TITLE

Periodic minimizers of the anisotropic Ginzburg–Landau model

AUTHOR(S)
Alama, Stan; Bronsard, Lia; Sandier, Etienne
PUB. DATE
November 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2009, Vol. 36 Issue 3, p399
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider the anisotropic Ginzburg–Landau model in a three-dimensional periodic setting, in the London limit as the Ginzburg–Landau parameter $${\kappa=1/{\epsilon}\to\infty}$$ . By means of matching upper and lower bounds on the energy of minimizers, we derive an expression for a limiting energy in the spirit of Γ-convergence. We show that, to highest order as $${\epsilon\to0}$$ , the normalized induced magnetic field approaches a constant vector. We obtain a formula for the lower critical field Hc1 as a function of the orientation of the external field $${h^\epsilon_{ex}}$$ with respect to the principal axes of the anisotropy, and determine the direction of the limiting induced field as a minimizer of a convex geometrical problem.
ACCESSION #
44500039

 

Related Articles

  • Plane-parallel nonisothermal filtration of a gas: the role of heat transfer. Bondarev’, É.; Argunova, K.; Rozhin, I. // Journal of Engineering Physics & Thermophysics;Nov2009, Vol. 82 Issue 6, p1073 

    The influence of the parameters of a mathematical model and of the type of boundary conditions on the dynamics of pressure and temperature fields in nonisothermal gas filtration has been investigated in a computational experiment. To describe the process, the nonlinear system of partial...

  • Influence of surface anisotropy on magnetization distribution in a single-domain particle. Usov, N. A.; Grebenshchikov, Yu. B. // Journal of Applied Physics;Aug2008, Vol. 104 Issue 4, p043903 

    The magnetization distribution in a single domain particle with appreciable surface anisotropy energy contribution is investigated for particles of cylindrical, spherical, and rectangular shapes. It is shown that the behavior of the particle in applied magnetic field can be described using...

  • ON A SIMILARITY SOLUTION OF MHD BOUNDARY LAYER FLOW OVER A MOVING VERTICAL CYLINDER. Amkadni, Maryem; Azzouzi, Adnane // Differential Equations & Nonlinear Mechanics;2006, p1 

    The steady flow of an incompressible electrically conducting fluid over a semi-infinite moving vertical cylinder in the presence of a uniform transverse magnetic field is analyzed. The partial differential equations governing the flow are reduced to an ordinary differential equation, using the...

  • Investigation of MHD Flow of Compressible Fluid in a Channel with Porous Walls. Pourmahmoud, Nader; Mansoor, Mahtab; Eosboee, Mostafa Rahimi; Khameneh, Pedram Mohajeri // Australian Journal of Basic & Applied Sciences;2011, Vol. 5 Issue 6, p475 

    In this article magnetohydrodynamics (MHD) boundary layer flow of compressible fluid in a channel with porous walls is researched. In this study it will be shown that the nonlinear Navier- Stokes equations can be reduced to an ordinary differential equation, using the similarity transformations...

  • Remarks on the spectrum of the Neumann problem with magnetic field in the half-space. Morame, Abderemane; Truc, Françoise // Journal of Mathematical Physics;Jan2005, Vol. 46 Issue 1, p012105 

    We consider a Schrödinger operator with a constant magnetic field in a one-half three-dimensional space, with Neumann-type boundary conditions. It is known from the works by Lu–Pan and Helffer–Morame that the lower bound of its spectrum is less than b, the intensity of the...

  • Cylindrical Taylor states conserving total absolute magnetic helicity. Low, B. C.; Fang, F. // Physics of Plasmas;2014, Vol. 21 Issue 9, p1 

    The Taylor state of a three-dimensional (3D) magnetic field in an upright cylindrical domain V is derived from first principles as an extremum of the total magnetic energy subject to a conserved, total absolute helicity Habs. This new helicity [Low, Phys. Plasmas 18, 052901 (2011)] is distinct...

  • Solution of time Varying Magnetic field by Applying Absorbing Boundary Condition. Afjei, E.; Shokri-Razaghi, H.; Torkaman, H.; Siadatan, A. // AIP Conference Proceedings;8/13/2009, Vol. 1148 Issue 1, p766 

    The need for absorbing boundary condition and coordinate stretching arises when one wishes to simulate the extension to infinity on a finite domain of computation for a problem. This paper poses a time varying magnetic field problem in cylindrical coordinate for two regions under consideration...

  • Flow and Heat Transfer in Sisko Fluid with Convective Boundary Condition. Malik, Rabia; Khan, Masood; Munir, Asif; Khan, Waqar Azeem // PLoS ONE;Oct2014, Vol. 9 Issue 10, p1 

    In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a non-isothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations...

  • Upwind finite difference method for miscible oil and water displacement problem with moving boundary values. Yuan, Yi-rang; Li, Chang-feng; Yang, Cheng-shun; Han, Yu-ji // Applied Mathematics & Mechanics;Nov2009, Vol. 30 Issue 11, p1365 

    The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model...

  • ASYMPTOTIC ANALYSIS OF CONTINUOUS OPINION DYNAMICS MODELS UNDER BOUNDED CONFIDENCE. BORRA, DOMENICA; LORENZI, TOMMASO // Communications on Pure & Applied Analysis;May2013, Vol. 12 Issue 3, p1487 

    This paper deals with the asymptotic behavior of mathematical models for opinion dynamics under bounded confidence of Deffuant-Weisbuch type. Focusing on the Cauchy Problem related to compromise models with homogeneous bound of confidence, a general well-posedness result is provided and a...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics