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Dispersion Relation (dispersion + relation)
Selected AbstractsDispersion relation of the optical phonon frequencies in AlN/GaN superlatticesPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 7 2005S.K. Medeiros Abstract In this work we study the dispersion relation of the phonon frequencies in heterojunctions composed by III-V nitride materials (GaN and AlN). We are concerned with the superlattice structure, namely /substrate /AlN /AlxGa1,xN/GaN/AlxGa1,xN/,, where the substrate is here considered to be a transparent dielectric medium like sapphire. We make use of a model based on the Fröhlich Hamiltonian, taking into account the macroscopic theory known as the continuum dielectric model. The optical phonon modes are modelled considering only the electromagnetic boundary conditions, in the absence of charge transfer between ions. Numerical results of the confined optical phonon dispersion are presented, characterizing three distinct optical phonon classes designated as interface (IF), half-space (HS) and propagating (PR) modes. Furthermore, due to the dielectric anisotropy presented in the nitride, some additional peculiarities will be presented, like dispersive confined modes. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Dispersion of Dust Acoustic Modes and Perturbations of Plasma Flux BalanceCONTRIBUTIONS TO PLASMA PHYSICS, Issue 3 2007V. Tsytovich Abstract Previous considerations of dust acoustic waves is demonstrated to be inconsistent - the required equilibrium state for perturbations was not defined since balance of plasma fluxes was neglecting. The self-consistent treatment shows that plasma flux perturbations are accompanying any collective waves propagating in dusty plasmas and can play an important role in wave dispersion, wave damping and can create instabilities. This is illustrated by the derivation of dispersion relation for dust acoustic modes taking into account the plasma flux balances and plasma flux perturbations by waves. The result of this approach shows that the dust acoustic waves with linear dependence of wave frequency on the wave number exist only in restricted range of the wave numbers. Only for wave numbers larger than some critical wave number for low frequency modes the frequency can be have approximately a linear dependence on wave number and can be called as dust acoustic wave but the phase velocity of these waves is different from that which can be obtained neglecting the flux balance and depends on grain charge variations which are determined by the balance of fluxes. The presence of plasma fluxes previously neglected is the main typical feature of dusty plasmas. The dispersion relation in the range of small wave numbers is found to be mainly determined by the change of the plasma fluxes and is quite different from that of dust acoustic type, namely it is found to have the same form as the well known dispersion relation for the gravitational instability. This result proves in general way the existence of the collective grain attractions of negatively charged grains for for large distances between them and for any source of ionization. The attraction of grains found from dispersion relation of the dust acoustic branch coincides with that found previously for pair grain interactions using some models for the ionization source. For the existing experiments the effective Jeans length for such attraction is estimated to be about 8 , 10 times larger than the ion Debye length and the effective gravitational constant for the grain attraction is estimated to be several orders of magnitude larger than the usual gravitational constant. The grain attraction at large inter-grain distances described by the gravitationlike grain instability is considered as the simplest explanation for observed dust cloud clustering, formation of dust structures including the plasma crystals. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Giant magnons on , deformed AdS5 × S5FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 4-5 2008R.C. Rashkov Abstract In this short note we report on the dispersion relation of a new magnon type string solution in , deformed AdS5 × S5 background. Our magnon solution has one spin in AdS5 part and two in S5 part of the background. [source] Field theory on a non-commutative plane: a non-perturbative studyFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5 2004F. Hofheinz Abstract The 2d gauge theory on the lattice is equivalent to the twisted Eguchi,Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. The large N double scaling limit corresponds to the continuum limit of non-commutative gauge theory, so the observed large N scaling demonstrates the non-perturbative renormalizability of this non-commutative field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter. Next we investigate the 3d ,,4 model with two non-commutative coordinates and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d = 4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns. We further present results for the correlators and the dispersion relation. In non-commutative field theory the Lorentz invariance is explicitly broken, which leads to a deformation of the dispersion relation. In one loop perturbation theory