Field of a point source in a semi-infinite elastic medium

An exact solution for the tensor Green's function of a harmonic field for a semi-infinite elastic medium is presented in an easy-to-use form in the theory of wave scattering. The solution is derived in the form of a sum of the Green's functions for an infinite medium and the term satisfying the homogeneous wave equation for a semi-infinite elastic medium. The results reproduce the known far-field asymptotics containing longitudinal, transversal and surface Rayleigh-type wave modes. The near-field asymptotic is essentially different for the regions far and near the boundary.     

Focusing of a nonlinear phase-conjugate ultrasonic wave transmitted through a phase-inhomogeneous layer

The propagation of a nonlinear phase-conjugate ultrasonic wave through a layer introducing random phase aberrations is studied experimentally. The wave is generated by an overthreshold parametric phase-conjugating ultrasonic amplifier. It is shown that, with the extent of nonlinearity achieved for the conjugate wave, the phase locking of harmonics is retained and, as a consequence, a compensation of the distortions introduced by the layer takes place. The possibility of an automatic focusing of a nonlinear phase-conjugate wave propagating in an inhomogeneous medium is demonstrated, which is important for practical applications.     

Modelling and design of a novel air-spring for a suspension seat

Air-springs used in conjunction with auxiliary volumes provide both spring stiffness and damping. The damping is introduced through the flow restriction connecting the two air volumes. This article presents a simplified model of an air-spring with an auxiliary volume derived from first principles for simulation and design of an air-spring coupled to an auxiliary volume for a suspension seat. Tests were performed on an experimental apparatus to validate the model. The simulation model of the air-spring and auxiliary volume followed the trend predicted by the literature but showed approximately 27% lower transmissibility amplitude and 21% lower system natural frequency than that obtained by tests when using large diameter flow restrictions. This inaccuracy is assumed to be introduced by the simplified mass transfer equations defining the flow restriction between air-spring and auxiliary volume. The model showed closer correlation to the experimental results when the auxiliary volume size was decreased by two-thirds of the volume actually used for the experiment. A procedure, using the developed simulation model, for the design of a prototype air-spring and auxiliary volume, is presented for application in a typical articulated or rigid frame dump truck. The goal of the study was to design a suspension seat for this application and to obtain a SEAT value below 1.1. The design was optimised by varying auxiliary volume size and flow restriction diameters for different loads. A SEAT value of less than 0.9 was achieved, clearly indicating the effectiveness of using an auxiliary volume with an air-spring as seat suspension.     

Diffraction of a plane electromagnetic wave by a slot in a conducting screen with a transverse dielectric layer

The problem of diffraction of a plane electromagnetic wave by a slot in a planar perfectly conducting arbitrary thick screen with an infinite planar dielectric layer passing through the slot transversely to the screen is solved rigorously. In each of the field existence domains (two domains on either side of the screen and the interior of the slot), the solution is represented as an expansion in piecewise harmonic or exponential modes that allow for reflection and refraction at the boundaries of the dielectric layer. It is found that a set of functions describing such modes is complete enough to construct a solution satisfying all boundary conditions of the diffraction problem. The procedures of solution construction for the case at hand and for the same diffraction structure without the dielectric layer are compared.     

Transport through a constriction in a FQH-annulus

The flux periodicity of thermodynamic properties of an annulus in the fractional quantum Hall state with a constriction is considered. It is found that -periodicity is obtained due to transfer of fractionally charged particles or composite fermions between the edges of the annulus, respectively. The result for the finite magnitude of the persistent current across a very strong constriction is presented, as obtained with an extension of Wen’s edge state theory.     

Numerical studies of a granular gas in a host medium

The nonlinear dissipative Boltzmann equation for an granular gas diffusing in a elastically scattering host medium is investigated and numerically solved by means of direct stochastic simulation. The procedure requires an appropriate treatment of the two collision integrals involved, and of their different features. The algorithm is first tested versus exact results for macroscopic moments worked out in the Maxwellian-pseudo-molecules approximation, and then it is applied to the more realistic collision model of hard spheres for both elastic and inelastic encounters. When collisions with background are dominant, reliability of some hydrodynamic closures is then discussed by comparison of their outputs to the kinetic results achieved by the present DSMC approach.     

