Showing papers on "Dispersion relation published in 2007"

Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror

Abstract: Conventional surface plasmons have a wave vector exceeding that of light in vacuum, and therefore cannot be directly excited by light that is simply incident on the surface. However, we propose that a plasmon-polariton state can be formed at the boundary between a metal and a dielectric Bragg mirror that can have a zero in-plane wave vector and therefore can be produced by direct optical excitation. In analogy with the electronic states at a crystal surface proposed by Tamm, we call these excitations Tamm plasmons, and predict that they may exist in both the TE and TM polarizations and are characterized by parabolic dispersion relations.

Space-time dispersion of graphene conductivity

Abstract: We present an analytic calculation of the conductivity of pure graphene as a function of frequency ω, wave-vector k, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter γ≃3 eV, but much larger than the collision rate τ-1. The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for kv0≪ T≪ω is equal to σ(ω,k)=e2/4ħ and independent of the band structure parameters γ and v0. Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure.

Linear and nonlinear ion-acoustic waves in an unmagnetized electron-positron-ion quantum plasma

Abstract: The linear and nonlinear properties of the ion-acoustic waves (IAWs) are investigated by using the quantum hydrodynamic equations together with the Poisson equation in a three-component quantum electron-positron-ion plasma. For this purpose, a linear dispersion relation, a Korteweg-de Vries equation and an energy equation containing quantum corrections are derived. Computational investigations have been performed to examine the quantum mechanical effects on the linear and nonlinear waves. It is found that both the linear and nonlinear properties of the IAWs are significantly affected by the inclusion of the quantum corrections. The relevance of the present investigation to dense white dwarfs (where the electron-positron annihilation can be unimportant) is discussed.

Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes

Abstract: Wave propagation in carbon nanotubes (CNTs) is studied based on the proposed nonlocal elastic shell theory. Both theoretical analyses and numerical simulations have explicitly revealed the small-scale effect on wave dispersion relations for different CNT wavenumbers in the longitudinal and circumferential directions and for different wavelengths in the circumferential direction. The applicability of the proposed nonlocal elastic shell theory is especially explored and analyzed based on the differences between the wave solutions from local and nonlocal theories in numerical simulations. It is found that the newly proposed nonlocal shell theory is indispensable in predicting CNT phonon dispersion relations at larger longitudinal and circumferential wavenumbers and smaller wavelength in the circumferential direction when the small-scale effect becomes dominant and hence noteworthy. In addition, the asymptotic frequency, phase velocities and cut-off frequencies are also derived from the nonlocal shell theory. Moreover, an estimation of the scale coefficient is provided based on the derived asymptotic frequency. The research findings not only demonstrate great potential of the proposed nonlocal shell theory in studying vibration and phonon dispersion relations of CNTs but also signify limitations of local continuum mechanics in analysis of small-scale effects, and thus are of significance in promoting the development of nonlocal continuum mechanics in the design of nanostructures.

Negative birefraction of acoustic waves in a sonic crystal.

Abstract: Optical birefringence and dichroism are classical and important effects originating from two independent polarizations of optical waves in anisotropic crystals1. Furthermore, the distinct dispersion relations of transverse electric and transverse magnetic polarized electromagnetic waves in photonic crystals can lead to birefringence more easily2,3,4,5,6. However, it is impossible for acoustic waves in the fluid to show such a birefringence because only the longitudinal mode exists. The emergence of an artificial sonic crystal (SC) has significantly broadened the range of acoustic materials in nature7,8,9,10,11,12,13,14,15,16,17,18 that can give rise to acoustic bandgaps and be used to control the propagation of acoustic waves. Recently, negative refraction has attracted a lot of attention and has been demonstrated in both left-handed materials and photonic crystals19,20,21,22,23,24,25,26. Similar to left-handed materials and photonic crystals, negative refractions have also been found in SCs14,15,16,17,18. Here we report, for the first time, the acoustic negative-birefraction phenomenon in a two-dimensional SC, even with the same frequency and the same ‘polarization’ state. By means of this feature, double focusing images of a point source have been realized. This birefraction concept may be extended to other periodic systems corresponding to other forms of waves, showing great impacts on both fundamental physics and device applications.

On the Spectra of Carbon Nano-Structures

Abstract: An explicit derivation of dispersion relations and spectra for periodic Schrodinger operators on carbon nano-structures (including graphene and all types of single-wall nano-tubes) is provided.

The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for maxBCG Galaxy Clusters

Abstract: The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG-galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202 ± 10 km s-1 for small groups to more than 854 ± 102 km s-1 for large clusters. We show the scatter to be at most 40.5% ± 3.5%, declining to 14.9% ± 9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within 1 σ of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass-observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus, our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.

