J. Y. Tan

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

Monte Carlo method for polarized radiative transfer in gradient-index media

Abstract Light transfer in gradient-index media generally follows curved ray trajectories, which will cause light beam to converge or diverge during transfer and induce the rotation of polarization ellipse even when the medium is transparent. Furthermore, the combined process of scattering and transfer along curved ray path makes the problem more complex. In this paper, a Monte Carlo method is presented to simulate polarized radiative transfer in gradient-index media that only support planar ray trajectories. The ray equation is solved to the second order to address the effect induced by curved ray trajectories. Three types of test cases are presented to verify the performance of the method, which include transparent medium, Mie scattering medium with assumed gradient index distribution, and Rayleigh scattering with realistic atmosphere refractive index profile. It is demonstrated that the atmospheric refraction has significant effect for long distance polarized light transfer.

On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

Abstract Light transport in graded index media follows a curved trajectory determined by Fermats principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.

A deficiency problem of the least squares finite element method for solving radiative transfer in strongly inhomogeneous media

Abstract The accuracy and stability of the least squares finite element method (LSFEM) and the Galerkin finite element method (GFEM) for solving radiative transfer in homogeneous and inhomogeneous media are studied theoretically via a frequency domain technique. The theoretical result confirms the traditional understanding of the superior stability of the LSFEM as compared to the GFEM. However, it is demonstrated numerically and proved theoretically that the LSFEM will suffer a deficiency problem for solving radiative transfer in media with strong inhomogeneity. This deficiency problem of the LSFEM will cause a severe accuracy degradation, which compromises the performance of the LSFEM too much and makes it not a good choice to solve radiative transfer in strongly inhomogeneous media. It is also theoretically proved that the LSFEM using the one dimensional linear element is equivalent to a second order form of radiative transfer equation discretized by the central difference scheme.

Ab initio molecular dynamics study of temperature and pressure-dependent infrared dielectric functions of liquid methanol

The temperature and pressure-dependent dielectric functions of liquids are of great importance to the thermal radiation transfer and the diagnosis and control of fuel combustion. In this work, we apply the state-of-the-art ab initio molecular dynamics (AIMD) method to calculate the infrared dielectric functions of liquid methanol at 183–573 K and 0.1–160 MPa in the spectral range 10−4000 cm−1, and study the temperature and pressure effects on the dielectric functions. The AIMD approach is validated by the Infrared Variable Angle Spectroscopic Ellipsometry (IR-VASE) experimental measurements at 298 K and 0.1 MPa, and the proposed IR-VASE method is verified by comparison with paper data of distilled water. The results of the AIMD approach agrees well with the experimental values of IR-VASE. The experimental and theoretical analyses indicate that the temperature and pressure exert a noticeable influence on the infrared dielectric functions of liquid methanol. As temperature increases, the average molecular d...

Infrared optical constants of liquid palm oil and palm oil biodiesel determined by the combined ellipsometry-transmission method

The optical constants of vegetable oils and biodiesels are the basic input parameters in the study of the thermal radiation transfer and monitoring the productivity of vegetable oils converting to biodiesels. In this work, a combined ellipsometry-transmission method is presented to obtain the optical constants of palm oil and palm oil biodiesel between 20°C and 150°C in the spectral range 600-4100  cm-1 and to study the temperature effect on the optical constants. In the combined method, a modified ellipsometry method is used to measure the optical constants of palm oil and palm oil biodiesel for the whole researched wave bands. For the weak absorption regions in which the ellipsometry method cannot give precise absorption indices, the transmission method is conducted to get the absorption indices using the refractive indices obtained by the proposed ellipsometry method. Deionized water and methanol are taken as examples to verify the combined ellipsometry-transmission method. It is shown that the combined method can overcome the deficiencies of the traditional ellipsometry and transmission method, which can be used for the measurements of both strong and weak absorption wave bands. The experimental analyses indicate that temperature exerts a noticeable influence on the infrared optical constants of palm oil and palm oil biodiesel. With the increase of temperature, the refractive indices at certain wavenumbers decrease nearly linearly, and the amplitudes of dominant absorption peaks show a decreasing trend. The absorption peaks located around 3550  cm-1 show blueshift trends as temperature increases. Comparing these two kinds of oils, palm oil presents larger values in refractive indices and dominant absorption peaks.

The influence of bubble populations generated under windy conditions on the blue–green light transmission in the upper ocean: An exploratory approach

The “blue–green window” in the ocean plays an important role in functions such as communication between vessels, underwater target identification, and remote sensing. In this study, the transmission process of blue–green light in the upper ocean is analyzed numerically using the Monte Carlo method. First, the effect of total number of photons on the numerical results is evaluated, and the most favorable number is chosen to ensure accuracy without excessive costs for calculation. Then, the physical and mathematical models are constructed. The rough sea surface is generated under windy conditions and the transmission signals are measured in the far field. Therefore, it can be conceptualized as a 1D slab with a rough boundary surface. Under windy conditions, these bubbles form layers that are horizontally homogeneous and decay exponentially with depth under the influence of gravity. The effects of bubble populations on the process of blue–green light transmission at different wind speeds, wavelengths, angle ...

Hamiltonian adaptive resolution molecular dynamics simulation of infrared dielectric functions of liquids

Hamiltonian adaptive resolution scheme (H-AdResS), which allows to simulate materials by treating different domains of the system at different levels of resolution, is a recently proposed atomistic/coarse-grained multiscale model. In this work, a scheme to calculate the dielectric functions of liquids on account of H-AdResS is presented. In the proposed H-AdResS dielectric-function calculation scheme (DielectFunctCalS), the corrected molecular dipole moments are calculated by multiplying molecular dipole moment by the weighting fraction of the molecular mapping point. As the widths of all-atom and hybrid regions show different degrees of influence on the dielectric functions, a prefactor is multiplied to eliminate the effects of all-atom and hybrid region widths. Since one goal of using the H-AdResS method is to reduce computational costs, widths of the all-atom region and the hybrid region can be reduced considering that the coarse-grained simulation is much more timesaving compared to atomistic simulati...

Temperature-dependent optical constants of liquid isopropanol, n-butanol, and n-decane

Liquid isopropanol, n-butanol, and n-decane are combustible organic compounds that are frequently used in theoretical and experimental researches on fuel combustion. In this work, the temperature-dependent optical constants of liquid isopropanol, n-butanol, and n-decane in the region 500-5500  cm-1 at ambient pressure are measured using the combined ellipsometry-transmission method. In the combined method, the optical constants are first measured by a modified ellipsometry method, and then the absorption indices for weak absorption regions are obtained by the transmission method using the refractive indices measured by the modified ellipsometry method. The refractive indices of liquid isopropanol, n-butanol, and n-decane are within the range from 1.3 to 1.45 in the studied wavelength and temperature region. The absorption indices of these liquids range from 10-5 to 10-1. In the temperature range studied, the refractive indices decrease with increasing temperature in an approximately linear manner, but the effects of the temperature on the absorption indices are much smaller. The characteristic wavenumbers of the main absorption peaks are consistent with the vibrational frequencies of major functional groups.