Critical escape dynamics of an active particle moving on curved surfaces
Abstract
On the macroscopic scale, active (self-propelled) objects moving through complex environments are often subject to effects arising from both the curvature of the surrounding surface and external influences such as gravity. We study the Kramers escape problem for active Brownian particles in two settings: motion in an external potential driven solely by gradient forces, and motion on a curved manifold subject to an additional constant gravitational force. In the absence of translational noise, a sharp dynamical transition occurs when the self-propulsion velocity v0 reaches a critical velocity vc required for an escape. Above this threshold, the escape rate k follows a universal scaling form, k ∝ exp[−const(v0−vc)−γ], with an exponent γ=3/2 for the escape in a potential and γ=1/2 for the escape on a curved manifold in the presence of gravity. These distinct exponents reveal how the interplay of activity, surface curvature, and gravity determines the critical escape dynamics. Our theoretical predictions are verified by numerical simulations.
Related
- Geodesic Trapping and Escape of Active Particles on Curved Surfaces
- Poisson-shot-noise induced escape dynamics of a passive particle and a dimer
- Unsteady and inertial dynamics of a small active particle in a fluid
- Active particle dynamics in uniform and patterned electroosmotic flows
- Linear and nonlinear active microrheology of viscous, viscoelastic, and elastic media: A fluid particle dynamics approach
BibTeX
@misc{root2026critical,
title = {{Critical escape dynamics of an active particle moving on curved surfaces}},
author = {Maxim Root and Hartmut Löwen and Peter Sollich and Lorenzo Caprini and Alexander P. Antonov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30455},
eprint = {2609.30455},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30455},
}
RIS
TY - UNPB
TI - Critical escape dynamics of an active particle moving on curved surfaces
AU - Maxim Root
AU - Hartmut Löwen
AU - Peter Sollich
AU - Lorenzo Caprini
AU - Alexander P. Antonov
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30455
UR - https://arxiv.org/abs/2609.30455
AB - On the macroscopic scale, active (self-propelled) objects moving through complex environments are often subject to effects arising from both the curvature of the surrounding surface and external influences such as gravity. We study the Kramers escape problem for active Brownian particles in two settings: motion in an external potential driven solely by gradient forces, and motion on a curved manifold subject to an additional constant gravitational force. In the absence of translational noise, a sharp dynamical transition occurs when the self-propulsion velocity v_0 reaches a critical velocity v_c required for an escape. Above this threshold, the escape rate k follows a universal scaling form, k ∝ exp[−const(v_0−v_c)^−γ], with an exponent γ=3/2 for the escape in a potential and γ=1/2 for the escape on a curved manifold in the presence of gravity. These distinct exponents reveal how the interplay of activity, surface curvature, and gravity determines the critical escape dynamics. Our theoretical predictions are verified by numerical simulations.
ER -