this deformation involves an additional infrared divergent term. Our data agree with this perturbative result. We also confirm the recent observation by Ambjø rn and Catterall that stripes occur even in d = 2, although they imply the spontaneous breaking of the translation symmetry. [source] Non-commutative field theories beyond perturbation theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003W. Bietenholz We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we measure Wilson loops in 2d NC gauge theory of rank 1. It turns out that they are non-perturbatively renormalizable, and the phase follows an Aharonov-Bohm effect if we identify , = 1/B. Next we study the 3d , ,4 model with two NC coordinates, where we present new results for the correlators and the dispersion relation. We further reveal the explicit phase diagram. The ordered regime splits into a uniform and a striped phase, as it was qualitatively conjectured before. We also confirm the recent observation by Ambjø rn and Catterall that such stripes occur even in d = 2, although they imply the spontaneous breaking of translation symmetry. However, in d = 3 and d = 2 we observe only patterns of two stripes to be stable in the range of parameters investigated. [source] Dispersion analysis of the least-squares finite-element shallow-water systemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003D. Y. Le Roux Abstract The frequency or dispersion relation for the least-squares mixed formulation of the shallow-water equations is analysed. We consider the use of different approximation spaces corresponding to co-located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the dispersion of a non-orthogonal TLM cellINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 3 2008Zaiqing Li Abstract The numerical dispersion of a non-orthogonal transmission line matrix (TLM) algorithm is for the first time investigated. First of all, the dispersion relation is derived in the most general possible case. Then, the validation is carried out in the analysis of a simple one-dimensional example. Results show that the theory is in excellent agreement with the numerical simulation. Numerical results concerning various cell shape dispersion characteristics are presented and show some relatively weak numerical dispersion even for rather highly distorted cells. Finally, some indications concerning cell shape selection to minimize the non-orthogonal TLM cell are proposed. Copyright © 2007 John Wiley & Sons, Ltd. [source] Floating ladder track response to a steadily moving load,MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2007Roger J. Hosking Abstract Floating ladder rail tracks, which can significantly reduce traffic vibration and noise, have already been installed at several railway sites in and around Tokyo. The steel rails are fixed onto successive ladder-like sections with two parallel longitudinal reinforced concrete sleepers, which are then mounted upon discrete resilient supports on a concrete bed. A simple mathematical model in which a continuous horizontal Bernoulli,Euler beam on periodic discrete elastic supports represents each floating ,combined rail' (i.e. rail and longitudinal sleeper), used earlier to discuss the low-frequency free vibrations in the system, is again adopted to investigate the response due to a steadily moving load. We demonstrate that Fourier transforms can be invoked to obtain the forced deflexion, which depends upon the load speed. A contribution from the periodic supports determines the steady component of the deflexion moving with the load, and the other contributions from the supports produce oscillations. As is the case for a load moving over a beam or plate with continuous support, the response may be characterized using the free flexural wave dispersion relation,although there is now a countably infinite number of dispersion curves, corresponding to the existence of propagation bands in the periodic structure. The lowest wavenumber local minimum in the phase speed (coincident with the group speed) defines the primary critical load speed of most interest, at which the magnitude of the steady component accompanying the moving load becomes large. This primary critical load speed depends upon the relative elasticity of the discrete supports, which must not be too low if the floating ladder track is to be safe for fast rail systems. Copyright © 2007 John Wiley & Sons, Ltd. [source] Left-handed characteristic analysis of a split-ring resonator defected ground structure transmisson lineMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 10 2007Bian Wu Abstract The left-handed properties of a split-ring resonator defected ground structure transmission line (TL) is investigated in this article. Then the transmission zero location, dispersion relation, impedance characteristic as well as refraction index are derived in detail. The numerical and measurement results validate that, this type of TL unit has the left-handed properties with transmission zero. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2599,2602, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22752 [source] A kinetic approach to cosmic-ray-induced streaming instability at supernova shocksMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2009E. Amato ABSTRACT We show that a purely kinetic approach to the excitation of waves by cosmic rays in the vicinity of a shock front leads to predict the appearance of a non-Alfvénic fast-growing mode which has the same dispersion relation as that previously found by Bell in 2004 by treating the plasma in the magnetohydrodynamic approximation. The kinetic approach allows us to investigate the dependence of the dispersion relation of these waves on the microphysics of the current which compensates the cosmic ray flow. We also show that a resonant and a non-resonant mode may appear at the same time and one of the two may become dominant on the other depending on the conditions in the acceleration region. We discuss the role of the unstable modes for magnetic field amplification and particle acceleration in supernova remnants at different stages of the remnant evolution. [source] Surface trapping and leakage of low-frequency g modes in rotating early-type stars , I. Qualitative analysisMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2000R. H. D. Townsend A qualitative study of the surface trapping of low-frequency non-radial g modes in rotating early-type stars is undertaken within the Cowling, adiabatic and traditional approximations. A dispersion relation describing the local character of waves in a rotating star is derived; this dispersion relation is then used to construct propagation diagrams for a 7-M, stellar model, which show the location and extent of wave trapping zones inside the star. It is demonstrated that, at frequencies below a cut-off, waves cannot be fully trapped within the star, and will leak through the surface. Expressions for the cut-off frequency are derived in both the non-rotating and rotating cases; it is found from these expressions that the cut-off frequency increases with the rotation rate for all but prograde sectoral modes. While waves below the cut-off cannot be reflected at the stellar surface, the presence of a sub-surface convective region in the stellar model, owing to He ii ionization, means that they can become partially trapped within the star. The energy leakage associated with such waves, which are assigned the moniker virtual modes owing to their discrete eigenfrequencies, means that stability analyses which disregard their existence (by assuming perfect reflection at the stellar surface) may be in error. The results are of possible relevance to the 53 Per and SPB classes of variable star, which exhibit pulsation frequencies of the same order of magnitude as the cut-off frequencies found for the stellar model. It is suggested that observations either of an upper limit on variability periods (corresponding to the cut-off), or of line-profile variations owing to virtual modes, may permit asteroseismological studies of the outer layers of these systems. [source] Dispersion relation of the optical phonon frequencies in AlN/GaN superlatticesPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 7 2005S.K. Medeiros Abstract In this work we study the dispersion relation of the phonon frequencies in heterojunctions composed by III-V nitride materials (GaN and AlN). We are concerned with the superlattice structure, namely /substrate /AlN /AlxGa1,xN/GaN/AlxGa1,xN/,, where the substrate is here considered to be a transparent dielectric medium like sapphire. We make use of a model based on the Fröhlich Hamiltonian, taking into account the macroscopic theory known as the continuum dielectric model. The optical phonon modes are modelled considering only the electromagnetic boundary conditions, in the absence of charge transfer between ions. Numerical results of the confined optical phonon dispersion are presented, characterizing three distinct optical phonon classes designated as interface (IF), half-space (HS) and propagating (PR) modes. Furthermore, due to the dielectric anisotropy presented in the nitride, some additional peculiarities will be presented, like dispersive confined modes. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Magnetic field effects on the optical response of corrugated films: Voigt geometryPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 8 2003J. H. Jacobo-Escobar Abstract Using the Rayleigh,Fano modal theory it is investigated the interaction of p -polarized light with the corrugated surface of a metallic film. Calculations of the magnetoreflectance in the presence of an external magnetic field in the Voigt configuration are carried out. Studies are performed on the nonreciprocity property and the coupling of the incident light with the surface magnetoplasmons. It is found that the calculated dispersion relation of the surface magnetoplasmons predicts the possible experimental excitation of such modes. