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     

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)     

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.     

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.     

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.     

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)     

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.     

Interaction of a premixed flame with a liquid fuel film on a wall

In piston engines and in gas turbines, the injection of liquid fuel often leads to the formation of a liquid film on the combustor wall. If a flame reaches this zone, undesired phenomena such as coking may occur and diminish the lifetime of the engine. Moreover, the effect of such an interaction on maximum wall heat fluxes, flame quenching, and pollutant formation is largely unknown. This paper presents a numerical study of the interaction of a premixed flame with a cold wall covered with a film of liquid fuel. Simulations show that the presence of the film leads to a very rich zone at the wall in which the flame cannot propagate. As a result, the flame wall distance remains larger with liquid fuel than it is for a dry wall, and maximum heat fluxes are smaller. The nature of the interaction of flame wall interaction with a liquid fuel is also different from the classical flame/dry wall interaction: it is controlled mainly by chemical mechanisms and not by the thermal quenching effect observed for flames interacting with dry walls: the existence of a very rich zone created above the liquid film is the main mechanism controlling quenching.     

Relaxation of a dislocation in a nanocrystallite

Experimental studies of dislocations in nanoparticles are just beginning. The corresponding theoretical models are still lacking. In this context, the author analyzes relaxation of a dislocation in a nanoparticle. Mechanistically, this process is considered to occur primarily via dislocation drift induced by the stress-related image forces. Elementary dislocation displacements include the formation of a kink at one of the sides of the dislocation line, its diffusion along this line, and annihilation at the opposite side. For this mechanism, the dependence of the time of dislocation disappearance on the nanoparticle size has been identified.     

Inferring a Property of a Large System from a Small Number of Samples

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.     

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.     

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).     

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.     

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.     

Discrete accidental symmetry for a particle in a constant magnetic field on a torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the 1/r and r² potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the θ-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters θ_x and θ_y explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.     

Propagation of a localized wavepacket in a metamaterial with a negative index of refraction

Propagation properties of electromagnetic waves in a medium with a negative index of refraction are investigated. A model of a physical signal that combines simultaneously qualities of both a spatially-localized beam and a wavepacket was used as the incident wave. Such a choice was necessary because of the strong frequency dispersion of metamaterials in the spectral region with a negative index of refraction. An approximate analytical solution was derived that describes the propagation dynamics of such a signal through a slab made of material showing simultaneously a negative dielectric permittivity and magnetic permeability. Presented at the XIIIth International Conference “Physics of Pulse Discharges in Condensed Media,” August 21–25, 2007, Nikolaev, Ukraine. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 2, pp. 187–193, March–April, 2008.     

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.     

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.