Pinning of vortices and critical current in the presence of parallel twinning planes

Magnetic and transport properties of superconductors with a periodic array of twinning planes (TP's) are studied for the case of an increase of the critical temperature in the neighborhood of a TP. Based on the modified London model, the critical magnetic field H_c1, the barrier field H_s, and the critical current j_c(H) are calculated for low temperatures much less than T_c. For resonant vortex configurations, a peak in the curve j_c(H) is predicted with a peak value which cannot be larger than 10⁶ A/cm². Furthermore, the interplay of the bulk and surface pinning for TT_c as well as the magnetic and transport properties for T_c0c are studied.On leave from the Institute of Physics, Belgrade University, Belgrade, Yugoslavia. Also affiliated with Fachbereich Physik WE 5, Freie Universität Berlin, D-1000 Berlin 33.     

Peculiarities of the current-voltage characteristics of a Josephson medium in a YBCO high-temperature superconductor

The influence of a weak magnetic field (H < 150 Oe) on the current-voltage (I-U) characteristic of a YBa₂Cu₃O_{7 ? x} (YBCO) high-temperature superconductor (HTSC) near the superconducting transition temperature has been studied. It is established that there exist narrow (<0.2 K) temperature regions where the I-U curve exhibits sharp bending for H < 30 Oe and the ohmic behavior changes to a quadratic dependence of the voltage on current in a region of several milliamperes. At higher temperatures, the I-U curve bending exhibits smearing. This behavior is observed at a temperature below that corresponding to a zero critical current. Above a certain current, the temperature and magnetic field exhibit equivalent effects on the I-U curve of YBCO. Experimental results are explained by a sharp decrease in the critical currents of intergranular Josephson junctions under the action of magnetic field and by the current-induced formation of uncoupled (with respect to the order parameter) superconducting grains. Characteristic currents for the transition of the intergranular Josephson medium into an incoherent state are determined and the first critical fields in YBCO are evaluated.     

Influence of grain properties on the Abrikosov vortices interaction with Josephson junction

The problem of the displacement of an Abrikosov vortex is investigated when the magnetic field decreases to H _cl ^G in a grain of a type II superconductor. It is shown that near grain boundaries the vortex line generates an intergranular current which depends on the normalized grain size τ and the anisotropy ratio ν. These parameters strongly influence the conditions of the Josephson vortex generation as a result of the interaction of the Abrikosov vortex with the Josephson junction. We support our theory with calculations of the intergrain critical current taking into account two types of the vortex configuration, triangular and square, for different grain characteristics. The results are of interest for the charge transport in granular superconductors as well as the relaxation process in devices that contain Josephson junctions in micro- and nanoelectronics in magnetic field.     

The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet

The role of coherent vortices near the turbulent/non-turbulent (T/NT) interface in a turbulent plane jet is analysed by a direct numerical simulation (DNS). The coherent vortices near the jet edge consist of large-scale vortical structures (LSVSs) maintained by the mean shear and intense vorticity structures (IVSs) created by the background fluctuating turbulence field. The radius of the LSVS is equal to the Taylor micro-scale R(lsvs)≈λ, while the radius of the IVS is of the order of the Kolmogorov micro-scale R(ivs)~η. The LSVSs are responsible for the observed vorticity jump at the T/NT interface, being of the order of the Taylor micro-scale. The coherent vortices in the proximity of the T/NT interface are preferentially aligned with the tangent to the T/NT interface and are responsible for the viscous dissipation of kinetic energy near the T/NT interface and to the characteristic shape of the enstrophy viscous diffusion observed at that location.     

