One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909831189757952 |
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| author | Dolmaire, Théophile Hübner-Rosenau, Eleni |
| author_facet | Dolmaire, Théophile Hübner-Rosenau, Eleni |
| contents | We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient $r$, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision pattern, proving that it can be realized, despite its instability. We prove that we can associate to the four-particle dynamical system another dynamical system of smaller dimension, acting on $\{1,2,3\} \times \mathbb{S}^2$, and that encodes the collision orders of each trajectory. We provide different representations of this new dynamical system, and study numerically its $ω$-limit sets. In particular, the numerical simulations suggest that the orbits of such a system might be quasi-periodic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction Dolmaire, Théophile Hübner-Rosenau, Eleni Dynamical Systems Mathematical Physics We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient $r$, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision pattern, proving that it can be realized, despite its instability. We prove that we can associate to the four-particle dynamical system another dynamical system of smaller dimension, acting on $\{1,2,3\} \times \mathbb{S}^2$, and that encodes the collision orders of each trajectory. We provide different representations of this new dynamical system, and study numerically its $ω$-limit sets. In particular, the numerical simulations suggest that the orbits of such a system might be quasi-periodic. |
| title | One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction |
| topic | Dynamical Systems Mathematical Physics |
| url | https://arxiv.org/abs/2411.10324 |