Wong-Zakai Approximations for the Stochastic Landau-Lifshitz-Bloch Equation with Helicity
For temperatures below and beyond the Curie temperature, the stochastic Landau-Lifshitz-Bloch equation describes the evolution of spins in ferromagnetic materials. In this work, we consider the stochastic Landau-Lifshitz-Bloch equation driven by a real valued Wiener process and show Wong-Zakai type...
Gespeichert in:
| Veröffentlicht in: | Acta applicandae mathematicae 2024-10, Vol.193 (1), p.4, Article 4 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 1 |
| container_start_page | 4 |
| container_title | Acta applicandae mathematicae |
| container_volume | 193 |
| creator | Gokhale, Soham Sanjay |
| description | For temperatures below and beyond the Curie temperature, the stochastic Landau-Lifshitz-Bloch equation describes the evolution of spins in ferromagnetic materials. In this work, we consider the stochastic Landau-Lifshitz-Bloch equation driven by a real valued Wiener process and show Wong-Zakai type approximations for the same. We consider non-zero contribution from the helicity term in the energy. First, using a Doss-Sussmann type transform, we convert the stochastic partial differential equation into a deterministic equation with random coefficients. We then show that the solution of the transformed equation depends continuously on the driving Wiener process. We then use this result, along with the properties of the said transform to show that the solution of the originally considered equation depends continuously on the driving Wiener process. |
| doi_str_mv | 10.1007/s10440-024-00681-y |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3100377238</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3100377238</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-7c1e037370c62c0ce4eb6da8340b8840025800bf0dc6d691b598871aba1b067f3</originalsourceid><addsrcrecordid>eNp9kL1OwzAURi0EEqXwAkyRmA3XcWo7Y6kKRYrEAAjBYjmO07iUpLUdQXh6TIvExnSH-537cxA6J3BJAPiVJ5BlgCHNMAATBA8HaEQmPMU5UHaIRkAYxwJIfoxOvF8BAM0ZG6GX565d4lf1pmwy3Wxc92nfVbBd65O6c0loTPIQOt0oH6xOCtVWqseFrX1jwxe-XsdWMt_2OyT5sKFJFmZttQ3DKTqq1dqbs986Rk8388fZAhf3t3ezaYF1yiFgrokByikHzVIN2mSmZJUSNINSiAwgnQiAsoZKs4rlpJzkQnCiSkVKYLymY3SxnxuP3_bGB7nqetfGlZJGN5TzlIqYSvcp7TrvnanlxsVP3SAJyB-Fcq9QRoVyp1AOEaJ7yMdwuzTub_Q_1Dfyz3R_</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3100377238</pqid></control><display><type>article</type><title>Wong-Zakai Approximations for the Stochastic Landau-Lifshitz-Bloch Equation with Helicity</title><source>SpringerLink Journals</source><creator>Gokhale, Soham Sanjay</creator><creatorcontrib>Gokhale, Soham Sanjay</creatorcontrib><description>For temperatures below and beyond the Curie temperature, the stochastic Landau-Lifshitz-Bloch equation describes the evolution of spins in ferromagnetic materials. In this work, we consider the stochastic Landau-Lifshitz-Bloch equation driven by a real valued Wiener process and show Wong-Zakai type approximations for the same. We consider non-zero contribution from the helicity term in the energy. First, using a Doss-Sussmann type transform, we convert the stochastic partial differential equation into a deterministic equation with random coefficients. We then show that the solution of the transformed equation depends continuously on the driving Wiener process. We then use this result, along with the properties of the said transform to show that the solution of the originally considered equation depends continuously on the driving Wiener process.</description><identifier>ISSN: 0167-8019</identifier><identifier>EISSN: 1572-9036</identifier><identifier>DOI: 10.1007/s10440-024-00681-y</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Anisotropy ; Applications of Mathematics ; Approximation ; Calculus of Variations and Optimal Control; Optimization ; Computational Mathematics and Numerical Analysis ; Curie temperature ; Ferromagnetic materials ; Helicity ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations ; Probability Theory and Stochastic Processes ; Temperature</subject><ispartof>Acta applicandae mathematicae, 2024-10, Vol.193 (1), p.4, Article 4</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-7c1e037370c62c0ce4eb6da8340b8840025800bf0dc6d691b598871aba1b067f3</cites><orcidid>0000-0002-1001-003X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10440-024-00681-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10440-024-00681-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Gokhale, Soham Sanjay</creatorcontrib><title>Wong-Zakai Approximations for the Stochastic Landau-Lifshitz-Bloch Equation with Helicity</title><title>Acta applicandae mathematicae</title><addtitle>Acta Appl Math</addtitle><description>For temperatures below and beyond the Curie temperature, the stochastic Landau-Lifshitz-Bloch equation describes the evolution of spins in ferromagnetic materials. In this work, we consider the stochastic Landau-Lifshitz-Bloch equation driven by a real valued Wiener process and show Wong-Zakai type approximations for the same. We consider non-zero contribution from the helicity term in the energy. First, using a Doss-Sussmann type transform, we convert the stochastic partial differential equation into a deterministic equation with random coefficients. We then show that the solution of the transformed equation depends continuously on the driving Wiener process. We then use this result, along with the properties of the said transform to show that the solution of the originally considered equation depends continuously on the driving Wiener process.