Tunnelling process between a semiconductor or a metal and a polymer

The tunnelling lifetime of an electron lying in a p-type orbital localised at a given distance from a semiconductor or a metal is calculated by using Bardeen's method. It is then shown that even in the absence of broad bands, the hole injection process from semiconductors and metals into polymers should follow a Fowler-Nordheim dependence, provided that the current is not bulk-limited. In the semiconductor case, the current can be expressed by a fully analytical formula, and by an approximate one in the case of a metal. It is demonstrated that the effective Fowler-Nordheim barrier is not the mere difference between the metal work function or the semiconductor electron affinity and the HOMO level of the polymer, but a simple function of both levels. Received 6 April 2001 and Received in final form 29 May 2001     

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.     

Formation of a bistructure of a solid in a computer experiment

Molecular-dynamics was used to investigate the structural changes occurring in a three-dimensional solid when the solid is transferred from an amorphous into a crystalline state. Crystal cells of a new type — pentadecahedrons with five square lateral faces and ten regular triangular faces at the vertices of a cell — were found for the first time in a computer experiment. It is shown that a bistructure consisting of crystal cells of different types, including cells with five-fold symmetry axes, are stable in the solid. Fiz. Tverd. Tela (St. Petersburg) 40, 1919–1924 (October 1998)     

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.     

Rigorous solution of a problem for a cylindrical cavity containing a ferrite

Conclusions Equation (6) relates the complex frequency for a TM_nmo mode in a cylindrical cavity to the geometrical parameters, ferrite parameters, and volume and position of the specimen.Formula (6) is a generalization of characteristic equations previously derived [3, 4], which are of great value.The dispersion equation of (6) is of interest in that it allows one to calculate the effects of the dielectric parameters on the cavity, which is of value if a large tuning range is needed.Numerical results are rather laborious to obtain, but some valuable conclusions can be drawn in a relatively simple fashion, as will be shown in a forthcoming paper.     

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.     

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).     

Parastatistics and phase transition from a cluster as a fluctuation to a cluster as a distinguishable object

A phase transition of the first kind is a jump of a function, a phase transition of the second kind is a jump of its first derivative, a phase transition of the third kind, a jump of the second derivative. A phase transition from one statistic to another is very gradual, but finally it is as considerable as the phase transition of the first kind. However, we cannot introduce a clearly defined parameter to which this transition corresponds. This is due to the fact that the fluctuations near the critical point are huge, and this violates, in the vicinity of that point, the main law of equilibrium thermodynamics, which asserts that fluctuations are relatively small. The paper describes the transition in the supercritical fluid region of equilibrium thermodynamics from parastatistics to mixed statistics, in which the Boltzmann statistics is realized for long-living clusters. In economics this corresponds to a negative nominal credit rate. Examples of this non-standard situation are presented.     

Spectrum of a particle on a polyhedron enclosing a synthetic magnetic monopole

We consider a single particle hopping on a tight binding lattice formed by the vertices of a regular polyhedron and discuss the effect of a magnetic monopole enclosed in the polyhedron. The presence of the monopole induces phases on the hopping terms, given by Peierls substitution. By requiring the flux through each face of a regular polyhedron to be the same, Dirac’s quantization condition is obtained in this discrete setting. For each regular polyhedron, we calculate the energy spectrum for an arbitrary value of the flux through a Dirac string coming in from one of the faces. We find that the energy levels are degenerate only when the flux through the Dirac string corresponds to a quantized monopole. We show that the degeneracies in the presence of the monopole can be classified using the double group of the symmetry of the polyhedron and label all energy levels with corresponding irreducible representations.     

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.     

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)     

Vibration of a liquid with a free surface in a spinning spherical tank

The problem of forced fluid vibrations in a partially filled spinning spherical tank is solved numerically by using the finite element method. The governing equations include Coriolis acceleration and spatially homogeneous vorticity. An exponential instability is detected in the present simulation for fill ratios below 0·5 and centrifugal acceleration to thrust ratios less than 1·7. This fictitious instability appears in the model as a result of the homogeneous vortex assumption since the free slosh equations are neutrally stable in the Liapunov sense.     

Towards a predictive scenario of a burning accident in a mining passage

To reveal the inner mechanisms of a combustion accident in a coalmine, the key stages and characteristics of premixed flame front evolution such as the flame shapes, propagation speeds, acceleration rates, run-up distances and flame-generated velocity profiles are scrutinised. The theories of globally spherical, expanding flames and of finger-flame acceleration are combined into a general analytical formulation. Two-dimensional and cylindrical mining passages are studied, with noticeably stronger acceleration found in the cylindrical geometry. The entire acceleration scenario may promote the total burning rate by up to two orders of magnitude, to a near-sonic value. Starting with gaseous combustion, the analysis is subsequently extended to gaseous-dusty environments. Specifically, combustible dust (e.g. coal), inert dust (e.g. sand), and their combination are considered, and the influence of the size and concentration of the dust particles is quantified. In particular, small particles influence flame propagation more than large ones, and flame acceleration increases with the concentration of a combustible dust, until the concentration attains a certain limit.     

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.     

Testing a Bell-type inequality with a micromaser

We propose a phase-sensitive micromaser setup to demonstrate experimentally a violation of a Bell-type inequality. The interaction of atoms with the cavity field produces entanglement between the atoms and the cavity photons and therefore also between the atoms. We derive a Bell-type inequality for the atom-atom correlations and show that it can be violated not only in an idealized model but also under realistic circumstances when various sources of additional randomness are accounted for. Among them are the energy dissipation in the resonator and the Poissonian arrival statistics of the atoms.Prof. F.P. Schäfer on the occasion of his 65th birthday.     

Radiation of a Cascade near a Plane Interface and in a Planar Layer

In order to detect cosmic rays and ultrahigh-energy neutrinos, a number of experiments based on the detection of radio radiation of cascades initiated by these particles in dense media such as ground ice massifs or lunar regolith have been developed. In most of the experiments, radio radiation is detected at the emission to the atmosphere or cosmic space rather than in a dense medium. Consequently, it is necessary to calculate the radiation of a cascade taking into account an interface between two media. This problem is usually solved numerically by the Monte Carlo method. A simple analytical expression for a radiation field in the wave zone of the less dense medium has been obtained for the case of development of the cascade in the dense medium and the crossing of the interface between two media by radiation. The effect of the third, additional medium on the radiation field of the cascade has also been considered.     

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.     

Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary

We study the random motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary with a nonzero classical constant velocity in a direction parallel to the plane. We calculate the mean squared fluctuations in the velocity and position of the test particle taking into account both fluctuating electric and magnetic forces. Our results show that the influence of fluctuating magnetic fields is, in general, of the higher order than that caused by fluctuating electric fields and is thus negligible.     

Arbitrary tensor concomitants of a bivector and a metric in a space-time manifold

In the general theory of relativity the energy-momentum tensor due to an electromagnetic field is taken to be a symmetric rank-two tensor concomitant of a bivector and the metric tensor. As a step in the discussion of the possible uniqueness of this tensor we display a method for finding all tensor concomitants of a bivector and a metric in a space-time manifold.