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Showing papers on "Dispersion relation published in 1995"


Journal ArticleDOI
20 Dec 1995-EPL
TL;DR: In this paper, the phonon dispersion relations of diamond and graphite are calculated using an ab initio force constant method via a self-consistent supercell approach in the local density approximation in terms of the Hellmann-Feynman forces induced by the displacement of a single atom in the supercell.
Abstract: The phonon dispersion relations of diamond and graphite are calculated using an ab initio force constant method. The force constants are calculated via a self-consistent supercell approach in the local-density approximation in terms of the Hellmann-Feynman forces induced by the displacement of a single atom in the supercell. For diamond our ab initio results are in very good agreement with the neutron inelastic scattering and Raman data. For graphite we find good agreement with the neutron data for the low-energy modes as well as with the reflections electron energy loss spectroscopy (REELS) and optical data at higher energies. Significant differences to the predictions of semi-empirical models appear.

609 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed an algorithm to solve the elastic-wave equation by replacing the partial differentials with finite differences, which enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models.
Abstract: An algorithm is presented to solve the elastic-wave equation by replacing the partial differentials with finite differences. It enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models. The space derivatives are calculated using discrete convolution sums, while the time derivatives are replaced by a truncated Taylor expansion. A centered finite difference scheme in cartesian coordinates is used for the space derivatives leading to staggered grids. The use of finite difference approximations to the partial derivatives results in a frequency-dependent error in the group and phase velocities of waves. For anisotropic media, the use of staggered grids implies that some of the elements of the stress and strain tensors must be interpolated to calculate the Hook sum. This interpolation induces an additional error in the wave properties. The overall error depends on the precision of the derivative and interpolation operators, the anisotropic symmetry system, its orientation and the degree of anisotropy. The dispersion relation for the homogeneous case was derived for the proposed scheme. Since we use a general description of convolution sums to describe the finite difference operators, the numerical wave properties can be calculated for any space operator and an arbitrary homogeneous elastic model. In particular, phase and group velocities of the three wave types can be determined in any direction. We demonstrate that waves can be modeled accurately even through models with strong anisotropy when the operators are properly designed.

296 citations


Journal ArticleDOI
TL;DR: In this paper, a new plasma dispersion function is proposed, which is proportional to Gauss' hypergeometric function 2F1[1,2κ+2;κ+ 2;z] enabling the well-established theory of the hypergeometrical function to be used to manipulate dispersion relations.
Abstract: It is now well known that space plasmas frequently contain particle components that exhibit high, or superthermal, energy tails with approximate power law distributions in velocity space. Such nonthermal distributions, with overabundances of fast particles, can be better fitted, for supra‐ and superthermal velocities, by generalized Lorentzian or kappa distributions, than by Maxwellians or one of their variants. Employing the kappa distribution, with real values of the spectral index κ, in place of the Maxwellian we introduce a new plasma dispersion function expected to be of significant importance in kinetic theoretical studies of waves in space plasmas. It is demonstrated that this function is proportional to Gauss’ hypergeometric function 2F1[1,2κ+2;κ+2;z] enabling the well‐established theory of the hypergeometric function to be used to manipulate dispersion relations. The reduction, for integer values of κ, to the less general so‐called modified plasma dispersion function [Phys. Fluids B 3, 1835 (1991...

284 citations


Journal ArticleDOI
TL;DR: A novel density functional is presented, properly accounting for the static response function and the phonon-roton dispersion in the uniform liquid, used to study both structural and dynamical properties of superfluid helium in various geometries.
Abstract: We present a novel density functional for liquid 4 He, properly accounting for the static response function and the phonon-roton dispersion in the uniform liquid. The functional is used to study both structural and dynamical properties of superfluid helium in various geometries. The equilibrium properties of the free surface, droplets and films at zero temperature are calculated. Our predictions agree closely to the results of ab initio Monte Carlo calculations, when available. The introduction of a phenomenological velocity dependent interaction, which accounts for backflow effects, is discussed. The spectrum of the elementary excitations of the free surface and films is studied. PACS number:67.40