</description><subject>Anisotropy</subject><subject>Applications of Mathematics</subject><subject>Approximation</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Curie temperature</subject><subject>Ferromagnetic materials</subject><subject>Helicity</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Temperature</subject><issn>0167-8019</issn><issn>1572-9036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kL1OwzAURi0EEqXwAkyRmA3XcWo7Y6kKRYrEAAjBYjmO07iUpLUdQXh6TIvExnSH-537cxA6J3BJAPiVJ5BlgCHNMAATBA8HaEQmPMU5UHaIRkAYxwJIfoxOvF8BAM0ZG6GX565d4lf1pmwy3Wxc92nfVbBd65O6c0loTPIQOt0oH6xOCtVWqseFrX1jwxe-XsdWMt_2OyT5sKFJFmZttQ3DKTqq1dqbs986Rk8388fZAhf3t3ezaYF1yiFgrokByikHzVIN2mSmZJUSNINSiAwgnQiAsoZKs4rlpJzkQnCiSkVKYLymY3SxnxuP3_bGB7nqetfGlZJGN5TzlIqYSvcp7TrvnanlxsVP3SAJyB-Fcq9QRoVyp1AOEaJ7yMdwuzTub_Q_1Dfyz3R_</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Gokhale, Soham Sanjay</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-1001-003X</orcidid></search><sort><creationdate>20241001</creationdate><title>Wong-Zakai Approximations for the Stochastic Landau-Lifshitz-Bloch Equation with Helicity</title><author>Gokhale, Soham Sanjay</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-7c1e037370c62c0ce4eb6da8340b8840025800bf0dc6d691b598871aba1b067f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Anisotropy</topic><topic>Applications of Mathematics</topic><topic>Approximation</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Curie temperature</topic><topic>Ferromagnetic materials</topic><topic>Helicity</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Temperature</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gokhale, Soham Sanjay</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Acta applicandae mathematicae</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gokhale, Soham Sanjay</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Wong-Zakai Approximations for the Stochastic Landau-Lifshitz-Bloch Equation with Helicity</atitle><jtitle>Acta applicandae mathematicae</jtitle><stitle>Acta Appl Math</stitle><date>2024-10-01</date><risdate>2024</risdate><volume>193</volume><issue>1</issue><spage>4</spage><pages>4-</pages><artnum>4</artnum><issn>0167-8019</issn><eissn>1572-9036</eissn><abstract>For temperatures below and beyond the Curie temperature, the stochastic Landau-Lifshitz-Bloch equation describes the evolution of spins in ferromagnetic materials. In this work, we consider the stochastic Landau-Lifshitz-Bloch equation driven by a real valued Wiener process and show Wong-Zakai type approximations for the same. We consider non-zero contribution from the helicity term in the energy. First, using a Doss-Sussmann type transform, we convert the stochastic partial differential equation into a deterministic equation with random coefficients. We then show that the solution of the transformed equation depends continuously on the driving Wiener process. We then use this result, along with the properties of the said transform to show that the solution of the originally considered equation depends continuously on the driving Wiener process.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10440-024-00681-y</doi><orcidid>https://orcid.org/0000-0002-1001-003X</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0167-8019 |
| ispartof | Acta applicandae mathematicae, 2024-10, Vol.193 (1), p.4, Article 4 |
| issn | 0167-8019 1572-9036 |
| language | eng |
| recordid | cdi_proquest_journals_3100377238 |
| source | SpringerLink Journals |
| subjects | Anisotropy Applications of Mathematics Approximation Calculus of Variations and Optimal Control Optimization Computational Mathematics and Numerical Analysis Curie temperature Ferromagnetic materials Helicity Mathematics Mathematics and Statistics Partial Differential Equations Probability Theory and Stochastic Processes Temperature |
| title | Wong-Zakai Approximations for the Stochastic Landau-Lifshitz-Bloch Equation with Helicity |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-19T10%3A26%3A58IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Wong-Zakai%20Approximations%20for%20the%20Stochastic%20Landau-Lifshitz-Bloch%20Equation%20with%20Helicity&rft.jtitle=Acta%20applicandae%20mathematicae&rft.au=Gokhale,%20Soham%20Sanjay&rft.date=2024-10-01&rft.volume=193&rft.issue=1&rft.spage=4&rft.pages=4-&rft.artnum=4&rft.issn=0167-8019&rft.eissn=1572-9036&rft_id=info:doi/10.1007/s10440-024-00681-y&rft_dat=%3Cproquest_cross%3E3100377238%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3100377238&rft_id=info:pmid/&rfr_iscdi=true |