“Shallow-water” and “deep-water” approximations in the theory of the disruptive instability of thin current-carrying layers

Within the framework of the two-fluid hydrodynamics of plasmas it is shown that the problem instability of a thin current-carrying layer admits two limiting cases which allow analytic solutions and complement one another. These limits are analogous to the well-known shallow-water and deep-water approximations in the fluid mechanical “wave-breaking” instability. In this case, the long-wave limit coincides with the “quasi-Chaplygin” dynamic system of Bulanov and Sasorov, Fiz Plazmy 4, 746 (1978) [Sov. J. Plasma Phys. 4, 418 (1978)], while the short-wavelength limit corresponds to the phenomenological model of Trubnikov, Usp. Fiz. Nauk 160, 167 (1990) [Sov. Phys. Usp. 33, 87 (1990)], for the clumping of “elementary” currents. In the latter case, strong collapse is unavoidable with the appearance of current filaments that trap a finite current. Zh. éksp. Teor. Fiz. 113, 1313–1318 (April 1998)     

Two-particle correlations in 1D-lattice systems with δ-interactions

The problem of two interacting particles in finite closed and open chains is solved by the Lifshitz method. The “density-density” correlation function, the dependence of the “surface” energy on the two-particle interaction energy and number of links in the chain, and the two-particle distribution on the chain are found and the nature of the ground state is clarified. Fiz. Tverd. Tela (St. Petersburg) 40, 366–370 (February 1998)     

Activated drift motion of a classical particle with a dynamical pinning effect

A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of “ageing” effects. The depth of each trap increases with the time elapsed since the particle has fallen into it. The consequences of this dynamical pinning are studied, and velocity-force characteristics are numerically obtained. A special attention is paid to the situation where the particle is pulled with a spring to ensure a finite average velocity. In the low velocity regime, the presence of a broad distribution of trapping times leads to suppression of linear response, replaced by a threshold or by sublinear dynamics. A regime of strong fluctuations is obtained when the particle is driven at intermediate velocities. Received: 12 December 1997 / Accepted: 25 February 1998     

New types of inhomogeneous nuclear spin-spin resonance in thin antiferromagnetic films

Several new resonant size effects in the bulk nuclear-spin dynamics of a thin magnetic film are investigated theoretically. The physical mechanism responsible for their appearance in a finite magnet is the indirect exchange of nuclear spins through a field of virtual “Lamb” phonons. Fiz. Tverd. Tela (St. Petersburg) 39, 1817–1823 (October 1997)     

Critical velocity and event horizon in pair-correlated systems with “relativistic” fermionic quasiparticles

The condition for the appearance of an event horizon is considered in pair-correlated systems (superfluids and superconductors) in which the fermionic quasiparticles obey “relativistic” equations. In these systems the Landau critical velocity of superflow corresponds to the speed of light. In conventional systems, such as s-wave superconductors, the superflow remains stable even above the Landau threshold. We show, however, that, in “ relativistic” systems, the quantum vacuum becomes unstable and the superflow collapses after the “speed of light” is reached, so that the horizon cannot appear. Thus an equilibrium dissipationless superflow state and the horizon are incompatible on account of quantum effects. This negative result is consistent with the quantum Hawking radiation from the horizon, which would lead to a dissipation of the flow. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 124–129 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Influence of local dispersion on transient processes accompanying the generation of rf radiation by an electromagnetic shock wave

Transient processes accompanying the conversion of a video pulse into a radio pulse in a nonlinear transmission line having hysteretic properties are studied. It is established that the transition process leading to the establishment of “steady-state” (close in amplitude) oscillations has a minimum when the electromagnetic shock wave front is phase-matched with the wave excited by it at a frequency near the minimum local dispersion of the group velocity. Zh. Tekh. Fiz. 68, 89–95 (January 1998)     

Barkhausen effect in stepped motion of a plane domain boundary in gadolinium molybdate

