Related papers: A Lighthouse Illumination Problem
We present neutral hydrogen observations for a sample of eight nearby, late-type, edge-on galaxies. All of the galaxies have been well resolved in the radial direction, while six have also been well resolved in the vertical direction. We…
Diffraction limits the behaviour of light in optical systems and sets the smallest achievable line width at half the wavelength. With a novel subwavelength plasmonic lens to reduce the diffraction via an asymmetry and to generate and…
Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as…
We show that the maximum number of pairwise non-overlapping $k$-rich lenses (lenses formed by at least $k$ circles) in an arrangement of $n$ circles in the plane is $O\left(\frac{n^{3/2}\log{(n/k^3)}}{k^{5/2}} + \frac{n}{k} \right)$, and…
The Art Gallery Problem (AGP) is one of the classical problems in computational geometry. It asks for the minimum number of guards required to achieve visibility coverage of a given polygon. The AGP is well-known to be NP-hard even in…
In this note we introduce the problem of illumination of convex bodies in spherical spaces and solve it for a large subfamily of convex bodies. We derive from it a combinatorial version of the classical illumination problem for convex…
We discuss the problem of the reflection of light on spherical and quadric surface mirrors. In the case of spherical mirrors, this problem is known as the Alhazen problem. For the spherical mirror problem, we focus on the reflection…
Let $n\geq C$ for a large universal constant $C>0$, and let $B$ be a convex body in $R^n$ such that for any $(x_1,x_2,\dots,x_n)\in B$, any choice of signs $\varepsilon_1,\varepsilon_2,\dots,\varepsilon_n\in\{-1,1\}$ and for any permutation…
In the late 90's, Tom Wolff introduced the circle tangency counting problem in his expository article on the Kakeya conjecture. For collections of well-spaced circles, we break the $N^{3/2}$-barrier, proving that a set of $N$ well-spaced…
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…
We formulate a complex analog of the celebrated Levi-Hadwiger-Boltyanski illumination (or covering) conjecture for complex convex bodies in C^n, as well as its (non-comparable) fractional version. A key element in posing these problems is…
Illumination is the deliberate utilization of light to realize practical or aesthetic effects. The designers combine with the environmental considerations, energy-saving goals, and technology advances with fundamental physics to develop…
We prove a gravitational lensing theorem: the magnification of a source of uniform brightness by a foreground spherical lens is mu =1+pi(2R_E^2-R_L^2)/A, where A is the area of the source and R_E and R_L are the Einstein radius and size of…
We answer some questions concerning the so called sigma-game of Sutner. It is played on a graph where each vertex has a lamp, the light of which is toggled by pressing any vertex with an edge directed to the lamp. For example, we show that…
The Local Supercluster is an ideal laboratory to study distribution of luminous and dark matter in the nearby Universe. The 1100 small groups have been selected using algorithm based on assumption that a total energy of physical pair of…
Coherent light sources, such as free electron lasers, provide bright beams for biology, chemistry, physics, and advanced technological applications. Increasing the brightness of these sources requires progressively larger devices, with the…
The emission properties of a molecular light source depend on its optical and chemical environment. This dependence, however, is different for various light sources. We present a general classification of sources by introducing the concepts…
Various fields of science and engineering rely on linear algebra for large scale data analysis, modeling and simulation, machine learning, and other applied problems. Linear algebra computations often dominate the execution time of such…
Unscrupulous outdoor lighting produces a number of effects that are currently included under the term light pollution. Its consequences (e.g. loss of resources by energy waste), are being recognized for some time, as well as the possibility…
From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to…