Modeling a waveguide with a nonlinear insert with a quadratic nonlinearity

The scalar problem of the scattering of a wave from a nonlinear insertion lying in the interior of a waveguide is reduced by the incomplete Galerkin method to the boundary value problem for a Hamiltonian system. The cases in which this problem admits a solution in finite terms are indicated. Examples are given to illustrate specific phenomena due to the nonlinearity of the problem.     

Instability of a flat horizontal interface between a thin layer of a ferrofluid and a thin layer of a nonmagnetic liquid in the presence of a vertical magnetic field

An asymptotic analysis of the equations and boundary conditions of fluid dynamics is performed, and a nonlinear model is constructed for the onset of the development of Rosensweig instability in a thin horizontal ferrofluid layer at rest covered with a thin layer of a lighter nonmagnetic liquid. The surface of a nonmagnetized slab is the lower boundary of the ferrofluid, and the interface with a gas is the upper boundary of the nonmagnetic liquid. The pressure in the gas is constant. The instability being considered arises upon the application of a rather strong uniform vertical magnetic field. The proposed model involves five dimensionless parameters. The critical magnetization of the initial ferrofluid layer with a flat upper boundary and the threshold wave number are found. The effect of the governing parameters on the instability region and on the wavelength of the fastest growing mode is studied in the linear formulation of the problem.     

Surface polaritons in a dielectric at a boundary with a metal in a static electric field

The existence of surface polaritons in a dielectric at a boundary with an ideal metal or superconductor in a static electric field is predicted. The frequency regions in which polaritons exist are substantially different for opposite orientations of the electric field, so that a change in the direction of the field signifies “switching on” or “switching off” of surface polaritons with a fixed frequency. Pis'ma Zh. éksp. Teor. Fiz. 68, No. 12, 876–880 (25 December 1998)     

Application of a reflector with a nonuniform field in a mass-reflectron

The conditions under which the nonuniform compensating field of the reflector of the mass-reflectron can be generated with an acceptable accuracy at the symmetry axis of the reflector and extrapolated to the radial neighborhood of the axial line are determined. The plots that illustrate the distribution of the calculated nonuniform field of the reflector, the possibilities for implementation, and errors of focusing with respect to time of flight in the radial neighborhood are presented. Analytical expressions for the calculation of the time of flight of ions in the reflector in which the field distribution is described using a power series and analytical expressions for the calculation of the field distribution in the reflector in which the time of flight is determined using a power series are derived. A method for the analytical calculation of the compensating nonuniform field of the reflector based on the given dependence of the time of flight in the absence of such a field is proposed using a solution to the Abel integral equation. The solution to this equation yields analytical expressions for the calculation of the compensating field of the reflector in mass-reflectrons that contain the zero-field drift space and regions of acceleration (deceleration) of ions with a uniform field.     

Plasmons at a hole in a screen

The field distribution and the spectrum of plasma eigenmodes are determined for a circular hole in a screen having the form of a hyperboloid of revolution. The spectrum of plasmons is obtained for a planar screen with a circular hole. The symmetric mode with m=1 can be excited in the field of a dipole oriented along the screen plane, whereas the antisymmetric mode with m=0 can be excited by a dipole perpendicular to the screen plane.     

Admittance of a groove on a rigid surface under a grazing flow

The problem of sound diffraction by a groove on a rigid surface in the presence of a grazing flow is considered. The input admittance of the groove is calculated, and its real part is shown to be negative.     

Radiation from a source near a jet

The problem examined is that of analysing the field of sound radiation caused due to the presence of a source in the immediate neighbourhood of a cylindrical jet in motion. The general analysis is restricted to low Mach number flow and special consideration is given to the high and low frequency limiting behaviour of the sound in the far field. The reflexion coefficient obtained in the high frequency case is exactly the same as that obtained by previous investigators for a source in the neighbourhood of an interface in relative motion [1, 2]. Also predicted here, however, is the existence of a “zone of excess attenuation” surrounding the jet fluid in motion, on both sides, far beyond the location of the acoustic source.     

Annihilation of a neutrino pair into a muon-positron pair in a magnetic field

The cross section for the process $\nu _\mu + \bar \nu _e \to \mu ^ - + e^ + $ in a constant magnetic field is calculated with allowance for muon and positron polarizations. The asymptotic behavior of the cross section as a function of the kinematical and the field parameter is investigated in the case where a high-energy neutrino (antineutrino) is scattered by a low-energy antineutrino (neutrino). The effect of a weak field is especially important near the threshold for the free process. The spectrum and the total cross section for the process in a strong field differ markedly from the corresponding characteristics of the free process. Possible astrophysical applications are considered.     

Determination of a response function of a thermocouple using a short acoustic pulse

This paper reports on an experimental technique to determine a response function of a thermocouple using a short acoustic pulse wave. A pulse of 10 ms is generated in a tube filled with 1 bar helium gas. The temperature is measured using the thermocouple. The reference temperature is deduced from the measured pressure on the basis of a laminar oscillating flow theory. The response function of the thermocouple is obtained as a function of frequency below 50 Hz through a comparison between the measured and reference temperatures.     

