A Linear Structure from Magnetic-Dipole Systems and Its Geometry
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909941730639872 |
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| author | Lin, Bohuan Li, Fengping Zhang, Zhengya |
| author_facet | Lin, Bohuan Li, Fengping Zhang, Zhengya |
| contents | We investigate a class of algebras on $\mathbb{R}^3$ arising and generalized from the algebraic structure of magnetic gradient fields induced by systems of synchronous magnets with identical dipole moments (i.e., $\mathbf{M}_i=\mathbf{M},\,\forall i$). We show that when there is a $2$ dimensional sub-algebra, the linear structure associated to such an algebra admits a certain type of decompositions, which allows the locating of the dipole moment $\bar{\mathbf{M}}$ that yields the strongest translational force(s) on a test magnet $\mathfrak{m}$. Upper bounds to the strength of this magnetic force are then established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03408 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Linear Structure from Magnetic-Dipole Systems and Its Geometry Lin, Bohuan Li, Fengping Zhang, Zhengya Rings and Algebras Mathematical Physics 15A18, 15A42, 17A60, We investigate a class of algebras on $\mathbb{R}^3$ arising and generalized from the algebraic structure of magnetic gradient fields induced by systems of synchronous magnets with identical dipole moments (i.e., $\mathbf{M}_i=\mathbf{M},\,\forall i$). We show that when there is a $2$ dimensional sub-algebra, the linear structure associated to such an algebra admits a certain type of decompositions, which allows the locating of the dipole moment $\bar{\mathbf{M}}$ that yields the strongest translational force(s) on a test magnet $\mathfrak{m}$. Upper bounds to the strength of this magnetic force are then established. |
| title | A Linear Structure from Magnetic-Dipole Systems and Its Geometry |
| topic | Rings and Algebras Mathematical Physics 15A18, 15A42, 17A60, |
| url | https://arxiv.org/abs/2512.03408 |