Tangential Tensor Fields on Deformable Surfaces -- How to Derive Consistent $L^2$-Gradient Flows
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909145424199680 |
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| author | Nitschke, Ingo Sadik, Souhayl Voigt, Axel |
| author_facet | Nitschke, Ingo Sadik, Souhayl Voigt, Axel |
| contents | We consider gradient flows of surface energies which depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to guarantee a decrease in energy, the gauge of surface independence and the time derivative have to be chosen consistently. We demonstrate the results for a surface Frank-Oseen-Hilfrich energy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2209_13272 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tangential Tensor Fields on Deformable Surfaces -- How to Derive Consistent $L^2$-Gradient Flows Nitschke, Ingo Sadik, Souhayl Voigt, Axel Mathematical Physics Differential Geometry 53A45, 53A05, 70G75 We consider gradient flows of surface energies which depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to guarantee a decrease in energy, the gauge of surface independence and the time derivative have to be chosen consistently. We demonstrate the results for a surface Frank-Oseen-Hilfrich energy. |
| title | Tangential Tensor Fields on Deformable Surfaces -- How to Derive Consistent $L^2$-Gradient Flows |
| topic | Mathematical Physics Differential Geometry 53A45, 53A05, 70G75 |
| url | https://arxiv.org/abs/2209.13272 |