Control of a network of magnetic ellipsoidal samples

Shruti Agarwal; Gilles Carbou; Stéphane Labbé; Christophe Prieur

doi:10.3934/mcrf.2011.1.129

Article Contents

2011, Volume 1, Issue 2: 129-147. Doi: 10.3934/mcrf.2011.1.129

This issue Previous Article Next Article Global Carleman inequalities for Stokes and penalized Stokes equations

Control of a network of magnetic ellipsoidal samples

1.
Indian Institute of Technology Madras, Department of Mathematics, Chennai - 600 036
2.
IMB, Université Bordeaux, 351 cours la Libération, 33405 Talence
3.
Laboratoire Jean Kuntzmann, Université de Grenoble, Tour IRMA, 51 rue des Mathématiques, BP 53, 38041 Grenoble Cedex 9
4.
Department of Automatic Control, Gipsa-lab, 961 rue de la Houille Blanche, BP 46, 38402 Grenoble Cedex

Received: September 30, 2010

Revised: January 31, 2011

Published: May 2011

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Abstract

In this work, we present a mathematical study of stability and controllability of one-dimensional network of ferromagnetic particles. The control is the magnetic field generated by a dipole whose position and whose amplitude can be selected. The evolution of the magnetic field in the network of particles is described by the Landau-Lifschitz equation. First, we model a network of ellipsoidal shape ferromagnetic particles. Then, we prove the stability of relevant configurations and discuss the controllability by the means of the external magnetic field induced by the magnetic dipole. Finally some numerical results illustrate the stability and the controllability results.

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Mathematics Subject Classification: Primary: 93B05, 35Q93; Secondary: 93C10.

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References

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