Re-visiting the relations: Galactic thin disc age-velocity dispersion relation

Abstract: The velocity dispersion of stars in the solar neighbourhood thin disc increases with time after star formation. Nordstrom et al. (2004) is the most recent observational attempt to constrain the age-velocity dispersion relation. They fitted the age-velocity dispersion relations of each Galactic cardinal direction space velocity component, U (towards the Galactic centre), V (in the direction of Galactic rotation) and W (towards the North Galactic Pole), with power laws and interpreted these as evidence for continuous heating of the disc in all directions throughout its lifetime. We re-visit these relations with their data and use Famaey et al. (2005) to show that structure in the local velocity distribution function distorts the in-plane (U and V) velocity distributions away from Gaussian so that a dispersion is not an adequate parametrization of their functions. The age-sigma(W) relation can however be constrained because the sample is well phase-mixed vertically. We do not find any local signature of the stellar warp in the Galactic disc. Vertical disc heating does not saturate at an early stage. Our new result is that a power law is not required by the data: disc heating models that saturate after ~ 4.5 Gyr are equally consistent with observations.

Collective spin modes in monodimensional magnonic crystals consisting of dipolarly coupled nanowires

Abstract: Magnetization dynamics of dipolarly coupled nanowire arrays has been studied by Brillouin light scattering. Measurements performed in uniformly magnetized wires as a function of the transferred wave vector demonstrated the existence of several discrete collective modes, propagating through the structure with a periodic dispersion curve encompassing several Brillouin zones relative to the artificial spatial periodicity. This experimental evidence has been quantitatively explained by a theoretical model which permits the calculation of the dispersion relation for collective modes in patterned arrays through the numerical solution of an eigenvalue problem for an integral operator.

Revisiting the relations: Galactic thin disc age–velocity dispersion relation

Abstract: The velocity dispersion of stars in the solar neighbourhood thin disc increases with time after star formation. NordstrA¶m et al. performed the most recent observations to constrain the age–velocity dispersion relation. They fitted the age–velocity dispersion relations of each Galactic cardinal direction space velocity component, U (towards the Galactic Centre), V (in the direction of Galactic rotation) and W (towards the North Galactic Pole), with power laws and interpreted these as evidence for continuous heating of the disc in all directions throughout its lifetime. We revisit these relations with their data and use the results of Famaey et al. to show that structure in the local velocity distribution function distorts the in-plane (U and V) velocity distributions away from Gaussian so that a dispersion is not an adequate parametrization of their functions. The age'? W relation can however be constrained because the sample is well phase-mixed vertically. We do not find any local signature of the stellar warp in the Galactic disc. Vertical disc heating does not saturate at an early stage. Our new result is that a power law is not required by the data: disc heating models that saturate after ?4.5 Gyr are equally consistent with observations.

Damping of oscillations by ion-neutral collisions in a prominence plasma

Abstract: Aims. The role of collisions between ions, electrons and neutrals in a partially ionised plasma is assessed as a possible wave damping mechanism. The relevance of this mechanism in the damping of small amplitude prominence oscillations is evaluated. Methods. A one-fluid MHD set of equations taking into account various effects in a partially ionised solar plasma (collisions between different species and Joule dissipation) is derived. Assuming small perturbations, these equations are next linearised about a uniform equilibrium configuration and the dispersion relation of magnetoacoustic waves in an unbounded medium is obtained. Results. The presence of neutrals in the plasma only affects the fast wave in a relevant way. An approximate expression for the damping rate is obtained which shows that the strongest damping takes place in a medium with strong magnetic field, low density and low ionisation fraction. Wave attenuation arises mostly from collisions between ions and neutrals. Conclusions. Given the poor knowledge about the values of the density and ionisation fraction in prominences, it is hard to judge the importance of the physics of partial ionisation in the damping of fast waves in solar prominences. Nevertheless, note that a very idealised case, with no stratification and no equilibrium currents, is considered here, so the addition of these features to the model may change the results of this work.

Quantum Ion-Acoustic Waves in Single-Walled Carbon Nanotubes Studied with a Quantum Hydrodynamic Model

Abstract: The quantum ion-acoustic waves in single-wall carbon nanotubes are studied with the quantum hydrodynamic model, in which the electron and ion components of the nanotubes are regarded as a two-species quantum plasma system. An analytical expression of the dispersion relation is obtained for the linear disturbance. Numerical results show that the frequency of the ion-acoustic wave strongly depends on the nanotube's radius in the long-wavelength cases.

