Showing papers on "Dispersion relation published in 2010"
TL;DR: The first three dimensional (3D) dispersion relations and k spectra of magnetic turbulence in the solar wind at subproton scales are shown and it is conjecture that the turbulence undergoes a transition range, where part of the energy is dissipated into proton heating via Landau damping and the remaining energy cascades down to electron scales where electron LandAU damping may predominate.
Abstract: We show the first three dimensional (3D) dispersion relations and k spectra of magnetic turbulence in the solar wind at subproton scales We used the Cluster data with short separations and applied the k-filtering technique to the frequency range where the transition to subproton scales occurs We show that the cascade is carried by highly oblique kinetic Alfven waves with ω(plas) ≤ 01ω(ci) down to k(⊥) ρ(i)∼2 Each k spectrum in the direction perpendicular to B0 shows two scaling ranges separated by a breakpoint (in the interval [04,1]k(⊥)ρ(i): a Kolmogorov scaling k(⊥)⁻¹ⁱ⁷ followed by a steeper scaling ∼k(⊥)⁻⁴ⁱ⁵ We conjecture that the turbulence undergoes a transition range, where part of the energy is dissipated into proton heating via Landau damping and the remaining energy cascades down to electron scales where electron Landau damping may predominate
483 citations
TL;DR: In this article, the authors derive and validate a technique for predicting phonon dispersion relations and lifetimes from the atomic velocities in a crystal using the spectral energy density, which incorporates the full anharmonicity of the atomic interactions into the lifetime and frequency predictions.
Abstract: We derive and validate a technique for predicting phonon dispersion relations and lifetimes from the atomic velocities in a crystal using the spectral energy density. This procedure, applied here to carbon nanotubes, incorporates the full anharmonicity of the atomic interactions into the lifetime and frequency predictions. It can also account for nonperiodic interactions between phonons and nonbonded molecules near the solid surface. We validate the technique using phonon properties obtained from anharmonic lattice dynamics calculations and thermal conductivities obtained from nonequilibrium molecular-dynamics simulation.
285 citations
TL;DR: It is demonstrated that the Dzyaloshinskii-Moriya interaction breaks the degeneracy of spin waves and leads to an asymmetric spin-wave dispersion relation.
Abstract: The influence of the Dzyaloshinskii-Moriya interaction on the spin-wave dispersion in an Fe double layer grown on W(110) is measured for the first time It is demonstrated that the Dzyaloshinskii-Moriya interaction breaks the degeneracy of spin waves and leads to an asymmetric spin-wave dispersion relation An extended Heisenberg spin Hamiltonian is employed to obtain the longitudinal component of the Dzyaloshinskii-Moriya vectors from the experimentally measured energy asymmetry
224 citations
TL;DR: In this article, the effect of nonlinearities on harmonic wave propagation in one-dimensional nonlinear periodic structures is investigated through a novel perturbation analysis and accompanying numerical simulations, where several chain unit cells are considered featuring a sequence of masses connected by linear and cubic springs.
Abstract: Wave propagation in one-dimensional nonlinear periodic structures is investigated through a novel perturbation analysis and accompanying numerical simulations. Several chain unit cells are considered featuring a sequence of masses connected by linear and cubic springs. Approximate closed-form, first-order dispersion relations capture the effect of nonlinearities on harmonic wave propagation. These relationships document amplitude-dependent behavior to include tunable dispersion curves and cutoff frequencies, which shift with wave amplitude. Numerical simulations verify the dispersion relations obtained from the perturbation analysis. The simulation of an infinite domain is accomplished by employing viscous-based perfectly matched layers appended to the chain ends. Numerically estimated wavenumbers show good agreement with the perturbation predictions. Several example chain unit cells demonstrate the manner in which nonlinearities in periodic systems may be exploited to achieve amplitude-dependent dispersion properties for the design of tunable acoustic devices.
202 citations
TL;DR: In this article, the properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals (PPCs) are studied based on the continuous boundary condition of electromagnetic wave.
Abstract: Properties of obliquely incident electromagnetic wave in one-dimensional (1D) magnetized plasma photonic crystals (PPCs) are studied in this paper. Based on the continuous boundary condition of electromagnetic wave in 1D PPC, transfer matrix equation and dispersion equation of transverse magnetic polarization are deduced, and the properties of dispersion and transmission relation in terms of external magnetic field, collision frequency, and dielectric constant of dielectric and incident angles are investigated, respectively. Results show that gap location and gap width can be effectively controlled by adjusting external magnetic field as well as incident angle, and increasing collision frequency has little effect on gap width while larger dielectric constant of dielectric leads to more gaps.
