Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914849463730176 |
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| author | Bevilacqua, Giulia Lonati, Chiara |
| author_facet | Bevilacqua, Giulia Lonati, Chiara |
| contents | We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of minimizers. Indeed, choosing three different geometrical shapes for the cross-section, we derive Euler-Lagrange equations for a planar version of the Kirchhoff-Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06269 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem Bevilacqua, Giulia Lonati, Chiara Analysis of PDEs 49K10, 49Q05, 74G05, 74G55, 74P20 We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of minimizers. Indeed, choosing three different geometrical shapes for the cross-section, we derive Euler-Lagrange equations for a planar version of the Kirchhoff-Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium. |
| title | Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem |
| topic | Analysis of PDEs 49K10, 49Q05, 74G05, 74G55, 74P20 |
| url | https://arxiv.org/abs/2302.06269 |