Polaritons in hollow cylinders in the presence of a dc magnetic field

We study the effects of a dc external magnetic field on the polaritons propagating in hollow dielectric cylinders, taking into account the retardation effects. In solving Maxwell's equations we show that only the TM modes can propagate in these systems, and we obtain the dispersion relation of the confined-surface-polariton modes. The effects of geometric parameters and the external magnetic field on the propagation of surface-polariton modes are also analyzed and show significant influence on the behavior of the modes. Numerical results are presented for the dispersion relation of surface polaritons with GaAs as the optically active medium.     

Magnetoelastic stability of a superconducting ring in its own field

Summary The stability of the flexural vibrations of a superconducting ring in its own magnetic field is investigated. This problem is formulated as a perturbation problem: the final magnetic fields due to the deflected ring are considered as perturbations of the rigid-body fields. Both the rigid-body problem and the linearized perturbed prolem are solved analytically. These solutions are expressed in Legendre functions. A so-called ring equation for the in-plane flexural vibrations of the slender ring is constructed. From this equation a frequency-current dispersion relation is derived. It turns out that the ring is stable against in-plane vibrations and that the cigenfrequency increases with increasing current.     

A simple analysis of the Einstein relation in quantum confined non-parabolic semiconductors in the presence of a parallel magnetic field

An attempt is made to study the Einstein relation for the diffusivity-mobility ratio of the carriers in quantum confined non-parabolic semiconductors in the presence of a parallel magnetic field at low temperatures on the basis of new electron dispersion laws of quantum wells (QWs) and quantum wells wires (QWWs) of such materials. It is found, taking QW and QWWs of Hg_1–xCd_xTe and In_1–xGa_xAs_yP_1–y lattice-matched to InP as examples, that the diffusivity-mobility ratio increases with increasing electron concentration, decreasing alloy composition and decreasing film thickness in various oscillatory manners in both the cases. The magnetic field and the quantum wire structure enhance the numerical values of the same ratio. We have suggested an experimental method of determining the Einstein relation in degenerate materials having arbitrary dispersion laws. In addition, the corresponding well-known results of relatively wide-gap quantum confined materials in the absence of the magnetic field have been obtained as special cases of our generalized formulations, under certain limiting conditions.     

Cyclotron wave propagation in silver

Azbel'-Kaner cyclotron resonance in metals is accompanied by electromagnetic waves propagating in a direction perpendicular to the magnetic field. Taking into account the anisotropy of the silver Fermi surface, the dispersion relation for these waves is calculated in the limit where the wavelength is much smaller than the orbit diameter of the electrons. Thus it is shown that a number of previously observed oscillations in the surface impedance of a semiinfinite silver specimen arise from points of zero-group velocity on the dispersion relation. Physically, the oscillations reflect a matching of the electron-orbit diameter with an integer number of wavelengths. They may, therefore, be looked upon as geometric resonances in the surface impedance, complementary to the temporal cyclotron resonances. The surface impedance is calculated under the assumption of specular surface scattering. Satisfactory agreement with experiments is obtained by using an independent-particle model for the electron gas and band parameters based on APW calculations. The influence of the Fermi-surface geometry is demonstrated by comparing with calculations for a cylindrical and a spherical Fermi surface. The electric field in the metal is calculated for selected magnetic fields, and the expected result of a transmission experiment is presented. Finally, the absence of Fermi liquid effects in the experiments is briefly discussed.     

Polaritons in uniaxial materials propagating in hollow cylinders

The properties of polaritons propagating in hollow dielectric and magnetic cylinders embedded in an optically inert medium are studied. We pay special attention to those solutions of Maxwell's equations that give the behavior of the nonradiative modes (confined and localized) propagating in an optically active cylindrical medium. The dispersion relation of surface (localized) modes is obtained. Numerical results are presented for cylinders constituted by magnetic and dielectric materials, such as the uniaxial Heisenberg antiferromagnet MnF2 and the dielectric TiO2.     

Boundary element analysis of guided waves in a bar with an arbitrary cross-section

A boundary element method (BEM) is presented for analyzing the dispersion relation of guided waves in a bar with an arbitrary cross-section. A boundary integral equation for a harmonic motion in time and space is derived with respect to the boundary of the cross-section of the bar. By means of a collocation method, a homogeneous matrix equation which depends on the frequency and the wave number of the guided wave is obtained. The dispersion relation of guided waves is then obtained by finding nontrivial solutions of the matrix equation. The Newton's method is used to find the solution of the dispersion relation mode by mode for both propagating waves and nonpropagating waves. Numerical results are shown for a square bar, rectangular bars, and an L-shaped bar. Dispersive properties of guided waves in the bars are discussed in comparison with the results for Lamb modes in a 2D plate.     

