A multiple-timing analysis of temporal ratcheting
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916242190761984 |
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| author | Hashemi, Aref Gilman, Edward T. Khair, Aditya S. |
| author_facet | Hashemi, Aref Gilman, Edward T. Khair, Aditya S. |
| contents | We develop a two-timing perturbation analysis to investigate the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies $ω$ and $αω$, where $α$ is a rational number. It has been established, in other physical systems, that if $α$ is a ratio of odd and even integers (e.g., $\tfrac{2}{1}$, $\tfrac{3}{2}$, $\tfrac{4}{3}$), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order and third-order two-timing perturbation schemes predict the existence of temporal ratchets for, respectively, $α=2$ and $α=\tfrac{3}{2}$, $\tfrac{4}{3}$. More importantly, we find closed form formula for the magnitude and direction of the induced net velocities for these $α$ values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07555 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A multiple-timing analysis of temporal ratcheting Hashemi, Aref Gilman, Edward T. Khair, Aditya S. Applied Physics We develop a two-timing perturbation analysis to investigate the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies $ω$ and $αω$, where $α$ is a rational number. It has been established, in other physical systems, that if $α$ is a ratio of odd and even integers (e.g., $\tfrac{2}{1}$, $\tfrac{3}{2}$, $\tfrac{4}{3}$), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order and third-order two-timing perturbation schemes predict the existence of temporal ratchets for, respectively, $α=2$ and $α=\tfrac{3}{2}$, $\tfrac{4}{3}$. More importantly, we find closed form formula for the magnitude and direction of the induced net velocities for these $α$ values. |
| title | A multiple-timing analysis of temporal ratcheting |
| topic | Applied Physics |
| url | https://arxiv.org/abs/2210.07555 |