The Study on Surface Critical Magnetic Field of a Layered Magnetic Superconductors

2014 ◽  
Vol 979 ◽  
pp. 224-227 ◽  
Author(s):  
Sumitta Meakniti ◽  
Arpapong Changjan ◽  
Pongkaew Udomsamuthirun
Keyword(s):  
Magnetic Field ◽  
Magnetic Property ◽  
Variational Method ◽  
Critical Field ◽  
Landau Equation ◽  
Critical Magnetic Field ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Non Linear

In this research, we studied the surface critical magnetic field () of a layered magnetic superconductors by Ginzburg-Landau approach. After the 1st Ginzburg-Landau equation was calculated, a surface critical field was solved by variational method analytically. Our formula obtained was depended on the magnetic property of superconductor. We found that Hc3 of antiferromagnetism and paramagnetism superconductors were shown the same behaviour as non-magnetic superconductors. For diamagnetism and ferromagnetism superconductors, the higher and the lower values of critical magnetic field were found, respectively. However, the Hc3 was strongly depended on the non-linear of magnetic field intend of all kind magnetism.

Die Methode der Korrelationsfunktion in der Theorie der Supraleitung

1966 ◽  
Vol 21 (9) ◽  
pp. 1415-1425 ◽  
Author(s):  
Gerhart Lüders
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Diffusion Approximation ◽  
Landau Equation ◽  
Isotropic Scattering ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Special Cases ◽  
Method Of Correlation

The method of correlation function is, without complete justification, extended to superconductors in the presence of a magnetic field. Applying this method, we derive the linearized and generalized GINZBURG—LANDAU equation and DE GENNES’ diffusion approximation in simple way. The results agree with those obtained previously by DE GENNES, GORKOV, MAKI, TEWORDT, and others. In special cases (no magnetic field, pure superconductor or isotropic scattering) they can also be derived from WERTHAMER’S kernel. In connection with this kernel, we discuss the limits of validity of both the linearized and generalized GINZBURG—LANDAU equation and of the diffusion approximation.

scholarly journals BOUNDARY PROBLEMS FOR THE GINZBURG–LANDAU EQUATION

2005 ◽  
Vol 07 (05) ◽  
pp. 597-648 ◽  
Author(s):  
DAVID CHIRON
Keyword(s):  
Magnetic Field ◽  
Landau Equation ◽  
Travelling Waves ◽  
Ginzburg Landau ◽  
Boundary Problems ◽  
Ginzburg Landau Equation

We provide a study at the boundary for a class of equations including the Ginzburg–Landau equation as well as the equation of travelling waves for the Gross–Pitaevskii model. We prove Clearing-Out results and an orthogonal anchoring condition of the vortex on the boundary for the Ginzburg–Landau equation with magnetic field.

LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART II

1999 ◽  
Vol 01 (03) ◽  
pp. 295-333 ◽  
Author(s):  
SYLVIA SERFATY
Keyword(s):  
Magnetic Field ◽  
Critical Field ◽  
Critical Magnetic Field ◽  
Asymptotic Limit ◽  
Local Minimizers ◽  
Ginzburg Landau ◽  
London Equation ◽  
Stable Solutions

As in Part I, we study local minimizers of the Ginzburg–Landau energy (depending on κ → +∞) for superconductors in a prescribed magnetic field hex. For disc domains, we find and describe stable solutions of the associated equations and show how vortices appear as hex is raised from the first critical field Hc1. We also study the asymptotic limit κ→∞ for hex=Hc1 and prove that the limiting magnetic field in the superconductor satisfies the London equation.

scholarly journals Bacterial communication and relevance of quantum theory

2017 ◽  
Author(s):  
Sarangam Majumdar ◽  
Sisir Roy
Keyword(s):  
Kinematic Viscosity ◽  
Landau Equation ◽  
Bacterial Species ◽  
Thermal Fluctuations ◽  
Communication Process ◽  
Dinger Equation ◽  
Ginzburg Landau ◽  
Bacterial Communication ◽  
Ginzburg Landau Equation ◽  
Non Linear

The recent findings confirm that bacteria communicate each other through chemical and electrical signals. Bacteria use chemical signaling molecules which are called as quorum sensing molecules(QSMs) or autoinducers. Moreover, the ion channels in bacteria conduct a long-range electrical signaling within biofilm communities through propagated waves of potassium ions and biofilms attracts other bacterial species too. Both communication process are used by bacteria to make their own survival strategies. In this article, we model this bacterial communication mechanism by complex Ginzburg- Landau equation and discuss the formation of patterns depending on kinematic viscosity associated with internal noise. Again, the potassium wave propagation is described by the non-linear Schrödinger equation in a dissipative environment. By adding perturbation to non-linear Schrödinger equation one arrives at Complex Ginzburg-Landau equation. In this paper we emphasize that at the cellular level(bacteria) we use Complex Ginzburg - Landau equation as a perturbed Nonlinear Schrödinger equation to understand the bacterial communication as well as pattern formation in Biofilms for certain range of kinematic viscosity which can be tested in laboratory experiment. Here, the perturbation is due to the existence of non thermal fluctuations associated to the finite size of the bacteria. It sheds new light on the relevance of quantum formalism in understanding the cell to cell communication.