Asymptotic representations of the dispersion relation for a two-ply, pre-stressed incompressible elastic laminate

Summary The dispersion relation associated with small amplitude waves propagating along a common (in-plane) principal direction in a two layer perfectly bonded elastic structure is derived. Each layer is composed of a pre-stressed incompressible elastic solid. An asymptotic analysis is carried out in the high wave number region, giving phase speed as a function of harmonic number, pre-stress and wave number for each harmonic. These expansions concur very well with numerical results and indicate that the structure of the dispersion relation may, for certain forms of pre-stress, differ significantly from that associated with the analogous classical problem within which pre-stress is absent. The paper also includes a discussion of the stability of the structure, with the domain of linear stability being established.     

Dispersion characteristics of a rectangularly corrugated cylindrical slow-wave structure driven by a non-relativistic annular electron beam

The dispersion relation of a rectangularly periodic cylindrical slow-wave structure (SWS) with an annular electron beam of energy <100 keV and current around 200 A has been derived and solved numerically. This type of system is typically used in backward wave high-power microwave devices and linear accelerators. The dispersion relation is analysed for both the cold structure (for zero beam current) and structure with an annular beam. The cold structure dispersion relation is characterised by the real value of frequency and wavenumber. When an electron beam propagates through the structure and the beam energy and current are sufficient to produce instability, microwave radiation results. The strength of this radiation can be qualitatively approximated from the temporal growth rate of the instability, which is defined by the imaginary values of the frequency corresponding to the complex conjugate roots of the dispersion relation. The temporal growth rate for various beam parameters has been calculated. The proposed SWS is very easy to be fabricated and can be used in the real experiments for generating high-power microwaves     

The giant dispersion of critical currents in a superconductor with fractal clusters of a normal phase

The influence of fractal clusters of a normal phase on the dynamics of a magnetic flux trapped in a percolation superconductor is considered. The critical depinning current distribution and the current-voltage characteristics of fractal superconducting structures in the resistive state are determined for an arbitrary fractal dimension of the cluster boundaries. The interval of fractal dimensions is found in which the dispersion of critical currents exhibits unlimited growth. It is established that the fractality of clusters favors a decrease of the electric field arising during the magnetic flux motion, thus increasing the critical current value. The region featuring the giant dispersion of critical currents can be expected to provide for the maximum current-carrying capacity of a superconductor.     

Magnetic field contribution to the Lorentz model

The classical Lorentz model of dielectric dispersion is based on the microscopic Lorentz force relation and Newton's second law of motion for an ensemble of harmonically bound electrons. The magnetic field contribution in the Lorentz force relation is neglected because it is typically small in comparison with the electric field contribution. Inclusion of this term leads to a microscopic polarization density that contains both perpendicular and parallel components relative to the plane wave propagation vector. The modified parallel and perpendicular polarizabilities are both nonlinear in the local electric field strength.     

Electro-magneto-thermo-visco-elastic Plane Waves in Rotating Media with Thermal Relaxation

A study is made of the propagation of plane electro-magneto-thermo-visco-elastic harmonic waves in an unbounded isotropic conducting visco-elastic medium of Kelvin–Voigt type permeated by a primary uniform magnetic field when the entire medium rotates with a uniform angular velocity. The thermal relaxation time of heat conduction, the electric displacement current, the coupling between heat flow density and current density, and that between the temperature gradient and the electric current are included in the analysis. A more general dispersion relation is obtained to determine the effects of rotation, thermal relaxation time, visco-elastic parameters, and the external magnetic field on the phase velocity of the waves. Perturbation techniques are used to study the influence of small magneto-elastic and thermo-elastic couplings on the phase velocity of the waves. Cases of low and high frequencies are also analyzed to determine the effect of rotation, visco-elastic parameters, thermo elastic and magneto-elastic coupling, as well as thermal relaxation time of heat conduction on the waves.     

Surface modes at the interfaces between isotropic media and indefinite media

Characteristics of surface modes at the interface between an isotropic medium and an indefinite medium that has a dispersion relation of hyperbolic form are studied. Four cases for the isotropic medium, including normal, left-handed, magnetic (with negative permeability), and metallic media, are considered. The conditions for the existence of surface modes in each case are analyzed in detail, and the results are expressed explicitly, indicating that the existence of surface modes is determined by the nature of the indefinite medium as well as the orientation of the boundary surface of this anisotropic medium. The energy flows associated with the surface modes are also discussed.     

Effect of interaction on magnetic properties of a particulate medium

Samples of magnetic particles were prepared in dry powder form, as well as in a plastic binder system. Magnetic measurements were made on the samples as function of the volumetric packing factor. Coercive force Hc, squareness, and anhysteretic magnetization measurements are correlated with the uniformity of particle dispersion. It was found that the behavior of Hc, squareness, and the initial anhysteretic susceptibility as a function of the packing factor are good indications of the degree of dispersion of the particles. It is shown that if the particles are well dispersed, Hcincreased with increased dilution, and the initial anhysteretic susceptibility increased at both high and low dilutions. A mathematical model is developed to explain the observed results. The model consists of a double distribution of interaction fields to account for the well-dispersed and the agglomerated particles.     

