Dispersion Relation

Modes of ultra relativistic electron plasma embedded in a strong magnetic field are investigated for perpendicular propagation. Using Boltzmann-Vlasov equation, a general expression for the conductivity tensor is derived. An ultra-relativistic Maxwellian distribution function is employed to derive different modes for strong magnetic field limit. In particular, the dispersion relations for the ordinary mode and the extra ordinary mode (O-mode and X-mode) are obtained. Graphs of these dispersion relations and the imaginary parts of the frequency are drawn for some specific values of the parameters. It is observed that the damping rate increases gradually, reaches some maximum point and then decreases for larger wavenumbers. Further, increasing the strength of the magnetic field lowers the maximum value of the damping rate.

We study the electromagnetic properties of a system that consists of an electron background and a neutrino gas that may be moving or at rest, as a whole, relative to the background. The photon self-energy for this system is characterized by the usual transverse and longitudinal polarization functions, and two additional ones which are the focus of our calculations, that give rise to birefringence and anisotropic effects in the photon dispersion relations. Expressions for them are obtained, which depend on the neutrino number densities and involve momentum integrals over the electron distribution functions, and are valid for any value of the photon momentum and general conditions of the electron gas. Those expressions are evaluated explicitly for several special cases and approximations which are generally useful in astrophysical and cosmological settings. Besides studying the photon dispersion relations, we consider the macroscopic electrodynamic equations for this system, which involve the standard dielectric and permeability constants plus two additional ones related to the photon self-energy functions. As an illustration, the equations are used to discuss the evolution of a magnetic field perturbation in such a medium. This particular phenomena has also been considered in a recent work by Semikoz and Sokoloff as a mechanism for the generation of large-scale magnetic fields in the Early Universe as a consequence of the neutrino-plasma interactions, and allows us to establish contact with a specific application in a well defined context, with a broader scope and from a very different point of view.

Motivated by exploring spin-orbit coupled magnetism in 5d-based transition metal oxides (TMOs) beyond the iridates, we present a powder inelastic neutron scattering study of magnetic excitations in Ba2FeReO6-a member of the double perovskite family of materials which exhibit half-metallic behavior and high Curie temperatures Tc. We find clear evidence of two well-defined dispersing magnetic modes in its low temperature ferrimagnetic state. We develop a local moment model, which incorporates the interaction of Fe spins with spin-orbital locked magnetic moments on Re, and show that it captures our experimental observations. This allows us to extract moment sizes and exchange couplings, explain the magnitude of Tc, and to infer that magneto-structural locking terms are weak. Our study further opens up Re-based compounds as model systems to explore the interplay of strong correlations and spin-orbit coupling in 5d TMOs.

The nature of oscillations in the 1 kHz-60 MHz frequency range that have been observed during operation of Hall thrusters is quantitatively discussed. Contours of various plasma parameters measured inside the accelerating channel of a typical Hall thruster are used to evaluate the various stability criteria and dispersion relations of oscillations that are suspected to occur. A band by band up-to-date overview of the oscillations is carried out with a description of their observed behavior and a discussion of their nature and dependencies through comparison of the calculated contours to reported observations. The discussion encompasses the excitation of low frequency azimuthal drift waves that can form a rotating spoke, axially propagating ''transit-time'' oscillations, azimuthal drift waves, ionization instability-type waves, and wave emission peculiar to weakly ionized inhomogeneous plasmas in crossed electric and magnetic fields.

Quantum Zakharov equations are obtained to describe the nonlinear interaction between quantum Langmuir waves and quantum ion-acoustic waves. These quantum Zakharov equations are applied to two model cases, namely the four-wave interaction and the decay instability. In the case of the four-wave instability, sufficiently large quantum effects tend to suppress the instability.

The Fraunhofer diffraction pattern of an aperture function, which can be described in terms of the superposition of a known aperture function with a half plane, has an amplitude distribution which is real along one direction and complex along the orthogonal direction. The real and imaginary parts of the amplitude distribution are related by Hubert transforms (dispersion relations). These disper sion relations can be used to arrive at the diffraction patterns of a variety of apertures having symmetry properties. Theoretical results are presented to illustrate the diffraction pattern of various apertures.

