Generalized Dispersion Relations Research Articles

Low frequency dust acoustic drift instability in the equatorial electrojet

The dust acoustic drift instability has been investigated at the lower electrojet region of the dusty ionosphere by considering a linearized fluid model. The effect of dust-neutral collisions, electron–ion recombination at the surface of the dust particles, and electron and ion inertia on the onset and growth of the instability have been explored in minutiae. The perturbed densities are gleaned from the electron, ion, and dust dynamics, which engendered generalized dispersion relations. The generalized dispersion relation delineates the propagation of low-frequency dust acoustic drift waves. The dispersion relation is solved numerically for various cases of interest at the two different altitudes(∼90km and ∼100km) of the lower electrojet region. It has been found that the instability is unlikely to develop due to recombination alone, similar as observed in the case of laboratory dusty plasma. A significant reduction of the growth rate has been observed in the low-frequency mode due to the dust-neutral collision both in the presence and absence of an equilibrium electron density gradient. However, the effect of dust-neutral collision is not discernible in the relatively higher frequency mode, which exists at an altitude of 100km. Moreover, the presence of electron and ion inertia has a stabilizing effect on the instability. The analysis presented here is germane to the lower ionospheric dusty electrojet region in which electrons are magnetized, but ions and dust particles are unmagnetized.

Low regularity well-posedness of KP-I equations: The three-dimensional case

In this paper low regularity local well-posedness results for the Kadomtsev–Petviashvili–I equation posed in spatial dimension d=3 are proved. Periodic, non-periodic and mixed settings as well as generalized dispersion relations are considered. In the weak dispersion regime these initial value problems show a quasilinear behavior so that bilinear and energy estimates on frequency dependent time scales are used in the analysis.

Causality and passivity: From electromagnetism and network theory to metamaterials

In this review, we take an extensive look at the role that the principles of causality and passivity have played in various areas of physics and engineering, including in the modern field of metamaterials. The aim is not to provide a comprehensive list of references as that number would be in the thousands, but to review the major results and contributions which have animated these areas and to provide a unified framework which could be useful in understanding the developments in different fields. Towards these goals, we chart the early history of the field through its dual beginnings in the analysis of the Sellmeier equation and in Hilbert transforms, giving rise to the far reaching dispersion relations in the early works of Sokhotskii, Plemelj, Kramers, Kronig, and Titchmarsh. However, these early relations constitute a limited result as they only apply to a restricted class of transfer functions. To understand how this restriction can be lifted, we take a quick detour into the distributional analysis of Schwartz, and discuss the dispersion relations in the context of distribution theory. This approach expands the reach of the dispersion analysis to distributional transfer functions and also to those functions which exhibit polynomial growth properties. To generalize the results even further to tensorial transfer functions, we consider the concept of passivity — originally studied in the theory of electrical networks. We clarify why passivity implies causality and present generalized dispersion relations applicable to transfer functions which are distributional, tensorial, and possibly exhibiting polynomial growth. Subsequently, as special cases, we present examples of dispersion relations from several areas of physics including electromagnetism, acoustics, seismology, reflectance measurements, and scattering theory. We discuss sum rules which follow from the infinite integral dispersion relations and also how these integrals may be simplified either by truncating them under appropriate assumptions or by replacing them with derivative relations. These derivative relations, termed derivative analyticity relations, form the basis of the so called nearly-local approximations of the dispersion relations which are extensively employed in many fields including acoustics. Finally, we review the clever applications of ideas from causality and passivity to the recent field of metamaterials. In many ways, these ideas have provided limits to what can be achieved in metamaterial property design and metamaterial device performance.

Ordinary and extraordinary waves in hot nonextensive plasma

In this paper, a kinetic method based on particle velocity distribution function in the context of the nonextensive Tsallis statistics is presented for ordinary and extraordinary waves in a collisionless magnetized hot plasma. The components of the generalized dielectric tensor for perpendicular propagation in hot nonextensive plasma are derived in terms of generalized hypergeometric functions. The components are expressed as functions of different values of the nonextensive parameter q, which quantifies the degree of nonextensivity of the system. The dispersion relations of ordinary and extraordinary waves in hot plasma are obtained in the context of the nonextensive statistics. It is shown that in hot nonextensive plasma the generalized dispersion relations of these waves depend on q parameter, which means that the initial distribution function alters the properties of ordinary and extraordinary waves. For the hot nonextensive plasma, the ordinary and extraordinary wave experience resonances at cyclotron harmonics, whilst the upper hybrid resonance is eliminated due to thermal effects. However, cutoff frequencies shift to higher values as q parameter increases.

Dispersion relations for unphysical particles

Generalized dispersion relations are discussed for unphysical particles, e.g. confined degrees of freedom that are not present in the physical spectra but can give rise to observable bound states. While in general the propagator of the unphysical particles can have complex poles and cannot be reconstructed from the knowledge of the imaginary part, under reasonable assumptions the missing piece of information is shown to be in the rational function that contains the poles and must be added to the integral representation. For pure Yang-Mills theory, the rational part and the spectral term are identified in the explicit analytical expressions provided by the massive expansion of the gluon propagator. The multi particle spectral term turns out to be very small and the simple rational part provides, from first principles, an approximate propagator that is equivalent to the tree-level result of simple phenomenological models like the refined Gribov-Zwanziger model.

