We derive the hypoelliptic estimates for a kinetic equation of the form ∂tf + k · ∇xf = (−∆d)h, for (t, x, k) ∈ R× R × S, where d ≥ 1, β > 0, Sd is the unit sphere in Rd+1 and ∆d is the Laplace-Beltrami operator on Sd. Such equations arise in the modeling of high frequency waves in random media with long-range correlations. Assuming some (fractional) Sobolev regularity in the momentum variable ...

The fundamental phenomenological equations of radiative transfer, e.g., Lambert's cosine rule and the radiant transport equation, are derived from an analysis based on the Cauchy flux theory of continuum mechanics. For the classical case, where the radiance is distributed regularly over the unit sphere, it is shown that Lambert's rule follows from a balance law for the transfer of radiative pow...

Radiation absorption at the surjace of catalytic particles is the initial step of photocatalytic oxidation reactions currently considered for their potential effectiueness in the treatment of polluted water with traces of highly toxic organics. Owing to the presence of catalyst particles within the fluid phase, the radiation field within a photocatalytic reactor results from the absorption and ...

We present a largely improved version of CRASH, a 3-D radiative transfer code that treats the effects of ionizing radiation propagating through a given inhomogeneous H/He cosmological density field, on the physical conditions of the gas. The code, based on a Monte Carlo technique, self-consistently calculates the time evolution of gas temperature and ionization fractions due to an arbitrary num...

Using the methods of general relativity Lindquist derived the radiative transfer equation that is correct to all orders in v/c. Mihalas developed a method of solution for the important case of monotonic velocity fields with spherically symmetry. We have developed the generalized atmosphere code PHOENIX, which in 1-D has used the framework of Mihalas to solve the radiative transfer equation (RTE...

The radiative transfer phenomenon is modeled by an integro-differential equation known as Boltzmann equation. This equation describes mathematically the interaction of the radiation with the participating medium, i.e., a medium that may absorb, scatter and emit radiation. In this sense, this work presents a study regarding the estimation of radiative properties in a one-dimensional participatin...

In the near field, radiative heat transfer can exceed the prediction from Planck's law by several orders of magnitude, when the interacting materials support surface polaritons in the infrared range. However, if the emitter and absorber are made from two different materials, which support surface polariton resonances at different frequencies, the mismatch between surface polariton resonance fre...

This tutorial paper provides a general overview of the hierarchy of problems involving electromagnetic scattering by particles and clarifies the place of the radiative transfer theory and the theory of coherent backscattering in the context of classical electromagnetics. The self-consistent microphysical approach to radiative transfer is compared with the traditional phenomenological treatment....