Stability properties of steady-states for a network of ferromagnetic nanowires

Abstract : We investigate the problem of describing the possible stationary configurations of the magnetic moment in a network of ferromagnetic nanowires with length $L$ connected by semiconductor devices, or equivalently, of its possible $L$-periodic stationary configurations in an infinite nanowire. The dynamical model that we use is based on the one-dimensional Landau-Lifshitz equation of micromagnetism. We compute all $L$-periodic steady-states of that system, define an associated energy functional, and these steady-states share a quantification property in the sense that their energy can only take some precise discrete values. Then, based on a precise spectral study of the linearized system, we investigate the stability properties of the steady-states.
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Journal of Differential Equations, Elsevier, 2012, 253 (6), pp.1709-1728. 〈10.1016/j.jde.2012.06.005〉
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Stéphane Labbé, Yannick Privat, Emmanuel Trélat. Stability properties of steady-states for a network of ferromagnetic nanowires. Journal of Differential Equations, Elsevier, 2012, 253 (6), pp.1709-1728. 〈10.1016/j.jde.2012.06.005〉. 〈hal-00492758v2〉

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