Effects of Ions on the Propagation of Langmuir Oscillations in Cold Quantum Electron-Ion Plasmas

2008 ◽  
Vol 63 (7-8) ◽  
pp. 400-404 ◽  
Author(s):  
Hyun-Jae Rhee ◽  
Young-Dae Jung
Keyword(s):  
Phase Velocity ◽  
Quantum Effect ◽  
Frequency Mode ◽  
Wave Number ◽  
Propagation Mode ◽  
Quantum Electron ◽  
Quantum Plasmas ◽  
Phase And Group Velocities ◽  
Lower Frequency Mode ◽  
Group Velocities

The effects of ions on the propagation of Langmuir oscillations are investigated in cold quantum electron-ion plasmas. It is shown that the higher and lower frequency modes of the Langmuir oscillations would propagate in cold quantum plasmas according to the effects of ions. It is also shown that these two propagation modes merge into one single propagation mode if the contribution of ions is neglected. It is found that the quantum effect enhances the phase and group velocities of the higher frequency mode of the propagation. In addition, it is shown that the phase velocity of the lower frequency mode is saturated with increasing the quantum wavelength and further that the group velocity of the lower frequency mode has a maximum position in the domains of the wave number and quantum wavelength.

A Dispersive Nonlocal Model for In-Plane Wave Propagation in Laminated Composites With Periodic Structures

2015 ◽  
Vol 82 (3) ◽  
Author(s):  
H. Brito-Santana ◽  
Yue-Sheng Wang ◽  
R. Rodríguez-Ramos ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Díaz ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Phase Velocity ◽  
Incident Angle ◽  
Unit Cell ◽  
Wave Number ◽  
Periodic Distribution ◽  
Phase And Group Velocities ◽  
Group Velocities ◽  
Plane Wave Propagation

In this paper, the problem of in-plane wave propagation with oblique incidence of the wave in an isotropic bilaminated composite under perfect contact between the layers and periodic distribution between them is studied. Based on an asymptotic dispersive method for the description of the dynamic processes, the dispersion equations were derived analytically from the average model. Numerical examples show that the dispersion curves obtained from the present model agree with the exact solutions for a range of wavelengths. Detailed numerical simulations are provided to illustrate graphically the phase and group velocities. Such illustrations allow the identification and comparison of the effects of the unit cell size, wave number and incident angle. It was observed that, as the incident angle increases, the dimensionless quasi-longitudinal phase velocity increases, and the dimensionless quasi-shear phase velocity decreases. In addition, the phase and group velocities decrease as the size of the unit cell increases. The frequency band structure, as a function of the wave-vector components is calculated.

scholarly journals VELOCITIES AND TRAJECTORIES OF WAVE MOTION IN A TWO-LAYER HYDRODYNAMIC SYSTEM

2020 ◽  
pp. 30-37
Author(s):  
Y. Hurtovyi ◽  
O. Kuharenko
Keyword(s):  
Surface Tension ◽  
Phase Velocity ◽  
Internal Waves ◽  
Lower Layer ◽  
World Ocean ◽  
Capillary Waves ◽  
Wave Number ◽  
Hydrodynamic System ◽  
Phase And Group Velocities ◽  
Group Velocities

The paper deals with studying trajectories of motion of individual liquid particles in a two-layer hydrodynamic system with a finite layer thickness as well as analyzing phase and group velocities of internal waves in the system. The problem is modeled for an inviscid incompressible fluid under action of the gravity and surface tension forces in a dimensionless form. Solutions of the problem are sought in the form of progressive waves using the multi-scale method. The solutions are expanded in terms of the nonlinearity coefficient. Dependence of the dispersion ratio of the wavenumber is investigated for different values of the surface tension coefficient and the ratio of the layer densities. Formulas are obtained for the group and phase velocities for internal gravity-capillary waves as well as in the limiting case for capillary waves. A comparison of the values of the phase and group velocities of internal waves for different values of the wave number is carried out. It is proved that with an increase in the wave number, the group velocity begins to outstrip the phase velocity, and their equality occurs at the minimum phase velocity. It is shown that the trajectories are ellipses in which the horizontal semi axes are larger than the vertical ones. Formulas are obtained for the semi axes of elliptic trajectories for each of the layers. The character of the change in the semi axes of elliptical trajectories is analyzed depending on the distance from the interface between two liquid layers as well as on the values of the wave number. It is proved that the semi axes of ellipses decrease unevenly with increasing distance from the boundary. The asymmetry of the particle trajectories of each of the layers is shown for the case when the thickness of the lower layer differs from the thickness of the lower layer. The study of the kinematic characteristics of the particle motion makes it possible to simulate real physical wave processes in the World Ocean. The results are also relevant for creating a theoretical basis for experiments.