Breaking soliton equations and negative-order breaking soliton equations of typical and higher orders

We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models. We establish the distinct dispersion relation for each equation. We use the simplified Hirota’s method to obtain multiple soliton solutions for each developed breaking soliton equation. We also develop generalized dispersion relations for the typical breaking soliton equations and the generalized negative-order breaking soliton equations. The results provide useful information on the dynamics of the relevant nonlinear negative-order equations.

Characteristics of surface plasmon polaritons in a dielectrically chiral-metal-chiral waveguiding structure.

We demonstrate theoretically the characteristics of surface plasmon polaritons (SPPs) with an asymmetric chiral-metal-chiral (CMC) waveguide structure, under realistic frequency dependencies of the permittivity and chirality parameters. Generalized dispersion relations are derived which can be applied to the nonchiral SPPs. We find that the existence of cutoffs in different modes for the CMC structures may facilitate the design of mode-selective surface plasmon waveguides. CMC-SPPs also exhibit an interesting dependence of the polarization on the chiral strength. These novel characteristics of CMC-SPPs provide new possibilities for the design of more compact nanophotonic devices.

Generalized permittivity tensor for the description of waves in general relativistic plasma around a Schwarzschild black hole

The effects of gravitation on the permittivity tensor in the relativistic electron--positron or ions plasma in a frame of reformulated relativistic two-fluid equations by gravitational effects due to the event horizon using the 3 + 1 formalism of general relativity are investigated. The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The elements of the generalized permittivity tensor in this configuration are obtained. It is shown that the permittivity tensor could be written as a summation of two parts: Hermitian and non-Hermitian parts. Furthermore, the generalized dispersion relations are investigated for transverse and longitudinal modes. In the absence of gravitation effects, correctness of the obtained results is confirmed.

Quantum multiresolution: tower of scales

We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like equations. The numerical simulation demonstrates the formation of various (meta) stable patterns or orbits generated by internal hidden symmetry from generic high-localized fundamental modes. In addition, we can control the type of behaviour on the pure algebraic level by means of properly reduced algebraic systems (generalized dispersion relations).

Computation of generalized and exact dispersion relations for longitudinal plasma waves in nonextensive statistics and the effects of the nonextensivity on the oscillation modes and damps

We have derived generalized dispersion relations for longitudinal waves in collisionless thermal plasma using linear Vlasov-Poisson kinetic model and nonextensive distributions for electrons. The Maxwellian limit of the dispersion relations, where the q-nonextensive parameter tends to one, is calculated. The generalized dispersion relations are reduced to polynomials for some specific values of q. The well-known modes of oscillations such as the Langmuir and electron acoustic waves have been obtained by solving the dispersion relations. Some new modes of oscillation are also found. Finally, the dependence of the oscillation modes and damps on q is discussed.

Study of high frequency parallel propagating modes in a weakly magnetized relativistic degenerate electron plasma

Using the Vlasov-Maxwell’s model, the generalized dispersion relations for parallel propagating electromagnetic modes (R- and L-waves) and electrostatic mode (Langmuir wave) for weakly magnetized relativistic degenerate plasma are derived. The propagation characteristics of these modes are analyzed both analytically and graphically in order to highlight the relativistic and the ambient magnetic field effects in different degenerate plasma environments. Furthermore, the analytical expressions of these modes are extracted for the limiting cases, i.e., non-relativistic (pF/moc≪1) and ultra-relativistic (pF/moc≫1). It is noted that the relativistic effects shift the cut-off point towards the lower value of frequency and resultantly broaden the propagation domain. Moreover, the cut-off point of R-wave/L-wave move towards the higher/lower frequency as the strength of ambient magnetic field is increased. The shifting of frequency due to the ambient magnetic field becomes more prominent in the non-relativistic regime than in the highly relativistic one because the relativistic effect suppresses the contribution of the ambient magnetic field.

Linear stability of the 1D Saint-Venant equations and drag parameterizations

The stability of the homogeneous and steady flow based on the one-dimensional Saint-Venant equations for free surface and shallow-water flows of constant slope is derived and displayed through graphs. With a suitable choice of units, the small and large drag limits, respectively, correspond to the small and large spatio-temporal scales of a linear system only controlled by the Froude number and two other dimensionless numbers associated with the bottom drag parameterization. Between the small drag limit, with the two families of marginal and non-dispersive shallow-water waves, and the large drag limit, with the marginal and non-dispersive waves of the kinematic wave approximation, dispersive roll waves are detailed. These waves are damped or amplified, depending on the value of the three control parameters. The spatial generalized dispersion relations are also derived indicating that the roll-wave instability is of the convective type for all drag parameterizations.