198 citations
TL;DR: In this article, the authors demonstrate the waveguiding of Lamb waves in a locally resonant phononic crystal (LRPC) and present an analysis of the guiding of elastic waves in straight and bent waveguides.
Abstract: We demonstrate the waveguiding of Lamb waves in a locally resonant phononic crystal (LRPC) and we present an analysis of the guiding of elastic waves in straight and bent waveguides. The finite element method combined with the supercell technique was used to analyze the band gap and the dispersion relation of LRPC waveguides. Unlike the traditional phononic crystals, we show the possibility of guiding only one confined mode inside a LRPC waveguide. We discuss the confinement and the transmission of the guided mode as a function of the width of the waveguide based on both the band structure and the displacement field.
156 citations
TL;DR: In this paper, a viscoelastic model is proposed to describe the propagation of gravity waves into various types of ice cover, where the wave number is the closest to the open water value and attenuation rate is the least among all modes.
Abstract: [1] A viscoelastic model is proposed to describe the propagation of gravity waves into various types of ice cover. The ice-ocean system is modeled as a homogeneous viscoelastic fluid overlying an inviscid layer. Both layers have finite thickness. The viscosity is imagined to originate from the frazil ice or ice floes much smaller than the wavelength, and the elasticity from ice floes which are relatively large compared to the wavelength. A compact form of the dispersion relation is obtained. Under proper limiting conditions this dispersion relation can be reduced to several previously established models including the mass loading model, the viscous layer model and the thin elastic plate model. The full dispersion relation contains several propagating wave modes under the ice cover. The following two criteria are used to select the dominant wave mode: (1) wave number is the closest to the open water value and (2) attenuation rate is the least among all modes. The modes selected from those criteria coincide with the ones discussed in previous studies, which are shown to be limiting cases in small or large elasticity regimes of the present model. In the intermediate elasticity regime, however, it appears that there are three wave modes with similar wavelengths and attenuation rates. Implications of this intermediate elasticity range remain to be seen. The general viscoelastic model bridges the gap among existing models. It also provides a unified tool for wave-ice modelers to parameterize the polar regions populated with various types of ice cover.
156 citations
TL;DR: Nakamura et al. as mentioned in this paper showed that the Reissner-Nordstrom black hole in the five-dimensional anti-de Sitter space coupled to the Maxwell theory with the Chern-Simons term is unstable when the ChernSimons coupling is sufficiently large.
Abstract: In a previous paper [S. Nakamura, H. Ooguri, and C. S. Park, Phys. Rev. D 81, 044018 (2010)], we showed that the Reissner-Nordstrom black hole in the five-dimensional anti–de Sitter space coupled to the Maxwell theory with the Chern-Simons term is unstable when the Chern-Simons coupling is sufficiently large. In the dual conformal field theory, the instability suggests a spatially modulated phase transition. In this paper, we construct and analyze nonlinear solutions which describe the endpoint of this phase transition. In the limit where the Chern-Simons coupling is large, we find that the phase transition is of the second order with the mean field critical exponent. However, the dispersion relation with the Van Hove singularity enhances quantum corrections in the bulk, and we argue that this changes the order of the phase transition from the second to the first. We compute linear response functions in the nonlinear solution and find an infinite off-diagonal DC conductivity in the new phase.
154 citations
TL;DR: In this paper, the structural and optical properties of CuSe thin films were analyzed using the Wemple and Didomenico WDD model and the dispersion curve of the refractive index showed an anomalous dispersion in the absorption region and a normal dispersion on the transparent region.
140 citations
TL;DR: In this article, a dispersion relation describing coupled P-and SV-wave modes can be converted into a fourth-order scalar partial differential equation (PDE), which can be used to increase computational efficiency.
