UID:
almahu_9949462259202882
Umfang:
1 online resource (242 p.)
ISBN:
9783110307108
,
9783110494938
Serie:
De Gruyter Studies in Mathematics , 58
Inhalt:
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.
Anmerkung:
Frontmatter --
,
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
,
Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Studies in Mathematics eBook-Package, De Gruyter, 9783110494938
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013, De Gruyter, 9783110317350
In:
E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013, De Gruyter, 9783110317282
In:
E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013, De Gruyter, 9783110317275
Weitere Ausg.:
ISBN 9783110306996
Sprache:
Englisch
Fachgebiete:
Mathematik
DOI:
10.1515/9783110307108
URL:
https://doi.org/10.1515/9783110307108
URL:
https://www.degruyter.com/isbn/9783110307108