Josephson vortices in weakly-coupled superconductors as topological solitons of the sine-Gordon equations for phase differences

We present a mathematically rigorous solution of the problem of magnetic properties of weakly-coupled superconducting multilayers with an arbitrary number N≥2 of superconducting layers in external parallel magnetic fields H>0. By minimizing a relevant Gibbs free-energy functional, we show that the equilibrium vortex structure is given by a new class of soliton solutions: namely, topological solitons of a system of N−1 coupled static sine-Gordon equations for the phase differences in a finite spatial interval I=[−L, L]. A complete classification of the new soliton solutions is presented. For N=2,3, and N=∞, exact, closed-form analytical expressions are derived. The special case L=∞, H=0 is considered separately. Non-soliton solutions are also analyzed: they are shown to be saddle points of the Gibbs free-energy functional. A comparison with the experiment is drawn.     

Propagation of a planar shock thermal wave in a nonlinear medium

Conditions are analyzed for a strong discontinuity of a thermal field in a nonlinear medium, possessing thermal relaxation. The solution of the heattransfer equations is obtained in the region between the mobile boundaries and the front of the strong discontinuity.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 3, pp. 436–443, September, 1985.     

Stuart vortices in a stratified mixing layer: the Holmboe model

Asymptotic techniques are used to model the quasi-steady state vortices that have been observed in two-dimensional simulations of vortex roll-up in stratified shear layers. A time-independent nonlinear critical layer analysis is used to find a family of steady-state finite amplitude vortices in the Holmboe model of an inviscid stratified shear layer, with the vorticity inside closed streamlines based on the Stuart vortex. The vortices are compared to results of simulations and also an alternative model where the vorticity was constant inside closed streamlines.     

Effective electrical characteristics of a three-dimensional composite medium

The electrical characteristics of a three-dimensional composite consisting of components with strongly different conductivities, σ₁ and σ₂, are theoretically described. The quadratic field and current correlators at the percolation threshold are determined, and the distribution of the energy dissipated in the composite between the components is found. The lower limit of the critical index of the nonlinear effective conductivity is estimated.     

Specific features of a model with Josephson frustrated arrays

Using the model for layered superstructures with the Josephson bond and additional boundary conditions (frustration), the authors consider the dependence of the critical temperatureT _c ^(p) on the number P of evaporated layers. The characteristics defined through precise solutions of the Josephson functions functional distinctions on the fluxon latticeT _c ^(p) are presented.     

Fourier description of the propagation and focusing of an extraordinary beam in a planar uniaxial medium

The scalar-angular-spectrum approach is used to examine a focused extraordinary wave propagating along an arbitrary direction in a homogeneous uniaxial planar medium, and the Fraunhofer diffraction formula is generalized for this case. The size of the focal spot is found to be inversely proportional to an effective index, depending on the refractive indices and the propagation direction. The validity of the paraxial model is checked by nonparaxial (but scalar) numerical calculations. They show that the paraxial formulas predict the spot size correctly, but if the beam propagates neither parallel with nor perpendicular to the optic axis, they do not reproduce the symmetries of the amplitude distribution in the focal line.     

Light propagation in a multilayered medium for three-dimensional optical memory

We report on the optimization of film thicknesses in a multilayered medium to increase readout signal intensity. The multilayered medium consists of a stack of photosensitive and transparent films, arranged alternately. The thicknesses of the photosensitive and transparent films in the multilayered medium were optimized for a reflection confocal system to read out data by analyzing the propagation of light focused into a multilayered medium.     

Quantum creep of Josephson intergrain vortices in Bi2Sr2Ca2Cu3O10

Magnetic relaxation caused by the creep of Josephson intergrain vortices is studied in Bi₂Sr₂Ca₂Cu₃O₁₀ high-T_c superconductor in the temperature interval 1.8–30 K for applied magnetic fields between 15 and 25 Oe. It is found that the magnetic moment M logarithmically decays with time t. At high enough temperatures the normalized logarithmic decay rate S=−(1/M_J0)(dM_J/dlnt) linearly increases with temperature, while at T<T₀(H), a temperature-independent relaxation rate S≈1.7·10⁻³ is found, manifesting the occurrence of quantum creep of the Josephson vortices. The “crossover” temperature T₀ from the quantum tunneling to the classical thermally activated regime of the vortex motion rapidly decreases from T₀=10 K to T₀<2 K when the field is increased from H=15 Oe to H=25 Oe. No thermal enhancement of the tunneling rate was found in contrast to the quantum creep behavior of Abrikosov intragrain vortices measured in the same sample (Physica C 222 (1994) 149).     

