and both structured and unstructured elements are considered. The DSEM has properties such as hp-convergence, local conservation and its solutions are allowed to be discontinuous across interelement boundaries. The influences of different schemes for treatment of the interelement numerical flux on the performance of the DSEM are compared. The p-convergence characteristics of the DSEM are studied. Four various test problems are taken as examples to verify the performance of the DSEM, especially the performance to solve the problems with discontinuity in the angular distribution of radiative intensity. The predicted results by the DSEM agree well with the benchmark solutions. Numerical results show that the p-convergence rate of the DSEM follows exponential law, and the DSEM is stable, accurate and effective to solve multidimensional radiative transfer in semitransparent media

[en] The aim of this study is to contribute to the valorization of the tinctorial plants of Central Africa. A chemical characterization was conducted on three vegetable species presumed tinctorial. Grewia coriacea Mast (Malvaceae), Harungana madagascariensis Lamex Poir. (Hypericaceae), Annickia chlorantha Oliv. (Annonaceae) were selected because of their traditional use as colouring agents. The classical extractions were done by means of TLC, and quantified by usual methods. The antioxidant activity for the three species has also been assessed.(author)

[en] Because the optical plane defined by the incidence and reflection direction at a cylindrical surface has a complicated relation with the local azimuthal angle and zenith angle in the traditional cylindrical coordinate system, it is difficult to deal with the specular reflective boundary condition in the solution of the traditional radiative transfer equation for cylindrical system. In this paper, a new radiative transfer equation for graded index medium in cylindrical system (RTEGCN) is derived based on a newly defined cylindrical coordinate system. In this new cylindrical coordinate system, the optical plane defined by the incidence and reflection direction is just the isometric plane of the local azimuthal angle, which facilitates the RTEGCN in dealing with cylindrical specular reflective boundaries. A least squares finite element method (LSFEM) is developed for solving radiative transfer in single and multi-layer cylindrical medium based on the discrete ordinates form of the RTEGCN. For multi-layer cylindrical medium, a radial basis function interpolation method is proposed to couple the radiative intensity at the interface between two adjacent layers. Various radiative transfer problems in both single and multi-layer cylindrical medium are tested. The results show that the present finite element approach has good accuracy to predict the radiative heat transfer in multi-layer cylindrical medium with Fresnel surfaces.

[en] Both Galerkin finite element method (GFEM) and least squares finite element method (LSFEM) are developed and their performances are compared for solving the radiative transfer equation of graded index medium in cylindrical coordinate system (RTEGC). The angular redistribution term of the RTEGC is discretized by finite difference approach and after angular discretization the RTEGC is formulated into a discrete-ordinates form, which is then discretized based on Galerkin or least squares finite element approach. To overcome the RTEGC-led numerical singularity at the origin of cylindrical coordinate system, a pole condition is proposed as a special mathematical boundary condition. Compared with the GFEM, the LSFEM has very good numerical properties and can effectively mitigate the nonphysical oscillation appeared in the GFEM solutions. Various problems of both axisymmetry and nonaxisymmetry, and with medium of uniform refractive index distribution or graded refractive index distribution are tested. The results show that both the finite element approaches have good accuracy to predict the radiative heat transfer in semitransparent graded index cylindrical medium, while the LSFEM has better numerical stability.