262 citations


Journal ArticleDOI
TL;DR: In this paper, the authors compare causal theories, based on Kramers-Kronig relations, fractional calculus, and on those derived from new time domain causal relationships, to diverse data.
Abstract: This study compares causal theories, based on Kramers–Kronig relations, fractional calculus, and on those derived from new time domain causal relationships, to diverse data. All these theories are based on the assumptions that the functional form of the attenuation persists beyond the measurement range and that attenuation is much smaller than the wave number. The data, for lossy media with attenuation having a power‐law frequency dependence with an exponent y, include cases for both liquids and solids, ranging from acoustic to ultrasound frequencies. Data are in closer correspondence with the new theory which predicts decreasing dispersion as the power exponent y approaches zero or an even integer. Experimental results and supporting evidence show that the classical case of frequency‐squared attenuation is dispersionless. An approximate nearly local Kramers–Kronig theory is in agreement with the time causal theory when the exponent is close to one, but deviates for other values. The comprehensive time causal theory is shown to be equivalent to two other theories derived from exact Kramers–Kronig relations and from fractional calculus and it covers the y odd integer cases which are missing or incomplete in these approaches. Attenuation–dispersion relations are presented in two forms: one for a general frequency range and another for a finite range. It is demonstrated that complete velocity dispersion (within a signal bandwidth) can be predicted from knowledge of the attenuation data and velocity at a single frequency including the velocity at either zero frequency (y≳1) and or at a high‐frequency limit (0

256 citations


Journal ArticleDOI
Mario Rocca1
TL;DR: In this article, the authors reviewed recent progress in experimental and theoretical investigations of surface electronic excitations of metals with an emphasis on surface plasmon dispersion, highlighting present limitations and possible future developments.

226 citations


Journal ArticleDOI
TL;DR: In this paper, a comprehensive two-fluid model is developed for collective modes in a nonrelativistic electron-positron plasma, both in the presence and absence of a magnetic field.
Abstract: A comprehensive two-fluid model is developed for collective modes in a nonrelativistic electron-positron plasma. Longitudinal and transverse electrostatic and electromagnetic modes, both in the presence and absence of a magnetic field, are studied. Wave properties are discussed in terms of dispersion relations, wave normal surfaces, and cylindrical mirror analyzer clemmow-Mullaly-Allis diagrams. The results are extended to include the two-stream instability and ion acoustic solitary waves. For the two-stream instability, a similar result is found as in the electron-ion plasma. For ion acoustic solitary waves, only subsonic solutions are found to exist. Furthermore, their width is proportional to their amplitude, unlike the electron-ion plasma case, where the speed is proportional to the amplitude.

222 citations


Journal ArticleDOI
TL;DR: This simple model gives an example of a system with a temperature-dependent effective Hamiltonian and finds that to satisfy the thermodynamical relations in these systems, standard statistical mechanics formulas have to be supplemented by special requirements.
Abstract: The statistical mechanics for systems with a medium-dependent dispersion relation are formulated and applied to construct a model for the gluon plasma equation of state with a temperature-dependent particle mass. This simple model gives us an example of a system with a temperature-dependent effective Hamiltonian. We find that to satisfy the thermodynamical relations in these systems, standard statistical mechanics formulas have to be supplemented by special requirements. The self-consistent statistical model formulation is used to describe Monte Carlo lattice data for the thermodynamical functions of SU(2) and SU(3) gluon plasma.

152 citations


Journal ArticleDOI
TL;DR: In this article, a large and well-controlled sample of clusters of galaxies was used to investigate the relation between cluster velocity dispersions and X-ray temperatures of intra-cluster gas.
Abstract: Using a large and well-controlled sample of clusters of galaxies, we investigate the relation between cluster velocity dispersions and X-ray temperatures of intra-cluster gas. In order to obtain a reliable estimate of the total velocity dispersion of a cluster, independent of the level of anisotropies in galaxy orbits, we analyze the integrated velocity dispersion profiles over increasing distances from the cluster centers. Distortions in the velocity fields, the effect of close clusters, the presence of substructures, and the presence of a population of (spiral) galaxies not in virial equilibrium with the cluster potential are taken into account. Using our final sample of 37 clusters, for which a reliable estimate of the velocity dispersion could be obtained, we derive a relation between the velocity dispersions and the X-ray temperatures, with a scatter reduced by more than 30 % with respect to previous works. A chi square fit to the temperature-velocity dispersion relation does not exclude the hypothesis that the ratio between galaxy and gas energy density (the so-called spectral beta) is a constant for all clusters. In particular, the value of beta=1, corresponding to energy equipartition, is acceptable.

149 citations


Journal ArticleDOI
TL;DR: In this paper, the formulation of a nonlinear frequency domain parabolic mild-slope model is described, and the resulting model describes two-dimensional wave transformation and nonlinear coupling between frequency components.
Abstract: The formulation of a nonlinear frequency domain parabolic mild‐slope model is detailed. The resulting model describes two‐dimensional wave transformation and nonlinear coupling between frequency components. Linear dispersion and transformation characteristics are dictated by fully‐dispersive linear theory, an improvement over weakly‐dispersive Boussinesq theory. Both the present model and a weakly‐dispersive nonlinear frequency domain model are compared to laboratory data for both two‐dimensional wave transformation and pure shoaling. It is found that, in general, data‐model comparisons are enhanced by the present model, particularly in instances where the wave condition is outside the shallow water range.

131 citations


Journal ArticleDOI
TL;DR: In this article, the mode frequencies and Landau damping of two dominant ion-acoustic modes in CH plasmas are calculated by numerical solution of the kinetic dispersion relation.
Abstract: The kinetic theory of ion‐acoustic waves in multi‐ion‐species plasmas is discussed. Particular application is made to hydrocarbon (CH) plasmas, which are widely used in laser–plasma experiments. The mode frequencies and Landau damping of the two, dominant, ion‐acoustic modes in CH plasmas are calculated by numerical solution of the kinetic dispersion relation. In addition, some useful results are obtained analytically from expansions of the kinetic dispersion relation and from fluid models. However, these results disagree with the numerical results in domains of particular practical interest. When ion temperatures exceed two‐tenths of the electron temperature, the least damped mode is the one with the smaller phase velocity, and this mode is then found to dominate the ponderomotive response of the CH plasma.

Journal ArticleDOI
TL;DR: In this paper, a bright optical soliton described by a nonlinear Schrodinger equation can survive even in a positive dispersion region as long as the average dispersion has a negative value.
Abstract: A bright optical soliton described by a nonlinear Schrodinger equation can survive even in a positive dispersion region as long as the average dispersion has a negative value. This allows us to combine fibres with large positive and large negative dispersion, which in turn will enable us to introduce solitons in a commercial system.

Journal ArticleDOI
TL;DR: The existence and linear stability problem for the Stokes periodic wavetrain on fluids of finite depth is formulated in terms of the spatial and temporal Hamiltonian structure of the water-wave problem as mentioned in this paper.
Abstract: The existence and linear stability problem for the Stokes periodic wavetrain on fluids of finite depth is formulated in terms of the spatial and temporal Hamiltonian structure of the water-wave problem. A proof, within the Hamiltonian framework, of instability of the Stokes periodic wavetrain is presented. A Hamiltonian center-manifold analysis reduces the linear stability problem to an ordinary differential eigenvalue problem on ℝ4. A projection of the reduced stability problem onto the tangent space of the 2-manifold of periodic Stokes waves is used to prove the existence of a dispersion relation Λ(λ,σ, I 1, I 2)=0 where λ e ℂ is the stability exponent for the Stokes wave with amplitude I 1 and mass flux I 2 and σ is the “sideband’ or spatial exponent. A rigorous analysis of the dispersion relation proves the result, first discovered in the 1960's, that the Stokes gravity wavetrain of sufficiently small amplitude is unstable for F e (0,F0) where F 0 ≈ 0.8 and F is the Froude number.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a two-pole Sellmeier equation for binary tellurite glasses to find the chromatic dispersion behavior at any wavelength, particularly at the optical windows of optical fiber communication systems and femtosecond technology.
Abstract: Sellmeier coefficients are necessary to optimize the design parameters of optical devices. These coefficients are computed for binary tellurite glasses to find the chromatic dispersion behavior at any wavelength, particularly at the optical windows of optical fiber communication systems and femtosecond technology. A single-oscillator DiDomenico and Wemple's dispersion equation is not sufficient to represent accurately the measured refractive indexes throughout the transmission range. As a minimum, a two-pole Sellmeier equation is necessary to represent the data more accurately. Both the average electronic absorption band gap and the lattice absorption frequency, lying in the UV and IR region, respectively, affect the refractive indexes and their dispersion. Various other optical properties are discussed. A single-oscillator dispersion equation is unable to verify the existence of zero-dispersion wavelength.