Computer model of a porous medium

A computer model has been set up to represent a porous medium. The basis for this model is a two-dimensional square network (100×100) of channels that have randomly assigned widths between the value of zero (closed) and the value of one (open, unrestricted flow). The channel width assignments have been made by a random selection from five different distributions:f(q)=q, f(q)=sinq, f(q)=erf(q),f(q)=1–sinq, andf(q)=1 –erf(q). Diffusion of particles in the network has been studied by a random-walk procedure for each realization of the channel width assignments. The diffusivity is quite sensitive to the distribution of channel widths. The percolation properties of the networks obtained from the three most restrictive distributions have been investigated and the independent, linked clusters within the network have been determined. For cluster sizes that are less than the full width of the network, the network does not percolate and either the flow is not diffusive or the diffusivity is severely reduced. An approximate value for the percolation threshold has been determined in each case and the fractal dimension has been calculated also.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Weight function for an elliptical planar crack embedded in a homogeneous elastic medium

The method of simultaneous dual integral equations is used for obtaining the exact analytical solution for the weight function for an elliptical crack embedded in an infinite elastic solid. We show that the solution is unique and can be reduced to the known solutions for a number of particular cases.     

Algorithm for calculating the refraction patterns of a planar laser beam in an optically inhomogeneous medium

An algorithm for simulation of the distribution of a planar laser beam in a three-dimensional, optically inhomogeneous medium is proposed. A technique for numerical calculation of the trajectories of the beam in a geometrically optical approximation is described. A calculation of refraction patterns in probing of a thermal boundary layer near a cylindrically shaped heated body that takes into account edge effects is performed. Translated from Izmeritel’naya Tekhnika, No. 5, pp. 36–39, May, 2008.     

Zero-radius potential model for a planar waveguide in a photonic crystal

A zero-radius potential model is proposed to describe a waveguide in a planar crystal. Two-dimensional and three-dimensional cases are considered. Layers, waveguides, and coupled waveguides are described. Explicit model dispersion equations are derived and the spectral properties are described. Pis’ma Zh. Tekh. Fiz. 25, 45–49 (August 26, 1999)     

Nonparaxial diffraction-limited propagation of light in a graded-index planar medium with a hyperbolic secant refractive-index profile

Nonparaxial diffraction-limited propagation of light with amplitude distribution in hyperbolic functions through an inhomogeneous planar medium with a hyperbolic secant refractive-index profile is studied by means of the stationary phase method. The irradiance distribution at geometrical shadow, edge of shadow, and a geometrically illuminated region is analyzed for a particular case.     

Fast solution of the elasticity problem for a planar crack of arbitrary shape in 3D-anisotropic medium

A planar crack of arbitrary shape in a 3D-anisotropic elastic medium subjected to an arbitrary external stress field is considered. An efficient numerical method of the solution of the problem is proposed. The problem is reduced to an integral equation for the crack opening vector on the crack surface. For discretization of this equation, Gaussian (radial) approximation functions centered at a system of nodes that covers the crack surface are used. For such functions, the elements of the matrix of the discretized problem are calculated in a quasi analytical form that involves standard non-singular integrals. If the node grid is regular, the matrix of the discretized system has Teoplitz’s structure, and the Fast Fourier Transform algorithm may be used for the calculation of matrix-vector products with such a matrix. It accelerate substantially the process of the iterative solution of the discretized system. Examples of the solutions for a circular crack in a transversally isotropic elastic medium are presented.     

Diffusion of a passive impurity in a porous medium. Fractal model in the case of an unsaturated medium

The theory of fractal sets is used to describe convective diffusion in a partly-saturated porous medium.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 4, pp. 612–617, October, 1987.