[en] Highlights: • The calculated level energies for higher-lying rovibrational levels is more accurate than those obtained by Dunham expansion. • The potential energy curves of lower-lying electronic states are reconstructed by the RKR inversion procedure. • The partition functions, thermodynamic and spectral radiative properties of the N₂, N₂⁺, NO, O₂, CN, C₂, CO, and CO⁺ are given. • The calculated spectral radiative intensities are in good agreement with the available experimental results. The level energies of diatomic molecules calculated by the frequently used Dunham expansion will become less accurate for high-lying vibrational and rotational levels. In this paper, the potential curves for the lower-lying electronic states with accurate spectroscopic constants are reconstructed using the Rydberg–Klein–Rees (RKR) method, which are extrapolated to the dissociation limits by fitting of the theoretical potentials, and the rest of the potential curves are obtained from the ab-initio results in the literature. Solving the rotational dependence of the radial Schrödinger equation over the obtained potential curves, we determine the rovibrational level energies, which are then used to calculate the equilibrium and non-equilibrium thermodynamic properties of N₂, ${\mathrm{N}}_2^{+}$, NO, O₂, CN, C₂, CO and CO⁺. The partition functions and the specific heats are systematically validated by available data in the literature. Finally, we calculate the radiative source strengths of diatomic molecules in thermodynamic equilibrium, which agree well with the available values in the literature. The spectral radiative intensities for some diatomic molecules in thermodynamic non-equilibrium are calculated and validated by available experimental data.

[en] The radiative properties of soot aerosols largely depend on their mixing state and morphology factors. In this paper, we generated soot aggregates in four mixing states with sulfate, including bare soot, partly coated soot, heavily coated soot and soot with inclusion. The number of monomers and fractal dimension of soot were varied in each mixing state while the radius of monomers was fixed at 0.025 μm. Using the discrete dipole approximation method (DDA), we calculated optical parameters relevant for climate forcing simulation at mid-visible wavelength (0.55 μm). Internal mixing results in enhanced absorption, scattering cross sections as well as the single scattering albedo. The enhancement ratio of the absorption is largest for heavily coated soot, which ranges from 1.5 to 1.65 with a soot volume fraction of 0.15 and is larger for soot with larger fractal dimension. The scattering cross section can be dramatically increased by factors larger than 10 when soot is heavily coated. The increasing of both the scattering cross section and the single scattering albedo is larger for soot aggregates with smaller number of monomers and fractal dimension. The asymmetry parameter is insensitive to the fractal dimension for heavily coated soot and soot with inclusion. Two simplified models including the homogeneous sphere model (HS) and the core shell sphere model (CS) were examined using the DDA results as references. The performance of the HS and CS model largely depends on the morphology factors and the mixing state of soot. For bare and partly coated soot, both the HS and CS model can introduce relative errors as large as several tens percent. For heavily coated soot, the HS model predicts the absorption with relative errors within 10%, while it overestimates the absorption with relative errors no larger than 20% for soot with inclusion. The HS model predicts the single scattering albedo and the asymmetry parameter with relative errors no larger than 10% for heavily coated soot and soot with inclusion, which is much better than the prediction by the CS model. - Highlights: • Soot aggregates in different mixing states with sulfate were generated. • Morphological factors of soot aggregates in each mixing state were considered. • Radiative properties of aggregates were calculated by discrete dipole approximation. • The homogeneous sphere and the core shell sphere models were examined

[en] Highlights: • Growth dependent radiative properties of filamentous helix structure Spirulina platensis were experimentally studied. • Radiative properties of Spirulina platensis show good temporal scaling behavior. • The temporal scaling functions are nearly wavelength independent. • Results further demonstrate general validity of the temporal scaling law. The interaction of a cell with light is described by electromagnetic theory through parameters such as absorption cross-section, scattering cross-section and scattering phase function, which are essential radiative properties in radiative transfer theory for analysis of light transport in dispersed media. The radiative properties of microalgae vary with time due to the growth process of cell division and metabolism. In this paper, the growth-dependent radiative properties of Spirulina platensis (a microalgae with filamentous helix structure) was experimentally investigated in batch cultivation. The microalgae was cultivated in a flat-plate photobioreactor under dark and light cycle 12 h and 12 h with irradiance of 2000–2500 lx. The absorption and scattering cross-sections of Spirulina platensis were measured in the spectral region 380–850 nm at different growth time. The experimental results showed temporal scaling behavior of the radiative properties of this filamentous microalgae, which confirms the temporal scaling law of radiative properties of microalgae reported recently, namely, the temporal scaling function (TSF) defined as the ratio of spectral absorption or scattering cross-sections at different growth time to that at stationary phase is nearly wavelength independent. This paper is the first work on the temporal scaling behavior of radiative properties of Spirulina platensis, and also provides additional experimental evidence on the general validity of the temporal scaling law of radiative properties of microalgae cells.