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Semiclassical determination of exponentially small intermode transitions for 1 + 1 spacetime scattering systems,COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2007Alain Joye We consider the semiclassical limit of systems of autonomous PDEs in 1 + 1 spacetime dimensions in a scattering regime. We assume the matrix-valued coefficients are analytic in the space variable, and we further suppose that the corresponding dispersion relation admits real-valued modes only with one-dimensional polarization subspaces. Hence a BKW-type analysis of the solutions is possible. We typically consider time-dependent solutions to the PDE that are carried asymptotically in the past and as x , ,, along one mode only and determine the piece of the solution that is carried for x , +, along some other mode in the future. Because of the assumed nondegeneracy of the modes, such transitions between modes are exponentially small in the semiclassical parameter; this is an expression of the Landau-Zener mechanism. We completely elucidate the spacetime properties of the leading term of this exponentially small wave, when the semiclassical parameter is small, for large values of x and t, when some avoided crossing of finite width takes place between the involved modes. © 2006 Wiley Periodicals, Inc. [source] Delayed reflection of the energy flow at a potential step for dispersive wave packetsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2004F. Ali Mehmeti Abstract We study Klein,Gordon equations with constant coefficients and different dispersion relations on two one-dimensional semi-infinite media coupled with transmission conditions. We obtain lower and upper bounds of the reflected part of the energy flow at the connecting point when the frequency band involved in the initial signal is sufficiently narrow. We detect a phenomenon of delayed reflection for low frequency wave packets, which is in accordance with the recent experiments of Haibel and Nimtz. The result is then generalized for a star-shaped network of n semi-infinite branches connected at one point. Copyright © 2004 John Wiley & Sons, Ltd. [source] Uniaxial dielectric media with hyperbolic dispersion relationsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2006Tom G. Mackay Abstract Planewave propagation with hyperbolic/hyperboliclike characteristics in uniaxial dielectric media is investigated. The phase velocity is positive with respect to the time-averaged Poynting vector for both evanescent and nonevanescent propagation in nondissipative media. A conceptualization of a uniaxial medium, which exhibits hyperboliclike planewave characteristics as a homogenized composite medium, is presented. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 363,367, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21350 [source] Wideband finite-difference,time-domain beam propagation methodMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 4 2002J. J. Lim Abstract A wide-band finite-difference,time-domain beam propagation method (FD TD-BPM) based on Padé approximants is introduced to improve the bandwidth of the conventional TD-BPM. Numerical dispersion relations for the TD-BPM are derived to demonstrate the increase in bandwidth of the wide-band TD-BPM. The effects of the spatial and time step sizes on the numerical dispersion are also investigated. It is shown that the wide-band TD-BPM is less sensitive to the choice of spatial step size and allows a larger time step size to be used compared to the finite-difference time-domain (FD-TD) method. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 243,247, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10428 [source] Coherent phases and magnetoexcitons in graphenePHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 5 2009Yu. E. Lozovik Abstract Unique band structure peculiarities of graphene imply that near Fermi level electrons are described by two-dimensional Dirac equation for massless particles. We investigate how these peculiarities manifest in electron,hole pairing and properties of indirect magnetoexcitons in two spatially separated, independently gated graphene layers. For electron,hole pairing, we derive asymptotical expressions for the gap in energy spectrum and discuss system behavior at various controlling parameters. We derive dispersion relations for magnetoexcitons and their effective-mass decompositions, and also discuss a possibility of magnetoexcitonic superfluidity. The systems under consideration can reveal coherent properties, dissipationless currents and Josephson phenomena at room temperature. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Lattice dynamics of chalcopyrite semiconductors LiAlTe2, LiGaTe2 and LiInTe2PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2009A. V. Kosobutsky Abstract Within density functional perturbation theory using norm-conserving pseudopotentials and a plane-wave basis set calculations of phonon dispersion relations and densities of states of LiAlTe2, LiGaTe2 and LiInTe2 compounds being crystallized into the tetragonal chalcopyrite structure have been performed. Theoretical values of phonon mode frequencies in LiGaTe2 and LiInTe2 are in good agreement with the experimental data available for these crystals obtained by the methods of Raman and infrared spectroscopies. The similarity of the physical and chemical properties of the crystals concerned manifests itself in the similarity of their phonon spectra that are especially close to each other in low- and high-frequency ranges. Phonon modes of the upper phonon band are predominantly caused by the lithium sublattice vibrations and have an upper bound of 350,370 cm,1. In a mid-frequency range a significant downshift of the vibrational frequencies is observed on going from LiAlTe2 to LiGaTe2 and LiInTe2 that is a consequence of the third group cation mass reduction. From calculated electron density maps it follows that Li-containing chalcopyrites are characterized by a less pronounced bond between the first group cation and anion as compared with the Cu- and Ag-based analogs due to the absence of pd-hybridization. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Vibrational modes in a square cross-section InAs/InP nanowire superlatticePHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 2 2010Seiji Mizuno Abstract We study theoretically the phonon modes in a square cross-section nanowire superlattice (NWSL) consisting of InAs and InP. The phonon modes in the NWSL composed of cubic materials are classified into five types, i.e., A1, A2, B1, B2, and E modes. We calculate the dispersion relations of each phonon mode and corresponding displacement fields for this NWSL. The A1, A2, B1, B2, and E modes have features of dilatational, torsional, stretching, shear, and flexural modes, respectively. We examine the effects of both the superlattice modulation along the wire axis and lateral confinement of phonons. (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] One- and two-dimensional porous silicon photonic crystals: momentum dispersion relations and stopbands analysisPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 7 2009Nadav Gutman Abstract We report on a novel approach to analyze and measure the optical properties of one- and two -dimensional photonic crystals (PCs) in all spatial directions inlcluding the symmetry axis of the PCs. The analysis is based on calculating momentum dispersion relations between the ordinary and the Bloch components of the wavevector and finding momentum stop-bands of the PC. This method provides a direct way to analyze the angular dependence of the reflection and the diffraction pattern of a monochromatic optical beam approaching the PC. Measurements have been performed on 1D PCs, e.g., 1D periodic structures of micro-porous silicon and 2D periodic arrays of macro-porous silicon. The periodicity of these PCs is about 2.5 to 4 ,m so that their momentum stop-bands fall in the mid-infrared (IR) wavelengths. We analyze several geometries, including slabs and prisms, to map the momentum dispersion relations and stopbands associated with guided and radiation modes. Angular reflection and diffraction measurements using a tunable CO2 laser showed a good agreement with the calculated momentum dispersion relations. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Spin densities in parabolic quantum wires with Rashba spin-orbit interactionPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 12 2006Sigurdur I. Erlingsson Abstract Using canonical transformations we diagonalize approximately the Hamiltonian of a gaussian wire with Rashba spin-orbit interaction. This proceedure allows us to obtain the energy dispersion relations and the wavefunctions with good accuracy, even in systems with relatively strong Rashba coupling. With these eigenstates one can calculate the non-equilibrium spin densities induced by applying bias voltages across the sample. We focus on the z -component of the spin density, which is related to the spin Hall effect. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Linear waves in a symmetric equatorial channelTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 624 2007C. Erlick Abstract Using a scaling that allows us to separate the effects of the gravity wave speed from those of boundary location, we reduce the equations for linear waves in a zonal channel on the equatorial beta-plane to a single-parameter eigenvalue problem of the Schrödinger type with parabolic potential. The single parameter can be written , = (,,)2/,1/2, where , = gH(2,R),2, ,, is half the channel width, g is the acceleration due to gravity, H is the typical height of the troposphere or ocean, , is the Earth's rotational frequency, and R is the Earth's radius. The Schrödinger-type equation has exact analytical solutions in the limits , , 0 and , , ,, and one can use these to write an approximate expression for the solution that is accurate everywhere to within 4%. In addition to the simple expression for the eigenvalues, the concise and unified theory also yields explicit expressions for the associated eigenfunctions, which are pure sinusoidal in the , , 0 limit and Gaussian in the , , , limit. Using the same scaling, we derive an eigenvalue formulation for linear waves in an equatorial channel on the sphere with a simple explicit formula for the dispersion relation accurate to O{(,,)2}. From this, we find that the phase velocity of the anti-Kelvin mode on the sphere differs by as much as 10% from , ,1/2. Integrating the linearized shallow-water equations on the sphere, we find that for for larger , and ,,, the phase speeds of all of the negative modes differ substantially from their phase speeds on the beta-plane. Furthermore, the dispersion relations of all of the waves in the equatorial channel on the sphere approach those on the unbounded sphere in a smooth asymptotic fashion, which is not true for the equatorial channel on the beta-plane. Copyright © 2007 Royal Meteorological Society [source] | ||||||||||||||||||||||||||||