Diffusion, subdiffusion, and trapping of active particles in heterogeneous media

We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles avoid. Obstacle avoidance is characterized by the particle turning speed $γ$. We show, through simulations and analytical calculations, that the mean square displacement of particles exhibits two regimes as function of the density of obstacles $ρ_o$ and $γ$. We find that at low values of $γ$, particle motion is diffusive and characterized by a diffusion coefficient that displays a minimum at an intermediate obstacle density $ρ_o$. We observe that in high obstacle density regions and for large $γ$ values, spontaneous trapping of active particles occurs. We show that such trapping leads to genuine subdiffusive motion of the active particles. We indicate how these findings can be used to fabricate a filter of active particles.

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