dispersion relation


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dispersion relation

[də′spər·zhən ri‚lā·shən]
(nuclear physics)
A relation between the cross section for a given effect and the de Broglie wavelength of the incident particle, which is similar to a classical dispersion formula.
(physics)
An integral formula relating the real and imaginary parts of some function of frequency or energy, such as a refractive index or scattering amplitude, based on the causality principle and the Cauchy integral formula.
(plasma physics)
A relation between the radian frequency and the wave vector of a wave motion or instability in a plasma.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
By expressing the Lagrangian displacements [[xi].sub.ir] and [[xi].sub.er] in both media via the derivatives of corresponding Bessel functions and by applying the boundary conditions for continuity of the pressure perturbation [p.sub.tot] and [[xi].sub.r] across the interface, r = a, one obtains the dispersion relation of normal MHD modes propagating in a flowing compressible jet surrounded by a static compressible plasma [65, 83, 84]
For Figure 1, with wave vectors [[bar.k].sup.i.sup.TE] = [??][k.sup.TE.sub.0x] + [??][k.sup.TE.sub.y] (incident) and [[bar.k].sub.r.sup.TE] = [??][k.sup.TE.sub.0x] + [??][k.sup.TE.sub.y] (reflection) in the isotropic medium and [[bar.k].sub.t.sup.TE] = [??][k.sup.TE.sub.tx] (transmission) in the biaxial anisotropic medium, the dispersion relations can be expressed as
The dispersion relation of Love-type wave has been obtained and coincides with the classical dispersion relation of Love wave in particular cases.
Although the number of the data is limited, we are able to say that the linear dispersion relation can be used ordinarily for the ocean waves except for the special cases where very steep waves are generated by extremely strong wind.
Dispersion relations have been obtained separately in the cases of electrical open circuit and short circuit.
We have used the expressions of [eta], [[phi].sup.(1)], [[phi].sup.(2)], [[psi].sup.(1)], [[psi].sup.(2)], and -[p.sup.v.sub.1] + [p.sup.v.sub.2] in (34) to find the dispersion relation which is a quadratic equation expressed as follows:
The condition of nontrivial solution of the above system gives the following biquadratic dispersion relation:
It is not easy to achieve fast electrokinetic mode in presence of drifting carriers in the medium; hence, we will study this dispersion relation under slow electrokinetic mode situation only.
In order to obtain the propagation constants for the EH0i , [EH.sub.11], and [EH.sub.-11] modes, we solve the dispersion relation as stated in (7) for the range of [beta].
This results in an unusual hyperbolic dispersion relation for the medium and consequently many interesting phenomena such as hyperlensing [2-5], control of the electromagnetic fields [6], all-angle zero reflection [7, 8], all-direction pulse compression [9] and all-angle zero reflection-zero transmission [10] can be happened.
In particular, the exact dispersion relation of the plasma column loaded cylindrical waveguide was presented in different forms with different notations in [15, 48, 51, 52].
The dispersion relation for TM waves in the infinite periodic structure, which relates the frequency [omega], the longitudinal wave number [k.sub.x] and the Bloch wave number [bar.k], can be written as [9]