The nonlinear coupling of intense, monochromatic, e1ectromagnetic radiation with plasma is considered in a number of special cases. The first part of the thesis serves as an introduction to three-wave interactions. A general formulation of the stimulated scattering of transverse waves by longitudinal modes in a warm, unmagnetized, uniform plasma is c9nstructed. We derive a general dispersion relation that describes Raman and, Brillouin scattering, modulational instability, and induced Thomson scattering. 'J ' J J J then we obtain the linearized coupled mode equations We thus consider all three waves on an equal basis. MUch work has been done on these equations in various limi. ts. 18-21 In the limit that la21,laJI« lall, the coupled set of equations reduces to two equations describing the evolution in space and time of the field quanti ties ai x, t) and a J C x, t) coupled by the pwnp whose amplitude is assumed constant. ll ,12,22-24 The research on various

In this paper propagation properties of a parallel-plate waveguide with tunable artificial impedance surfaces as sidewalls are studied both analytically and numerically. The impedance surfaces comprise an array of patches over a dielectric slab with embedded metallic vias. The tunability of surfaces is achieved with varactors. Simple design equations for tunable artificial impedance surfaces as well as dispersion equations for the TE and TM modes are presented. The propagation properties are studied in three different regimes: a multi-mode waveguide, a single-mode waveguide, and below-cutoff waveguide. The analytical results are verified with numerical simulations.

The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides analytic solutions, or which can be treated with more general spectrum generating algebraic methods. We find dynamical symmetries for which we derive the transfer matrices and dispersion relations. Both compact and non-compact groups are found to play a role.

On the basis of Braaten and Segel's representation of the electro-magnetic dispersion relations in a QED plasma we check the numerical accuracy of several published analytic approximations to the plasma neutrino emission rates. As we find none of them satisfactory we de-rive a ...

To cite this article: Sourabh Bal and M Bose 2010 J. Phys.: Conf. Ser. 208 012081 View the article online for updates and enhancements. Related content Effect of dust particles on kinetic Alfven wave in earth's magnetoplasma P Varma, Nidhi Shukla, Priyanka Agarwal et al. -Collisional effects on the electrostatic ion cyclotron instability in a dusty plasma R Bharuthram, P Singh, M Rosenberg et al. -Kelvin-Helmholtz instability of magnetized plasmas with surface tension and dust particles R P Prajapati and R K Chhajlani -This content was downloaded from IP address 34.203.241.206 on 29/03

The finite-difference time-domain method is applied to the calculation of dispersion relations of acoustic waves in two-dimensional ͑2D͒ phononic lattices, i.e., periodic solid-solid, solid-liquid, and solid-vacuum composites, for which the conventional plane-wave-expansion method fails or converges very slowly. Numerical examples are developed for 2D structures with polyethylene, mercury, and vacuum cylinders forming a square lattice in an aluminum matrix. The implication of the calculated dispersion relations for ultrasound transmission experiments is discussed.

We investigate the binding surface along the Bain path and phonon dispersion relations for the cubic phase of the ferromagnetic binary alloys Fe3X (X = Ni, Pd, Pt) for L12 and DO22 ordered phases from first principles by means of density functional theory. The phonon dispersion relations exhibit a softening of the transverse acoustic mode at the M-point in the L12-phase in accordance with experiments for ordered Fe3Pt. This instability can be associated with a rotational movement of the Fe-atoms around the Ni-group element in the neighboring layers and is accompanied by an extensive reconstruction of the Fermi surface. In addition, we find an incomplete softening in [111] direction which is strongest for Fe3 Ni. We conclude that besides the valence electron density also the specific Fe-content and the masses of the alloying partners should be considered as parameters for the design of Fe-based functional magnetic materials.

Mechanisms of transition to chaotic behavior in generalized versions of the Verhulst map, based on a parametrization suggested by the Bjorken scaling limit of the phase dispersion relations are investigated. Intermittency within phenomenologically acceptable regions can be observed under rather strong simplifying assumptions.

