We consider the problem of radiative transfer in stellar atmospheres where the index of refraction departs from unity and is a function of density and temperature. We present modified Feautrier and Lambda-iteration methods to solve the equation of radiative transfer with refraction in a plane parallel atmosphere. These methods are general and can be used in any problem with 1-D geometry where t...

Hamiltonian Monte Carlo (HMC) is a successful approach for sampling from continuous densities. However, it has difficulty simulating Hamiltonian dynamics with non-smooth functions, leading to poor performance. This paper is motivated by the behavior of Hamiltonian dynamics in physical systems like optics. We introduce a modification of the Leapfrog discretization of Hamiltonian dynamics on piec...

Diffusion waves form the basis of several measurement technologies in materials science as well as in biological systems. They are, however, so heavily damped that their observation is a real challenge to the experimentalist. We show that accurate information about the refraction-like and reflection-like behavior of diffusion waves can be obtained by studying diffusion fronts. For this we use h...

Electro-optic switching of reflection and refraction is experimentally demonstrated in metasurface liquid crystal cell. Negative metasurface is fabricated by focused-ion-beam milling, and twisted nematic cells are constructed with complementary double-split ring resonator and V-shape slot antenna metasurface. By application of an external voltage, electro-optic switchings are achieved in reflec...

Surprisingly colourful views are possible from sparkling white snow. It is well known that similarly colourful features can exist in the sky whenever appropriate ice crystals are around. However, the transition of light reflection and refraction from ice crystals in the air to reflection and refraction from those in snow on the ground is not trivial. Photographs and videos from brilliant colour...

Constructions on unbounded domains are more difficult as energy tends to radiate to infinity. It tends to leave the domain where the periodic variations can be amplifying. The examples we know use a ray, trapped by reflection or refraction ([C1], [C3], [CR], [PR]). The paper [PR] gives a definitive analysis for rays trapped by reflection using fine tools from microlocal analysis. [CR] has no bo...