Weak Solutions of a Stochastic Landau-Lifshitz-Gilbert Equation
نویسندگان
چکیده
منابع مشابه
Weak Solutions of the Stochastic Landau-lifshitz-gilbert Equation
Abstract. The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative spacedependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere S. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert e...
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A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of GinzburgLandau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear...
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In our contribution, we extend a P1 finite element scheme for the discretization of the Landau-LifshitzGilbert equation (LLG), which has originally been proposed by Alouges [1] for a simpler model problem. Unlike prior works [2], [5], we allow arbitrary contributions to the effective field and elaborate the circumstances under which weak subconvergence towards a weak solution can mathematically...
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Institut Neel, CNRS-UJF, Nanosciences Department, 25 Av. des Martyrs, BP 166, 38042 Grenoble cedex 9, France Institut National Polytechnique de Grenoble, 46 Av. Félix Viallet, 38031 Grenoble cedex 1, France Laboratoire SPINTEC, CEA-CNRS-UJF-INPG, Bât. 1005, 17 Rue des Martyrs, 38054 Grenoble cedex 9, France Département de Mathématiques, Faculté des Sciences d'Orsay, Université Paris-Sud 11, Bât...
متن کاملGeneralization of the Landau-Lifshitz-Gilbert equation for conducting ferromagnets.
We propose an extension of the Landau-Lifshitz-Gilbert (LLG) equation by explicitly including the role of conduction electrons in magnetization dynamics of conducting ferromagnets. The temporal and spatial dependent magnetization order parameter m(r,t) generates both electrical and spin currents that provide dissipation of the energy and angular momentum of the processing magnet. The resulting ...
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ژورنال
عنوان ژورنال: Applied Mathematics Research eXpress
سال: 2012
ISSN: 1687-1200,1687-1197
DOI: 10.1093/amrx/abs009