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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.05984 |
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| _version_ | 1866914182908084224 |
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| author | Deeb, Omar El |
| author_facet | Deeb, Omar El |
| contents | We develop a minimal nonlinear model to investigate the oscillatory dynamics of Saturn's F ring under dual-moon forcing from Prometheus and Pandora. The model extends classical predator--prey dynamics by incorporating both a nonlinear mass aggregation term $kM^n$ and explicit dual-frequency forcing, capturing how higher-order coagulation physics interacts with multi-moon perturbations. Through extensive numerical integration and dynamical systems analysis, including time-series, spectral, stroboscopic mapping, and rotation number diagnostics, we identify distinct dynamical regimes controlled by the parameters $n$ and $k$.
For moderate nonlinearity $(n=1.28, k=0.54)$, the system exhibits regular quasi-periodic motion on a two-torus, characterized by smooth amplitude modulation and discrete spectral lines. As nonlinearity increases $(n=1.30, k=0.62)$, the dynamics transition to strongly modulated oscillations with intermittent phase slips, broadened Poincaré bands, and sideband-rich spectra. A rotation number heatmap reveals organized structures in parameter space, with smooth quasi-periodic regions bounded by near-locking bands analogous to Arnold tongues.
Our results demonstrate that the F ring's complex morphology can emerge from deterministic multi-frequency dynamics rather than stochastic processes, with the system operating near critical boundaries where small parameter variations can trigger macroscopic reorganization. The model provides a framework for understanding pattern formation in other driven granular systems while offering testable predictions for ring observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dual-moon forced dynamics and nonlinear aggregation in Saturn's F ring: From quasi-periodicity to modulated oscillations Deeb, Omar El General Physics We develop a minimal nonlinear model to investigate the oscillatory dynamics of Saturn's F ring under dual-moon forcing from Prometheus and Pandora. The model extends classical predator--prey dynamics by incorporating both a nonlinear mass aggregation term $kM^n$ and explicit dual-frequency forcing, capturing how higher-order coagulation physics interacts with multi-moon perturbations. Through extensive numerical integration and dynamical systems analysis, including time-series, spectral, stroboscopic mapping, and rotation number diagnostics, we identify distinct dynamical regimes controlled by the parameters $n$ and $k$. For moderate nonlinearity $(n=1.28, k=0.54)$, the system exhibits regular quasi-periodic motion on a two-torus, characterized by smooth amplitude modulation and discrete spectral lines. As nonlinearity increases $(n=1.30, k=0.62)$, the dynamics transition to strongly modulated oscillations with intermittent phase slips, broadened Poincaré bands, and sideband-rich spectra. A rotation number heatmap reveals organized structures in parameter space, with smooth quasi-periodic regions bounded by near-locking bands analogous to Arnold tongues. Our results demonstrate that the F ring's complex morphology can emerge from deterministic multi-frequency dynamics rather than stochastic processes, with the system operating near critical boundaries where small parameter variations can trigger macroscopic reorganization. The model provides a framework for understanding pattern formation in other driven granular systems while offering testable predictions for ring observations. |
| title | Dual-moon forced dynamics and nonlinear aggregation in Saturn's F ring: From quasi-periodicity to modulated oscillations |
| topic | General Physics |
| url | https://arxiv.org/abs/2512.05984 |