Dispersion relations for acoustic surface waves in piezoelecirics with periodic metal strips applied to the surface are developed. Particular emphasis is given to the modification in effective piezoelectric coupling due to strip geometry, and the details of the dispersion relations around the stop bands. The general results are applied to discuss devices such as multistrip directional couplers and strip-coupled amplifiers.

The energy of any bound state of the hydrogen molecule ion Hq+ has an expansion in inverse powers of the internuclear distance R of the form E(R) yg'+'{2R)-+e "~" y A'~{ 2R) N N +e i"~g B' '(2R) n+ln(R) germs pie "gC +(2R) N N Rayleigh-Schrodinger perturbation theory (RSPT) gives the coefficients E' ' but is otherwise unable to treat the exponentially small series, which in part are characteristic of the double-well aspect of H2+. (Here n denotes the hydrogenic principal quantum number. } %e develop a quasisemiclassical method for solving the Schrodinger equation that gives all the exponentially small subseries. The RSPT series diverges: for the ground state E' '--(%+1)!/e for large N. The E' ' asymptotics are governed via a dispersion relation by the imaginary e 2"~" series, which itself is given by the square of the e " " series times a "normalization integral. " That the expansion itself contains imaginary terms might seem inconsistent with the reality of the H2+ eigenvalues. In fact, the RSPT series is Sorel summable for R complex. The Sorel sum has a cut on the real R axis, and its limit from above or below the positive R axis is complex. The imaginary e 2"~" (and higher) series consist of just the counterterms to cancel the imaginary part of the Sorel sum. Extensive numerical examples are given. Of interest is a weak (down by a factor N } alternating-sign contribution to E' ', which is uncovered both theoretically and numerically. Also of interest is the identification of the Borel sum of the RSPT series with nonphysical boundary conditions. This too is illustrated both theoretically and numerically.

Knowledge of the dispersal mechanisms used by plants is important in phylogenetic, ecological, biogeographical, and conservation studies. Here we attempt to assign dispersal mechanisms to the entire flora-2595 plant species of the New Zealand Botanical Region. Anemochory is the most frequent dispersal mechanism, utilised by 79% of species. The next most frequent mechanisms are endozoochory (33%), hydrochory (28%), epizoochory (26%), and ballistic (8%). Polychory is common, particularly in monocotyledonous and dicotyledonous families and hydrochorous, epizoochorous, and ballistically dispersed species. Epizoochory is more common in New Zealand than in other regions, and species using this dispersal mechanism are over-represented among threatened species. Frugivory is less common than previously reported, and is under-represented among threatened species. Some mechanisms are poorly known, and entanglement and capsulivory are dispersal mechanisms apparently unique to New Zealand. Dispersal mechanisms reflective of New Zealand's distinctive assemblages of large flightless birds and reptiles are not apparent. A pattern of reduction in dispersal-related structures is evident in some genera. The mechanisms utilised by some species are ambiguous. Thus there remains a need for further investigation of the dispersal mechanisms utilised by plants in New Zealand.

In this thesis, consisting of two main parts, we study observational signatures of cosmic (super)strings in the context of D-brane inflation and properties of scalar perturbations on generic homogeneous inflating backgrounds. In the first part we study the production, nature and decay processes of cosmic superstrings in two widely used effective models of D-brane inflation, namely the $D3/D7$ and $D3/\bar{D}3$ models. Specifically, we show that the strings produced in $D3/D7$ are of local axionic type and we place constraints on the tension while arguing that the supersymmetry breaking mechanism of the model needs to be altered according to supergravity constraints on constant Fayet-Iliopoulos terms. Moreover, we study radiative processes of cosmic superstrings on warped backgrounds. We argue that placing the string formation in a natural context such as $D3/\bar{D}3$ inflation, restricts the forms of possible radiation from these objects. Motivated by these string models, which inevitably result in the presence of heavy moduli fields during inflation, in the second part, using the Effective Field Theory (EFT) of inflation, we construct operators that capture the effects of massive scalars on the low energy dynamics of inflaton perturbations. We compute the energy scales that define the validity window of the EFT such as the scale where ultra violet (UV) degrees of freedom become operational and the scale where the EFT becomes strongly coupled. We show that the low energy operators related to heavy fields induce a dispersion relation for the light modes admitting two regimes: a linear and a non linear/dispersive one. Assuming that these modes cross the Hubble scale within the dispersive regime, we compute observables related to two- and three-point correlators and show how they are directly connected with the scale of UV physics.

Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmitted wave can appear in the form of a frozen mode with very large diverging amplitude and either zero, or purely tangential energy flux. The field amplitude in the transmitted wave can exceed that of the incident wave by several orders of magnitude. There are two qualitatively different kinds of frozen mode regime. The first one is associated with a stationary inflection point of electromagnetic dispersion relation. This phenomenon has been analyzed in our previous papers. Now, our focus is on the frozen mode regime related to a degenerate photonic band edge. An advantage of this phenomenon is that it can occur in much simpler periodic structures. This spectacular effect is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in a variety of practical applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc.

We obtain a covariant decomposition of the motion of a relativistic charged particle into parallel motion and perpendicular gyration, and transform to guiding-center coordinates using Lie transforms. The natural guiding-center Poisson bracket structure and Hamiltonian are derived. The guiding-center equations of motion are presented to one order higher than the usual drifts, and the correction to the gyromomentum is given.

A linear stability analysis is presented for a liquid sheet that includes the eects of the surrounding gas, surface tension and the liquid viscosity on the wave growth process. An inviscid dispersion relation is used to identify the transition from a long wavelength regime to a short wavelength regime, analogous to the ®rst and second wind induced breakup regimes of cylindrical liquid jets. This transition, which is found to occur at a gas Weber number of 27/16, is used to simplify the viscous dispersion relation for use in multi-dimensional simulations of sheet breakup. The resulting dispersion relation is used to predict the maximum unstable growth rate and wave length, the sheet breakup length and the resulting drop size for pressure-swirl atomizers. The predicted drop size is used as a boundary condition in a multi-dimensional spray model. The results show that the model is able to accurately predict liquid spray penetration, local Sauter mean diameter and overall spray shape. #

Optical transmission measurements are commonly used for the routine determination of thin film optical constants. This paper presents an overview of the different methods of evaluating these transmission data, leading to values for the complex refractive index. Three different groups of methods are distinguished using: (1) at least two different optical measurements; (2) dispersion relations or general physical constraints to

A comprehensive theoretical and experimental study is presented of the magnetic susceptibility versus temperature \chi(T) of spin S = 1/2 two- and three-leg Heisenberg ladders and ladder oxide compounds. Extensive quantum Monte Carlo simulations of \chi(T) were carried out for both isolated and coupled two-leg ladders with spatially anisotropic intraladder exchange. Accurate fits to these and related literature QMC data were obtained. We have also calculated the one- and two-magnon dispersion relations and the dynamical spin structure factor for anisotropic isolated 2 x 12 ladders. The exchange constants in the two-leg ladder compound SrCu2O3 are estimated from LDA+U calculations. We report the detailed crystal structure of SrCu2O3 and of the three-leg ladder compound Sr2Cu3O5. New experimental \chi(T) data are reported for the two-leg ladder cuprates SrCu2O3 and LaCuO_{2.5}, and for the (nominally) two-leg ladder vanadates CaV2O5 and MgV2O5. The new and literature \chi(T) data for these compounds and for Sr2Cu3O5 are modeled using our QMC \chi(T) simulation fits, and the exchange coupling constants between the spins-1/2 are thereby estimated for each material. The surpisingly strong spatial anisotropy of the bilinear intraladder exchange constants in the cuprate compounds is discussed together with the results of other experiments sensitive to this anisotropy. Recent theoretical predictions are discussed including those which indicate that a four-spin cyclic exchange interaction within a Cu4 plaquette is important to determining the magnetic properties and which can significantly influence the exchange interactions estimated from \chi(T) data assuming the presence of only bilinear exchange.

