Related papers: The reflection coefficient of a fractional reflect…
We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's equations,…
We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on $(x_1 \partial_{x_1} f(x) ,..., x_n \partial_{x_n}f(x))$, where $f(x)$ is the phase function. We prove a theorem which provides estimates…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for the purpose of using the intensity scattered from them to obtain the Hurst exponent and topothesy that characterize the self-affine roughness. By…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
This is a theoretical study of the interplay of optical phase-conjugation and multiple scattering. We calculate the intensity of light reflected by a phase-conjugating mirror when it is placed behind a disordered medium. We compare the…
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
We consider the possibility that most of the reflection component, observed in the hard X-ray spectra of Seyfert galaxies, could be formed on an extended medium, at large distance from the central source of primary radiation (e.g. on a…
Particle accelerations by a 1D, EM, dispersive pulse in an external magnetic field are investigated. It is found that the well-known cyclotron resonance may be classified into three regimes as the length and/or the amplitude of the pulse…
The electromagnetic scattering resonances of a non-magnetic object much smaller than the incident wavelength in vacuum can be either described by the electroquasistatic approximation of the Maxwell's equations if its permittivity is…
In this paper, first we present a review of experimental data corresponding to phase retardation per reflection of interferential mirrors. Then, we report our new measurements on both commercial and tailor-made mirrors. To be able to…
The flow phenomena around a rotating elliptic cylinder in a channel is studied numerically. The value of the confinement parameter \beta is varied as \frac{1}{k}, where k = 2, 4, 6, and 8 respectively, to demonstrate the vortex-shedding…
The average power spectrum of a pulse reflected by a disordered medium embedded in an N-mode waveguide decays in time with a power law t^(-p). We show that the exponent p increases from 3/2 to 2 after N^2 scattering times, due to the onset…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave,…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and…
We study theoretically mode conversion and resonant overreflection of magnetohydrodynamic waves in an inhomogeneous plane-stratified plasma in the presence of a nonuniform shear flow, using precise numerical calculations of the reflection…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…