Robust Causality Characterization via Generalized Dispersion Relations

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The self-consistency of frequency responses obtained via numerical simulations or measurements is of paramount importance in the analysis and design of linear systems. In particular, tabulated responses with flaws and causality violations have been demonstrated to be the root cause for numerical problems and unreliability in modeling and simulation tasks. In this work, we present the generalized dispersion relations as a robust and reliable tool for the causality characterization of frequency responses. Several applications are presented, including causality and passivity verification for tabulated data and causality-controlled interpolation schemes. Practical examples illustrate the excellent performance of the proposed techniques. </para>

Ducted compressional waves in the magnetosphere in the double-polytropic approximation

Abstract. Small-amplitude compressional magnetohydrodynamic-type waves are studied in the magnetosphere. The magnetosphere is treated as a rarefied plasma with anisotropy in the kinetic pressure distribution. The parallel and perpendicular pressures are defined by general polytropic pressure laws. This double-polytropic model can be considered as a natural extension of the magnetohydrodynamic (MHD) model when the plasma is collisionless. Generalized dispersion relations for surface and body waves are derived and analyzed for an isolated magnetic slab. The waves are confined to the slab. For specific polytropic indices, the results obtained in the (i) Chew-Goldberger-Low (CGL) double-adiabatic and (ii) double-isothermal approximations are recovered.Key words. Magnetospheric physics (MHD waves and in-stabilities; plasma sheet; plasma waves and instabilities)

Generalized dispersive Alfvén waves

Generalized dispersion relations for Alfvén waves are derived, accounting for arbitrary values of ω/ωci, k⊥ρi, and k⊥λe, where ω(ωci) is the wave (ion gyro) frequency, k⊥ = 2π/λ⊥ the perpendicular (to the external magnetic field line) wavenumber, and ρi(λe) the ion gyroradius (electron skin depth). Our dispersion relations are appropriate for deducing the relationships of the dispersive (inertial and kinetic) Alfvén waves with other plasma modes. The present results can be considered as a prerequisite for understanding some salient features of the broadband electromagnetic/electrostatic waves that are frequently observed by the Freja and FAST spacecraft in the auroral zone of the Earth's ionosphere.

Dispersion Theory for Two-phase Layered-Geometry Nanocomposites

A dispersion theory for linear optical properties of two-phase layered-geometry nanocomposites is presented. Generalized dispersion relations and sum rules are stated using the results from complex analysis. The concept of Lorentzian linear susceptibility is exploited in theoretical treatment of the effective linear susceptibility of the nanocomposite. The meromorphism of total reflectance in the case of effective meromorphic nonlinear susceptibility was observed.

Localized tearing modes in the magnetotail driven by curvature effects

The stability of collisionless tearing modes is examined in the presence of curvature drift resonances and the trapped particle effects. A kinetic description for both electrons and ions is employed to investigate the stability of a two‐dimensional equilibrium model. The main features of the study are to treat the ion dynamics properly by incorporating effects associated with particle trajectories in the tail fields and to include the linear coupling of trapped particle modes. Generalized dispersion relations are derived in several parameter regimes by considering two important sublayers of the reconnecting region. For a typical choice of parameters appropriate to the current sheet region, we demonstrate that localized tearing modes driven by ion curvature drift resonance effects are excited in the current sheet region with growth time of the order of a few seconds. Also, we examine nonlocal characteristics of tearing modes driven by curvature effects and show that modes growing in a fraction of a second arise when mode widths are larger than the current sheet width. Further, we show that trapped particle effects, in an interesting frequency regime, significantly enhance the growth rate of the tearing mode. The relevance of this theory for substorm onset phase and other features of the substorms is briefly discussed.

Characterization of thin films using generalized lamb wave dispersion relations

Note: Part 3 Reference LNNME-ARTICLE-1993-002View record in Web of Science Record created on 2007-04-23, modified on 2016-08-08

Generalized dispersion relations for nonlinear slab-guided waves

The propagation of nonlinear guided waves in a slab configuration with arbitrary intensity-dependent dielectric functions is considered. General expressions for the dispersion relations and the guided power flux are derived without explicit integration of the nonlinear Helmholtz equations. One example is investigated in greater detail.

Generalized Dispersion Relations for Surface Polaritons in Uniaxial Antiferromagnetic Crystals

physica status solidi (b)Volume 126, Issue 2 p. K131-K134 Short Note Generalized Dispersion Relations for Surface Polaritons in Uniaxial Antiferromagnetic Crystals N. B. Ivanov, N. B. Ivanov Section of Low Temperature Physics, Department of Physics, Moscow State University Search for more papers by this author N. B. Ivanov, N. B. Ivanov Section of Low Temperature Physics, Department of Physics, Moscow State University Search for more papers by this author First published: 1 December 1984 https://doi.org/10.1002/pssb.2221260242Citations: 2 11 7234 Moscow, USSR. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume126, Issue21 December 1984Pages K131-K134 RelatedInformation