Abstract: Reverse time migration (RTM) images reflectors by using time-extrapolation modeling codes to synthesize source and receiver wavefields in the subsurface. Asymptotic analysis of wave propagation in transversely isotropic (TI) media yields a dispersion relation describing coupled P- and SV-wave modes. This dispersion relation can be converted into a fourth-order scalar partial differential equation (PDE). Increased computational efficiency can be achieved using equivalent coupled second-order PDEs. Analysis of the corresponding dispersion relations as matrix eigenvalue systems allows one to characterize all possible coupled linear second-order systems equivalent to a given linear fourth-order PDE and to determine which ones yield optimally efficient finite-difference implementations. Setting the shear velocity along the axis of symmetry to zero yields a simpler approximate TI wave equation that is more efficient to implement. This simpler approximation, however, can become unstable for some plausible combinations of anisotropic parameters. The same eigensystem analysis can be applied using finite vertical shear velocity to obtain solutions that avoid these instability problems.
137 citations
TL;DR: In this article, a logarithmic correction to the quantum wave equation is introduced and the emergence of evolution time from the group of automorphisms of the von Neumann algebra governed by this nonlinear correction is demonstrated.
Abstract: Starting from a generic generally covariant quantum theory, we introduce a logarithmic correction to the quantum wave equation. We demonstrate the emergence of evolution time from the group of automorphisms of the von Neumann algebra governed by this nonlinear correction. It turns out that such a parametrization of time is essentially energy-dependent and becomes global only asymptotically, as the energies become very small as compared to the effective quantum gravity scale. A similar thing happens to Lorentz invariance: in the resulting theory it becomes an asymptotic low-energy phenomenon. We show how the logarithmic nonlinearity deforms the vacuum wave dispersion relations and explains certain features of the astrophysical data coming from the recent observations of high-energy cosmic rays. In general, the estimates imply that, ceteris paribus, particles with higher energy propagate slower than those with lower energy, therefore, for a high-energy particle the mean free path, lifetime in a high-energy state and thus the travel distance from the source can be significantly larger than one would expect from the conventional theory. In addition, we discuss the possibility and conditions of transluminal phenomena in the physical vacuum such as Cherenkov-type shock waves.
TL;DR: In this paper, the authors measured the spectrum of small-amplitude perturbations growing on the rim of a liquid sheet and showed that the generation of secondary droplets results from a Rayleigh-Plateau instability of the rim, whose shape is almost cylindrical.
Abstract: The impact of a drop onto a liquid layer produces a splash that results from the ejection and dissolution of one or more liquid sheets, which expand radially from the point of impact. In the crown splash parameter regime, secondary droplets appear at fairly regularly spaced intervals along the rim of the sheet. By performing many experiments for the same parameter values, we measure the spectrum of small-amplitude perturbations growing on the rim. We show that for a range of parameters in the crown splash regime, the generation of secondary droplets results from a Rayleigh–Plateau instability of the rim, whose shape is almost cylindrical. In our theoretical calculation, we include the time dependence of the base state. The remaining irregularity of the pattern is explained by the finite width of the Rayleigh-Plateau dispersion relation. Alternative mechanisms, such as the Rayleigh–Taylor instability, can be excluded for the experimental parameters of our study.
TL;DR: In this paper, a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere was developed, where the authors derived the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions and derived equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave.
Abstract: [1] We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.
TL;DR: In this article, the role of optical phonons in thermal conductivity prediction was investigated and a procedure to calculate three-phonon scattering time-scales with the inclusion of Optical Phonons was described and implemented.
Abstract: The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures T200 K, longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50‐200 K) and to increase it at high temperature 200 K, especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures. DOI: 10.1115/1.4000447
TL;DR: This technique enables to recover accurately guided wave phase velocity dispersion curves and was designed to overcome limitations of spatio-temporal Fourier transform for receiver array of limited spatial extent as in the case of clinical assessment of cortical bone in axial transmission.
Abstract: This paper is devoted to a method of extraction of guided waves phase velocities from experimental signals. Measurements are performed using an axial transmission device consisting of a linear arrangement of emitters and receivers placed on the surface of the inspected specimen. The technique takes benefit of using both multiple emitters and receivers and is validated on a reference wave guide. The guided mode phase velocities are obtained using a projection in the singular vectors basis. The singular vectors are determined by the singular values decomposition (SVD) of the response matrix between the two arrays in the frequency domain. This technique enables to recover accurately guided wave phase velocity dispersion curves. The SVD based approach was designed to overcome limitations of spatio-temporal Fourier transform for receiver array of limited spatial extent as in the case of clinical assessment of cortical bone in axial transmission.
