scholarly journals Schauder-Tychonoff Fixed-Point Theorem in Theory of Superconductivity

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Mariusz Gil ◽  
Stanisław Wędrychowicz
Keyword(s):  
Magnetic Field ◽  
Banach Space ◽  
Fixed Point ◽  
Global Attractivity ◽  
Mild Solutions ◽  
Time Dependent ◽  
Ginzburg Landau ◽  
Superconducting Sample ◽  
Tdgl Equations ◽  
Theory Of Superconductivity

We study the existence of mild solutions to the time-dependent Ginzburg-Landau ((TDGL), for short) equations on an unbounded interval. The rapidity of the growth of those solutions is characterized. We investigate the local and global attractivity of solutions of TDGL equations and we describe their asymptotic behaviour. The TDGL equations model the state of a superconducting sample in a magnetic field near critical temperature. This paper is based on the theory of Banach space, Fréchet space, and Sobolew space.

Dynamics of vortex–antivortex creation and annihilation in current-driven mesoscopic superconducting squares

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1550247
Author(s):  
Xiao-Meng Liang ◽  
Guo-Qiao Zha
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Landau Theory ◽  
Symmetric Case ◽  
Time Dependent ◽  
Dynamical Process ◽  
Applied Bias ◽  
Ginzburg Landau ◽  
Dc Drive ◽  
Vortex Velocity

In this paper, based on the time-dependent Ginzburg–Landau theory, we study the dynamics of vortex–antivortex (V–Av) pairs in a mesoscopic superconducting square with a small hole under applied bias currents. For the sample with a centered hole, a V–Av pair can nucleate at the hole edges and moves in opposite directions perpendicular to applied constant DC drive. The influence of the external magnetic field on the (anti)vortex velocity and the lifetime of V–Av pairs is mainly investigated. Different modes in the dynamical process of the V–Av collision and annihilation are identified. Moreover, in the case when the hole is displaced from the center of the square, the V–Av dynamics behaves quite differently from the symmetric case due to the shift of the V–Av creation point.

scholarly journals Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity

2005 ◽  
Vol 2005 (8) ◽  
pp. 863-887
Author(s):  
Fouzi Zaouch
Keyword(s):  
Magnetic Field ◽  
Existence And Uniqueness ◽  
Uniform Boundedness ◽  
Strong Solutions ◽  
Time Dependent ◽  
Dynamical Process ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations ◽  
Uniformly Bounded ◽  
Weak And Strong Solutions

The time-dependent Ginzburg-Landau equations of superconductivity with a time-dependent magnetic fieldHare discussed. We prove existence and uniqueness of weak and strong solutions withH1-initial data. The result is obtained under the “φ=−ω(∇⋅A)” gauge withω>0. These solutions generate a dynamical process and are uniformly bounded in time.

scholarly journals Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mixed Type ◽  
Evolution Operator ◽  
Mild Solutions ◽  
Integral Operators ◽  
Periodic Systems ◽  
Time Varying ◽  
Type Integral ◽  
Generating Operators

A class of semilinear impulsive periodic systems with time-varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. Showing the compactness ofPoincaréoperator and using a new generalized Gronwall inequality with mixed type integral operators given by us, we utilize Leray-Schauder fixed point theorem to prove the existence ofT0-periodicPC-mild solutions. Our method is an innovation and it is much different from methods of other papers. At last, an example is given for demonstration.

scholarly journals On solutions of semilinear evolution integrodifferential equations with nonlocal conditions

2009 ◽  
Vol 40 (3) ◽  
pp. 257-269 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Contraction Principle ◽  
Theory Of Evolution ◽  
Banach’S Contraction Principle

In this paper, by using the theory of evolution families, Banach's contraction principle and Schauder's fixed point theorem, we prove the existence of mild solutions of a class of semilinear evolution integrodifferential equations with nonlocal conditions in Banach space. An example is provided to illustrate the obtained results.

TRANSPORT PHENOMENA IN THE MIXED STATE AND FLUCTUATION REGIME IN (Bi1.6Pb0.4)Sr2Ca1-xHox(Cu1-yZny)2O8+d

2001 ◽  
Vol 15 (21) ◽  
pp. 929-934
Author(s):  
G. ILONCA ◽  
A. V. POP ◽  
R. STIUFIUC ◽  
G. STIUFIUC ◽  
C. LUNG ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Mixed State ◽  
Landau Theory ◽  
Hole Concentration ◽  
Transport Coefficients ◽  
Time Dependent ◽  
Ginzburg Landau ◽  
Metallic Behavior ◽  
Fluctuation Effects ◽  
Longitudinal Resistivity

Measurements of the magnetoresistivity, Seebeck, Nernst and Hall coefficients in Bi:2212 superconductors doped with Ho and Zn are reported. The critical temperature and the transport coefficients depend strongly on the Ho and Zn contents. The tails of the transport coefficients versus temperature curves are caused by fluctuation effects, which increase with increasing magnetic field. An anomalous suppression of superconductivity at x = 0.25–0.35 and y = 0.025–0.032 was also found when the hole concentration per Cu is P H = 1/8 and the transport properties exhibit metallic behavior. It was found that dB c2 /dT = -2.4 ± 0.2 T/K , corresponding to a Ginzburg–Landau coherence length ξ = 15 Å. The Hall resistivity ρxy scaling with the longitudinal resistivity ρxx as [Formula: see text] with α ≈ 1.8 is in agreement with the theory of Vinokur et al. The experimental data in the mixed state are in agreement with the prediction of the time-dependent Ginzburg–Landau theory.

Theoretical prediction of the minimum height for negligible demagnetization field in a superconducting sample

2015 ◽  
Vol 29 (34) ◽  
pp. 1550225
Author(s):  
J. Barba-Ortega ◽  
Miryam R. Joya ◽  
Paulo de Tarso C. Freire
Keyword(s):  
External Field ◽  
Theoretical Prediction ◽  
Cross Section ◽  
Magnetic Induction ◽  
Time Dependent ◽  
Lateral Size ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Minimum Height ◽  
Superconducting Sample

The limit below which the magnetization curve of a mesoscopic superconducting prism of square cross-section and finite height approximates the characteristic bi-dimensional limit, e.g. long prism, which with both the magnetic induction and the superconducting electron density are invariant along the direction where the magnetic external field is applied, was numerically found. Using the three- and two-dimensional time-dependent Ginzburg–Landau models, we have determined an analytical dependence of this height limit as a function of the lateral size of the sample.

scholarly journals Existence of Mild Solutions for the Elastic Systems with Structural Damping in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongxia Fan ◽  
Yongxiang Li ◽  
Pengyu Chen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Elastic System ◽  
Mild Solutions ◽  
Structural Damping ◽  
Initial Value ◽  
Operator Semigroups ◽  
Elastic Systems ◽  
Theoretical Results

This paper deals with the existence and uniqueness of mild solutions for a second order evolution equation initial value problem in a Banach space, which can model an elastic system with structural damping. The discussion is based on the operator semigroups theory and fixed point theorem. In addition, an example is presented to illustrate our theoretical results.

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