Stability analysis for active Brownian particle models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915686515736576 |
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| author | Zelati, Michele Coti Ertzbischoff, Lucas Gerard-Varet, David |
| author_facet | Zelati, Michele Coti Ertzbischoff, Lucas Gerard-Varet, David |
| contents | We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are Fokker-Planck type equations in position-orientation and are known to exhibit motility-induced phase separation. We fully characterize the linear stability and instability regimes, with an explicit threshold depending on the effective speed of the particles. In this way, we rigorously confirm a conjecture on phase separation originating in the physics and applied literature. Our sharp and quantitative (in)stability results are valid both in the non-diffusive case and in the case of small angular diffusion. In the stable non-diffusive regime, we uncover a mixing mechanism reminiscent of Landau damping for the Vlasov equation, albeit with significantly weaker decay. This decay is non-integrable in time and gives rise to substantial mathematical difficulties; in particular, it prevents the use of classical perturbative arguments to treat the case of small angular diffusion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_17649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability analysis for active Brownian particle models Zelati, Michele Coti Ertzbischoff, Lucas Gerard-Varet, David Analysis of PDEs We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are Fokker-Planck type equations in position-orientation and are known to exhibit motility-induced phase separation. We fully characterize the linear stability and instability regimes, with an explicit threshold depending on the effective speed of the particles. In this way, we rigorously confirm a conjecture on phase separation originating in the physics and applied literature. Our sharp and quantitative (in)stability results are valid both in the non-diffusive case and in the case of small angular diffusion. In the stable non-diffusive regime, we uncover a mixing mechanism reminiscent of Landau damping for the Vlasov equation, albeit with significantly weaker decay. This decay is non-integrable in time and gives rise to substantial mathematical difficulties; in particular, it prevents the use of classical perturbative arguments to treat the case of small angular diffusion. |
| title | Stability analysis for active Brownian particle models |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.17649 |