Barkhausen pulses generated in stepped motion of a single plane domain boundary (PDB) are investigated experimentally in single-crystalline wafers of the extrinsic ferroelastic ferroelectric gadolinium molybdate containing artificial pinning centers of the “field inhomogeneity” type near the edges of the sample. Two scenarios of the evolution of a PDB in interaction with “defects” are proposed on the basis of analyzing the shape of the pulses in a linearly increasing field: small changes of the pulse shape in a weak field and the generation of wedge domains in a strong field. The proposed mechanism of PDB motion due to the generation of steps near the edge of the sample and their longitudinal motion provides a means for explaining the experimentally observed linear field dependence of the PDB velocity and for determining the velocity of the steps. Fiz. Tverd. Tela (St. Petersburg) 41, 301–305 (February 1999)     

Effective interaction potential and ordered structures of dust particles in a gas-discharge plasma

An effective potential is proposed for the interaction between dust particles in a gas-discharge plasma which takes account of the following physical factors: the spatial dependence of the particle charges on the floating potential of the plasma, anisotropy of the interaction, resulting from focusing of the negatively charged particles of the drift ion current, and aspects of screening of the dust particles by plasma electrons and ions which interact strongly with them and recombine faster in their vicinity and on their surface. Monte Carlo calculations explain the formation of threadlike structures of dispersed particles, and also “transverse crystallization” of these “threads” in a stratified gas-discharge plasma. Zh. éksp. Teor. Fiz. 115, 819–836 (March 1999)     

Nearly spherical vesicles: Shape fluctuations

Isolated vesicles with “insufficient” area have a finite surface tension and spherical shapes, whereas vesicles with “excess” area are necessarily aspherical. We consider the crossover behavior between both kinds of vesicles occurring as the equilibrium area increases. In the mean field approximation it is a second-order phase transition from the spherical to aspherical shape. We demonstrate the fluctuations smear the transition. The critical behavior of the amplitudes of fluctuations and of their characteristic times is investigated. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 203–208 (10 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On the problem of the relation between phason elasticity and phason dynamics in quasicrystals

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals [S. Francoual et al. Phys. Rev. Lett. 91, 225501 (2003); A. Létoublon et al. 54, 753 (2001)]. We will show that the data reported call for a more detailed development of the elasticity theory of Jarić and Nelsson [M.V. Jarić and D.R. Nelsson, Phys. Rev. B 37, 4458 (1988)] in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a “satellite position” at a distance q from each Bragg peak; that (2) has an intensity that scales with the intensity of the corresponding Bragg peak; (3) falls off as 1/q²; and (4) has a time decay constant that is proportional to 1/Dq². It is thus superfluous to call for a picture of “phason waves” in order to explain such data, especially as such “waves” violate many physical principles.     

Magnetic anisotropy of a system of nanocrystalline BaO·6Fe2O3 particles

The anisotropy of a system of barium ferrite particles with an average diameter of 60 nm has been studied. The effective anisotropy constant has been determined in the temperature range from 4.2 K to T _c by the law governing approach to saturation magnetization. The observed deviation from the magnetocrystalline anisotropy constant is explained as due to a negative contribution of the “surface” anisotropy constant. An estimate is made of this contribution as a function of particle size. Fiz. Tverd. Tela (St. Petersburg) 40, 1894–1897 (October 1998)     

Ionization of a two-electron atom in a strong electromagnetic field

A one-dimensional model of a helium atom in an intense field of a femtosecond electromagnetic pulse has been constructed using the Hartree technique. “Exact” calculations have been compared to the approximations of “frozen” and “passive” electrons. A nonmonotonic dependence of the single-electron ionization probability on the radiation intensity has been detected. Minima in the ionization probability are due to multiphoton resonances between different atomic states due to the dynamic Stark effect. We suggest that the ionization suppression is due to the interference stabilization in this case. Zh. éksp. Teor. Fiz. 112, 470–482 (August 1997)     

