One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability
We study a model system with nematic and magnetic order, within a channel geometry modeled by an interval, $[-D, D]$. The system is characterized by a tensor-valued nematic order parameter ${{Q}}$ and a vector-valued magnetization ${{M}}$, and the observable states are modeled as stable critical poi...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2022
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| _version_ | 1826307771807563776 |
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| author | Dalby, J Farrell, PE Majumdar, A Xia, J |
| author_facet | Dalby, J Farrell, PE Majumdar, A Xia, J |
| author_sort | Dalby, J |
| collection | OXFORD |
| description | We study a model system with nematic and magnetic order, within a channel geometry modeled by an interval, $[-D, D]$. The system is characterized by a tensor-valued nematic order parameter ${{Q}}$ and a vector-valued magnetization ${{M}}$, and the observable states are modeled as stable critical points of an appropriately defined free energy which includes a nemato-magnetic coupling term, characterized by a parameter $c$. We (i) derive $L^\infty$ bounds for ${{Q}}$ and ${{M}}$; (ii) prove a uniqueness result in specified parameter regimes; (iii) analyze order reconstruction solutions, possessing domain walls, and their stabilities as a function of $D$ and $c$ and; (iv) perform numerical studies that elucidate the interplay of $c$ and $D$ for multistability. |
| first_indexed | 2024-03-07T07:08:06Z |
| format | Journal article |
| id | oxford-uuid:a836fa02-a040-4c19-b0f8-fed21973b8a3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:08:06Z |
| publishDate | 2022 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:a836fa02-a040-4c19-b0f8-fed21973b8a32022-05-24T10:43:08ZOne-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistabilityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a836fa02-a040-4c19-b0f8-fed21973b8a3EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2022Dalby, JFarrell, PEMajumdar, AXia, JWe study a model system with nematic and magnetic order, within a channel geometry modeled by an interval, $[-D, D]$. The system is characterized by a tensor-valued nematic order parameter ${{Q}}$ and a vector-valued magnetization ${{M}}$, and the observable states are modeled as stable critical points of an appropriately defined free energy which includes a nemato-magnetic coupling term, characterized by a parameter $c$. We (i) derive $L^\infty$ bounds for ${{Q}}$ and ${{M}}$; (ii) prove a uniqueness result in specified parameter regimes; (iii) analyze order reconstruction solutions, possessing domain walls, and their stabilities as a function of $D$ and $c$ and; (iv) perform numerical studies that elucidate the interplay of $c$ and $D$ for multistability. |
| spellingShingle | Dalby, J Farrell, PE Majumdar, A Xia, J One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability |
| title | One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability |
| title_full | One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability |
| title_fullStr | One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability |
| title_full_unstemmed | One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability |
| title_short | One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability |
| title_sort | one dimensional ferronematics in a channel order reconstruction bifurcations and multistability |
| work_keys_str_mv | AT dalbyj onedimensionalferronematicsinachannelorderreconstructionbifurcationsandmultistability AT farrellpe onedimensionalferronematicsinachannelorderreconstructionbifurcationsandmultistability AT majumdara onedimensionalferronematicsinachannelorderreconstructionbifurcationsandmultistability AT xiaj onedimensionalferronematicsinachannelorderreconstructionbifurcationsandmultistability |