Trail-Mediated Self-Interaction

Abstract

A number of microorganisms leave persistent trails while moving along surfaces. For single-cell organisms, the trail-mediated self-interaction will influence its dynamics. It has been discussed recently [Kranz \textit{et al.} Phys. Rev. Lett. \textbf{117}, 8101 (2016)] that the self-interaction may localize the organism above a critical coupling ${\chi }_c$ to the trail. Here we will derive a generalized active particle model capturing the key features of the self-interaction and analyze its behavior for smaller couplings $\chi <{\chi }_c$. We find that fluctuations in propulsion speed shift the localization transition to stronger couplings.

arXiv comment7 pages, 2 figures; minor improvments

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• Active Phases for Particles on Resource Landscapes
• Current fluctuations of a self-interacting diffusion on a ring
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• Extension and dynamical phases in random walkers depositing and following chemical trails
• Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems