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The method of retarded potentials is used to derive the Biot-Savart law, taking into account the correction that describes the chaotic motion of charged particles in rectilinear currents. Then this method is used for circular currents and…
We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture,…
A fast and practical method is described for calculating the microlensed flux variance of an arbitrary source by uncorrelated stars. The required inputs are the mean convergence and shear due to the smoothed potential of the lensing galaxy,…
Relativistic current sheets have been proposed as the sites of dissipation in pulsar winds, jets in active galaxies and other Poynting-flux dominated flows. It is shown that the steady versions of these structures differ from their…
The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface…
We study rotation-induced asymmetry of far-field emission from optical microcavities, based on which a new scheme of rotation detection may be developed. It is free from the "dead zone" caused by the frequency splitting of standing-wave…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
A uniformly accelerated point charge which moves neither in a straight line nor in a circle, but in a cusp, is investigated. We find the angular distribution of the Larmor radiation, the constant power, and the intensity in the maximal…
We expand the off-resonant scattering theory for particle diffusion in magnetized current filaments that can be typically compared to astrophysical jets, including active galactic nucleus jets. In a high plasma beta region where the…
This paper models light scattering through flat surfaces with finite transmission, reflection and absorption rates, with wave packets approaching the mirror from both sides. While using the same notion of photons as in free space, our model…
A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands…
We develop a Markov process viewpoint for discrete circular distributions motivated by directional-statistics settings where angles are observed on a finite grid and evolve over time. On the $m$-point discrete circle, the cycle graph, we…
Any charged particle moving faster than light through a medium emits Cherenkov radiation. We show that charged particles moving faster than light through the v a c u u m emit Cherenkov radiation. How can a particle move faster than light?…
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit…
A natural modification of the equations of covariantly-constant vector fields (CCVF) in Weyl geometry leads us to consider a metric compatible geometry possessing conformal curvature and torsion fully determined by its trace. The latter is…
Transient radio signals of astrophysical origin present an avenue for studying the dynamic universe. With the next generation of radio interferometers being planned and built, there is great potential for detecting and studying large…
We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral…
We have developed a maximum likelihood source detection method capable of detecting ultra-faint streaks with surface brightnesses approximately an order of magnitude fainter than the pixel level noise. Our maximum likelihood detection…
Two methods are developed for solving the steady-state spherically symmetric radiative transfer equation for resonance line radiation emitted by a point source in the Intergalactic Medium. One method is based on solving the ray and moment…
Cherenkov radiation in uniformly moving homogenous isotropic medium without dispersion is studied. Formula for the spectrum of Cherenkov radiation of fermion was derived for the case when the speed of the medium is less than the speed of…