Oscillatory instability in an Ostwald ripening process
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916660509671424 |
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| author | Wilkinson, Michael |
| author_facet | Wilkinson, Michael |
| contents | This paper considers an Ostwald ripening process in which new droplets are injected at a constant rate, with a fixed distribution of radii, and in which droplets are removed when they grow to a specified maximum radius. This process exhibits a transition from a steady state to a limit cycle as a parameter is varied. The instability is shown to be related to the roots of the Laplace transform of a response kernel. A model is described which gives a good approximation of the period of the limit cycle. The model may also exhibit chaotic behaviour. The relevance of the model to atmospheric precipitation is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Oscillatory instability in an Ostwald ripening process Wilkinson, Michael Statistical Mechanics This paper considers an Ostwald ripening process in which new droplets are injected at a constant rate, with a fixed distribution of radii, and in which droplets are removed when they grow to a specified maximum radius. This process exhibits a transition from a steady state to a limit cycle as a parameter is varied. The instability is shown to be related to the roots of the Laplace transform of a response kernel. A model is described which gives a good approximation of the period of the limit cycle. The model may also exhibit chaotic behaviour. The relevance of the model to atmospheric precipitation is discussed. |
| title | Oscillatory instability in an Ostwald ripening process |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2503.18194 |