Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910621824450560 |
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| author | Cristiani, Emiliano Loy, Nadia Menci, Marta Tosin, Andrea |
| author_facet | Cristiani, Emiliano Loy, Nadia Menci, Marta Tosin, Andrea |
| contents | In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19700 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions Cristiani, Emiliano Loy, Nadia Menci, Marta Tosin, Andrea Mathematical Physics Statistical Mechanics Numerical Analysis 35Q20, 35Q70, 92D50 In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms. |
| title | Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions |
| topic | Mathematical Physics Statistical Mechanics Numerical Analysis 35Q20, 35Q70, 92D50 |
| url | https://arxiv.org/abs/2310.19700 |