Related papers: Dispersion relation for transverse waves in a line…
Binary complex plasmas consist of microparticles of two different species and can form two-dimensional square lattices under certain conditions. The dispersion relations of the square lattice waves are derived for the longitudinal and…
We derive the dispersion relation for linearized small-amplitude gravity waves for various choices of non-constant vorticity. To the best of our knowledge, this relation is only known explicitly in the case of constant vorticity. We provide…
The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…
The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the…
We present the complete set of constitutive relations and field equations for the linear thermoelastic relaxed micromorphic continuum and investigate its variants for wave propagation. It is found that the additional thermal effects give…
We derive dispersion relations for a system of identical particles confined in a two-dimensional annular harmonic well and which interact through a Yukawa potential, e.g., a dusty plasma ring. When the particles are in a single chain (i.e.,…
The distributions of the angular transmission coefficient and of the total transmission are calculated for multiple scattered waves. The calculation is based on a mapping to the distribution of eigenvalues of the transmission matrix. The…
Propagation of Alfven waves in the solar plasma has been a topic of scientific interest for a long time. We have derived a dispersion relation for shear Alfven waves in a viscous and diffusive plasma.
Since the famous 1926 paper by Richardson, the relative diffusion of two particles in a turbulent liquid has attracted a lot of interest. The motion of a single particle on the other hand is usually considered not to be especially…
The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly…
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
Modern, high-fidelity numerical simulations have shown an apparently anomalous result: a longitudinal elastodynamic wave travelling perpendicular to the forcing direction. Numerical simulations, in combination with an analytical model, are…
We consider a linearly polarized electromagnetic wave incident on an opaque screen with square aperture of edge a. An application of Faraday's law to a loop parallel to the screen, on the side away from the source, shows that the wave must…
A prior work (see Chapter 8 of the book, ``Graphs and Networks: Transfinite and Nonstandard,'' Birkhauser-Boston, Cambridge, Mass., USA, 2004) examined the propagation of an electromagnetic wave on a transfinite transmission line,…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
A localized perturbation of a magnetic flux tube produces a pair of wave trains that propagate in opposite directions along the tube. These wave packets disperse as they propagate, where the extent of dispersion depends on the physical…
The dispersion relation of surface waves of a magnetic fluid in a magnetic field is studied experimentally. We verify the theoretically predicted existence of a non-monotonic dispersion relation. In particular, we demonstrate the existence…
The dispersion relation of an electromagnetic wave in an unmagnetized neutral plasma is well known to be w^2=wp^2+(ck)^2. A modified dispersion relation is presented taking into account the ion restoring force in the transverse direction.
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…