On the asymmetry of a random walk in the presence of a field

Any ensemble of random walks with symmetric transition probabilities will have symmetric properties. However, any single realization of such a random walk may be asymmetric. In an earlier paper, Weiss and Weissman developed a measure of asymmetry and applied it to random walks in the absence of a field, showing that the degree of asymmetry (in the diffusion limit) is independent of time and that the most probable degree of asymmetry corresponds to the maximum possible. We show in the present paper how the presence of a symmetric field can change this result, both in making the degree of asymmetry depend on time, and driving the random walk toward a more symmetric state.     

Effect of the field of a nonlinear electromagnetic wave on the shape of a soliton in a semiconductor superlattice

The effect of the electric component of the field of a high-frequency (HF) nonlinear electromagnetic (EM) wave on the propagation of a solitary EM wave (soliton) in a quantum semiconductor superlattice is studied. It is noted that in the collisionless approximation, the solution of the modified sine-Gordon equation corresponding to the amplification of an EM pulse that, with allowance made for interminiband electron transitions, transforms into a dissipative soliton is possible. The effect of electron collisions with irregularities of the crystal lattice on the soliton dynamics under the action of the field of a HF nonlinear wave is considered. The condition for an increase in the traveling time of the solitary wave is found.     

Self-consistent solutions of the problem of the interaction of a two-frequency field with a system of three-level atoms in the form of a phase-modulated simulton and a Raman soliton

This paper discusses features of the interaction of a system of three-level atoms with a bichromatic electromagnetic field. Steady-state solutions are found in the form of unimodal and nonunimodal solitary waves corresponding to a pair of pulses in the form of a simulton or a Raman soliton. An analytic form of the solutions is found, corresponding to a phase-modulated simulton and a Raman soliton. The conditions are determined for exciting them. The resulting solutions are of interest from the standpoint of the mechanism for forming the two-frequency coupled excitations observed in various experiments. Zh. éksp. Teor. Fiz. 113, 747–762 (February 1998)     

Anisotropy of the oscillation dynamics of a breather on a trap in the electroconvective twist structure of a nematic

The oscillation dynamics of dislocations with a dissociated nucleus in the electroconvective twist structure of a nematic liquid crystal has been studied. The initial state of the roll twist structure is unstable. One of the origins of this is the helical flows of the nematic in the neighboring rolls with the antiparallel axial velocity components. As a result, oscillating or “breathing” defects are formed, which have the properties of breathers and are described by the sine-Gordon equation. It has been demonstrated that the space-time anisotropy of the character of motion of the dislocations in opposite directions orthogonal to the roll structure takes place in such a nonstationary system.     

Theoretical analysis of the formation of a layered ice structure at the surface of a plate placed in a flow of a supercooled water aerosol

The motion of the front of crystallization and the growth of a film at the surface of a plate are analyzed in the case of a laminar and in the case of a turbulent flow mode. Conditions are determined under which there occurs a transition from a matt inhomogeneous structure to a transparent homogeneous structure of ice. It is shown that, for a film to be steadily preserved at the plate surface, the film thickness must be larger than a critical equilibrium-thickness value h _b.c, in which case a transparent homogeneous structure of ice is formed. Otherwise, the film at the plate surface is unstable and disappears in the course of time. The icing of aircrafts is the most important application of the results obtained in this study.     

On the theory of the alignment of a polar molecule in a non-polar solvent

The alignment average of a dilute polar substance dissolved in a non-polar solvent may be derived from the NMR spectrum of the polar component. Likewise, the Kerr effect is related to this quantity.In this paper a series expansion of the alignment of a polar molecule in a non-polar solvent is presented for a rigid-lattice model, first introduced by Van Vleck for the dielectric constant of a very dilute solution. Different results up to second order in the dipolar interaction are obtained for a simple, a body centred, or a face centred cubic lattice and a lattice whose lattice points are uniformly distributed in a continuum. The latter formula is compared with that calculated on the basis of the Lorentz local field model and with that of Buckingham in which the interaction between the dipoles themselves is neglected.     

