Related papers: On resonances generated by conic diffraction
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…
Heavy ion collisions at RHIC/LHC energies are well described by the (nearly ideal) hydrodynamics. Last year this success has been extended to higher angular harmonics, $v_n,n=3..9$ induced by initial-state perturbations, in analogy to…
The beamed emission by relativistic sources moving along the magnetic dipolar field lines occur in the direction of tangents to the field lines. To receive such a beamed radiation line-of-sight must align with the tangent within the beaming…
We study the resonance line emission from the rotating plane optically thick accretion disc, consisting of free electrons and resonant atoms. We use the standard assumption that the source of continuum radiation is located near central…
Refraction is the predominant mechanism causing spatially inhomogeneous surface gravity wave fields. However, the complex interplay between depth- and current-induced wave refraction remains poorly understood. Assuming weak currents and…
The kinetic theory for the cylindrical plasma, produced by the cylindrically symmetric (azimuthal mode number m=0) helicon wave, is developed with accounting for the cylindrical geometry and the radial inhomogeneity of the helicon wave and…
Coupling of two dielectric wires with rectangular cross-section gives rise to bonding and anti-bonding resonances. The latter is featured by extremal narrowing of the resonant width for variation of the aspect ratio of the cross-section and…
The existence of triadic resonances in the magnetized spherical Couette system (MSC) is related to the development of modulated rotating waves, which are quasiperiodic flows understood in terms of bifurcation theory in systems with…
Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
We observe and analyze d-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the d-wave resonance emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for…
A Riemannian or Finsler metric on a compact manifold M gives rise to a length function on the free loop space \Lambda M, whose critical points are the closed geodesics in the given metric. If X is a homology class on \Lambda M, the minimax…
The aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance…
In this paper, we try to put the results of Smilansky and al. on "Topological resonances" on a mathematical basis.A key role in the asymptotic of resonances near the real axis for Quantum Graphs is played by the set of metrics for which…
We study a hard regime of stimulation of two-frequency oscillations in the main resonance equation with a fast oscillating external force: $ \ve i \psi' + |\psi|^2\psi = \exp\big(it^2/ (2\ve)\big), 0<\ve\ll1$. This phenomenon is caused by…
We investigate the Helmholtz equation in a two dimensional open waveguide with a thin and high contrast core layer. We develop an asymptotic analysis of the Green function of the problem, and through it we identify and characterize the…
Mutual dependencies of mass and orbital moment increase for rotating bodies of various configurations (a string with uniform mass distribution, a string with squared mass distribution or a sphere with uniform mass distribution, double…
A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…
Analogues of the classical affine-projective correspondence are developed in the context of statistical manifolds compatible with a radiant vector field. These utilize a formulation of Einstein equations for special statistical structures…
The structure of the density singularity formed in a relativistically large amplitude plasma wave close to the wavebreaking limit leads to a refraction coefficient which has a coordinate dependence with discontinuous derivatives. This…