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Stability properties of steady-states for a network of ferromagnetic nanowires. (English) Zbl 1247.35173

Summary: 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.

MSC:

35Q82 PDEs in connection with statistical mechanics
35B35 Stability in context of PDEs
82D37 Statistical mechanics of semiconductors
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