125 research outputs found
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 Josephson junctions
Numerical modeling of dependences ``critical current -- external magnetic
field'' for geometrically symmetric 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 and dilaton mass , 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
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
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
and quantity 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
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
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