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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.12088 |
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| _version_ | 1866911060372488192 |
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| author | He, Shuhui Whale, Ben Wheeler, Glen Wheeler, Valentina-Mira |
| author_facet | He, Shuhui Whale, Ben Wheeler, Glen Wheeler, Valentina-Mira |
| contents | In this paper we propose and study a curvature-based mathematical model for dorsal closure in embryonic drosophila. Using an analysis that mixes maximum-principle and integral-estimates, we establish global existence and convergence for data that mimics the initial geometry of a dorsal closure event. Further, we present a numerical approximation scheme for the flow, establishing stability, consistence, and convergence. We also give sample simulations of the flow with initial configurations that include experimentally observed data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A curvature flow approach to dorsal closure modelling He, Shuhui Whale, Ben Wheeler, Glen Wheeler, Valentina-Mira Analysis of PDEs Differential Geometry 35Q92 (Primary) 35K93, 65M12, 65M22 (Secondary) In this paper we propose and study a curvature-based mathematical model for dorsal closure in embryonic drosophila. Using an analysis that mixes maximum-principle and integral-estimates, we establish global existence and convergence for data that mimics the initial geometry of a dorsal closure event. Further, we present a numerical approximation scheme for the flow, establishing stability, consistence, and convergence. We also give sample simulations of the flow with initial configurations that include experimentally observed data. |
| title | A curvature flow approach to dorsal closure modelling |
| topic | Analysis of PDEs Differential Geometry 35Q92 (Primary) 35K93, 65M12, 65M22 (Secondary) |
| url | https://arxiv.org/abs/2507.12088 |