Related papers: A Lighthouse Illumination Problem
It is shown that every simple polygon in general position with $n$ walls can be illuminated from a single point light source $s$ after at most $\lfloor (n-2)/4\rfloor$ diffuse reflections, and this bound is the best possible. A point $s$…
When a light bulb is turned on, light moves away from it at speed $c$, by definition. When light from this bulb illuminates a surface, however, this illumination front is not constrained to move at speed $c$. A simple proof is given that…
We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…
The illumination problem is a popular topic in recreational mathematics: In a mirrored room, is every region illuminable from every point in the region? So-called \enquote{unilluminable rooms} are related to \enquote{trapped sets} in…
It was conjectured by Levi, Hadwiger, Gohberg and Markus that the boundary of any convex body in ${\mathbb R}^n$ can be illuminated by at most $2^n$ light sources, and, moreover, $2^n-1$ light sources suffice unless the body is a…
Highly accurate numerical solutions to the problem of Black Holes surrounded by uniformly rotating rings in axially symmetric, stationary spacetimes are presented. The numerical methods developed to handle the problem are discussed in some…
Sub-diffraction-limit resolution, or super-resolution, had been successfully demonstrated by recent theoretical and experimental studies for two-point sources with ideal equal-brightness and strict incoherenceness. Unfortunately, practical…
We study the problem of arithmetic billiards from a new perspective. We first raise a similar problem about reflecting lights inside grids. For the solution to this problem, we will give three proofs. Next, we consider a similar problem in…
In the present work, the problem about shadow, generalized on domains of space $\mathbb{R}^n$, $n\le 3$, is investigated. Here the shadow problem means to find the minimal number of balls satisfying some conditions an such that every line…
The vast majority of physical objects we are dealing with are almost exclusively made of atoms. Due to their discrete level structure, single atoms have proved to be emitters of light which is incompatible with the classical description of…
First geometric calculus alongside its description of equiangular spirals, reflections and rotations is introduced briefly. Then single and double reflections at such a spiral are investigated. It proves suitable to distinguish incidence…
In this paper we consider the problem of packing a fixed number of identical circles inside the unit circle container, where the packing is complicated by the presence of fixed size circular prohibited areas. Here the objective is to…
A simple, analytical fitting-formula for a photometric light curve of a source of light orbiting around a black hole is presented. The formula is applicable for sources on a circular orbit with radius smaller than 45 gravitational radii…
Localized radiation sources are analyzed with respect to the relation of nonclassicality and quantum entanglement of the emitted light. The source field parts of the radiation emitted in different directions are closely related to each…
Given a set of $n\geq 1$ unit disk robots in the Euclidean plane, we consider the fundamental problem of providing mutual visibility to them: the robots must reposition themselves to reach a configuration where they all see each other. This…
The sustained increase of emissions of artificial light is causing a progressive brightening of the night sky in most of the world. This process represents a threat for the long-term sustainability of the scientific and educational activity…
Problems, related to the determination of the minimal number of balls that generate a shadow at a fixed point in the multi-dimensional Euclidean space $ \mathbb{R}^n $, are considered in present work. Here, the statement "a system of balls…
We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of diffuse reflections sufficient to illuminate the interior of any simple polygon with $n$ walls from any interior point light source is $\lfloor n/2 \rfloor - 1$.…
The diffuse light within galaxy groups and clusters provides valuable insight into the growth of massive cosmic structures. Groups are particularly interesting in this context, because they represent the link between galactic haloes and…
The interference phenomenon of light is a common but most important effect in physics. In this article, we compare and analyse the interference effects of both coherent and incoherent light; in particular, the interference of spatially…