159 research outputs found
The vortex dynamics of a Ginzburg-Landau system under pinning effect
It is proved that the vortices are attracted by impurities or inhomogeities
in the superconducting materials. The strong H^1-convergence for the
corresponding Ginzburg-Landau system is also proved.Comment: 23page
A hierarchy of models for superconducting thin films
A hierarchy of models for type-II superconducting thin films is presented. Through appropriate asymptotic limits this hierarchy passes from the mesoscopic Ginzburg--Landau model to the London model with isolated vortices as -function singularities to vortex-density models and finally to macroscopic critical-state models. At each stage it is found that a key nondimensional parameter is , where is the penetration depth of the magnetic field, a material parameter, and d and L are a typical thickness and lateral dimension of the film,respectively. The models simplify greatly if this parameter is large or small
Nonuniform Self-Organized Dynamical States in Superconductors with Periodic Pinning
We consider magnetic flux moving in superconductors with periodic pinning
arrays. We show that sample heating by moving vortices produces negative
differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in
the voltage-current characteristic (VI curve). The uniform flux flow state is
unstable in the NDR region of the VI curve. Domain structures appear during the
NDR part of the VI curve of an N type, while a filamentary instability is
observed for the NDR of an S type. The simultaneous existence of the NDR of
both types gives rise to the appearance of striking self-organized (both
stationary and non-stationary) two-dimensional dynamical structures.Comment: 4 pages, 2 figure
Dynamics of filaments of scroll waves
This has been written as a chapter for "Engineering Chemical Complexity II",
and as such does not have an abstract.Comment: 18 pages, 10 figure
Ginzburg-Landau vortex dynamics with pinning and strong applied currents
We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on
a bounded two-dimensional domain with an electric current applied on the
boundary and a pinning potential term. This is meant to model a superconductor
subjected to an applied electric current and electromagnetic field and
containing impurities. Such a current is expected to set the vortices in
motion, while the pinning term drives them toward minima of the pinning
potential and "pins" them there. We derive the limiting dynamics of a finite
number of vortices in the limit of a large Ginzburg-Landau parameter, or \ep
\to 0, when the intensity of the electric current and applied magnetic field
on the boundary scale like \lep. We show that the limiting velocity of the
vortices is the sum of a Lorentz force, due to the current, and a pinning
force. We state an analogous result for a model Ginzburg-Landau equation
without magnetic field but with forcing terms. Our proof provides a unified
approach to various proofs of dynamics of Ginzburg-Landau vortices.Comment: 48 pages; v2: minor errors and typos correcte
Ultra-fast Kinematic Vortices in Mesoscopic Superconductors: The Effect of the Self-Field
Within the framework of the generalized time-dependent Ginzburg-Landau
equations, we studied the influence of the magnetic self-field induced by the
currents inside a superconducting sample driven by an applied transport
current. The numerical simulations of the resistive state of the system show
that neither material inhomogeneity nor a normal contact smaller than the
sample width are required to produce an inhomogeneous current distribution
inside the sample, which leads to the emergence of a kinematic
vortex-antivortex pair (vortex street) solution. Further, we discuss the
behaviors of the kinematic vortex velocity, the annihilation rates of the
supercurrent, and the superconducting order parameters alongside the vortex
street solution. We prove that these two latter points explain the
characteristics of the resistive state of the system. They are the fundamental
basis to describe the peak of the current-resistance characteristic curve and
the location where the vortex-antivortex pair is formed.Comment: 9 pages, 6 figures. Accepted for publication in Scientific Report
Negative differential resistivity in superconductors with periodic arrays of pinning sites
We study theoretically the effects of heating on the magnetic flux moving in
superconductors with a periodic array of pinning sites (PAPS). The
voltage-current characteristic (VI-curve) of superconductors with a PAPS
includes a region with negative differential resistivity (NDR) of S-type (i.e.,
S-shaped VI-curve), while the heating of the superconductor by moving flux
lines produces NDR of N-type (i.e., with an N-shaped VI-curve). We analyze the
instability of the uniform flux flow corresponding to different parts of the
VI-curve with NDR. Especially, we focus on the appearance of the filamentary
instability that corresponds to an S-type NDR, which is extremely unusual for
superconductors. We argue that the simultaneous existence of NDR of both N- and
S-type gives rise to the appearance of self-organized two-dimensional dynamical
structures in the flux flow mode. We study the effect of the pinning site
positional disorder on the NDR and show that moderate disorder does not change
the predicted results, while strong disorder completely suppresses the S-type
NDR.Comment: 10 pages, 1 table, 7 figure
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