Polarization and energy ellipsoids for an introductory visualization of tensors
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915024012836864 |
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| author | Alves, Danilo T. Queiroz, Lucas Silva, Jeferson Danilo L. |
| author_facet | Alves, Danilo T. Queiroz, Lucas Silva, Jeferson Danilo L. |
| contents | In ``The Feynman Lectures on Physics'' is discussed an introduction to tensors by means of the polarization tensor, including a way of ``visualizing'' this tensor via the energy ellipsoid, which is drawn by the electric fields which produce the same polarization energy density in an anisotropic crystal. Here, we discuss an alternative way of visualizing the polarization tensor, by means of the polarization ellipsoid, which is based on the ideas of Lamé's stress ellipsoid and is drawn by the polarization vectors produced by electric fields having the same magnitude. We compare both ellipsoids as a first introductory way of visualizing the polarization tensor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polarization and energy ellipsoids for an introductory visualization of tensors Alves, Danilo T. Queiroz, Lucas Silva, Jeferson Danilo L. Physics Education Classical Physics In ``The Feynman Lectures on Physics'' is discussed an introduction to tensors by means of the polarization tensor, including a way of ``visualizing'' this tensor via the energy ellipsoid, which is drawn by the electric fields which produce the same polarization energy density in an anisotropic crystal. Here, we discuss an alternative way of visualizing the polarization tensor, by means of the polarization ellipsoid, which is based on the ideas of Lamé's stress ellipsoid and is drawn by the polarization vectors produced by electric fields having the same magnitude. We compare both ellipsoids as a first introductory way of visualizing the polarization tensor. |
| title | Polarization and energy ellipsoids for an introductory visualization of tensors |
| topic | Physics Education Classical Physics |
| url | https://arxiv.org/abs/2407.18464 |