TL;DR: In this article, the dispersion relation for electrostatic oscillations in a zero-temperature quantum plasma, in which degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations, is derived.
Abstract: We present a derivation of the dispersion relation for electrostatic oscillations in a zero-temperature quantum plasma, in which degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations. The Poisson equation determines the electrostatic wave potential. We consider parameters ranging from semiconductor plasmas to metallic plasmas and electron densities of compressed matter such as in laser compression schemes and dense astrophysical objects. Owing to the wave diffraction caused by overlapping electron wave function because of the Heisenberg uncertainty principle in dense plasmas, we have the possibility of Landau damping of the high-frequency electron plasma oscillations at large enough wavenumbers. The exact dispersion relations for the electron plasma oscillations are solved numerically and compared with the ones obtained by using approximate formulas for the electron susceptibility in the high- and low-frequency cases.
TL;DR: In this paper, the response of EPs is studied nonperturbatively and both local and nonlocal dispersion relations of EGAMs are derived assuming a single pitch angle slowing-down energetic ion equilibrium distribution function.
Abstract: Excitation of energetic-particle (EP)-induced geodesic acoustic modes (EGAMs) by velocity space anisotropy is investigated taking into account the coupling to the GAM continuous spectrum. The response of EPs is studied nonperturbatively and both local and nonlocal dispersion relations of EGAM are derived assuming a single pitch angle slowing-down energetic ion equilibrium distribution function. For a sharply localized EP source, it is shown that the mode is self-trapped where the EP drive is strongest, with an exponentially small damping due to the tunneling coupling to the GAM continuous spectrum. (Some figures in this article are in colour only in the electronic version)
TL;DR: In this paper, a robust signal processing technique using linear mapping for removing dispersion of Lamb waves is presented, based on the assumption that the dispersion relation characteristic can be removed.
Abstract: A robust signal processing technique using linear mapping for removing dispersion of Lamb waves is presented in this article. Based on the assumption that the dispersion relation characteristic can...
TL;DR: The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems and results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.
Abstract: A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin-1/2, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin-1/2 contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.
TL;DR: In this article, the authors analyzed the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density and quantified the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.
TL;DR: The dispersion relations for the nonlinear propagation of high-intensity surface plasmon polaritons are calculated, predicting a nonlinearity-induced cutoff and vanishing group velocity.
Abstract: We analyze an inherent nonlinearity of surface plasmon polaritons at the interface of Fermi-Dirac metal plasma, stemming from the depletion of electron density in high-intensity regions. The derived optical nonlinear coefficients are comparable with the experimental values for metals. We calculate the dispersion relations for the nonlinear propagation of high-intensity surface plasmon polaritons, predicting a nonlinearity-induced cutoff and vanishing group velocity.
TL;DR: In this paper, integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS3 × S3 completely up to a phase.
Abstract: We show that integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS3 × S3completely up to a phase Using semi-classical methods we evaluate the phase to the leading and to the one-loop approximation in the strong coupling expansion We then show that the phase obeys the unitarity constraint implied by the crossing relations to the one-loop order We also verify that the dispersion relation obeyed by these magnons is one-loop exact at strong coupling which is consistent with their BPS nature
TL;DR: In this paper, a point-particle relativistic lagrangians are constructed that generate the momentum velocity and dispersion relations for quantum wave packets in Lorentz-violating effective field theory.
TL;DR: In this article, the dispersion degree of the longitudinal wave in nanoplates with small scale effects was analyzed with different wave numbers and scale coefficients, and it was shown that the effect of small-scale effects can be strengthened by increasing the scale coefficient and the wave number.
Abstract: In this paper, the propagation characteristics of the longitudinal wave in nanoplates with small scale effects are studied. The equation of the longitudinal wave is obtained using the nonlocal elastic theory. The phase velocity and the group velocity are derived, respectively. The dispersion relation is analyzed with different wave numbers and scale coefficients. It can be observed from the results that the dispersion properties of the longitudinal wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the longitudinal wave in nanoplates can also be tuned by these factors.
TL;DR: Experimental observation of a normal incidence phononic band gap in one-dimensional periodic (SiO(2)/poly(methyl methacrylate)) multilayer film at gigahertz frequencies using Brillouin spectroscopy is reported.