The nature of running penumbral waves revealed

Abstract: We seek to clarify the nature of running penumbral (RP) waves: are they chromospheric trans-sunspot waves or a visual pattern of upward-propagating waves? Full Stokes spectropolarimetric time series of the photospheric Si I λ10827 line and the chromospheric He I λ10830 multiplet were inverted using a Milne-Eddington atmosphere. Spatial pixels were paired between the outer umbral/inner penumbral photosphere and the penumbral chromosphere using inclinations retrieved by the inversion and the dual-height pairings of line-of-sight velocity time series were studied for signatures of wave propagation using a Fourier phase difference analysis. The dispersion relation for radiatively cooling acoustic waves, modified to incorporate an inclined propagation direction, fits well the observed phase differences between the pairs of photospheric and chromospheric pixels. We have thus demonstrated that RP waves are in effect low-β slow-mode waves propagating along the magnetic field.

Analysis and Numerical Approximation of an Integro-differential Equation Modeling Non-local Effects in Linear Elasticity

Abstract: Long-range interactions for linearly elastic media resulting in nonlinear dispersion relations are modeled by an initial-value problem for an integro-differential equation (IDE) that incorporates non-local effects. Interpreting this IDE as an evolutionary equation of second order, well-posedness in L ∞(ℝ) as well as jump relations are proved. Moreover, the construction of the micromodulus function from the dispersion relation is studied. A numerical approximation based upon quadrature is suggested and carried out for two examples, one involving jump discontinuities in the initial data corresponding to a Riemann-like problem.

Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation

Abstract: The relaxation of a dewetting contact line is investigated theoretically in the so-called ‘Landau–Levich’ geometry in which a vertical solid plate is withdrawn from a bath of partially wetting liquid. The study is performed in the framework of lubrication theory, in which the hydrodynamics is resolved at all length scales (from molecular to macroscopic). We investigate the bifurcation diagram for unperturbed contact lines, which turns out to be more complex than expected from simplified ‘quasi-static’ theories based upon an apparent contact angle. Linear stability analysis reveals that below the critical capillary number of entrainment, Cac, the contact line is linearly stable at all wavenumbers. Away from the critical point, the dispersion relation has an asymptotic behaviour σ∝|q| and compares well to a quasi-static approach. Approaching Cac, however, a different mechanism takes over and the dispersion evolves from ∼|q| to the more common ∼q2. These findings imply that contact lines cannot be described using a universal relation between speed and apparent contact angle, but viscous effects have to be treated explicitly.

The low energy electronic band structure of bilayer graphene

Abstract: We employ the tight binding model to describe the electronic band structure of bilayer graphene and we explain how the optical absorption coefficient of a bilayer is influenced by the presence and dispersion of the electronic bands, in contrast to the featureless absorption coefficient of monolayer graphene. We show that the effective low energy Hamiltonian is dominated by chiral quasiparticles with a parabolic dispersion and Berry phase 2π. Layer asymmetry produces a gap in the spectrum but, by comparing the charging energy with the single particle energy, we demonstrate that an undoped, gapless bilayer is stable with respect to the spontaneous opening of a gap. Then, we describe the control of a gap in the presence of an external gate voltage. Finally, we take into account the influence of trigonal warping which produces a Lifshitz transition at very low energy, breaking the isoenergetic line about each valley into four pockets.

Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains

Abstract: The dispersion relations of the surface plasmon modes of metal nanoparticle chains are measured, and compared with theory. The theoretical model includes the effects of retardation, radiative damping and dynamic depolarization due to the finite size of the nanoparticles. The results reveal that, in addition to one longitudinal and one transverse mode, there is a third mode, which has not been previously reported.

The Weibel instability in relativistic plasmas. I. Linear theory

Abstract: Aims. We discuss the linear theory of the Weibel instability in a relativistic plasma driven by ultra-relativistic beams, describing the physics of the generation of magnetic fields in the ultra-relativistic shocks associated with Gamma Ray Bursts (GRBs). We perform a detailed analysis of the linear dispersion relation for the benefit of non-linear calculations that we discuss in the companion paper. Methods. We use a covariant approach, where the linear response of the beam-plasma system is determined from the polarization tensor. This tensor relates the four-current density to the four-potential of the electromagnetic field. Showing that two approaches, one based on a fluid model and one on a kinetic description that uses a waterbag distribution for the phase-space density of the beam particles, yield essentially the same result, we compare our results to those obtained by other approaches. We mainly consider the symmetric case of two counterstreaming (but otherwise identical) beams. Results. We show that the effect of an asymmetry in the beam densities is small for typical parameters, and briefly discuss the effect of an ambient magnetic field. The dispersion relation of the Weibel instability driven by ultra-relativistic beams is rather insensitive to the model used to describe the plasma. The properties of the instability, such as the growth rate and the range of unstable wavelengths, are governed by only two parameters: the ratio of the plasma frequency squared of the beam and hot background plasma, and a “Mach number”, which is essentially the ratio of the beam momentum and the momentum associated with thermal velocity (∼sound speed) in the beam plasma. We also show that, at least for the parameters associated with the ultra-relativistic shocks in GRBs, the influence of the magnetic field is small, and the results for an unmagnetized plasma can be used. Conclusions.

