Comparison of the potential energy for different equilibrium configurations of symmetric and asymmetric floating drops
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913174586916864 |
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| author | Mault, Mason Treinen, Ray |
| author_facet | Mault, Mason Treinen, Ray |
| contents | We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value problems, and at each iterative step a Chebyshev spectral collocation method is employed. The problems considered here are those that can be described by using generating curves, and include problems in $\mathbb{R}^2$ and $\mathbb{R}^3$.
The resulting nine-dimensional space of physical parameters is explored, and examples are given that highlight the potential energy of centrally located drops, wall-bound drops, and asymmetrical configurations in $\mathbb{R}^2$. Non-uniqueness of solutions to the corresponding Euler-Lagrange equations is displayed, and also strong evidence of non-uniqueness of energy minimizers is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10120 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comparison of the potential energy for different equilibrium configurations of symmetric and asymmetric floating drops Mault, Mason Treinen, Ray Fluid Dynamics Numerical Analysis Mathematical Physics We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value problems, and at each iterative step a Chebyshev spectral collocation method is employed. The problems considered here are those that can be described by using generating curves, and include problems in $\mathbb{R}^2$ and $\mathbb{R}^3$. The resulting nine-dimensional space of physical parameters is explored, and examples are given that highlight the potential energy of centrally located drops, wall-bound drops, and asymmetrical configurations in $\mathbb{R}^2$. Non-uniqueness of solutions to the corresponding Euler-Lagrange equations is displayed, and also strong evidence of non-uniqueness of energy minimizers is given. |
| title | Comparison of the potential energy for different equilibrium configurations of symmetric and asymmetric floating drops |
| topic | Fluid Dynamics Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2602.10120 |