Localization of Long-Wavelength Acoustic Phonons in a Disordered Anomalous Soft Solid with Parabolic Dispersion Relation

2009 ◽  
Vol 78 (4) ◽  
pp. 044602
Author(s):  
Masaki Goda ◽  
Manabu Okamura ◽  
Shinya Nishino
Keyword(s):  
Dispersion Relation ◽  
Acoustic Phonons ◽  
Long Wavelength ◽  
Parabolic Dispersion

Magnetic Superlattice: Localized Magnetostatic Waves and Magnetic Polaritons

2003 ◽  
Vol 17 (15) ◽  
pp. 829-839
Author(s):  
R. T. Tagiyeva ◽  
M. Saglam
Keyword(s):  
Magnetic Material ◽  
Electromagnetic Wave ◽  
Dispersion Relation ◽  
Wave Theory ◽  
Frequency Region ◽  
Long Wavelength ◽  
Magnetostatic Waves ◽  
General Dispersion ◽  
Magnetic Polaritons ◽  
Magnetic Superlattice

Localized magnetostatic waves and magnetic polaritons at the junction of the magnetic material and magnetic superlattice composed of the alternating ferromagnetic or ferromagnetic and nonmagnetic layers are investigated in the framework of the electromagnetic wave theory in Voigt geometry. The general dispersion relation for localized magnetic polaritons and magnetostatic waves (MW) are derived in the long-wavelength limit. The dispersion curves and frequency region of the exsistence of the localized MW and magnetic polaritons are calculated numerically.

Stability of strong electromagnetic waves in overdense plasmas against long-wavelength perturbations

1985 ◽  
Vol 33 (2) ◽  
pp. 285-301 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Modulation Depth ◽  
Longitudinal Direction ◽  
Transverse Component ◽  
Ion Density ◽  
Long Wavelength ◽  
The Stability ◽  
Two Parameters

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

Electromagnetic instability supported by a rippled, magnetically focused relativistic electron beam

1984 ◽  
Vol 31 (2) ◽  
pp. 239-251 ◽  
Author(s):  
S. Cuperman ◽  
F. Petran ◽  
A. Gover
Keyword(s):  
Electron Beam ◽  
Dispersion Relation ◽  
Growth Rates ◽  
Relativistic Electron Beam ◽  
Electron Beams ◽  
Wave Instability ◽  
Electrostatic Waves ◽  
Long Wavelength ◽  
Ripple Amplitude ◽  
Electromagnetic Instability

The coupling of volume, long-wavelength TM electromagnetic and longitudinal space charge (electrostatic) waves by the rippling of magnetically focused electron beams is examined analytically. The dispersion relation is obtained and then solved for these types of wave. Instability, with growth rates proportional to the relative ripple amplitude of the beam, is found and discussed.

On capillary waves in the gradient theory of interfaces

1985 ◽  
Vol 63 (2) ◽  
pp. 131-134 ◽  
Author(s):  
Luis de Sobrino ◽  
Jože Peternelj
Keyword(s):  
Dispersion Relation ◽  
Thermal Effects ◽  
Equations Of Motion ◽  
Capillary Waves ◽  
Gradient Theory ◽  
Two Phase ◽  
Long Wavelength ◽  
Phase Solution

We have solved the equations of motion for an inhomogeneous, nondissipative fluid linearized about a two-phase solution in order to determine the dispersion relation for capillary waves of long wavelength. The solution is reasonably rigorous in that no physical assumptions have been introduced. We find that, in accordance with the results of Turski and Langer and contrary to other workers' claims, the dispersion relation agrees with classical capillary theory only if thermal effects are included.

Propagation of Low-Frequency Elastic Disturbances in a Composite Material

1974 ◽  
Vol 41 (1) ◽  
pp. 97-100 ◽  
Author(s):  
W. Kohn
Keyword(s):  
Composite Material ◽  
Wave Equation ◽  
Dispersion Relation ◽  
Displacement Field ◽  
Low Frequency ◽  
Local Strain ◽  
Airy Functions ◽  
Low Frequencies ◽  
One Dimensional ◽  
Long Wavelength

In the limit of low frequencies the displacement u(x, t) in a one-dimensional composite can be written in the form of an operator acting on a slowly varying envelope function, U(x, t): u(x, t) = [1 + v1(x)∂/∂x + …] U(x, t). U(x, t) itself describes the overall long wavelength displacement field. It satisfies a wave equation with constant, i.e., x-independent, coefficients, obtainable from the dispersion relation ω = ω(k) of the lowest band of eigenmodes: (∂2/∂t2 − c¯2∂2/∂x2 − β∂4/∂x4 + …) U(x, t) = 0. Information about the local strain, on the microscale of the composite laminae, is contained in the function v1(x), explicitly expressible in terms of the periodic stiffness function, η(x), of the composite. Appropriate Green’s functions are constructed in terms of Airy functions. Among applications of this method is the structure of the so-called head of a propagating pulse.

DISPERSION OF ACOUSTIC PHONONS IN QUASIPERIODIC SUPERLATTICES

2004 ◽  
Vol 11 (06) ◽  
pp. 541-551 ◽  
Author(s):  
R. K. MISHRA ◽  
K. D. MISRA ◽  
R. P. TIWARI
Keyword(s):  
Dispersion Relation ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Acoustic Phonon ◽  
Multilayered Structure ◽  
Angle Of Incidence ◽  
Semiconducting Materials ◽  
Acoustic Phonons ◽  
Normal Angle

The aim of this work is to present an up-to-date study of acoustic phonon excitations that can propagate in multilayered structure with constituents arranged in quasiperiodic fashion. In this paper, the dispersion relation of acoustic phonons for the quasiperiodic superlattice using different semiconducting materials, with the help of transfer matrix method, is derived at normal angle of incidence. Calculation is presented for (a) Ge / Si and (b) Nb / Cu semiconductor superlattices from 5th to 9th generations and dispersion diagrams are plotted using the famous Kronning–Penny model obtained from the transfer matrix of the structure. The concept of allowed and forbidden bands with the help of these dispersion curves in various generations of Fibonacci superlattices and the relation between imaginary value of propagation vector and the existence of forbidden bands is demonstrated.

Propagation of Acoustic Phonons in Amorphous Superlattices

1986 ◽  
Vol 77 ◽  
Author(s):  
P. V. Santos ◽  
L. Ley ◽  
J. Mebert ◽  
J. Koblinger
Keyword(s):  
Raman Spectrum ◽  
Light Scattering ◽  
Dispersion Relation ◽  
Brillouin Zone ◽  
Phonon Dispersion ◽  
Transmission Spectra ◽  
Acoustic Phonons ◽  
Longitudinal Acoustic ◽  
Energy Gaps

ABSTRACTWe have investigated the Raman and the phonon transmission spectra of a-Si:H/a-SiNx:H super lattices. At low wavenumbers, the Raman spectrum shows sharp peaks corresponding to the excitation of modes from the folded branches of the dispersion relation for longitudinal acoustic phonons propagating perpendicular to the layers. Energy gaps in the folded phonon dispersion occur at the center and at the boundary of the mini-Brillouin zone due to the differences in the acoustic impedances of the layers. The size of the lowest gaps was determined by light scattering. The phonon transmission spectra show transmission minima that we attribute to the frequency gaps in the dispersion of transversal acoustic phonons. The position and width of these minima are compared with the dispersion obtained from the Raman data.

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