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PreprintarXiv licencearXiv

Geodesic Trapping and Escape of Active Particles on Curved Surfaces

  • Yuzhu Chen
  • Vishal P. Patil
  • David Saintillan
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Abstract

Active particles on curved surfaces can become trapped along closed geodesics even without physical barriers. We show that escape from these geometric traps exposes a fundamental distinction between continuous and discrete reorientation. At high Péclet numbers, active Brownian particles escape efficiently through rotational diffusion, whereas run-and-tumble particles remain trapped much longer; at low Péclet numbers, both reduce to passive diffusion. Gaussian curvature controls escape by focusing or defocusing neighboring geodesics, producing distinct asymptotic scalings of the mean exit time.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026geodesic,
  title = {{Geodesic Trapping and Escape of Active Particles on Curved Surfaces}},
  author = {Yuzhu Chen and Vishal P. Patil and David Saintillan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09649},
  eprint = {2609.09649},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09649},
}
RIS
TY  - UNPB
TI  - Geodesic Trapping and Escape of Active Particles on Curved Surfaces
AU  - Yuzhu Chen
AU  - Vishal P. Patil
AU  - David Saintillan
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09649
UR  - https://arxiv.org/abs/2609.09649
AB  - Active particles on curved surfaces can become trapped along closed geodesics even without physical barriers. We show that escape from these geometric traps exposes a fundamental distinction between continuous and discrete reorientation. At high Péclet numbers, active Brownian particles escape efficiently through rotational diffusion, whereas run-and-tumble particles remain trapped much longer; at low Péclet numbers, both reduce to passive diffusion. Gaussian curvature controls escape by focusing or defocusing neighboring geodesics, producing distinct asymptotic scalings of the mean exit time.
ER  -