We analyse prospects for the use of Bose-Einstein condensates as condensedmatter systems suitable for generating a generic 'effective metric', and for mimicking kinematic aspects of general relativity. We extend the analysis due to Garay et al Phys. Rev. Lett. 85 4643, 2001 Phys. Rev. A 63 023611). Taking a long-term view, we ask what the ultimate limits of such a system might be. To this end, we consider a very general version of the nonlinear Schrödinger equation (with a 3-tensor position-dependent mass and arbitrary nonlinearity). Such equations can be used, for example, in discussing Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We demonstrate that at low momenta linearized excitations of the phase of the condensate wavefunction obey a (3 + 1)-dimensional d'Alembertian equation coupling to a (3 + 1)-dimensional Lorentzian-signature 'effective metric' that is generic, and depends algebraically on the background field. Thus at low momenta this system serves as an analogue for the curved spacetime of general relativity. In contrast, at high momenta we demonstrate how one can use the eikonal approximation to extract a well controlled Bogoliubovlike dispersion relation, and (perhaps unexpectedly) recover non-relativistic Newtonian physics at high momenta. Bose-Einstein condensates appear to be an extremely promising analogue system for probing kinematic aspects of general relativity.

We report a systematic first principles density functional study on the electronic structure, elastic and optical properties of nitrogen based solid hydrogen storage materials LiNH 2 , NaNH 2 , KNH 2 , and RbNH 2 . The ground state structural properties are calculated by using standard density functional theory, and also dispersion corrected density functional theory. We find that van der Waals interactions are dominant in LiNH 2 whereas they are relatively weak in other alkali metal amides. The calculated elastic constants show that all the compounds are mechanically stable and LiNH 2 is found to be a stiffer material among the alkali metal amides. The melting temperatures are calculated and follow the order RbNH 2 < KNH 2 < NaNH 2 < LiNH 2 . The electronic band structure is calculated by using the Tran-Blaha modified Becke-Johnson potential and found that all the compounds are insulators, with a considerable band gap. The [NH 2 ] − derived states completely dominate in the entire valence band region while the metal atom states occupy the conduction band. The calculated band structure is used to analyze the different interband optical transitions occurring between valence and conduction bands. Our calculations show that these materials have considerable optical anisotropy.

The origin and properties of the transverse non-reciprocal magneto-optical (nMO) effect were studied. The transverse nMO effect occurs in the case when light propagates perpendicularly to the magnetic field. It was demonstrated that light can experience the transverse nMO effect only when it propagates in the vicinity of a boundary between two materials and the optical field at least in one material is evanescent. The transverse nMO effect is pronounced in the cases of surface plasmons and waveguiding modes. The magnitude of the transverse nMO effect is comparable to or greater than the magnitude of the longitudinal nMO effect. In the case of surface plasmons propagating at a boundary between the transition metal and the dielectric it is possible to magnify the transverse nMO effect and the magneto-optical figure-of-merit may increase from a few percents to above 100%. The scalar dispersion relation, which describes the transverse MO effect in cases of waveguide modes and surface plasmons propagating in a multilayer MO slab, was derived.

A new higher-order spectral element (SE) is developed for wave propagation analysis of a functionally graded material (FGM) beam in the presence of thermal and mechanical loading. The element is based on first order shear deformation theory (FSDT) and takes into account the depthwise contraction due to Poisson’s ratio. A new method of element formulation is employed, which is the most general one and devoid of all previous cumbersome wavenumber and wave amplitude computation. The beam can be subjected to temperature variation in depth direction. This variation is found by solving the one-dimensional heat conduction equation uncoupled from the elasticity equation. The effect of the computed temperature field is subsequently superimposed on the mechanical loading in the form of an equivalent nodal load. Numerical examples are directed towards highlighting the effect of the Poisson’s contraction on the structural response and stress wave. The spectrum and the dispersion relation are studied in detail. The stress field generated by the element and its difference from the FSDT stress field is outlined. The response of an FGM beam to thermo-mechanical loading is analysed and the effect of thermal loading on the overall response is elicited.