Resonant electron-positron pair photoproduction on a nucleus in a pulsed light field

The resonant photoproduction of an electron-positron pair on a nucleus in the field of a pulsed light wave is studied theoretically. The approximation where the electromagnetic pulse duration is much longer than the characteristic time of wave oscillations is considered. The interaction of the electron and positron with the Coulomb potential of the nucleus is considered in the Born approximation. An analytical expression for the resonant differential cross section is derived for the range of moderately strong external fields. This cross section contains a resonant peak whose height and width are determined by the external pulsed wave characteristics. The resonant cross section for pair photoproduction on a nucleus in a pulsed laser field can exceed the corresponding cross section for pair photoproduction on a nucleus in the absence of an external field by an order of magnitude.     

Diffraction loss analysis of a plane-parallel optical cavity with a phase step and a slit aperture

A model for calculating the round trip diffraction loss in a plane-mirror cavity with an intracavity phase step and an infinite slit aperture is developed. The round trip remaining intensity fraction for the low order transverse cavity modes can be calculated for any given location of the slit aperture and the phase step along the cavity and for any given phase delay on the phase step. The diffraction loss on the slit aperture is found to be a periodic function of the phase delay on the phase step. Transformation of the lasing spectrum emitted from a broadband pulsed dye laser on moving the phase step along the oscillator cavity is reproduced theoretically. The lasing spectrum affected by the phase step is interpreted as the wavelength dependence of the remaining intensity fraction for the principal transverse mode.     

Collective excitations of a degenerate Fermi vapour in a magnetic trap

We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law is obtained for the vapour in the collisional regime inside a spherical trap of frequency , with n the number of radial nodes and the orbital angular momentum. The low-energy excitations are also treated in the case of an axially symmetric harmonic confinement. The collisionless regime is discussed with main reference to a Landau-Boltzmann equation for the Wigner distribution function: this equation is solved within a variational approach allowing an account of non-linearities. A comparative discussion of the eigenmodes of oscillation for confined Fermi and Bose vapours is presented in an Appendix. Received 23 February 1999 and Received in final form 21 April 1999     

Flows in a rotating elastico-viscous fluid induced by torsional oscillations of a plate acting for a finite time

Unsteady flows in an electrically conducting rotating elastico-viscous liquid in the presence of a uniform magnetic field and induced by small amplitude torsional oscillations, acting for a finite time, of an infinite, rigid, non-conducting plate, are discussed. This analysis indicates the general features of the steady and unsteady velocity field, and the structure of the associated boundary layers on the plate including the effect of rotation, hydromagnetic and elastic parameters involved in the problem. The velocity field related to small elastic parameter is calculated with physical significance. It is further shown that the Ekman suction velocity, which is responsible for the generation of an axial inflow toward the bounadry layer, does not appear unless the plate is subject to oscillations for an indefinite period. Several limiting results are found to follow as special cases of this analysis.     

Emission of a photon by an electron in a radiation-dominant universe

The process by which a photon is emitted by an electron in a radiation-dominant universe is considered, under the assumption that an arbitrary number of pairs are produced from a vaccum. In a flat space this process is forbidden by the laws of conservation. The dependence of the probability and the mean number of created particles on the energy of the initial electron is investigated. In the limiting cases (initial electron with high or low energies), approximate expressions are found for the probability that a photon is emitted by an electron as well as for the total probability of the process, including production of photons and pairs from a vacuum. Approximate expressions are obtained for the mean number of particles that are produced in the course of inelastic scattering of an electron in the early Universe. Biy State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 98–102, September, 1996.     

Plasmons and polaritons in a semi-infinite plasma and a plasma slab

Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions. Known results are re-obtained in much a more direct manner and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The dielectric response and the electron energy loss are computed. The surface contribution to the energy loss exhibits an oscillatory behaviour in the transient regime near the surfaces. The propagation of an electromagnetic wave in these plasmas is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved and the reflected and refracted waves are computed, as well as the reflection coefficient. For the slab we compute also the transmitted wave and the transmission coefficient. Generalized Fresnel's relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient for a semi-infinite plasma exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection). Similarly, apart from characteristic oscillations, the reflection and transmission coefficients for a plasma slab exhibit an appreciable enhancement in the damped regime.     

Incommensurate structure as a nonlinear resonance between an atomic chain and a field

The general condition for the commensurate-incommensurate phase transition in an atomic chain is considered. The potential energy of atoms consists of a next-neighbour interaction and an external periodic field. This condition reveals itself in the so-called nonlinear resonance for an equivalent dynamical system.     

