Related papers: The Geometry of Light Paths for Equiangular Spiral…
The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the…
Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of…
We propose geometric tools that are suitable for studying the behavior of a billiard trajectory in a homogeneous force field. Two examples are considered: a vertical plane with an open top and with a parabolic or right angle boundary at the…
New techniques to evaluate the clock effect using light are described. These are based on the flatness of the cylindrical surface containing the world lines of the rays constrained to move on circular trajectories about a spinning mass. The…
We revisit the GSC5249-01240 light curve obtained during its occultation by Saturn's North polar region. In addition to refractive scintillations, the power spectrum of intensity fluctuations shows an enhancement of power between refractive…
The evolution of the interface propagation in a slowly rotating half-filled horizontal cylinder is studied using MRI. Initially, the cylinder contains two axially segregated bands of small and large particles with a sharp interface. The…
We review the topic of rotation curves of spiral galaxies emphasizing the standard interpretation as evidence for the existence of dark matter halos. Galaxies other than spirals and late-type dwarfs may also possess great amounts of dark…
We present an ab-initio numerical investigation of the internal conical refraction of structured light beams in a biaxial crystal. Starting from the solutions of the Fresnel equation, a theoretical analysis is developed without assuming any…
Reflected diffusions in convex polyhedral domains arise in a variety of applications, including interacting particle systems, queueing networks, biochemical reaction networks and mathematical finance. Under suitable conditions on the data,…
As one type of incidence theory, the geometry of pentagram map seems quite classical at first. However, this is an excellent example of such a classical idea developed into a marvellous insight by some modern approach. We introduce an…
The notion of optical geometry, introduced more than twenty years ago as a formal tool in quantum field theory on a static background, has recently found several applications to the study of physical processes around compact objects. In…
Rotation curves of interacting galaxies often show that velocities are either rising or falling in the direction of the companion galaxy. We seek to reproduce and analyse these features in the rotation curves of simulated equal-mass…
It is standard practice to study the lensing of gravitational waves (GW) using the geometric optics regime. However, in many astrophysical configurations this regime breaks down as the wavelength becomes comparable to the Schwarzschild…
To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance…
The axial propagation of circularly polarized light in an optically active structurally chiral medium is exactly solved via full electromagnetic analysis. Some symmetries of the system's characteristic matrix reveal new insights, which are…
Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrical optics is…
We study geometric properties of linear strata of uni-singular curves. The singularities of closures of the strata are resolved and the resolutions are represent as projective bundles. This enables to study their geometry. In particular we…
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…
Spirals in galaxies have long been thought to be caused by gravitational instability in the stellar component of the disk, but discerning the precise mechanism had proved elusive. Tidal interactions, and perhaps bars, may provoke some…
The light curve of an isolated bright spot in a Keplarian orbit is studied to investigate the signature of the firewall around the event horizon of the black hole. An increase in total observed flux is found. In addition to that, for…