The ab initio method within the local-density approximation is applied to calculate the Hellmann-Feynman forces for the cubic and elongated supercells of the polar MgO crystal. From these forces, using the direct method, the phonon dispersion relations and the phonon density of states are derived. The LO/TO splitting was extracted from phonon frequencies found within the elongated supercell. ᭧

The refractive index of GaAs has been measured in the wavelength range from 0.97 to 17 m, which covers nearly the entire transmission range of the material. Linear and quadratic temperature coefficients of the refractive index have been fitted to data measured between room temperature and 95°C. In the midinfrared, the refractive index and temperature dependence are obtained from analysis of etalon fringes measured by Fourier-transform spectroscopy in undoped GaAs wafers. In the near infrared, the refractive index is deduced from the quasiphasematching ͑QPM͒ wavelengths of second-harmonic generation in orientation-patterned GaAs crystals. Two alternative empirical expressions are fitted to the data to give the refractive index as a function of wavelength and temperature. These dispersion relations agree with observed QPM conditions for midinfrared difference-frequency generation and second-harmonic generation. Predictions for various nonlinear optical interactions are presented, including tuning curves for optical parametric oscillators and amplifiers. Also, accurate values are predicted for QPM conditions in which extremely large parametric gain bandwidths can be obtained.

In this letter we present a method for calculation of linear heat flow in inhomogeneous solids. The method is based on the evaluation of transfer matrices for each layer in a multilayered structure from the Laplace transformation of the partial differential equation of heat conduction. The multilayered structure is then described by a matrix obtained as a chain of products of individual layer transfer matrices and corresponding boundary thermal resistivity matrices. The analytic expression for the nth power of the multilayered transfer matrix is found, describing a periodic multilayered structure composed of n equal multilayered structures. The application of the presented method for calculation of photothermal signals is also shown. Dispersion relation for the thermal waves in inhomogeneous solids is obtained from the matrix elements of the transfer matrix. Finally, from the dispersion relation explicit expressions for the effective values of thermal diffusivity and conductivity of both the discontinuously and continuously inhomogeneous solids are evaluated.

. Gullies locally termed dongas are a characteristic feature of the landscape in central KwaZulu-Natal and are highly associated with widespread, stratified colluvial sediments and the buried palaeosols that have formed in this material. Research objectives were to find out which sediment property or properties contribute most to the vulnerability of the colluvium to gully erosion; to study the erosion susceptibility of the sequence of buried stratigraphic layers and palaeosols; and to improve understanding of the relationship between erosion susceptibility of the colluvial layers and palaeosols and their disposition in the landscape. Materials from several colluvial layers and palaeosols exposed in the donga sidewall of the Dabekazi donga, 13 km north of Nqutu in central KwaZulu-Natal, were subjected to chemical and mineralogical analyses, several dispersion and erodibility tests and were characterized physically. Exchangeable sodium Ž . percentages ESP ranged from 0% to 23% and the dispersivity and erodibility tests revealed a range of dispersion potential and erodibility across the sequence of colluvial layers and palaeosols. However, a poor correlation was found between the results of different dispersion tests, as well as between dispersion tests and dispersion-related properties. Dispersion tests showed significant correlation with silt content. An erodibility test using a flume showed very strong correlation with Ž . Ž . electrical conductivity EC and sodium adsorption ratio SAR of the saturated paste extract and ESP values. The plasticity index ranged from 0% to 0.23 and estimated hydraulic conductivities ranged from 33 to 0.7 mrday. High correlation with ESP and EC suggests that dispersion plays an important role in the erodibility of the materials under conditions of short duration, turbulent water ) Corresponding author. 0341-8162r00r$ -see front matter q 2000 Published by Elsevier Science B.V. All rights reserved.

Organic solar cells with copper pthalocyanine (CuPC) and fullerene (C60) blends with efficiency around 5% have already been demonstrated. However, the data of reliable optical constants of these organic materials and their blends in thin films are not readily available. In this paper, we discuss thin films of CuPC and C60 fabricated using multiple evaporation cells at a base pressure b 10 − 8 torr are studied using spectroscopic ellipsometry. Ellipsometric data were obtained in the spectral range of 0.75 eV to 4.5 eV for determining the optical constants. We model CuPC and C60 using Tauc-Lorentz dispersion relation. The blend at the composition ratio of 1:1 were modelled by Maxwell-Garnett and Bruggeman effective medium approximations. In addition, a new approach is taken to model the blend by adding separately all the oscillators for each energy transition for both the composites and were found to fit the raw data better than the Maxwell-Garnett and Bruggeman effective medium approximations. The obtained refractive index data by this approach is then presented. We find that the Q-band and B-band of CuPC and the broad absorption of C60 around 3.56 eV still maintain their optical identity in the blend.

