Josephson Lattices of the Optimal Size

The stability of the bound states of the magnetic flux in a Josephson resistive lattices is investigated numerically. It is shown that for a simple relationship between the geometrical parameters of the lattice the range of bias current is the widest.Comment: 11 pages, latex, 13 figures, typos adde

On the solution of the modified Ginzburg-Landau type equation for one-dimensional superconductor in presence of a normal layer

We perform an analytical and numerical study of the crossover from the Josephson effect to the bulk superconducting flow for two identical one-dimensional superconductors, co-existing with a layer of normal material. A generalized Ginzburg-Landau (GL) model, proposed by S.J. Chapman, Q. Du and M.D. Gunzburger was used in modeling the whole structure. When the thickness of the normal layer is very small, the introduction of three effective potentials of specified strength leads to an exact analytical solution of the modified stationary GL equation. The resulting current density-phase offset relation is analyzed numerically. We show that the critical Josephson current density corresponds to a bifurcation of the solutions of the nonlinear boundary value problem coupled with the modified GL-equation. The influence of the second term in the Fourier-decomposition of the supercurrent density-phase relation is also investigated. We derive also a simple analytical formula for the critical Josephson current.Comment: 9 pages, 7 figures, submitted to Euro. Jnl. of Apll. Mat

Josephson Junctions with Minimal Length

The minimal length of ``one-dimensional'' Josephson junctions, in which the specific bound states of the magnetic flux retain their stability is discussed numerically. Thereby, we consider as ``long'' every Josephson junction, in which there exists at least one nontrivial stable distribution of the magnetic flux for fixed values of all the physical and the geometrical parameters. Our results can be applied for optimization of the sizes of devices containing Josephson junctions for different operating conditions.Comment: 11 pages, amstex, 13 figures, submitted to Superconductor Science and Technolog

Critical relations in symmetric 0−π0-\pi Josephson junctions

Numerical modeling of dependences ``critical current -- external magnetic field'' for geometrically symmetric $0-\pi$ Josephson junctions is performed. The calculation of critical current is reduced to non-linear eigenvalue problem. The critical curve of the contact is obtained as an envelope of the bifurcation curves of different distributions of the magnetic flux. The structure of vortices in contact is observed explicitly and the dependence of the basic physical characteristics of these vortices on junction's length is explored. The comparison of numerical results and known experimental data shows good qualitative and quantitative conformity.Comment: 7 pages (twocolumn), 16 figure

Numerical Modeling of Charged Black Holes with Massive Dilaton

In this paper the static, spherically symmetric and electrically charged black hole solutions in Einstein-Born-Infeld gravity with massive dilaton are investigated numerically. The Continuous Analog of Newton Method (CANM) is used to solve the corresponding nonlinear multipoint boundary value problems (BVPs). The linearized BVPs are solved numerically by means of collocation scheme of fourth order. A special class of solutions are the extremal ones. We show that the extremal horizons within the framework of the model satisfy some nonlinear system of algebraic equations. Depending on the charge $q$ and dilaton mass $\gamma$, the black holes can have no more than three horizons. This allows us to construct some Hermite polynomial of third order. Its real roots describe the number, the type and other characteristics of the horizons.Comment: talk given at V International Congress on Mathematical Modeling, Sep. 30 -- Oct. 6, Dubna, Russia, 2002: http://www.jinr.ru/vicmm/ latex file, 17 pages, 14 figure

Vortex structure in long Josephson junction with two inhomogeneities

A report of numerical experiment results on long Josephson junction with one and two rectangular inhomogeneities in the barrier layer is presented. In case of one inhomogeneity we demonstrate the existence of the asymmetric fluxon states. The disappearance of mixed fluxon-antifluxon states when the position of inhomogeneity shifted to the end of the junction is shown. In case with two inhomogeneities the change of the amplitude of Josephson current through the inhomogeneity at the end of junction makes strong effect on the stability of the fluxon states and smoothes the maximums on the dependence ``critical current - magnetic field''.Comment: Presented for M2S, Dresden, July 9-14, 200

Coordinate transformation in the model of long Josephson junctions: geometrically equivalent Josephson junctions

The transition from the model of a long Josephson junction of variable width to the model of a junction with a coordinate-dependent Josephson current amplitude is effected through a coordinate transformation. This establishes the correspondence between the classes of Josephson junctions of variable width and quasi-one-dimensional junctions with a variable thickness of the barrier layer. It is shown that for a junction of exponentially varying width the barrier layer of the equivalent quasi-one-dimensional junction has a distributed resistive inhomogeneity that acts as an attractor for magnetic flux vortices. The curve of the critical current versus magnetic field for a Josephson junction with a resistive microinhomogeneity is constructed with the aid of a numerical simulation, and a comparison is made with the critical curve of a junction of exponentially varying width. The possibility of replacing a distributed inhomogeneity in a Josephson junction by a local inhomogeneity at the end of the junction is thereby demonstrated; this can have certain advantages from a technological point of view.Comment: 9 pages, 6 figure

New Numerical Algorithm for Modeling of Boson-Fermion Stars in Dilatonic Gravity

We investigate numerically a models of the static spherically symmetric boson-fermion stars in scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem with unknown internal boundary. We employ the Continuous Analogue of Newton Method (CANM) which leads on each iteration to two separate linear boundary value problems with different dimensions inside and outside the star, respectively. Along with them a nonlinear algebraic system for the spectral parameters - radius of the star $R_{s}$ and quantity $\Omega$ is solved also. In this way we obtain the behaviour of the basic geometric quantities and functions describing dilaton field and matter fields which build the star.Comment: 13 pages, amstex, 6 figure

Numerical investigation of the second harmonic effects in the LJJ

We study the long Josephson junction (LJJ) model which takes into account the second harmonic of the Fourier expansion of Josephson current. The sign of second harmonic is important for many physical applications. The influence of the sign and value of the second harmonic on the magnetic flux distributions is investigated. At each step of numerical continuation in parameters of the model, the corresponding nonlinear boundary problem is solved on the basis of the continuous analog of Newton's method with the 4th order Numerov discretization scheme. New solutions which do not exist in the traditional model have been found. The influence of the second harmonic on stability of magnetic flux distributions for main solutions is investigated.Comment: 7 pages, 4 figures, to be published in Proc. of FDM10, June 28 - July 2, 2010, Lozenetz, Bulgari

A Free Boundary Problem in the Theory of the Stars

We investigate numerically models of the static spherically symmetric boson-fermion stars in the scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem with unknown internal boundary. To solve this problem the Continuous Analogue of Newton Method is used.Comment: 5 pages, amstex, 2 figure