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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Banas, Lubomir, author. aut http://id.loc.gov/vocabulary/relators/aut Stochastic Ferromagnetism : Analysis and Numerics / Andreas Prohl, Lubomir Banas, Zdzislaw Brzezniak, Mikhail Neklyudov. Berlin ; Boston : De Gruyter, [2013] ©2014 1 online resource (242 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 58 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Ferromagnetism Mathematics. Magnetization Mathematical models. Stochastische Differentialgleichungen. MATHEMATICS / Differential Equations / General. bisacsh Ginzburg-Landau type penalization. Macroscopic deterministic equation. Macrospin magnetization dynamics. Magnetization dynamics. Stochastic Landau-Lifshitz-Gilbert equation. Brzezniak, Zdzislaw, author. aut http://id.loc.gov/vocabulary/relators/aut Neklyudov, Mikhail, author. aut http://id.loc.gov/vocabulary/relators/aut Prohl, Andreas, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013 9783110317350 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013 9783110317282 ZDB-23-DMI Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013 9783110317275 ZDB-23-DMP print 9783110306996 https://doi.org/10.1515/9783110307108 https://www.degruyter.com/isbn/9783110307108 Cover https://www.degruyter.com/document/cover/isbn/9783110307108/original |
language |
English |
format |
eBook |
author |
Banas, Lubomir, Banas, Lubomir, Brzezniak, Zdzislaw, Neklyudov, Mikhail, Prohl, Andreas, |
spellingShingle |
Banas, Lubomir, Banas, Lubomir, Brzezniak, Zdzislaw, Neklyudov, Mikhail, Prohl, Andreas, Stochastic Ferromagnetism : Analysis and Numerics / De Gruyter Studies in Mathematics , 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 |
author_facet |
Banas, Lubomir, Banas, Lubomir, Brzezniak, Zdzislaw, Neklyudov, Mikhail, Prohl, Andreas, Brzezniak, Zdzislaw, Brzezniak, Zdzislaw, Neklyudov, Mikhail, Neklyudov, Mikhail, Prohl, Andreas, Prohl, Andreas, |
author_variant |
l b lb l b lb z b zb m n mn a p ap |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Brzezniak, Zdzislaw, Brzezniak, Zdzislaw, Neklyudov, Mikhail, Neklyudov, Mikhail, Prohl, Andreas, Prohl, Andreas, |
author2_variant |
z b zb m n mn a p ap |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Banas, Lubomir, |
title |
Stochastic Ferromagnetism : Analysis and Numerics / |
title_sub |
Analysis and Numerics / |
title_full |
Stochastic Ferromagnetism : Analysis and Numerics / Andreas Prohl, Lubomir Banas, Zdzislaw Brzezniak, Mikhail Neklyudov. |
title_fullStr |
Stochastic Ferromagnetism : Analysis and Numerics / Andreas Prohl, Lubomir Banas, Zdzislaw Brzezniak, Mikhail Neklyudov. |
title_full_unstemmed |
Stochastic Ferromagnetism : Analysis and Numerics / Andreas Prohl, Lubomir Banas, Zdzislaw Brzezniak, Mikhail Neklyudov. |
title_auth |
Stochastic Ferromagnetism : Analysis and Numerics / |
title_alt |
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 |
title_new |
Stochastic Ferromagnetism : |
title_sort |
stochastic ferromagnetism : analysis and numerics / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2013 |
physical |
1 online resource (242 p.) Issued also in print. |
contents |
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 |
isbn |
9783110307108 9783110494938 9783110238570 9783110238471 9783110637205 9783110317350 9783110317282 9783110317275 9783110306996 |
issn |
0179-0986 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QC - Physics |
callnumber-label |
QC761 |
callnumber-sort |
QC 3761.5 |
url |
https://doi.org/10.1515/9783110307108 https://www.degruyter.com/isbn/9783110307108 https://www.degruyter.com/document/cover/isbn/9783110307108/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
530 - Physics |
dewey-ones |
538 - Magnetism |
dewey-full |
538/.440151922 |
dewey-sort |
3538 9440151922 |
dewey-raw |
538/.440151922 |
dewey-search |
538/.440151922 |
doi_str_mv |
10.1515/9783110307108 |
oclc_num |
979585367 |
work_keys_str_mv |
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status_str |
n |
ids_txt_mv |
(DE-B1597)207098 (OCoLC)979585367 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013 Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013 Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013 |
is_hierarchy_title |
Stochastic Ferromagnetism : Analysis and Numerics / |
container_title |
Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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