A limiting model for a low Reynolds number swimmer with N passive elastic arms
We consider a low Reynolds number artificial swimmer that consists of an active arm followed by $ N $ passive springs separated by spheres. This setup generalizes an approach proposed in Montino and DeSimone, Eur. Phys. J. E, vol. 38, 2015. We further study the limit as the number of springs tends t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023087?viewType=HTML |
| _version_ | 1797448885528952832 |
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| author | François Alouges Aline Lefebvre-Lepot Jessie Levillain |
| author_facet | François Alouges Aline Lefebvre-Lepot Jessie Levillain |
| author_sort | François Alouges |
| collection | DOAJ |
| description | We consider a low Reynolds number artificial swimmer that consists of an active arm followed by $ N $ passive springs separated by spheres. This setup generalizes an approach proposed in Montino and DeSimone, Eur. Phys. J. E, vol. 38, 2015. We further study the limit as the number of springs tends to infinity and the parameters are scaled conveniently, and provide a rigorous proof of the convergence of the discrete model to the continuous one. Several numerical experiments show the performances of the displacement in terms of the frequency or the amplitude of the oscillation of the active arm. |
| first_indexed | 2024-03-09T14:16:54Z |
| format | Article |
| id | doaj.art-90e5f22d8a174215b1d56a4675aa5ed2 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-09T14:16:54Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-90e5f22d8a174215b1d56a4675aa5ed22023-11-29T01:14:05ZengAIMS PressMathematics in Engineering2640-35012023-05-015512010.3934/mine.2023087A limiting model for a low Reynolds number swimmer with N passive elastic armsFrançois Alouges 0Aline Lefebvre-Lepot1 Jessie Levillain21. Centre Borelli, ENS Paris-Saclay, CNRS, Université Paris-Saclay, 91190 Gif-sur-Yvette, France2. CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France2. CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, FranceWe consider a low Reynolds number artificial swimmer that consists of an active arm followed by $ N $ passive springs separated by spheres. This setup generalizes an approach proposed in Montino and DeSimone, Eur. Phys. J. E, vol. 38, 2015. We further study the limit as the number of springs tends to infinity and the parameters are scaled conveniently, and provide a rigorous proof of the convergence of the discrete model to the continuous one. Several numerical experiments show the performances of the displacement in terms of the frequency or the amplitude of the oscillation of the active arm.https://www.aimspress.com/article/doi/10.3934/mine.2023087?viewType=HTMLlow reynolds number swimmerspartial differential equationsordinary differential equationsdiscrete modelcontinuous modelconvergence |
| spellingShingle | François Alouges Aline Lefebvre-Lepot Jessie Levillain A limiting model for a low Reynolds number swimmer with N passive elastic arms Mathematics in Engineering low reynolds number swimmers partial differential equations ordinary differential equations discrete model continuous model convergence |
| title | A limiting model for a low Reynolds number swimmer with N passive elastic arms |
| title_full | A limiting model for a low Reynolds number swimmer with N passive elastic arms |
| title_fullStr | A limiting model for a low Reynolds number swimmer with N passive elastic arms |
| title_full_unstemmed | A limiting model for a low Reynolds number swimmer with N passive elastic arms |
| title_short | A limiting model for a low Reynolds number swimmer with N passive elastic arms |
| title_sort | limiting model for a low reynolds number swimmer with n passive elastic arms |
| topic | low reynolds number swimmers partial differential equations ordinary differential equations discrete model continuous model convergence |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023087?viewType=HTML |
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