Optical spin orientation of a single manganese atom in a quantum dot

The magnetic state of a single magnetic atom (Mn) embedded in an individual semiconductor quantum dot is optically probed using micro-spectroscopy. A high degree of spin polarization can be achieved for an individual Mn atom localized in a quantum dot using quasi-resonant or fully-resonant optical excitation at zero magnetic field. Optically created spin polarized carriers generate an energy splitting of the Mn spin and enable magnetic moment orientation controlled by the photon helicity and energy. The dynamics and the magnetic field dependence of the optical pumping mechanism shows that the spin lifetime of an isolated Mn atom at zero magnetic field is controlled by a magnetic anisotropy induced by the built-in strain in the quantum dots. The Mn spin distribution prepared by optical pumping is fully conserved for a few microseconds. This opens the way to full optical control of the spin state of an individual magnetic atom in a solid state environment.     

Investigation of the efficient coupling between a highly elliptical Gaussian profile output from a laser diode and a single mode fiber using a hyperbolic-shaped microlens

A tapered hyperbolic-shaped microlens has been improved for efficient the coupling of the output from a laser diode into an optical fiber. A tapered hemispherical-end fiber microlens is also evaluated for comparison purposes. The Fresnel diffraction theory is used to evaluate laser to fiber coupling using microlenses. Experimental results demonstrate that, for an elliptical Gaussian laser diode with an aspect ratio of 1:1.5, the coupling efficiencies for the hyperbolic-shaped microlenses and the hemispherical-end fiber microlenses are 87% and 62%, respectively. Simulation results show excellent agreement with the measurements. The research results illustrate that a hyperbolic-shaped microlens has a much higher coupling efficiency than a hemispherical-end microlens due to efficient mode matching and phase matching.     

Production of a pair by a polarized photon in a uniform constant electromagnetic field

The total probability of production of an electron-positron pair by a polarized photon in a constant uniform electromagnetic field of an arbitrary configuration is determined using the imaginary part of the diagonalized polarization operator. Approximate expressions are derived for this probability in four ranges of photon energy. In the high-energy range, the corrections to the standard semiclassical approximation are calculated. In the range of intermediate energies, in which this approximation is inapplicable, the probability of the process is calculated using the steepest descent method. It is shown that in the range of photon energies higher than the pair production threshold in a magnetic field, a weak electric field removes root divergences in the probability of production of the particles at the Landau levels. For relatively low photon energies, a low-energy approximation is developed. At such energies, the effect of the electric field on the process is decisive, while the effect of the magnetic field is associated with its interaction with the magnetic moment of the particles being produced. Such an interaction is manifested, in particular, in the difference in the probabilities of production of a pair by an external field for scalar and spinor particles.     

The electromagnetic initial boundary value problem in a domain with a chiral filling

The problem of the excitation of electromagnetic oscillations by given charge and current distributions in a domain with a nonhomogeneous chiral filling is investigated. The domain where the problem is considered may be both a finite one bounded by an ideally conducting surface and an infinite supplement to an ideally conducting bounded object. The initial boundary value problem is shown to arise, for which the generalized formulation in a special functional space is given. The existence of a unique weak solution to the problem is proven using the Galerkin method.     

Thermal entanglement in a two-spin-qutrit system under a nonuniform external magnetic field

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction under a magnetic field in an arbitrary direction is investigated. Negativity, the measurement of entanglement, is calculated. We find that for any temperature the evolvement of negativity is symmetric with respect to magnetic field. The behavior of negativity is presented for four different cases. The results show that for different temperature, different magnetic field give maximum entanglement. Both the parallel and antiparallel magnetic field cases are investigated qualitatively (not quantitatively) in detail, we find that the entanglement may be enhanced under an antiparallel magnetic field.     

Quantum diffusion of a particle in a periodic potential with ohmic dissipation

The motion of a particle in a periodic potential is studied at low temperatures where transitions between the potential wells are caused by quantum tunnelling. The theory accounts for the dissipative interaction with an environment which for a wide range of parameters leads to incoherent tunnelling at a rate with a nonanalytic temperature dependence. The influence of an external force is determined and a nonanalytic response is found at T = 0. The case of a biased double-well system is treated too.     

Nonlinear analysis of a wave motion on the surface of a jet moving in a dielectric medium placed in a longitudinal electric field

The possibility of degenerate internal nonlinear resonance interaction between capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid is demonstrated. The jet moves in an ideal incompressible dielectric medium collinearly with an external uniform electrostatic field. It is shown, in particular, that six different resonance situations take place for axisymmetric waves in which primary waves and waves due to the nonlinearity of the equations of hydrodynamics exchange energy.