Related papers: Random reflections in a high dimensional tube
The reflections caused by common semi-reflectors, such as glass windows, can impact the performance of computer vision algorithms. State-of-the-art methods can remove reflections on synthetic data and in controlled scenarios. However, they…
We address the concept of three-dimensional light bullet formation in structures where nonlinearity and dispersion are contributed by different materials, including metamaterials, which are used at their best to create suitable conditions…
We investigate the spontaneous emission of a two-level system, e.g. an atom or atomlike object, coupled to a single-end, i.e., semi-infinite, one-dimensional photonic waveguide such that one end behaves as a perfect mirror while light can…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semiclassical laser rate equations, accounting for (coherent) stimulated and (incoherent) spontaneous emission.…
Propagation of light in a highly scattering medium is among the most fascinating optical effect that everyone experiences on an everyday basis and possesses a number of fundamental problems which have yet to be solved. Conventional wisdom…
We study the well-known Ptolemy-Alhazen problem on reflection of light at the surface of a spherical mirror in the case when the source of light is very far from the mirror.
It is proposed that the propagation of light in disordered photonic lattices can be harnessed as a random projection that preserves distances between a set of projected vectors. This mapping is enabled by the complex evolution matrix of a…
Relativistic flying mirrors in plasmas are realized as thin dense electron (or electron-ion) layers accelerated by high-intensity electromagnetic waves to velocities close to the speed of light in vacuum. The reflection of an…
We show that theory predictions for volume reflection in bent crystals agree with recent experimental data. This makes possible to predict volume reflection angle and efficiency in a broad range of energy for various crystals. A simple…
This paper models light scattering through flat surfaces with finite transmission, reflection and absorption rates, with wave packets approaching the mirror from both sides. While using the same notion of photons as in free space, our model…
We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move…
We calculate the probability distribution of the Andreev reflection eigenvalues R_n at the Fermi level in the circular ensemble of random-matrix theory. Without spin-rotation symmetry, the statistics of the electrical conductance G depends…
The analytical description of the volume reflection of the charged ultrarelativistic particles in bent single crystals is considered. The relation describing the angle of volume reflection as a function of the transversal energy is…
We consider the quantum radiation from a partially reflecting moving mirror for the massless scalar field in 1+1 Minkowski space. Partial reflectivity is achieved by localizing a delta-type potential at the mirror's position. The radiated…
While the absorption of light is ubiquitous in nature and in applications, the question remains how absorption modifies the transmission channels in random media. We present a numerical study on the effects of optical absorption on the…
We consider contractivity for diffusion semigroups w.r.t. Kantorovich ($L^1$ Wasserstein) distances based on appropriately chosen concave functions. These distances are inbetween total variation and usual Wasserstein distances. It is shown…