Stochastic Ferromagnetism : : Analysis and Numerics / / Andreas Prohl, Lubomir Banas, Zdzislaw Brzezniak, Mikhail Neklyudov.
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 invar...
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Superior document: | Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2013] ©2014 |
Year of Publication: | 2013 |
Language: | English |
Series: | De Gruyter Studies in Mathematics ,
58 |
Online Access: | |
Physical Description: | 1 online resource (242 p.) |
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100 | 1 | |a Banas, Lubomir, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Stochastic Ferromagnetism : |b Analysis and Numerics / |c Andreas Prohl, Lubomir Banas, Zdzislaw Brzezniak, Mikhail Neklyudov. |
264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2013] | |
264 | 4 | |c ©2014 | |
300 | |a 1 online resource (242 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
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490 | 0 | |a De Gruyter Studies in Mathematics , |x 0179-0986 ; |v 58 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Introduction -- |t Chapter 1. The role of noise in finite ensembles of nanomagnetic particles -- |t Chapter 2. The stochastic Landau-Lifshitz-Gilbert equation -- |t Chapter 3 Effective equations for macrospin magnetization dynamics at elevated temperatures -- |t Bibliography |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) | |
650 | 0 | |a Ferromagnetism |x Mathematics. | |
650 | 0 | |a Magnetization |x Mathematical models. | |
650 | 4 | |a Stochastische Differentialgleichungen. | |
650 | 7 | |a MATHEMATICS / Differential Equations / General. |2 bisacsh | |
653 | |a Ginzburg-Landau type penalization. | ||
653 | |a Macroscopic deterministic equation. | ||
653 | |a Macrospin magnetization dynamics. | ||
653 | |a Magnetization dynamics. | ||
653 | |a Stochastic Landau-Lifshitz-Gilbert equation. | ||
700 | 1 | |a Brzezniak, Zdzislaw, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
700 | 1 | |a Neklyudov, Mikhail, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
700 | 1 | |a Prohl, Andreas, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Studies in Mathematics eBook-Package |z 9783110494938 |o ZDB-23-GSM |
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