Journal ArticleDOI
TL;DR: In this paper, the dispersion characteristics of sound waves propagating in a tunnel with an array of Helmholtz resonators connected axially are examined. And the validity of the continuum approximation for distribution of the resonators is discussed in terms of dispersion relations, though subjected intrinsically not only to weak damping due to the dissipative effects but also to the weak dispersion due to wall friction.
Abstract: This paper examines dispersion characteristics of sound waves propagating in a tunnel with an array of Helmholtz resonators connected axially. Assuming plane waves over the tunnel’s cross section except a thin boundary layer, weakly dissipative effects due to the wall friction and the thermoviscous diffusivity of sound are taken into account. Sound propagation in such a spatially periodic structure may be termed ‘‘acoustic Bloch waves.’’ The dispersion relation derived exhibits peculiar characteristics marked by emergence of ‘‘stopping bands’’ in the frequency domain. The stopping bands inhibit selectively propagation of sound waves even if no dissipative effects are taken into account, and enhance the damping pronouncedly even in a dissipative case. The stopping bands result from the resonance with the resonators as side branches and also from the Bragg reflection by their periodic arrangements. In the ‘‘passing bands’’ outside of the stopping bands, the sound waves exhibit dispersion, though subjected intrinsically not only to the weak damping due to the dissipative effects but also to the weak dispersion due to the wall friction. Taking a plausible example, the dispersion relation and the Bloch wave functions for the pressure are displayed. Finally the validity of the continuum approximation for distribution of the Helmholtz resonators is discussed in terms of the dispersion relations.

Journal ArticleDOI
TL;DR: In this paper, the authors extended the fully relativistic limit for a circularly polarized light for which one derives the dispersion relation in a one-dimensional plasma, and showed that the nonlinear stage of the instability results in a strong heating of the electron distribution function.
Abstract: A large amplitude electromagnetic wave propagating in a plasma is known to be subject to severe modulational and Raman instabilities. Previous works were devoted to the weakly relativistic limit and applied mainly to a cold underdense plasma. One extends these works to include the fully relativistic limit for a circularly polarized light for which one derives the dispersion relation in a one‐dimensional plasma. The characteristics of the instabilities are also calculated in the case where the plasma is classically overdense, with 1<(ωp/ω0)2<γ, where ωp is the plasma frequency, ω0 is the laser frequency, and γ is the relativistic factor of an electron in the laser field. Particle‐in‐cell simulations confirm the results of the numerical solutions of the dispersion relation. For (ωp/ω0)2/γ=0.57 the growth rate can be as large as 0.52ω0. The nonlinear stage of the instability results in a strong heating of the electron distribution function. The theory is further extended to the case of an initially hot plasm...

Journal ArticleDOI
TL;DR: In this article, a non-linear theory of dispersion is proposed to describe hydrodynamic dispersion in porous media, which is based on the assumption of a linear dependance of a solute dispersive mass flux on its concentration gradient.

Journal ArticleDOI
TL;DR: In this article, a scanning interference pattern produced by intersecting two cw lasers generates the density variation (acoustic phonons) through the thermal expansion for a light absorbing liquid.
Abstract: We have developed a new method of phonon spectroscopy using forced Brillouin scattering: A scanning interference pattern produced by intersecting two cw lasers generates the density variation (acoustic phonons) through the thermal expansion for a light-absorbing liquid. When the dispersion relation of phonons is satisfied, phonons are generated resonantly in the liquid. Continuous tuning of the frequency difference between the two lasers enables us to measure a resonance spectrum of light-excited phonons using light scattering phenomena. We demonstrate that this resonance spectrum is equivalent to the Brillouin spectrum of thermal phonons both experimentally and theoretically.

