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| In this article, we present a mathematical study of stability properties of steady states for a three-dimensional network of ferromagnetic particles of ellipsoidal shapes. The dynamics of magnetization inside the material is governed by the Landau-Lifschitz equation of micromagnetism which is non-linear and parabolic in nature. We prove that under certain condition on the shape of the samples and on the network geometry, the stability property for the relevant configurations can be achieved. More precisely, we establish a sufficient condition on the volume of the ellipsoidal samples and on the distance between the samples for particular configuration to be locally asymptotically stable using variational estimate technique. In this talk, we will also discuss about the controllability of these relevant configurations in which the control is the magnetic field generated by a dipole whose position and
amplitude can be selected. |
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