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

Propagation of Impact-Induced Longitudinal Waves in Mechanical Systems With Variable Kinematic Structure

1993 ◽  
Vol 115 (1) ◽  
pp. 1-8 ◽  
Author(s):  
A. A. Shabana ◽  
W. H. Gau
Keyword(s):  
Mechanical Systems ◽  
Wave Number ◽  
Jump Discontinuity ◽  
Harmonic Waves ◽  
Kinematic Structure ◽  
System Configuration ◽  
Longitudinal Waves ◽  
Phase And Group Velocities ◽  
Group Velocities ◽  
System Topology

In previous publications by the authors of this paper it was shown that elastic media become dispersive as the result of the coupling between the finite rotation and the elastic deformation. Impact-induced harmonic waves no longer travel, in a rotating rod, with the same phase velocity and consequently the group velocity becomes dependent on the wave number. In this investigation, the propagation of impact-induced longitudinal waves in mechanical systems with variable kinematic structure is examined. The configuration of the mechanical system is identified using two different sets of modes. The first set describes the system configuration before the change in the system topology, while the second set describes the configuration of the system after the topology changes. In the analysis presented in this investigation, it is assumed that collision between the system components occurs first, followed by a change in the system topology. Both events are assumed to occur in a very short-lived interval of time such that the system configuration does not appreciably change. By using the first set of modes, the jump discontinuity in the system velocities is predicted using the algebraic generalized impulse momentum equations. The propagation of the impact-induced wave motion after the change in the system topology is described using the Fourier method. The series solution obtained is used to examine the effect of the topology change on the propagation of longitudinal elastic waves in constrained mechanical systems. It is shown that, while, for a nonrotating rod, mass capture or mass release has no effect on the phase and group velocities, in rotating rods the phase and group velocities depend on the change in the system topology. In particular the phase velocities of low harmonic longitudinal waves are more affected by the change in the system topology as compared to high frequency harmonic waves.

scholarly journals Dispersion and attenuation of a longitudinal wave propagating in a metamaterial defined as a mass-to-mass chain

2019 ◽  
pp. 6-18
Author(s):  
V I Erofeev ◽  
D A Kolesov ◽  
V L Krupenin
Keyword(s):  
Phase Velocity ◽  
Longitudinal Wave ◽  
Group Velocity ◽  
Mass Density ◽  
Deformable Body ◽  
Mass Model ◽  
Positive Direction ◽  
Normal Dispersion ◽  
Phase And Group Velocities ◽  
Group Velocities

We study the features of propagation of a longitudinal wave in an acoustic (mechanical) metamaterial, modeled as a one-dimensional chain, containing equal masses, connected by elastic elements (springs), and having the same rigidity. Each mass contains within itself a series connection of another mass and viscous element (damper). The mass-to-mass model is free from the drawbacks of a number of other mechanical models of metamaterials: i.e. it eliminates the need to have the property of a deformable body to possess a negative mass, density, and (or) a negative elastic modulus. It is shown that the model under consideration makes it possible to describe the dispersion and frequency-dependent attenuation of a longitudinal wave, the character of which essentially depends on the ratio of the external and internal mass of the metamaterial. The behavior of the phase and group velocities of the wave is studied, as well as the evolution of its profile, both in the low-frequency and high-frequency ranges. The mass ratios were found at which the phase velocity exceeds the group velocity (normal dispersion) in magnitude and those at which the group velocity exceeds the phase velocity (anomalous dispersion) in a wide frequency range. Having the same asymptotic values when the frequency tends to infinity, the phase and group velocities have significant differences in behavior, namely, that the phase velocity is a monotonic function of frequency, and the group velocity has a maximum. In addition, in the region of normal dispersion, the group velocity may be negative, i.e. the so-called “reverse wave” effect is true, when, despite the fact that the phase velocity is directed in the positive direction of the spatial axis, the energy in such a wave is transferred in the negative direction.

