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 Physics , 2011, DOI: 10.1016/j.jqsrt.2011.11.002 Abstract: Light transport in graded index media follows a curved trajectory determined by the Fermat's 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.
 Physics , 1999, Abstract: A Monte Carlo model of radiative transfer in multi-phase dusty media is applied to the situation of stars and clumpy dust in a sphere or a disk. The distribution of escaping and absorbed photons are shown for various filling factors and densities. Analytical methods of approximating the escaping fraction of radiation, based on the Mega-Grains approach, are discussed. Comparison with the Monte Carlo results shows that the escape probability formulae provide a reasonable approximation of the escaping/absorbed fractions, for a wide range of parameters characterizing a clumpy dusty medium. A possibly more realistic model of the interstellar medium is one in which clouds have a self-similar hierarchical structure of denser and denser clumps within clumps, resulting in a fractal distribution of gas and dust. Monte Carlo simulations of radiative transfer in such multi-phase fractal media are compared with the two-phase clumpy case.
 Mathematics , 2012, DOI: 10.1063/1.4790409 Abstract: The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical scatterers. To model this, we consider two optically random media, with the second medium obtained by shifting the first medium in some local region. We derive the radiative transfer equation for the cross-correlation of the wave fields in the media. Then we derive its diffusion approximation. In both the radiative transfer and the diffusion regimes, we relate the correlation of speckle patterns to the solutions of the radiative transfer and the diffusion equations. We present numerical simulations based on our model which are in agreement with recent experimental measurements.
 Physics , 2014, DOI: 10.1016/j.wavemoti.2014.08.001 Abstract: In this paper we develop a multiple scattering model for elastic waves in random anisotropic media. It relies on a kinetic approach of wave propagation phenomena pertaining to the situation whereby the wavelength is comparable to the correlation length of the weak random inhomogeneities--the so-called weak coupling limit. The waves are described in terms of their associated energy densities in the phase space position x wave vector. They satisfy radiative transfer equations in this scaling, characterized by collision operators depending on the correlation structure of the heterogeneities. The derivation is based on a multi-scale asymptotic analysis using spatio-temporal Wigner transforms and their interpretation in terms of semiclassical operators, along the same lines as Bal [Wave Motion 43, 132-157 (2005)]. The model accounts for all possible polarizations of waves in anisotropic elastic media and their interactions, as well as for the degeneracy directions of propagation when two phase speeds possibly coincide. Thus it embodies isotropic elasticity which was considered in several previous publications. Some particular anisotropic cases of engineering interest are derived in detail.
 Physics , 2002, Abstract: We describe the method we have used to parallelize our spherically symmetric special relativistic short characteristics general radiative transfer code PHOENIX. We describe some possible parallelization strategies and show why they would be inefficient. We discuss the multiple parallelization strategy techniques that we have adopted. We briefly discuss generalizing these strategies to full 3-D (spatial) radiation transfer codes.
 Physics , 2014, DOI: 10.1016/j.jqsrt.2014.11.005 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.
 Physics , 2014, DOI: 10.1103/PhysRevB.91.115406 Abstract: We obtain a fluctuation--dissipation theorem describing thermal electromagnetic fluctuation effects in nonlinear media that we exploit in conjunction with a stochastic Langevin framework to study thermal radiation from Kerr ($\chi^{(3)}$) photonic cavities coupled to external environments at and out of equilibrium. We show that that in addition to thermal broadening due to two-photon absorption,the emissivity of such cavities can exhibit asymmetric,non-Lorentzian lineshapes due to self-phase modulation. When the local temperature of the cavity is larger than that of the external bath, we find that the heat transfer into the bath exceeds the radiation from a corresponding linear black body at the same local temperature. We predict that these temperature-tunable thermal processes can be observed in practical, nanophotonic cavities operating at relatively small temperatures.
 Physics , 2011, DOI: 10.1016/j.jcp.2012.08.020 Abstract: 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. Comput. Phys. 214 (2006) 12-40 (where it was termed SAAI), 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.
 Physics , 2012, DOI: 10.1016/j.jqsrt.2012.04.005 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 too much of the performance of the LSFEM and makes it not a good choice to solve radiative transfer in strongly inhomogeneous media. It is also theoretically proved that the LSFEM is equivalent to a second order form of radiative transfer equation discretized by the central difference scheme.
 Mathematics , 2014, Abstract: The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the convergence relies on a formal Hilbert expansion and the estimation of the remainder. The Hilbert expansion has to be done up to order 3 to overcome some diffculties caused by the random noise.
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