Related papers: The problem of camouflaging via mirror reflections
This work presents a framework for billiards in convex domains on two dimensional Riemannian manifolds. These domains are contained in connected, simply connected open subsets which are totally normal. In this context, some basic properties…
Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the…
We consider the determination of a conductivity function in a two-dimensional domain from the Cauchy data of the solutions of the conductivity equation on the boundary. We prove uniqueness results for this inverse problem, posed by…
One of the most fascinating ideas coming from particle physics is the concept of mirror matter. Mirror matter is a new form of matter which is predicted to exist if mirror symmetry is respected by nature. At the preset time evidence that…
It is proved that one can choose a control function on an arbitrary small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number…
One of the deepest unsolved puzzles of subatomic physics is why Nature prefers the left particles to the right ones. Mirror matter is an attempt to understand this mystery by assuming the existence of a "parallel''world where this…
We study the geometry of reflection of a massive point-like particle at conic section boundaries. Thereby the particle is subjected to a central force associated with either a Kepler or Hooke potential. The conic section is assumed to have…
A cylindrical wave expansion method is developed to obtain the scattering field for an ideal two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up to solve the boundary problem at the inner…
In this paper we will consider an unknown binary image, of which the length of the boundary and the area of the image are given. These two values together contain some information about the general shape of the image. We will study two…
Polygonalization of any smooth billiard boundary can be carried out in several ways. We show here that the semiclassical description depends on the polygonalization process and the results can be inequivalent. We also establish that…
Light's internal reflectivity near a critical angle is very sensitive to the angle of incidence and the optical properties of the external medium near the interface. Novel applications in biology and medicine of subcritical internal…
We prove Poisson limit laws for open billiards where the holes are on the boundaries of billiard tables (rather than some abstract holes in the phase space of a billiard). Such holes are of the main interest for billiard systems, especially…
Total internal reflection occurs for large angles of incidence, when light is incident from a high-refractive-index medium onto a low-index medium. We consider the situation where the low-index medium is active. By invoking causality in its…
We prove that, for arbitrary three-dimensional transformation-based invisibility cloaking of an object above a ground plane or of isolated object, there are practical constraints that increase with the object size. In particular, we show…
We tackle the problem of reflectance estimation from a set of multi-view images, assuming known geometry. The approach we put forward turns the input images into reflectance maps, through a robust variational method. The variational model…
Physicists have used billiards to understand and explore both classical and quantum chaos. Recently, in 2001, a group at the University of Texas introduced an experimental set up for modeling the wedge billiard geometry called optical…
The renowned Fagnano problem asks for the inscribed triangle of minimal perimeter within a given reference triangle. Equivalently, it seeks a billiard trajectory inside the triangle that closes after three reflections. In this note, we…
Mirror matter is a self-collisional dark matter candidate. If exact mirror parity is a conserved symmetry of the nature, there could exist a parallel hidden (mirror) sector of the Universe which has the same kind of particles and the same…
Let $K$ be a convex body in $\mathbb{R} ^d$, with $d = 2,3$. We determine sharp sufficient conditions for a set $E$ composed of $1$, $2$, or $3$ points of ${\rm bd}K$, to contain at least one endpoint of a diameter of $K$ (for $d=2,3$). We…
Consider an opaque medium which contains 3D particles. All particles are convex bodies of the same shape, but they vary in size. The particles are randomly positioned and oriented within the medium and cannot be observed directly. Taking a…