Related papers: The concentrated toroidal wave
In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical…
An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…
Properties of solitary waves in pre-compressed Hertzian chains of particles are studied in the long wavelength limit using a well-known continuum model. Several main results are obtained by parameterizing the solitary waves in terms of…
We discuss the linear response to low-frequency tidal forcing of fluid bodies that are slowly and uniformly rotating, are neutrally stratified and may contain a solid or fluid core. This problem may be regarded as a simplified model of…
The paper presents a new and simple range characterization for the spherical mean transform of functions supported in the unit ball in even dimensions. It complements the previous work of the same authors, where they solved an analogous…
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a…
This paper presents an analytical approach of the propagation of an acoustic wave through a normally distributed disordered lattice made up of Helmholtz resonators connected to a cylindrical duct. This approach allows to determine…
New type of tomographic probability distribution, which contains complete information on the density matrix (wave function) related to the Fresnel transform of the complex wave function, is introduced. Relation to symplectic tomographic…
In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in…
Standard power series are used to construct and analyze angular and radial spheroidal functions, which are necessary for solving boundary value problems for Helmholtz equation in a spheroid. With an advanced approach the low-lying energy…
We introduce nonparaxial spatially accelerating waves whose two-dimensional transverse profiles propagate along semicircular trajectories while approximately preserving their shape. We derive these waves by considering imaginary…
Coastal erosion describes the displacement of sand caused by the movement induced by tides, waves or currents. Some of its wave phenomena are modeled by Helmholtz-type equations. Our purposes, in this paper are, first, to study optimal…
We study the one-dimensional Helmholtz equation with (possibly perturbed) quasiperiodic coefficients. Quasiperiodic functions are the restriction of higher dimensional periodic functions along a certain (irrational) direction. In classical…
Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of…
There is great interest in the development of novel nanomachines that use charge, spin, or energy transport, to enable new sensors with unprecedented measurement capabilities. Electrical and thermal transport in these mesoscopic systems…
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
The fundamental problem of optical wave propagation is the determination of the field at an observation point, given a disturbance specified over some finite aperture. In both vacuum and inhomogeneous media, the solution of this problem is…
This work concerns the analysis of wave propagation in random media. Our medium of interest is sea ice, which is a composite of a pure ice background and randomly located inclusions of brine and air. From a pulse emitted by a source above…
We study Sobolev spaces of radial functions on spherically symmetric Riemannian manifolds. Using geodesic polar coordinates, we give a sharp one-dimensional reduction: a radial function belongs to the Sobolev space on the manifold if and…