Abstract: We report experimental observation of a normal incidence phononic band gap in one-dimensional periodic (SiO(2)/poly(methyl methacrylate)) multilayer film at gigahertz frequencies using Brillouin spectroscopy. The band gap to midgap ratio of 0.30 occurs for elastic wave propagation along the periodicity direction, whereas for inplane propagation the system displays an effective medium behavior. The phononic properties are well captured by numerical simulations. The porosity in the silica layers presents a structural scaffold for the introduction of secondary active media for potential coupling between phonons and other excitations, such as photons and electrons.
TL;DR: In this paper, the influence of electron-electron scattering on the distribution function and transport characteristics of intrinsic monolayer graphene was investigated via an ensemble Monte Carlo simulation, and it was found that pair-wise collisions in graphene do not conserve the ensemble average velocity in contrast to conventional semiconductors with parabolic energy bands.
Abstract: The influence of electron-electron scattering on the distribution function and transport characteristics of intrinsic monolayer graphene is investigated via an ensemble Monte Carlo simulation. Due to the linear dispersion relation in the vicinity of the Dirac points, it is found that pair-wise collisions in graphene do not conserve the ensemble average velocity in contrast to conventional semiconductors with parabolic energy bands. Numerical results indicate that electron-electron scattering can lead to a decrease in the low field mobility by more than a factor of 2 for moderate electron densities. The corresponding degradation in the saturation velocity is more modest at around 15%. At high densities, the impact gradually diminishes due to increased degeneracy.
TL;DR: A geometric Doppler effect manifested by a spin-split dispersion relation of thermal radiation is observed and the observation of the spin-symmetry breaking in thermal radiation may be utilized for manipulation of spontaneous or stimulated emission.
Abstract: A geometric Doppler effect manifested by a spin-split dispersion relation of thermal radiation is observed. A spin-dependent dispersion splitting was obtained in a structure consisting of a coupled thermal antenna array. The effect is due to a spin-orbit interaction resulting from the dynamics of the surface waves propagating along the structure whose local anisotropy axis is rotated in space. The observation of the spin-symmetry breaking in thermal radiation may be utilized for manipulation of spontaneous or stimulated emission.
TL;DR: In this article, a straightforward analysis proposed by Swanepoel based on the use of the maxima and minima of the interference fringes has been used to drive the film thickness, d, the complex index of refraction, n, and the extinction coefficient, k.
Abstract: Amorphous As
x
Se70Te30−x
thin films with (0≤x≤30 at.%) were deposited onto glass substrates by using thermal evaporation method. The transmission spectra T(λ) of the films at normal incidence were measured in the wavelength range 400–2500 nm. A straightforward analysis proposed by Swanepoel based on the use of the maxima and minima of the interference fringes has been used to drive the film thickness, d, the complex index of refraction, n, and the extinction coefficient, k. The dispersion of the refractive index is discussed in terms of the single-oscillator Wemple and DiDomenico model (WDD). Increasing As content is found to affect the refractive index and the extinction coefficient of the As
x
Se70Te30−x
films. With increasing As content the optical band gap increases while the refractive index decreases. The optical absorption is due to allowed indirect transition. The chemical bond approach has been applied successfully to interpret the increase of the optical gap with increasing As content.
TL;DR: In this paper, an in-depth investigation of the propagation of harmonic plane waves in elastic media in the context of the linear theory of two-temperature generalized thermoelasticity is presented.
TL;DR: In this paper, a general dispersion equation is obtained in terms of Kummer's functions for the approximation of weak and uniform internal twist, which is a good initial working model for flux tubes in solar applications.
Abstract: The oscillatory modes of a magnetically twisted compressible flux tube embedded in a compressible magnetic environment are investigated in cylindrical geometry. Solutions to the governing equations to linear wave perturbations are derived in terms of Whittaker’s functions. A general dispersion equation is obtained in terms of Kummer’s functions for the approximation of weak and uniform internal twist, which is a good initial working model for flux tubes in solar applications. The sausage, kink and fluting modes are examined by means of the derived exact dispersion equation. The solutions of this general dispersion equation are found numerically under plasma conditions representative of the solar photosphere and corona. Solutions for the phase speed of the allowed eigenmodes are obtained for a range of wavenumbers and varying magnetic twist. Our results generalise previous classical and widely applied studies of MHD waves and oscillations in magnetic loops without a magnetic twist. Potential applications to solar magneto-seismology are discussed.