Journal ArticleDOI
TL;DR: In this article, the existence of magneto-acoustic modes in different frequency regimes in a magnetized dusty plasma consisting of electrons, ions and dust particles is investigated using an effective two-fluid MHD-like model which allows for the non-frozen motion of the component fluids.
Abstract: The existence of various types of (fast) magnetoacoustic modes in different frequency regimes in a magnetized dusty plasma consisting of electrons, ions and dust particles is investigated. The analysis is carried out using an effective two-fluid MHD-like model which allows for the non-frozen motion of the component fluids. For frequencies much smaller than the dust particle gyro- frequency, we obtain a magnetoacoustic mode that is a generalization of the usual compressional fast hydromagnetic wave in an electron—ion plasma. In the higher-frequency regimes, we show the existence of two new types of modes called ‘Dust-magnetoacoustic waves’. Both modes are accompanied by compressional magnetic field and plasma number density perturbations, and are the electromagnetic generalizations of the dust-acoustic waves in an unmagnetized dusty plasma with thermal electrons and ions. For a two- component plasma, all three modes degenerate into the same fast magneto- acoustic wave found in the usual electron—ion plasmas. We also obtain another novel type of magneto-acoustic mode called a ‘dust—ion-magneto- acoustic wave’, which is an electromagnetic generalization of the dust—ion- acoustic wave. The dispersion relations as well as the frequency regimes for the existence of the various modes are explicitly obtained. An alternative derivation of the relevant governing equations using an approach similar to that employed in so-called ‘electron magnetohydrodynamics’ (EMHD) is also presented.

Journal ArticleDOI
TL;DR: In this article, a method for developing an accurate temperature-dependent dispersion model is described, which combines a room-temperature Sellmeier model with temperaturedependent refractive index measurements at a few wavelengths to predict the refractive indices over a wide temperature and wavelength region.
Abstract: A method for developing an accurate temperature-dependent dispersion model is described. It combines a room-temperature Sellmeier dispersion model with temperature-dependent refractive index measurements at a few wavelengths to predict the refractive index over a wide temperature and wavelength region. The method is applied to nine well-characterized materials to give dispersion over a wide temperature and wavelength region.

Journal ArticleDOI
TL;DR: In this article, a non-destructive technique for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves is described for measuring material properties.
Abstract: A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/µs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.

Journal ArticleDOI
TL;DR: In this article, a multaper technique was used to estimate the off-great-circle arrival angles of long-period surface waves (2 80 s) as a function of frequency, which can be reliably measured using a multitaper technique.
Abstract: SUMMARY In the current generation of global dispersion maps of surface waves, the longwavelength structure seems to be very well determined. There is general agreement in the patterns of global phase velocity anomalies up to harmonic degree 1-6. However, the shorter-wavelength structure varies significantly between published maps, and it appears that this part of the models depends strongly on the inversion technique and on the data set of surface-wave dispersion (usually phase measurements). Polarization data depend on the lateral gradient of phase velocity and hence are more sensitive to shorter-wavelength structure than phase data; thus, including these data should enhance resolution. In this paper, I demonstrate that polarization data of long-period surface waves (2 80 s), as a function of frequency, can be reliably measured using a multitaper technique. The resulting off-great-circle arrival angles of the surface-wave packets are relatively easy to interpret within a ray-theoretical framework. Our data base of threecomponent recordings is now large enough to provide useful constraints on global dispersion maps, particularly on the shorter-wavelength parts. Apart from the phase velocity model itself, a possible misorientation of the horizontal components at each station is included in a non-linear inversion as an additional independent model parameter. This gives a significant improvement in the fit to the data. Misorientations of more than 3" are probable for at least four of the 37 stations investigated.

Journal ArticleDOI
TL;DR: In this article, the authors measured the traveling and standing-wave characteristics of a helicon discharge using a five-turn, balanced magnetic probe movable along the discharge axis z, and the damping rate of the helicon wave is consistent with theoretical predictions based on collisions alone.
Abstract: Traveling‐ and standing‐wave characteristics of the wave fields have been measured in a helicon discharge using a five‐turn, balanced magnetic probe movable along the discharge axis z. Helical and plane‐polarized antennas were used, and the magnitude and direction of the static magnetic field were varied, yielding three primary results. (1) As the density varies along z, the local wavelength agrees with the local dispersion relation. (2) Beats in the z variation of the wave intensity do not indicate standing waves, but instead are caused by the simultaneous excitation of two radial eigenmodes. Quantitative agreement with theory is obtained. (3) The damping rate of the helicon wave is consistent with theoretical predictions based on collisions alone.

