On the application of Lorentz-Finsler geometry to model wave propagation
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911191348019200 |
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| author | Pendás-Recondo, Enrique |
| author_facet | Pendás-Recondo, Enrique |
| contents | The recent increasing interest in the study of Lorentz-Finsler geometry has led to several applications to model real-world physical phenomena. Our purpose is to provide a simple, step-by-step review on how to build and implement such a geometric model to describe the propagation of a classical wave satisfying Fermat's and Huygens' principles in an anisotropic and rheonomic (time-dependent) medium. The model is based on identifying the individual wave trajectories as lightlike pregeodesics of a specific Lorentz-Finsler metric, which obey a simple ODE system and can therefore be easily computed in real time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03206 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the application of Lorentz-Finsler geometry to model wave propagation Pendás-Recondo, Enrique Differential Geometry Mathematical Physics 53C80, 53C22, 53C60 The recent increasing interest in the study of Lorentz-Finsler geometry has led to several applications to model real-world physical phenomena. Our purpose is to provide a simple, step-by-step review on how to build and implement such a geometric model to describe the propagation of a classical wave satisfying Fermat's and Huygens' principles in an anisotropic and rheonomic (time-dependent) medium. The model is based on identifying the individual wave trajectories as lightlike pregeodesics of a specific Lorentz-Finsler metric, which obey a simple ODE system and can therefore be easily computed in real time. |
| title | On the application of Lorentz-Finsler geometry to model wave propagation |
| topic | Differential Geometry Mathematical Physics 53C80, 53C22, 53C60 |
| url | https://arxiv.org/abs/2408.03206 |