Anomaly-free quantization of a string in two-dimensional space-time

An anomaly-free quantum theory of a relativistic string is constructed in two-dimensional space-time. The states of the string are found to be similar to the states of a massless chiral quantum particle. This result is obtained by generalizing the concept of an “operator” in quantum field theory. Zh. éksp. Teor. Fiz. 113, 1566–1578 (May 1998)     

A Colorimetric and Ratiometric Fluorescent Chemosensor for Fluoride Based on Proton Transfer

N-Phenyl-N’-(3-quinolinyl)urea (1) has been developed as a highly selective colorimetric and ratiometric fluorescent chemosensor for fluoride ion based on a proton transfer mechanism. Evidences for the mechanism were provided by UV-vis and fluorescence titration and especially ¹H and ¹⁹F NMR experiments. The sensor gave the largest ratiometric fluorescent response reported so far (R_max/R_min = 2620) to fluoride. Taking H⁺ as the “recovering reagent”, the sensor can be reversibly “used” and “recovered” for several cycles with only a slight decay of the response ability.     

On the properties of small-world network models

We study the small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder strength. We show that any finite value of the disorder is able to trigger a “small-world” behaviour as soon as the initial lattice is big enough, and study the crossover between a regular lattice and a “small-world” one. These results are corroborated by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region. In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite. [0.5cm] Received 29 March 1999 and Received in final form 21 May 1999     

Dynamic properties of moderately concentrated magnetic liquids

On the basis of statistical analysis, we derive expressions for the dynamic susceptibility, magnetization relaxation times, and the effective rheological characteristics of a moderately concentrated homogeneous ferrocolloid consisting of identical spherical ferroparticles suspended in a Newtonian liquid. The magnetic moment of a particle is assumed constant and rigidly “frozen” into the body of the particle. We also estimate how the magnetodipole and hydrodynamic interactions of the particles influence the effective dynamic properties of the ferrocolloid. Zh. éksp. Teor. Fiz. 114, 892–909 (September 1998)     

Theory of one-dimensional and quasi-one-dimensional heat conduction

It is shown that the heat conduction process in a one-dimensional flow of a fluid moving with a velocity V in a constant temperature field follows a law that is considerably more complicated than an “ordinary” exponential law. It is demonstrated that in the quasi-one-dimensional case the heat conduction process in an abstract space of dimension 1+ɛ, where ɛ varies from zero to unity, is described by a modified Fourier equation. Its solution for an infinite space is found. Zh. Tekh. Fiz. 67, 8–12 (July 1997)     

The impact of collisions on platelet distribution in the blood flow

The impact of platelet collisions on their distribution in a viscous liquid flow has been analyzed. It has been shown that platelet distribution in the flow perpendicular to current lines resulting from their collisions can be described as “shear” diffusion. In the wide physiological range of shear velocities specific for blood, the coefficient of “shear” diffusion is much larger than the coefficient of “Brownian” diffusion. For a parabolic fluid velocity profile (Poiseuille flow) in cylindrical vessel “shear” diffusion causes uneven radial distribution of platelets over the vessel radius. “Shear” diffusion causes platelet concentration to grow from the wall toward the center (vessel axis). This effect appears to be a consequence of the specific distribution of platelet collision frequency reaching its maximum at the vessel wall.     

Electronic spectrum of a two-dimensional Fibonacci lattice

The electronic spectrum and wave functions of a new quasicrystal structure—a two-dimensional Fibonacci lattice—are investigated in the tight-binding approximation using the method of the level statistics. This is a self-similar structure consisting of three elementary structural units. The “central” and “nodal” decoration of this structure are examined. It is shown that the electronic energy spectrum of a two-dimensional Fibonacci lattice contains a singular part, but in contrast to a one-dimensional Fibonacci lattice the spectrum does not contain a hierarchical gap structure. The measure of allowed states (Lebesgue measure) of the spectrum is different from zero, and for “central” decoration it is close to 1. The character of the localization of the wave functions is investigated, and it is found that the wave functions are “critical.” Zh. éksp. Teor. Fiz. 116, 1834–1842 (November 1999)