Journal ArticleDOI
TL;DR: In this paper, a method of deriving the discrete Green function for the analysis of surface acoustic wave propagation and excitation under metallic-grating structures with finite thickness was proposed.
Abstract: This paper proposes a method of deriving the discrete Green function for the analysis of surface acoustic wave (SAW) propagation and excitation under metallic-grating structures with finite thickness. The method uses the finite-element method (FEM) for the analysis of the grating electrode region, while the spectral domain analysis (SDA) is used for the analysis of the substrate region. This approach takes account of the mass-loading effect of grating electrodes as part of electrical quantities in a substrate, and makes it possible to employ Bltekjaer et al.'s theory for rapid computation. Rayleigh SAWs and leaky SAWs propagating under metallic-grating structures on 128°YX- LiNbO3 and 36°YX- LiTaO3 (36-LT), respectively, were analysed. The dispersion relation calculated by the present method agreed very well with that obtained by the perturbation theory. It is also shown that the electromechanical coupling factor for leaky SAWs on 36-LT increases with the thickness of grating electrodes, which is primarily due to the change in the SAW energy concentration near the surface.

Journal ArticleDOI
TL;DR: In this article, the linear stage of the Farley-Buneman instability in the ionospheric E region is reexamined based on a consistent kinetic theory for electrons developed earlier.
Abstract: The linear stage of the Farley-Buneman instability in the ionospheric E region is reexamined. Unlike previous theories, the present analysis is based on a consistent kinetic theory for electrons developed earlier which takes into account such important factors as the non-Maxwellian nature of the perturbed electron distribution, different rates for electron momentum and energy relaxation, and the velocity dependence of the electron-neutral collision frequency. The dispersion relation obtained using this theory is applicable for wave frequencies small compared to the ion-neutral collision frequency and for sufficiently low altitudes where the electron-electron collisions are negligible. The threshold conditions prove to be strongly modified compared to those resulting from the earlier simplified theories. For strong electric fields which can occur in the auroral regions, unstable long-wave waves excited along the bisector between the directions of the electric field E0 and E0×B drift velocity are predicted at low atitudes. The excitation of such waves becomes possible due to a new kinetic mechanism associated with the perturbed electron current caused by the Pedersen conductivity.

Journal ArticleDOI
TL;DR: A method of periodic Green's functions with a propagation factor exp(i/spl beta/x), unknown in advance, was used to calculate dispersion curves and attenuation coefficients for Rayleigh- and leaky- waves propagating in a periodic system of thin electrodes on a piezoelectric surface as mentioned in this paper.
Abstract: A method of periodic Green's functions with a propagation factor exp(i/spl beta/x), unknown in advance, is used to calculate dispersion curves and attenuation coefficients for Rayleigh- and leaky- waves propagating in a periodic system of thin electrodes on a piezoelectric surface. To describe the charge distribution on the electrodes both a step approximation and Chebyshev polynomials are used, the last being more adequate in most cases. Numerically determined values of the Green's function are used and interpolated either linearly or using a modified variant of Ingebrigtsen's formula. Such basic parameters as stopband width, stopband center frequency, wave velocity and attenuation in the stopband are found. These parameters can be used in the coupling-of-modes (COM) analysis and design of SAW devices. The analysis includes bulk wave radiation and scattering. The dependence of the corresponding attenuation coefficient on frequency is determined. Results obtained allow the determination directly and properly of the COM parameters and the design of SAW devices having large number of electrodes most precisely and rapidly. Numerical results for Rayleigh waves on YZ-LiNbO/sub 3/ and leaky waves on 36/spl deg/YX-LiTaO/sub 3/ substrates are presented. >

Journal ArticleDOI
TL;DR: In this article, the joint frequency-wavenumber spectrum is recovered from wavefields measured by two or more satellites via spectral methods based on wavelet transforms, and the impact of nonlinear processes on wave propagation at the Earth's foreshock is revealed.
Abstract: The joint frequency-wavenumber spectrum is one of the basic quantities for analyzing plasma turbulence It is shown how the full spectrum can be recovered from wavefields measured by two or more satellites via spectral methods based on wavelet transforms Compared to standard cross-correlation techniques, different branches in the dispersion relation can be resolved and quasi-stationary wavefields can be accessed Using this new approach, low frequency magnetic field data from the AMPTE-UKS and AMPTE-IRM spacecraft are investigated and the impact of nonlinear processes on wave propagation at the Earth's foreshock is revealed

Journal ArticleDOI
TL;DR: In this article, the Helmholtz free energy and the stress associated with general constitutive equations of a simple continuum are proposed to model dispersive effects of an inherent material characteristic length.
Abstract: Modifications of the Helmholtz free energy and the stress associated with general constitutive equations of a simple continuum are proposed to model dispersive effects of an inherent material characteristic length. These modifications do not alter the usual restrictions on the unmodified constitutive equations imposed by the first and second laws of thermodynamics. The special case of a thermoelastic compressible Newtonian viscous fluid is considered with attention focused on uniaxial strain. Within this context, the linearized problems of wave propagation in an infinite media and free vibrations of a finite column are considered for the simple case of elastic response. It is shown that the proposed model predicts the dispersive effects observed in wave propagation through a chain of springs and masses as the wavelength decreases. Also, the nonlinear problems of steady wave propagation of a soliton in the absence of viscosity and of a shock wave in the presence of viscosity are discussed. In particular it is shown that the presence of the dispersive terms can cause the stress in a shock wave to overshoot the Hugoniot stress by as much as 50%. This phenomenon may cause an underprediction of the threshold level for failure determined by analysis of stress in shock experiments.

Journal ArticleDOI
TL;DR: In this article, a characterization of scattering data for the potentials from the Schwartz class S = C∞(∞)(ℝ2) is given under the small norm assumption, and a family of two-dimensional spherically-symmetric real potentials S transparent at a given energy.
Abstract: For the two-dimensional Schrodinger equation $$[ - \Delta + v(x)]\psi = E\psi , x \in \mathbb{R}^2 , E = E_{fixed} > 0 (*)$$ at a fixed positive energy with a fast decaying at infinity potentialv(x) dispersion relations on the scattering data are given. Under “small norm” assumption using these dispersion relations we give (without a complete proof of sufficiency) a characterization of scattering data for the potentials from the Schwartz classS=C∞(∞)(ℝ2). For the potentials with zero scattering amplitude at a fixed energyEfixed (transparent potentials) we give a complete proof of this characterization. As a consequence we construct a family (parametrized by a function of one variable) of two-dimensional spherically-symmetric real potentials from the Schwartz classS transparent at a given energy. For the two-dimensional case (without assumption that the potential is small) we show that there are no nonzero real exponentially decreasing, at infinity, potentials transparent at a fixed energy. For any dimension greater or equal to 1 we prove that there are no nonzero real potentials with zero forward scattering amplitude at an energy interval. We show that KdV-type equations in dimension 2+1 related with the scattering problem (*) (the Novikov-Veselov equations) do not preserve, in general, these dispersion relations starting from the second one. As a corollary these equations do not preserve, in general, the decay rate faster than |x|−3 for initial data from the Schwartz class.

Journal ArticleDOI
TL;DR: In this paper, the authors analyse how the loss cone feature (as determined by the loss-cone index or indices) influences the growth of instabilities in a fully ionized, homogeneous, hot plasma in a uniform magnetic field.
Abstract: Electromagnetic and electrostatic instabilities driven by loss-cone particle distributions have been invoked to explain a variety of plasma phenomena observed in space and in the laboratory. In this paper we analyse how the loss- cone feature (as determined by the loss-cone index or indices) influences the growth of such instabilities in a fully ionized, homogeneous, hot plasma in a uniform magnetic field. Specifically, we consider three loss-cone distributions: a generalized Lorentzian (kappa) loss-cone distribution, the Dory—Guest—Harris distribution and the Ashour-Abdalla-Kennel distribution (involving a subtracted Maxwellian). Our findings are common to all three distributions. We find that, for parallel propagation, electromagnetic instabilities are only affected by the loss-cone indices in terms of their occurrence in the temperature anisotropy. However, for oblique propagation, even including propagation at small angles to the ambient magnetic field, the loss-cone indices do independently affect the growth of instabilities for electromagnetic waves, in contrast to certain claims in the literature. For electrostatic waves such that 1, where kx is the component of the wave vector perpendicular to the ambient magnetic field and pLa is the Larmor radius for particle species