Non-Gaussian behaviour of a self-propelled particle on a substrate

• Date: 2009
• Main Authors: ten Hagen, B., van Teeffelen, S., Löwen, H.
• Format: Article
• Language: English
• Published: Інститут фізики конденсованих систем НАН України 2009
• Series: Condensed Matter Physics
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/120556
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Non-Gaussian behaviour of a self-propelled particle on a substrate / B. ten Hagen, S. van Teeffelen, H. Löwen // Condensed Matter Physics. — 2009. — Т. 12, № 4. — С. 725-738. — Бібліогр.: 42 назв. — англ.

The overdamped Brownian motion of a self-propelled particle which is driven by a projected internal force is studied by solving the Langevin equation analytically. The active particle under study is restricted to move along a linear channel. The direction of its internal force is orientationally diffusing on a unit circle in a plane perpendicular to the substrate. An additional time-dependent torque is acting on the internal force orientation. The model is relevant for active particles like catalytically driven Janus particles and bacteria moving on a substrate. Analytical results for the rst four time-dependent displacement moments are presented and analysed for several special situations. For a vanishing torque, there is a significant dynamical non-Gaussian behaviour at finite times t as signalled by a non-vanishing normalized kurtosis in the particle displacement which approaches zero for long time with a 1/t long-time tail.