Related papers: Exact Analytical Solution of the One-Dimensional T…
Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a…
We demonstrate that the spatial resolution of images in optical tomography is not limited to the fundamental length scale of one transport mean free path. This result is facilitated by the introduction of novel corrections to the standard…
In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies…
Cosmic rays (CR), constrained by scattering on magnetic irregularities, are believed to propagate diffusively. But a well-known defect of diffusive approximation whereby some of the particles propagate unrealistically fast has directed…
We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…
The difficulty of description of the radiative transfer in disordered photonic crystals arises from the necessity to consider on the equal footing the wave scattering by periodic modulations of the dielectric function and by its random…
The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The…
The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of the so-called \textquotedblleft convexification" method, which…
We present benchmark problems and solutions for the continuum radiative transfer (RT) in a 2D disk configuration. The reliability of three Monte-Carlo and two grid-based codes is tested by comparing their results for a set of well-defined…
A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a…
We have obtained new solutions and methods for the process of thermal Comptonization. We modify the solution to the kinetic equation of Sunyaev \& Titarchuk to allow its application up to mildly relativistic electron temperatures and…
We solve the integral equation describing the propagation of light in an isothermal plane-parallel atmosphere of optical thickness $\tau^*$, adopting a uniform thermalization parameter $\epsilon$. The solution given by the ALI method,…
In a medium where the dielectric permittivity is perturbed in the presence of an acoustic wave, optical scattering generates frequency-shifted light. In this paper we consider the inverse problem of recovering the optical properties of this…
When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…
Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods…
The Monte Carlo method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. The main drawback of the standard Monte Carlo radiative equilibrium methods is that they require iteration, which makes…
Employing tight-binding approximation we derive a transfer matrix formalism for one-dimensional single photon transport through a composite scattering center, which consists of parallel connected resonator optical waveguides. By solving the…
It was recently shown [Y. Suzuki, L. Lacombe, K. Watanabe, and N. T. Maitra, Phys. Rev. Lett. 119, 263401 (2017)] that peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory are…
Motivated by applications in quantitative photoacoustic imaging, we study inverse problems to a semilinear radiative transport equation (RTE) where we intend to reconstruct absorption coefficients in the equation from single and multiple…
The radiative transfer equation (RTE) for polarized light accepts a convenient exponential solution when the absorption matrix commutes with its integral. We characterize some of the matrix depth variations which are compatible with the…