scholarly journals Instabilities in a Non-Uniformly Rotating Medium with Stratification of the Temperature in an External Uniform Magnetic Field

2019 ◽  
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Uniform Magnetic Field ◽  
Landau Equation ◽  
Stationary Convection ◽  
Vertical Temperature Gradient ◽  
Vertical Temperature ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
The Stability

In this paper the stability of the non-uniformly rotating cylindrical plasma in the axial uniform magnetic field with the vertical temperature gradient is investigated. In the approximation of geometrical optics a dispersion equation for small axisymmetric perturbations is obtained with the effects of viscosity, ohmic and heat conductive dissipation taken into account. The stability criteria for azimuthal plasma flows are obtained in the presence of the vertical temperature gradient and the constant magnetic field. The Rayleigh-Benard problem for stationary convection in the non-uniformly rotating layer of the electrically conducting fluid in the axial uniform magnetic field is considered. In the linear theory of stationary convection the critical value of the Rayleigh number subject to the profile of the inhomogeneous rotation (Rossby number) is obtained. It is shown that the negative values of the Rossby number have a destabilizing effect, since the critical Rayleigh number becomes smaller, than in the case of the uniform rotation , or of the rotation with positive Rossby numbers . To describe the nonlinear convective phenomena the local Cartesian coordinate system was used, where the inhomogeneous rotation of the fluid layer was represented as the rotation with a constant angular velocity and azimuthal shear with linear dependence on the coordinate. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number a nonlinear Ginzburg-Landau equation was obtaned. This equation describes the evolution of the finite amplitude of perturbations by utilizing the solution of the Ginzburg-Landau equation. It is shown that the weakly nonlinear convection based on the equations of the six-mode Lorentz model transforms into the identical Ginzburg-Landau equation. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various profiles of the angular velocity of the rotation of electrically conductive fluid.

scholarly journals Chebyshev wavelet collocation method for Ginzburg-Landau equation

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 57-65
Author(s):  
Aydin Secer ◽  
Yasemin Bakir
Keyword(s):  
Collocation Method ◽  
Landau Equation ◽  
Linear Equations ◽  
Operational Matrix ◽  
Ginzburg Landau ◽  
Chebyshev Wavelets ◽  
Ginzburg Landau Equation ◽  
Wavelet Collocation Method ◽  
Non Linear ◽  
Chebyshev Wavelet

The main aim of this paper is to investigate the efficient Chebyshev wavelet collocation method for Ginzburg-Landau equation. The basic idea of this method is to have the approximation of Chebyshev wavelet series of a non-linear PDE. We demonstrate how to use the method for the numerical solution of the Ginzburg-Landau equation with initial and boundary conditions. For this purpose, we have obtained operational matrix for Chebyshev wavelets. By applying this technique in Ginzburg-Landau equation, the PDE is converted into an algebraic system of non-linear equations and this system has been solved using MAPLE computer algebra system. We demonstrate the validity and applicability of this technique which has been clarified by using an example. Exact solution is compared with an approximate solution. Moreover, Chebyshev wavelet collocation method is found to be acceptable, efficient, accurate and computational for the non-linear or PDE.

scholarly journals The Effect of Modulation on Heat Transport by a Weakly Nonlinear Thermal Instability in the Presence of Applied Magnetic Field and Internal Heating

2020 ◽  
Vol 25 (4) ◽  
pp. 96-115
Author(s):  
S.H. Manjula ◽  
Palle Kiran ◽  
G. Narsimlu ◽  
R. Roslan
Keyword(s):  
Magnetic Field ◽  
Heat Transport ◽  
Applied Magnetic Field ◽  
Landau Equation ◽  
Thermal Modulation ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
The Real ◽  
Ginzburg Landau Equation ◽  
Gravity And Magnetic

AbstractThe present paper deals with a weakly nonlinear stability problem under an imposed time-periodic thermal modulation. The temperature has two parts: a constant part and an externally imposed time-dependent part. We focus on stationary convection using the slow time scale and quantify convective amplitude through the real Ginzburg-Landau equation (GLE). We have used the classical fourth order Runge-Kutta method to solve the real Ginzburg-Landau equation. The effect of various parameters on heat transport is discussed through GLE. It is found that heat transport analysis is controlled by suitably adjusting the frequency and amplitude of modulation. The applied magnetic field (effect of Ha) is to diminish the heat transfer in the system. Three different types of modulations thermal, gravity, and magnetic field have been compared. It is concluded that thermal modulation is more effective than gravity and magnetic modulation. The magnetic modulation stabilizes more and gravity modulation stabilizes partially than thermal modulation.

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