The present paper deals with the investigation of the propagation of harmonic plane waves with assigned frequency by employing the thermoelasticity theory with dual-phase-lags (Tzou [7], Chandrasekharaiah [10]). The exact dispersion relation solutions for the plane wave are obtained analytically and asymptotic expressions of several characterizations of the wave fields, such as phase velocity, specific loss, penetration depth and amplitude ratios are obtained for both the high frequency as well as low frequency values. In order to illustrate the analytical results, the computational tool Mathematica is used to find the numerical values of different wave fields at intermediate values of frequency and results are depicted in different figures. A detailed analysis of the effects of phase-lags on plane wave is presented on the basis of analytical and numerical results and significant points are highlighted.

We study the propagation and dissipation of Alfvén gravity waves in the solar corona, considering viscosity as a damping mechanism, and derive a general dispersion relation for Alfvén gravity waves under WKB and Boussinesq approximation. We find that in the presence of viscosity, the wave normal surfaces do not differ significantly from the results obtained in an ideal MHD. From dissipation point of view, we find that for the wave frequency less than the Brunt-Väisälä frequency (i.e., ω¯<1) there are two types of damping, one is strong damping when LD ˜ λ and the other is weak damping when LD ≫ λ. For the wave frequencies greater than the Brunt-Väisälä frequency (i.e., ω¯>1), however, we get only weak damped oscillations. Thus, Brunt-Väisälä frequency separates regimes of wave frequency in which damping is weak or strong.

Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined as the expectation value of the electromagnetic term in the Einstein-Maxwell Hamiltonian constraint, regularized in the manner of Thiemann, with respect to a would-be semiclassical state. The resulting energy dispersion relations entail Planck scale corrections to those in flat spacetime. Both the helicity dependent contribution of Gambini and Pullin and, for a value of a parameter of our approximation, that of Ellis and co-workers are recovered. The electric-magnetic asymmetry in the regularization procedure yields nonlinearities only in the magnetic sector which are briefly discussed. Observations of cosmological gamma ray bursts might eventually lead to the needed accuracy to study some of these quantum gravity effects.

The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variational density-functional perturbation theory, with ab initio pseudopotentials and a plane-wave basis set. Comparison with the results previously obtained for barium titanate shows that the change of a single constituent (Ba to Pb, Ti to Zr) has profound effects on the character and dispersion of unstable modes, with significant implications for the nature of the phase transitions and the dielectric and piezoelectric responses of the compounds. Examination of the interatomic force constants in real space, obtained by a transformation which correctly treats the long-range dipolar contribution, shows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersions. These trends suggest the possibility of the transferability of force constants to predict the lattice dynamics of perovskite solid solutions.

A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of the group and phase velocity are analyzed.

Propagation of both low and high frequency waves in a plasma consisting of electrons, ions, positrons and charged dust particles have been theoretically studied. The characteristics of dust acoustic wave propagating through the plasma has been analysed and the dispersion relation deduced is a generalization of that obtained by previous authors. It is found that nonlinear localization of high frequency electromagnetic field in such a plasma generates magnetic field. This magnetic field is seen to depend on the temperatures of electrons and positrons and also on their equilibrium density ratio. It is suggested that the present model would be applicable to find the magnetic field generation in space plasma.

Plasmons in metallic nanomaterials exhibit very strong size and shape effects, and thus have recently gained considerable attention in nanotechnology, information technology, and life science. In this review, we overview the fundamental properties of plasmons in materials with various dimensionalities and discuss the optical functional properties of localized plasmon polaritons in nanometer-scale to atomic-scale objects. First, the pioneering works on plasmons by electron energy loss spectroscopy are briefly surveyed. Then, we discuss the effects of atomistic charge dynamics on the dispersion relation of propagating plasmon modes, such as those for planar crystal surface, atomic sheets and straight atomic wires. Finally, standing-wave plasmons, or antenna resonances of plasmon polariton, of some widely used nanometer-scale structures and atomic-scale wires (the smallest possible plasmonic building blocks) are exemplified along with their applications.

In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos. * Electronic address: [email protected]