Stochastic ferromagnetism : analysis and numerics / Lubomír Baňas [and three others].

Format:

Book

Author/Creator:

Baňas, Lubomír, author.

Brzezniak, Z., author.

Neklyudov, Mikhail, author.

Prohl, Andreas, 1968- author.

Series:

De Gruyter studies in mathematics ; 58.

De Gruyter studies in mathematics ; 58

Language:

English

Subjects (All):

Ferromagnetism--Mathematics.

Ferromagnetism.

Magnetization--Mathematical models.

Magnetization.

Physical Description:

1 online resource (248 p.)

Edition:

1st ed.

Place of Publication:

Berlin : Walter de Gruyter GmbH & Co. KG, [2014]

Language Note:

English

Summary:

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.

Contents:

Front matter

Contents

Introduction

Chapter 1. The role of noise in finite ensembles of nanomagnetic particles

Chapter 2. The stochastic Landau-Lifshitz-Gilbert equation

Chapter 3 Effective equations for macrospin magnetization dynamics at elevated temperatures

Bibliography

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

9783110307108

3110307103

OCLC:

1013963523