[en] CoCrPt-SiO₂-based granular perpendicular media with dual-Ru intermediate layers were studied in the paper. The effects of gas pressures, such as argon pressure for the top Ru layer, oxygen partial pressure ratio and the total gas pressure for the magnetic layer, on the magnetic properties and recording performance of the media were systematically investigated. The results show that all these gas pressure parameters have significant effects on the magnetic properties and recording performance of the media to different extents. Combined with the results by X-ray diffraction, transmission electron microscopy, magnetic force microscopy, magneto-optical polar Kerr magnetometer and Guzik spin-stand tester, the growth mechanism of the perpendicular media and the functions of the gas pressure parameters for certain individual layer were demonstrated

[en] Highlights: • Finding of temporal scaling behavior of the radiative properties of microalgae. • Both theoretical proof and experimental examination are presented. • Concept of temporal scaling function is introduced to characterize temporal scaling. • Temporal scaling relation shows temporal scaling function is wavelength independent. • Radiative properties at any time can be calculated using those at stationary phase. The optical properties of microalgae are basic parameters for analyzing light field distribution in photobioreactors (PBRs). With the growth of microalgae cell, their optical properties will vary with growth time due to accumulation of pigment and lipid, cell division and metabolism. In this work, we report a temporal scaling behavior of the growth dependent optical properties of microalgae cell suspensions with both experimental and theoretical evidence presented. A new concept, the temporal scaling function (TSF), defined as the ratio of absorption or scattering cross-sections at growth phase to that at stationary phase, is introduced to characterize the temporal scaling behavior. The temporal evolution and temporal scaling characteristics of the absorption and scattering cross-sections of three example microalgae species, Chlorella vulgaris, Chlorella pyrenoidosa, and Chlorella protothecoides, were experimentally studied at spectral range 380–850 nm. It is shown that the TSFs of the absorption and scattering cross-sections for different microalgae species are approximately constant at different wavelength, which confirms theoretical predictions very well. With the aid of the temporal scaling relation, the optical properties at any growth time can be calculated based on those measured at stationary phase, hence opens a new way to determine the time-dependent optical properties of microalgae. The findings of this work will help the understanding of time dependent optical properties of microalgae and facilitate their applications in light field analysis in PBRs design.

[en] Many species of microorganisms possess spine-like surface structures. In this paper, we built a sphere with surface spines (SSS) model to represent such featured particles. The volume fraction of surface spines varied from 0% to 22% and the effects of the relative length, number, and radius of the spines on the radiation characteristics were studied using the discrete dipole approximation method with a complex relative refractive index of m=1.05+0.005i. Meanwhile, the approximations by the equivalent volume sphere (EVS) and the core shell sphere (CSS) models were examined. Surface spines led to increased scattering and absorption cross sections and asymmetry parameter. The EVS model overestimated the scattering cross section and underestimated the asymmetry parameter of SSS, the relative errors of which can exceed 10%, but EVS predicted the absorption cross section well. The CSS model combined with the Maxwell-Garnett mixing rule predicted the integral radiation parameters with relative errors less than 5% in all the cases, which was also valid for relative refractive indices with an imaginary part up to 0.1 and a real part up to 1.2. The resonance peaks of the phase function and Mueller matrix elements in the back scattering directions were damped out due to the existence of surface spines for size parameters larger than 10, which could not be captured by either the EVS or the CSS models. - Highlights: • Models were built to represent microorganisms with spine-like surface structure. • The radiative properties were calculated by the DDA method. • Approximations by two simplified equivalent models were investigated. • The core shell sphere predicts well for the integral radiative parameters.