Mathematical Control and Related Fields (MCRF)

Control of a network of magnetic ellipsoidal samples

Pages: 129 - 147, Volume 1, Issue 2, June 2011      doi:10.3934/mcrf.2011.1.129

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Shruti Agarwal - Indian Institute of Technology Madras, Department of Mathematics, Chennai - 600 036, India (email)
Gilles Carbou - IMB, Université Bordeaux, 351 cours la Libération, 33405 Talence, France (email)
Stéphane Labbé - Laboratoire Jean Kuntzmann, Université de Grenoble, Tour IRMA, 51 rue des Mathématiques, BP 53, 38041 Grenoble Cedex 9, France (email)
Christophe Prieur - Department of Automatic Control, Gipsa-lab, 961 rue de la Houille Blanche, BP 46, 38402 Grenoble Cedex, France (email)

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.

Keywords:  Ferromagnetic material, Landau-Lifschitz equation, Control.
Mathematics Subject Classification:  Primary: 93B05, 35Q93; Secondary: 93C10.

Received: October 2010;      Revised: February 2011;      Available Online: June 2011.