scholarly journals Дисперсия объемных волн в структуре "графен--диэлектрик--графен"

2019 ◽  
Vol 126 (2) ◽  
pp. 224
Author(s):  
А.С. Абрамов ◽  
Д.А. Евсеев ◽  
И.О. Золотовский ◽  
Д.И. Семенцов
Keyword(s):  
Electric Field ◽  
Phase Velocity ◽  
Waveguide Mode ◽  
Chemical Potential ◽  
Dielectric Film ◽  
Dispersion Characteristics ◽  
Graphene Layers ◽  
Waveguide Modes ◽  
Phase And Group Velocities ◽  
Group Velocities

AbstractWe investigate the dispersion properties of the first waveguide modes in a dielectric film that is coated with graphene layers having different chemical potential values. The control over the phase and group velocities of the first waveguide mode is considered. Spectral intervals in which the phase velocity of the waveguide modes is small, while their group velocity is negative, are revealed. We show that the dispersion characteristics of the waveguide modes can be rearranged using an external electric field.

The combined effects of transverse isotropy and inhomogeneity on Love waves

1973 ◽  
Vol 63 (1) ◽  
pp. 49-57
Author(s):  
V. Thapliyal
Keyword(s):  
Half Space ◽  
Transverse Isotropy ◽  
Frequency Equation ◽  
Love Waves ◽  
Anisotropy Factor ◽  
Wave Number ◽  
Elastic Parameters ◽  
Short Period ◽  
Phase And Group Velocities ◽  
Group Velocities

abstract The characteristic frequency equation for Love waves propagating in a finite layer overlying an anisotropic and inhomogeneous half-space is derived. This frequency equation takes into account the arbitrary variation of density, elastic parameters, and degree of anisotropy factor in the half-space. In fact, the problem of deriving the frequency equation has been reduced to finding the solution of the equation of motion subject to the appropriate boundary conditions. To illustrate the method, the author has derived the frequency equation for a generalized power law variation of density and elastic parameters with the depth, in the halfspace. As a step toward the systematic investigation of the effects of anisotropy and inhomogeneity, the relationship between the wave number and phase and group velocities has been worked out for increasing, uniform and decreasing anisotropy factor. The pronounced effects of anisotropy have been noticed in the long-period range compared to the short-period one. The numerical analysis shows that for a given phase velocity (or group velocity), the period of propagation depends on the sign and magnitude of power of variation of the density and anisotropy factor in the half-space. For the increased positive rate of variation of the anisotropy factor, the values of phase and group velocities have been found higher whereas the reverse is found true for an increasing negative rate of variation of the anisotropy factor.

Graphical Study of the Dispersion of Electro-Magneto-Ionic Waves

1949 ◽  
Vol 2 (2) ◽  
pp. 307
Author(s):  
VA Bailey ◽  
JA Roberts
Keyword(s):  
Graphical Method ◽  
Wave Number ◽  
Refractive Indices ◽  
General Effect ◽  
Wave Groups ◽  
Positive Ions ◽  
Phase And Group Velocities ◽  
The Waves ◽  
Special Case ◽  
Group Velocities

A graphical method for approximating to all the eight roots of the equation of dispersion, corresponding to any numerically specified case, is described. This method uses curves drawn with ω and l as coordinates to give readily the following information about the waves which can exist in the medium : (i) the frequency- bands in which undamped waves or wave-groups can grow as they progress, (ii) the wave-number bands in which unattenuated waves can grow in time, (iii) the phase- and group-velocities, refractive indices, and coefficients of positive and negative attenuation and damping, (iv) the general effect of collisions between electrons and other particles on the attenuation or damping of a wave or wave-group. Several illustrative examples are given. The same method is also applied to a special case of the more comprehensive equation of dispersion which includes the effects due to the motions of the positive ions, and it is shown that there can then exist unattenuated waves which grow with the lapse of time.

scholarly journals Frequency derivative of Rayleigh wave phase velocity for fundamental mode dispersion inversion: parametric study and experimental application

2020 ◽  
Vol 224 (1) ◽  
pp. 649-668
Author(s):  
A Wang ◽  
D Leparoux ◽  
O Abraham ◽  
M Le Feuvre
Keyword(s):  
Phase Velocity ◽  
Rayleigh Wave ◽  
Group Velocity ◽  
Fundamental Mode ◽  
Deep Layer ◽  
Wave Phase Velocity ◽  
Phase And Group Velocities ◽  
Velocity Derivative ◽  
Rayleigh Wave Phase Velocity ◽  
Group Velocities

SUMMARY Monitoring the small variations of a medium is increasingly important in subsurface geophysics due to climate change. Classical seismic surface wave dispersion methods are limited to quantitative estimations of these small variations when the variation ratio is smaller than 10 per cent, especially in the case of variations in deep media. Based on these findings, we propose to study the contributions of the Rayleigh wave phase velocity derivative with respect to frequency. More precisely, in the first step of assessing its feasibility, we analyse the effects of the phase velocity derivative on the inversion of the fundamental mode in the simple case of a two-layer model. The behaviour of the phase velocity derivative is first analysed qualitatively: the dispersion curves of phase velocity, group velocity and the phase velocity derivative are calculated theoretically for several series of media with small variations. It is shown that the phase velocity derivatives are more sensitive to variations of a medium. The sensitivity curves are then calculated for the phase velocity, the group velocity and the phase velocity derivative to perform quantitative analyses. Compared to the phase and group velocities, the phase velocity derivative is sensitive to variations of the shallow layer and the deep layer shear wave velocity in the same wavelength (frequency) range. Numerical data are used and processed to obtain dispersion curves to test the feasibility of the phase velocity derivative in the inversion. The inversion results of the phase velocity derivative are compared with those of phase and group velocities and show improved estimations for small variations (variation ratio less than 5 per cent) of deep layer shear wave velocities. The study is focused on laboratory experiments using two reduced-scale resin-epoxy models. The differences of these two-layer models are in the deep layer in which the variation ratio is estimated as 16.4 ± 1.1 per cent for the phase velocity inversion and 17.1 ± 0.3 per cent for the phase velocity derivative. The latter is closer to the reference value 17 per cent, with a smaller error.

Generalized velocity approximation

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. C27-C40 ◽  
Author(s):  
Alexey Stovas ◽  
Sergey Fomel
Keyword(s):  
Phase Velocity ◽  
Functional Form ◽  
Transversely Isotropic ◽  
P Wave ◽  
Transversely Isotropic Medium ◽  
Numerical Examples ◽  
P Wave Velocity ◽  
Phase And Group Velocities ◽  
Group Velocities ◽  
Velocity Approximation

We have developed a new approximation for P-wave velocity that has the same functional form for phase and group velocities. We call it the generalized velocity approximation (GVA) because it is similar to the generalized moveout approximation. The 2D GVA has five parameters, and the 3D GVA has 12 parameters. Our approximation is exact for the phase velocity in a transversely isotropic medium. The parameters of the 3D version of the proposed approximation are defined in all of the symmetry planes in the same fashion. Numerical examples indicate that our approximation has the same accuracy as recently proposed anelliptic approximation, but it has fewer parameters.

Sign in / Sign up

Export Citation Format

Share Document