Propagation of waves in magneto-thermo-viscoelastic solids subjected to a uniform magnetic field

The propagation of magneto-thermo-mechanical (MTM) plane waves in electrically and thermally conductive magneto-thermo-viscoelastic (MTVE) unbounded solids is investigated with account for the mutual effects of the magnetic, thermal and strain fields. Concerning the mutual and thermo-electric effects in isotropic solids the governing equations are first linearized. In the linearization, the material is assumed to be subjected to a uniform and primary magnetic field in any direction while the material undergoes infinitesimal deformations. It is shown that the governing equations at the intermediate state are fulfilled by the presumed MTM-fields. Furthermore, the dispersion relation which allows us to consider the entire frequency range, the effect of the magnetic field and some nondimensional material parameters is obtained. Therefore, several modes of MTM-waves arise depending upon the direction of the magnetic field such as the uncoupled magnetic and mechanical S-mwaves, the coupled S-wave, the modified mechanical $\text{P}$-and thermal waves, and the modified and coupled MTM-waves. It is seen that all modes of the wave are dispersive and dissipative due to the conductivity and the viscosity of the material. Then the phase velocities and the attenuation constants for the coupling modes are obtained, and some limiting values are discussed. From the expressions follow, in particular, the results for the elastic case, the propagation of mechanical waves in nonconductive materials.     

Experiments on nonlinear acoustics in3He-B

Observations and applications of nonlinear acoustic phenomena in superfluid³He-B are reported. Two-phonon absorption (TPA) by the real squashing (rsq) mode has been detected under several experimental conditions below p = 3.5 bar, using two coincident sound pulses. The attenuation peak height has been investigated as a function of the energy densities of the two sound waves. We discovered the five-fold Zeeman splitting of TPA by parallel sound pulses in an applied magnetic field and the two-fold dispersion splitting due to the finite wave vector of the mode when the two sound pulses are mutually perpendicular. The dispersion relation of the real squashing mode has been investigated at zero pressure and in zero magnetic field by exciting the mode with two parallel, perpendicular, or antiparallel sound waves. Experimental values for the parameters that determine the collective-mode velocities have been extracted from the positions of the observed attenuation maxima. An anomalous structure has been observed in the attenuation and phase velocity spectra of a single high-intensity sound wave near the threshold for pair breaking by two phonons; in an applied magnetic field the phase velocity anomaly splits into a triplet.     

Energy bands and Landau levels of ultracold fermions in the bilayer honeycomb optical lattice

We investigate the spectrum and eigenstates of ultracold fermionic atoms in the bilayer honeycomb optical lattice. In the low energy approximation the dispersion relation has parabolic form and the quasiparticles are chiral. In the presence of the effective magnetic field, which is created for the system with optical means, the energy spectrum shows an unconventional Landau level structure. Furthermore, the experimental detection of the spectrum is proposed with the Bragg scattering techniques.     

Influence of variable permeability on the dispersion of a chemically reacting solute in porous media

In this paper in the first part, the influence of variable permeability on the two MHD basic flows in porous media is studied numerically. It is seen that the variable permeability due to random packing causes the hydromagnetic channelling in both the flows. Further, it is also observed that the flow in both the cases is retarded for any increase in the magnetic parameter.

In the second part, the influence of variable permeability and the effects of homogeneous and heterogeneous reactions on the dispersion of a solute in the above two basic flows are investigated. In the case of diffusion with a first order homogeneous reaction, in both the flows, the variation of permeability increases the effective dispersion coefficient while it decreases with increase in the magnetic parameter. In the case of diffusion combined with homogeneous and heterogeneous chemical reactions, the variation in permeability again increases the effective dispersion coefficient while with increase in magnetic parameter causes a decrease in the effective dispersion coefficient. Several earlier results follow as particular cases of the present study.     

A generalized formula for induced magnetic flux in a playback head

The usual reciprocity relation in magnetic reproduction is shown to be one form of a more general expression. This generalization incorporates an arbitrary tensor permeability which represents well oriented recording media. One useful alternate form of reciprocity is shown to involve only the irreversible or remanent recorded magnetization.     

Viscoelastic characterization of poly(butylene terephthalate) using longitudinal resonances

The viscoelastic constants of poly(butylene terephthalate) were determined as a function of temperature using the harmonic dispersion of longitudinal resonances. Measured quantities were Young's modulus, Poisson's ratio and the logarithmic decrement, from which the bulk and shear moduli were derived. It was found that a dispersion relation used by Schwarzl and Struik can be employed to compensate for frequency dispersion of the modulus using no adjustable parameters. Measured quantities agree well with previously published values. Appendices are included which derive the resonant frequency shift due to damping in our specific experiment and which estimate the error introduced by the Schwarzl-Struik dispersion relation.