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Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector…
In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function…
Hidden photons, gauge bosons of a U(1) symmetry of a hidden sector, can constitute the dark matter of the universe and a smoking gun for large volume compactifications of string theory. In the sub-eV mass range, a possible discovery…
A static, spherically symmetric, asymptotically flat spacetime may allow for circular, closed null-geodesics which are said to belong to a photon sphere. In the context of gravitational lensing in the strong deflection regime, the presence…
In most theories of diffraction by a diaphragm, the amplitude of the diffracted wave, and hence the position wave function of the associated particle, is calculated directly without prior calculation of the quantum state. Few models express…
The properties of light in the presence of electromagnetic and gravitational fields are compared. Once one takes account of the fact that clock rates vary with distance from a massive object, it is argued that in an absolute sense light…
We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…
Occultation and microlensing are different limits of the same phenomena of one body passing in front of another body. We derive a general exact analytic expression which describes both microlensing and occultation in the case of spherical…
Pushed by a number of advances, electromagnetic observatories have now reached the horizon scale of supermassive black holes. The existence and properties of horizons in our universe is one of the outstanding fundamental issues that can now…
In a variety of astronomical situations, there is a relatively high probability that a single isolated lens will produce a detectable event. The high probability is caused by some combination of a large Einstein angle, fast angular motion,…
In this paper, we first discuss the concept of an emission wave. In the history of science, this is the first time we have discovered a new way in which (transverse) waves are realized in nature. It can therefore be expected to lead to…
We present here a brief overview of recent models describing the photon-photon cross-section into hadrons. We shall show in detail results from the eikonal minijet model, with and without soft gluon summation.
We discuss the geometry behind classical Heisenberg model at the level suitable for third or fourth year students who did not have the opportunity to take a course on differential geometry. The arguments presented here rely solely on…
The phenomenon of microlensing has successfully been used to detect extrasolar planets. By observing characteristic, rare deviations in the gravitational microlensing light curve one can discover that a lens is a star--planet system. In…
Presence-only data, point locations where a species has been recorded as being present, are often used in modeling the distribution of a species as a function of a set of explanatory variables---whether to map species occurrence, to…
We consider the Euler-Poisson system for ions where the electrons are given by a Maxwell-Boltzmann distribution, and we investigate the existence of one-dimensional periodic traveling waves. More precisely, we first establish the existence…
Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point…
We study the optical properties of crystals with spatial dispersion and show that the usual Fresnel approach becomes invalid near frequencies where the group velocity of the wave packets inside the crystal vanishes. Near these special…
When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie on its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly…
The optical reflection coefficient of a dielectric medium moving uniformly in the plane spanned by its surface is rigorously calculated using classical electrodynamics and special relativity, and expressed in the Fourier domain, as a…