### Abstract

Original language | English |
---|---|

Title of host publication | Proceedings of the Comsol Conference |

Editors | Lars Gregersen |

Number of pages | 150 |

Place of Publication | Copenhagen, Denmark |

Publisher | COMSOL Inc. |

Publication date | 2006 |

Pages | 75-78 |

ISBN (Print) | 87-989426-1-1 |

Publication status | Published - 2006 |

Event | Nordic Comsol Conference - Kgs. Lyngby, Denmark Duration: 1 Jan 2006 → … |

### Conference

Conference | Nordic Comsol Conference |
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City | Kgs. Lyngby, Denmark |

Period | 01/01/2006 → … |

### Keywords

- nonlinear dynamics
- phase transition
- Ginzburg-Landau model
- Superconductivity

### Cite this

*Proceedings of the Comsol Conference*(pp. 75-78). Copenhagen, Denmark: COMSOL Inc..

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*Proceedings of the Comsol Conference.*COMSOL Inc., Copenhagen, Denmark, pp. 75-78, Nordic Comsol Conference, Kgs. Lyngby, Denmark, 01/01/2006.

**The Ginzburg-Landau Equation Solved by the Finite Element Method.** / Alstrøm, Tommy Sonne; Sørensen, Mads Peter; Pedersen, Niels Falsig; Madsen, Søren.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research

TY - GEN

T1 - The Ginzburg-Landau Equation Solved by the Finite Element Method

AU - Alstrøm, Tommy Sonne

AU - Sørensen, Mads Peter

AU - Pedersen, Niels Falsig

AU - Madsen, Søren

PY - 2006

Y1 - 2006

N2 - Around 1950 V.L. Ginzburg and L.D. Landau proposed a phenomenological theory for phase transitions1. The theory is based on a phenomenological Schrödinger equation with a φ-4 potential and a kinetic term involving the momentum operator. One of the more successful applications of the theory is to superconductivity and in particular to superconductors placed in a magnetic field. Superconductors expel magnetic fields from the inside bulk by setting up screening currents in the surface (type I superconductors). However, some supercon-ductors allow for magnetic field penetration through quantized current vortices when the magnetic field exceeds a threshold value. These superconductors are called type II supercon-ductors. In this article we solve numerically the time dependent Ginzburg-Landau equation coupled to a magnetic field for type II superconductors of complex geometry, where the finite element method is particularly suited.

AB - Around 1950 V.L. Ginzburg and L.D. Landau proposed a phenomenological theory for phase transitions1. The theory is based on a phenomenological Schrödinger equation with a φ-4 potential and a kinetic term involving the momentum operator. One of the more successful applications of the theory is to superconductivity and in particular to superconductors placed in a magnetic field. Superconductors expel magnetic fields from the inside bulk by setting up screening currents in the surface (type I superconductors). However, some supercon-ductors allow for magnetic field penetration through quantized current vortices when the magnetic field exceeds a threshold value. These superconductors are called type II supercon-ductors. In this article we solve numerically the time dependent Ginzburg-Landau equation coupled to a magnetic field for type II superconductors of complex geometry, where the finite element method is particularly suited.

KW - nonlinear dynamics

KW - phase transition

KW - Ginzburg-Landau model

KW - Superconductivity

M3 - Article in proceedings

SN - 87-989426-1-1

SP - 75

EP - 78

BT - Proceedings of the Comsol Conference

A2 - Gregersen, Lars

PB - COMSOL Inc.

CY - Copenhagen, Denmark

ER -