World-sheet scattering in AdS_5 x S^5 at two loops

Abstract: We study the AdS_5 x S^5 sigma-model truncated to the near-flat-space limit to two-loops in perturbation theory. In addition to extending previously known one-loop results to the full SU(2|2)^2 S-matrix we calculate the two-loop correction to the dispersion relation and then compute the complete two-loop S-matrix. The result of the perturbative calculation can be compared with the appropriate limit of the conjectured S-matrix for the full theory and complete agreement is found.

Ion acoustic solitary wave with weakly transverse perturbations in quantum electron-positron-ion plasma

Abstract: The characteristics and stability of ion acoustic solitary wave with transverse perturbations are examined in ultracold quantum magnetospheric plasma consisting of electrons, positrons, and ions. Using the quantum hydrodynamic model, a dispersion relation in the linear regime, and the Kadomtsev-Petviashvili equation in the nonlinear regime are derived. The quantum corrections are studied through quantum statistics and diffraction effects. It is found that compressive solitary wave can propagate in this system. The quantum effects are also studied graphically for both linear and nonlinear profiles of ion acoustic wave. Using energy consideration method, conditions for existence of stable solitary waves are obtained. It is found that stable solitary waves depend on quantum corrections, positron concentration, and direction cosine of the wave vector k along the x axis.

Rossby waves in "shallow water" magnetohydrodynamics

Abstract: Aims. The influence of a toroidal magnetic field on the dynamics of Rossby waves in a thin layer of ideal conductive fluid on a rotating sphere is studied in the “shallow water” magnetohydrodynamic approximation for the first time. Methods. Dispersion relations for magnetic Rossby waves are derived analytically in Cartesian and spherical coordinates. Results. It is shown that the magnetic field causes the splitting of low order (long wavelength) Rossby waves into two different modes, here denoted fast and slow magnetic Rossby waves. The high frequency mode (the fast magnetic Rossby mode) corresponds to an ordinary hydrodynamic Rossby wave slightly modified by the magnetic field, while the low frequency mode (the slow magnetic Rossby mode) has new and interesting properties since its frequency is significantly smaller than that of the same harmonics of pure Rossby and Alfven waves.

Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron-positron-ion plasmas

Abstract: The nonlinear amplitude modulation of electromagnetic waves propagating in pair plasmas, e.g., electron-positron or fullerene pair-ion plasmas, as well as three-component pair plasmas, e.g., electron-positron-ion plasmas or doped (dusty) fullerene pair-ion plasmas, assuming wave propagation in a direction perpendicular to the ambient magnetic field, obeying the ordinary (O-) mode dispersion characteristics. Adopting a multiple scales (reductive perturbation) technique, a nonlinear Schrodinger-type equation is shown to govern the modulated amplitude of the magnetic field (perturbation). The conditions for modulation instability are investigated, in terms of relevant parameters. It is shown that localized envelope modes (envelope solitons) occur, of the bright- (dark-) type envelope solitons, i.e., envelope pulses (holes, respectively), for frequencies below (above) an explicit threshold. Long wavelength waves with frequency near the effective pair plasma frequency are therefore unstable, and may evolve into bright solitons, while higher frequency (shorter wavelength) waves are stable, and may propagate as envelope holes.

Collisionless magnetohydrodynamics with gyrokinetic effects

Abstract: Anisotropic magnetohydrodynamics equations, which also capture the dynamics of quasi-transverse small scales obeying the gyrokinetic ordering, are derived using fourth-rank moment closures, based on a refined description of linear Landau damping and finite Larmor radius (FLR) corrections. This “FLR-Landau fluid model” reproduces the dispersion relation of low-frequency waves, up to scales that, in the case of quasi-transverse kinetic Alfven waves, can be much smaller than the ion gyroradius. The mirror instability, which requires temperature anisotropy, is also captured, together with its quenching at small scales. This model that accurately reproduces the collisionless dissipation of low-frequency modes, should provide an efficient tool to simulate mesoscale turbulence in a magnetized collisionless plasma.