Design of a suspension of a training sulky

A design study based on a modelling approach was used to optimise the characteristics of a new concept of suspension for training sulkies. The numerical model of sulky including the suspension and, in a second stage, a mechanical model of driver, allowed the definition of technical specifications. They were used to manufacture a prototype of suspension mounted on a current production model of sulky. The prototype of suspension was then tested in the lab and in a racecourse in real conditions of use.The resulting vibration exposure was assessed from vibration measurements. It was slightly lower than the limit value enacted in the European Vibration directive (1.15 m s²), but drastically reduced in comparison with the exposure measured on the original sulky (2.56 m s²). The prototype and moreover the design procedure is currently in a transfer process towards sulky manufacturers.     

Quantum transport of a single photon through a subwavelength hole by a single atom

The localization and transport of a photon through a subwavelength hole with the help of a neutral atom are studied. A method proposed and realized in the study is based on the absorption of a photon by a neutral atom directly in front of a subwavelength hole, the flight of the atom through the hole, and photon emission on the other side of the screen. The influence of the interaction of the excited atom flying through the subwavelength channel with the screen material is estimated. The estimate showed that the atomic excitation can be quenched in holes with diameters smaller than 200 nm, which affects the photon transport efficiency.     

Growth of a nonuniform ripple on a Gaussian beam in a plasma

In the present paper we have investigated the growth of a radially symmetrical ripple, superimposed on a Gaussian beam propagating in a plasma. The effect of the position and the width of the ripple on its growth has been studied in some detail. The present analysis considers two mechanisms for the redistribution of carriers in the plasma and the effect of redistribution on the growth of the ripple; the two mechanisms are nonuniform collision dominated heating of the carriers and the ponderomotive force arising on account of nonuniform intensity distribution. Work supported by NSF (USA) and CSIR (India).     

Reflection of a surface mode from a break in a dielectric waveguide

The problem of surface mode reflection from a break in a dielectric waveguide of arbitrary cross section is solved by a variational method. The dependences of the reflection coefficient on the size and cross-sectional shape of the waveguide are examined. Comparisons with results obtained by other methods, including the data calculated for the 2-D problem (a break in a dielectric plate), are presented. P. L. Kapitsa Institute of Physical Problems, Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 8, pp. 1004–1018, August, 1997.     

Conductance of a junction between a normal metal and a Berezinskii superconductor

The conductance of a junction between a normal metal and a superconductor having the symmetry proposed by Berezinskii is studied theoretically. The main feature of this symmetry is the odd frequency dependence of the anomalous Green’s function, which makes possible the s-wave triplet superconducting state (the Berezinskii superconductor). The Andreev reflection (which links positive and negative energies) is sensitive to the energetic symmetry; as a result, the conductance of the junction involving the Berezinskii superconductor is qualitatively different from the case of a conventional superconductor. Experimentally, the obtained results can be employed to test the possibility of the Berezinskii superconductivity proposed for Na _x CoO₂ and to identify the odd-ω component predicted for superconductor-ferromagnet systems. The text was submitted by the author in English.     

Thermodynamics of a gas-coal massif and a nonuniform gas distribution in a coal bed

The thermodynamic potential of a coal bed is calculated, and the gas pressure in the crack-pore system of the bed is shown to be nonuniformly distributed. This pressure is high in “weak“ regions in the bed, i.e., at the sites of a high porosity, low elastic moduli, and low solubility, as well as at high bearing pressure sites. All these phenomena are caused by the elastic interaction of a gas with a solid-state coal frame and the possibility of the formation of a solid solution in the coal. The relative increase in the gas pressure at these sites is estimated. The results obtained can be used to predict the localization of explosive and outburst regions in coal beds.     

Optimum coupling of a Gaussian beam to a corner reflector with a four-wavelength antenna

The coupling of a Gaussian radiation beam to a corner reflector with a four-wavelength long wire antenna was studied theoretically and experimentally. The antenna configuration in conjunction with a Schottky barrier diode is recently used widely as a fast submillimeter wave detector. The optimum angle focusing the radiation to the antenna has been obtained and is 11° (half-width at the 8.7dB points).     

Pressures for a One-Component Plasma on a Pseudosphere

The classical (i.e., non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a pseudosphere (an infinite surface of constant negative curvature) is considered. In the case of a flat space, it is known that, for a one-component plasma, there are several reasonable definitions of the pressure, and that some of them are not equivalent to each other. In the present paper, this problem is revisited in the case of a pseudosphere. General relations between the different pressures are given. At one special temperature, the model is exactly solvable in the grand canonical ensemble. The grand potential and the one-body density are calculated in a disk, and the thermodynamic limit is investigated. The general relations between the different pressures are checked on the solvable model.     

Self-consistent treatment of a phase transition in a system with a vector order parameter

The problem of the continuation of the Hartree approximation below the transition temperature is considered for a system with a vector order parameter, In contrast to the case of a scalar order parameter, considered in a previous paper, it is found that a self-consistent and gapless approximation can be constructed in the limit of a very large number of vector components. The results agree with those of the spherical model.