A variational analysis of nematic axisymmetric films: the covariant derivative case
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914071942529024 |
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| author | Bevilacqua, Giulia Lonati, Chiara Lussardi, Luca Marzocchi, Alfredo |
| author_facet | Bevilacqua, Giulia Lonati, Chiara Lussardi, Luca Marzocchi, Alfredo |
| contents | Nematic surfaces are thin fluid structures, ideally two-dimensional, endowed with an in-plane nematic order. In 2012, two variational models have been introduced by Giomi [11] and by Napoli and Vergori [29,28]. Both penalize the area of the surface and the gradient of the director: in [11] the covariant derivative of the director is considered, while [28] deals with the surface gradient. In this paper, a complete variational analysis of the model proposed by Giomi is performed for revolution surfaces spanning two coaxial rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A variational analysis of nematic axisymmetric films: the covariant derivative case Bevilacqua, Giulia Lonati, Chiara Lussardi, Luca Marzocchi, Alfredo Analysis of PDEs 49J05, 49Q10, 76A15 Nematic surfaces are thin fluid structures, ideally two-dimensional, endowed with an in-plane nematic order. In 2012, two variational models have been introduced by Giomi [11] and by Napoli and Vergori [29,28]. Both penalize the area of the surface and the gradient of the director: in [11] the covariant derivative of the director is considered, while [28] deals with the surface gradient. In this paper, a complete variational analysis of the model proposed by Giomi is performed for revolution surfaces spanning two coaxial rings. |
| title | A variational analysis of nematic axisymmetric films: the covariant derivative case |
| topic | Analysis of PDEs 49J05, 49Q10, 76A15 |
| url | https://arxiv.org/abs/2405.20154 |