On the dynamics of a particle on a cone

A detailed study of the classical and quantum mechanics of a free particle on a double cone and a particle bound to its tip by a harmonic oscillator potential is presented.     

Calculation of the characteristics of the radiation from a generator with a virtual cathode

A three-dimensional computer model, described by a system of Maxwell-Vlasov equations, for the interaction of a plasma with the electromagnetic field was used to calculate the excitation of a field by a relativistic electron beam with a virtual cathode oscillating in a resonance chamber. The characteristics of the generator radiation are investigated. Zh. Tekh. Fiz. 69, 87–92 (February 1999)     

Influence of the Porosity of the Surface of a Graphite Furnace on the Atomization of a Sample

The influence of the wear of a tube graphite furnace and the morphological features of its surface on the formation of an atomic-absorption signal has been investigated. Electron-microscopic and mass-spectrometric investigations have shown that, prior to atomization, copper in the form of elementary metal microparticles is found not only on the surface of the furnace but also in the bulk of its pores. Free atoms are formed as a result of the concurrent processes of atomization of a sample on the surface of the furnace and in the bulk of its pores. The change in the apparent energy of formation of free atoms of metals interacting actively with graphite in the process of atomization and the inflection on their Arrhenius plot have been explained qualitatively.     

On the initiation of a corona discharge near the surface of a nonlinearly oscillating liquid layer on the surface of a charged hailstone

An expression is derived for the electric field strength near a wet hailstone in an approximation quadratic in the oscillation amplitude of a charged liquid layer on its surface. It is found that the electric field strength in a small neighborhood of the capillary wave crests grows with the number of a mode governing the initial deformation of the equilibrium (spherical) shape of the liquid layer. Even if the charge is small (when the Rayleigh parameter of the hailstone equals one-hundredth of the value critical for stability against the self-charge), the electric field near the hailstone is high enough for initiating a corona discharge in its vicinity.     

Investigation of the interaction of a shock wave with the zone of a pulsed surface discharge in a rectangular channel

This study concerns the effect of the zone of a plane surface energy deposition on a gas-dynamic flow with a shock wave of M = 2.3–2.7 in a channel with a rectangular cross section. The source of the pulsed energy is a distributed sliding nanosecond discharge that develops in an approximately 1-mm-thick layer on a surface of 100 × 30 mm². The results of a 3D numerical simulation of the problem on the basis of the Navier-Stokes equations for a compressed gas are presented and compared with the experimental shadow images.     

Influence of the polarity of a medium on the photonics of a merocyanine dye with a high quadratic polarizability

The influence of the polarity of a medium on the spectral and luminescent properties of 2-[(2E,4E)-6-(1,3,3-trimethyl-2,3-dihydro-1H-2-indolyliden)-2,4-hexadienyliden]malononitrile (THDM) in solutions and polymer matrices is studied at room temperature under conditions of steady-state and pulsed laser excitation. A large bathochromic shift of the absorption spectra observed upon an increase in the polarity of a solvent is caused by a strong increase in the molecular dipole moment μ due to a transition of molecules from the ground state (μ_g = 7.6 D) to an excited Franck-Condon state (μ^FC = 33.5 D). Based on the solvatochromic data, the quadratic polarizability was calculated to be β = (3.2 ± 0.6) × 10^?28 esu, which is close to the experimentally determined value β_ex = (3.9 ± 0.2) × 10^?28 esu. A strong narrowing of the fluorescence spectra in comparison with the absorption spectra is observed upon an increase in the solvent polarity. This narrowing is explained by a decrease in the bond length alternation parameter and by weakening of vibronic interactions in the singlet excited state. The dynamic solvatofluorochromism of THDM in the picosecond range is caused by reorientations of molecules of the polar environment occurring during a time period consistent with the dielectric relaxation time of these molecules.     

