A fractional equation to approximate wave dispersion relation in elastic rods

Strain ◽  
2017 ◽  
Vol 53 (4) ◽  
pp. e12228 ◽  
Author(s):  
Ramzi Othman
Keyword(s):  
Dispersion Relation ◽  
Wave Dispersion ◽  
Elastic Rods ◽  
Approximate Wave ◽  
Fractional Equation

Attenuation of longitudinal electro-acoustic waves in a plasma

1974 ◽  
Vol 11 (1) ◽  
pp. 37-49
Author(s):  
R. J. Papa ◽  
P. Lindstrom
Keyword(s):  
Dispersion Relation ◽  
Electric Field ◽  
Acoustic Waves ◽  
Collision Frequency ◽  
Wave Dispersion ◽  
Signal Frequency ◽  
Variable Theory ◽  
Longitudinal Waves ◽  
Confluent Hypergeometric Functions ◽  
Linearized Boltzmann Equation

There are several practical situations in partially ionized plasmas when both collisionless (Landau) damping and electron-neutral collisions contribute to the attenuation of longitudinal waves. The longitudinal-wave dispersion relation is derived from Maxwell's equations and the linearized Boltzmann equation, in which electron-neutral collisions are represented by a Bhatnagar–Gross–Krook model that conserves particles locally. (The dispersion relation predicts that, for a given signal frequency ώ), an infinite number of complex wavenumbers kn can exist. Using Fourier–Laplace transform techniques, an integral representation for the electric field of the longitudinal waves is readily derived. Then, using theorems from complex variable theory, a modal expansion of the electric field can be made in terms of an infinite sum of confluent hypergeometric functions, whose arguments are proportional to the complex wavenumbers kn. It is demonstrated numerically that the spatial integral of the square of the electric field amplitude decreases as the electron-neutral collision frequency increases. Also, the amount of energy contained in the first few (lowest) modes, and the coupling between the modes, is examined as a function of plasma frequency, signal frequency and collision frequency.

Kinetic theory of surface wave propagation along a hot plasma column

1976 ◽  
Vol 16 (1) ◽  
pp. 47-55 ◽  
Author(s):  
V. Atanassov ◽  
I. Zhelyazkov ◽  
A. Shivarova ◽  
Zh. Genchev
Keyword(s):  
Dispersion Relation ◽  
Plasma Column ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Displacement Vector ◽  
Electric Displacement ◽  
Wave Dispersion ◽  
Axially Symmetric ◽  
Surface Wave Propagation ◽  
Hot Plasma

In this paper we propose an exact solution of Vlasov and Maxwell's equations for a bounded hot plasma in order to derive the dispersion relation of the axially-symmetric surface waves propagating along a plasma column. Assuming specular reflexion of plasma particles from the boundary, expressions for the components of the electric displacement vector are obtained on the basis of the Vlasov equation. Their substitution in Maxwell's equations, neglecting the spatial dispersion in the transverse plasma dielectric function, allows us to determine the plasma impedance. The equating of plasma and dielectric impedances gives the wave dispersion relation which, in different limiting cases, coincides with the well-known results.

scholarly journals Extended Elliptic Mild Slope Equation Incorporating the Nonlinear Shoaling Effect

2016 ◽  
Vol 23 (s1) ◽  
pp. 44-51 ◽  
Author(s):  
Qian-lu Xiao ◽  
Chun-hui Li ◽  
Xiao-yan Fu ◽  
Mei-ju Wang
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Wave ◽  
Surf Zone ◽  
Wave Dispersion ◽  
Structure Design ◽  
Coastal Engineering ◽  
Wave Transformation ◽  
Flume Experiments ◽  
Mild Slope Equation ◽  
Wave Shoaling

Abstract The transformation during wave propagation is significantly important for the calculations of hydraulic and coastal engineering, as well as the sediment transport. The exact wave height deformation calculation on the coasts is essential to near-shore hydrodynamics research and the structure design of coastal engineering. According to the wave shoaling results gained from the elliptical cosine wave theory, the nonlinear wave dispersion relation is adopted to develop the expression of the corresponding nonlinear wave shoaling coefficient. Based on the extended elliptic mild slope equation, an efficient wave numerical model is presented in this paper for predicting wave deformation across the complex topography and the surf zone, incorporating the nonlinear wave dispersion relation, the nonlinear wave shoaling coefficient and other energy dissipation factors. Especially, the phenomenon of wave recovery and second breaking could be shown by the present model. The classical Berkhoff single elliptic topography wave tests, the sinusoidal varying topography experiment, and complex composite slopes wave flume experiments are applied to verify the accuracy of the calculation of wave heights. Compared with experimental data, good agreements are found upon single elliptical topography and one-dimensional beach profiles, including uniform slope and step-type profiles. The results indicate that the newly-developed nonlinear wave shoaling coefficient improves the calculated accuracy of wave transformation in the surf zone efficiently, and the wave breaking is the key factor affecting the wave characteristics and need to be considered in the nearshore wave simulations.

A surface wave dispersion relation for non-local media

1978 ◽  
Vol 28 (11) ◽  
pp. 927-929 ◽  
Author(s):  
Deva N. Pattanayak ◽  
Joseph L. Birman
Keyword(s):  
Surface Wave ◽  
Dispersion Relation ◽  
Wave Dispersion ◽  
Surface Wave Dispersion ◽  
Local Media ◽  
Non Local
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