This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). The first part of the book studies the role of noise in finite ensembles of nanomagnetic particles: we show geometric ergodicity of a unique invariant measure of Gibbs type and study related properties of approximations of the SLLG, including time discretization and Ginzburg-Landau type penalization. In the second part we propose an implementable space-time discretization using random walks to construct a weak martingale solution of the corresponding stochastic partial differential equation which describes the magnetization process of infinite spin ensembles. The last part of the book is concerned with a macroscopic deterministic equation which describes temperature effects on macro-spins, i.e. expectations of the solutions to the SLLG. Furthermore, comparative computational studies with the stochastic model are included.

We use constructive tools such as e.g. finite element methods to derive the theoretical results, which are then used for computational studies. The numerical experiments motivate an interesting interplay between inherent geometric and stochastic effects of the SLLG which still lack a rigorous analytical understanding: the role of space-time white noise, possible finite time blow-up behavior of solutions, long-time asymptotics, and effective dynamics.

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Yes, you can access Stochastic Ferromagnetism by Lubomir Banas, Zdzislaw Brzezniak, Mikhail Neklyudov, Andreas Prohl in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.

Information

Publisher

De Gruyter

Year

2013

ISBN

9783110307108

Edition

Topic

Mathematics

Subtopic

Differential Equations

Index

Mathematics

1 The role of noise in finite ensembles of nanomagnetic particles
2 The stochastic Landau-Lifshitz-Gilbert equation
3 Effective equations for macrospin magnetization dynamics
Bibliography