Related papers: A Conic Section Approach to the Relativistic Refle…
The relativistic Boltzmann equation in bounded domains has been widely used in physics and engineering, for example, Tokamak devices in fusion reactors.In spite of its importance, there has, to the best of our knowledge, been no…
The hemispherical Mueller matrix map for light reflected from a plane-parallel planetary atmosphere is shown to obey several symmetry properties that provide a straightforward method to check their physical realizability. The mirror…
The use of the generalized Snell's law opens wide possibilities for the manipulation of transmitted and reflected wavefronts. However, known structures designed to shape reflection wave fronts suffer from significant parasitic reflections…
Refraction and deflection of shear zones in layered granular materials was studied experimentally and numerically. We show, that (i) according to a recent theoretical prediction [T. Unger, Phys. Rev. Lett. 98, 018301 (2007)] shear zones…
We study projective stationary sets. The Projective Stationary Reflection principle is the statement that every projective stationary set contains an increasing continuous $\in$--chain of length $\omega_1$. We show that if Martin's Maximum…
We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions, both in the near and far field cases, when the input and output energies are prescribed.
We consider the possibility that most of the reflection component, observed in the hard X-ray spectra of Seyfert galaxies, could be formed on an extended medium, at large distance from the central source of primary radiation (e.g. on a…
It is proved that every convex body in the plane has a point such that the union of the body and its image under reflection in the point is convex. If the body is not centrally symmetric, then it has, in fact, three affinely independent…
For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available.…
We consider the asymptotic evolution of a relativistic spin-1/2-particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector)…
Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to an including quadratic terms in an angular velocity parameter using Darmois junction conditions. Einstein's equation's for the…
We establish effective convergence rates in the Doeblin-Lenstra law, describing the limiting distribution of approximation coefficients arising from continued fraction convergents of a typical real number. More generally, we prove…
This paper addresses the problem of inverse rendering from photometric images. Existing approaches for this problem suffer from the effects of self-shadows, inter-reflections, and lack of constraints on the surface reflectance, leading to…
Recently, adversarial imitation learning has shown a scalable reward acquisition method for inverse reinforcement learning (IRL) problems. However, estimated reward signals often become uncertain and fail to train a reliable statistical…
In accordance with Snel's law of refraction, whether a plane wave is refracted in the negative sense or positive sense at a planar boundary between two homogenous mediums is determined solely by the orientation of the real parts of the…
Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave,…
Electromagnetic wave control using the concept of a reflecting surface is first studied as a near-field and a far-field problem. Using a secondary source present in a wireless communication environment, such as a backscatter tag, it is…
Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R^d. The particle is accelerated by a constant external field; when colliding with an obstacle, the particle inelastically…
The inherent challenge of detecting symmetries stems from arbitrary orientations of symmetry patterns; a reflection symmetry mirrors itself against an axis with a specific orientation while a rotation symmetry matches its rotated copy with…
In his scientific treatise entitled De Lineis, Angulis et Figuris, seu Fractionibus et Reflexionibus Radiorum, Robert Grosseteste is discussing some qualitative geometric rules about reflection and refraction. However, he is also discussing…