On the motion of a charged particle in the field of a magnetic monopole

A quantum mechanical treatment of the motion of a charged particle in the field of a fixed magnetic monopole is given, based on a representation of the corresponding vector potential by means of a distribution. The results are closely similar to those obtained in the work of Wu and Yang, which stems from ideas borrowed from mathematical fiber bundle theory. We believe that our method follows more closely the usual quantum mechanical procedures and provides an alternative approach to that of Wu and Yang. Although the present paper deals with non-relativistic problem, it is clear that the extension to the case of a Pauli or Dirac particle can be easily done using spinor monopole harmonics.     

On the Mechanism of the Generation of Runaway Electrons after a Breakdown of a Gap

JETP Letters - Data that explain the generation of runaway electrons after the breakdown of a gap with a sharply inhomogeneous distribution of the electric field strength are presented. Using a...     

Effect of the shape of a particle heated to a high temperature on the gas-phase ignition of a liquid film

The process of gas-phase ignition of a liquid fuel film with incandescent small metal particles in the form of a parallelepiped, disk, or hemisphere was numerically simulated. The magnitude of influence of the particle shape on the delay time of ignition of a liquid fuel was determined. The range of parameters of the particle at which the effect of its shape on the ignition delay time is unimportant was established.     

Toward the theory of spin waves on the surface of a nanotube with a superlattice in a magnetic field

Electron spin waves on the surface of a semiconductor nanotube with a superlattice in a magnetic field have been considered. The spin-wave spectra and regions of collisionless wave damping have been found. It has been shown that the spin waves do not exhibit damping on small-radius tubes with a degenerate electron gas.     

Kinetics of the irreversible propagation of a thermal instability in the presence of a nonuniform temperature distribution over the cross section of a superconducting composite

The conditions for the irreversible propagation of a normal zone along a composite superconductor are investigated within the model of a continuous medium with consideration of its transverse thermal conductivity under the assumption of a uniform distribution of the current over the cross section of the wire. The numerical experiments performed for a currentcarrying element of circular cross section with variation of the cooling rate and the transverse dimensions are compared with known results of the one-dimensional theory. It is shown that the one-dimensional theory, as opposed to the two-dimensional theory, leads to underestimated values of the velocity of a thermal instability. The size effect modifies the propagation conditions of a normal zone to the greatest extent as the heat-transfer coefficient increases. This law is based on an increase in temperature at the center of the wire with a simultaneous decrease on its surface, as a result of which the mean temperature over the cross section of the composite increases as its radius increases. Zh. Tekh. Fiz. 68, 53–57 (January 1998)     

Validating a hypothesis of the form of a correlation function of a stationary random process

The problem of validating a statistical hypothesis stating that the correlation function of a stationary Gaussian random process possesses a specified form is considered for the case in which measurements of the process are performed at arbitrary moments of time. Anzhero-Sudzhen Division, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 10–15, April, 1998.     

On the interaction of a shear wave with a moving domain wall in a nonlinear response of the spin subsystem

A solution of the problem of parametric interaction between a plane monochromatic shear wave and a uniformly moving 180°-domain wall of a garnet-ferrite crystal is obtained in the exchangeless magnetostatic approximation by using the perturbation method under the conditions of a nonlinear response of the spin subsystem. It is shown that in a ferromagnetic resonance with magnetostatic oscillation of stray fields, the nonlinearity of the spin subsystem leads to the excitation of shear waves of triple frequency, which may have amplitudes comparable with that of the incident wave for oscillations doubly localized by a domain wall.     

Shortening of a laser pulse with a self-modulated phase at the focus of a lens

We found that, at the focus of a chromatic lens, a laser pulse with a self-modulated phase can be shortened due to the radial dependence of the group delay imposed by the lens. Normally, this group delay stretches a short pulse into a long pulse by spreading the arrival time of the pulse at the focus. However, for a pulse with a self-modulated phase, it causes the fields with different phases to overlap, thus resulting in destructive interference that shortens the pulse.