First-passage statistics of run-and-tumble particles with directional bias and stochastic trapping

Abstract

We numerically investigate the first-passage time statistics of active particles in confined one- and two-dimensional geometries, subject to stochastic trapping and directional bias. The dynamics alternate between persistent ballistic runs, trapping phases with power-law distributed waiting times, and stochastic reorientation events, providing a minimal framework for intermittent active transport in heterogeneous environments. We analyze how persistence, bias strength, and the trapping exponent jointly govern the mean first-passage time (MFPT) and its scaling with system size. In the absence of trapping, persistent motion exhibits the classical ballistic–diffusive crossover, while directional bias generates an effective drift that generally reduces the MFPT. Scaling behavior depends on dimensionality: in one dimension, the MFPT grows approximately linearly with system size, whereas in two-dimensional circular domains it shows sublinear scaling, reflecting more efficient spatial exploration. Heavy-tailed trapping times with diverging mean ( μ<1) produce intermittency-dominated dynamics and anomalous MFPT scaling, whereas finite-mean trapping ( μ⩾1) primarily renormalizes the search timescale. In the biased regime with strongly persistent runs ( γ<1), the MFPT can decrease only slowly with μ, revealing a nontrivial interplay between drift and intermittent immobilization. Overall, we identify persistence-, drift-, and trapping-dominated transport regimes and highlight how confinement geometry, directional bias, and temporal intermittency jointly control first-passage processes in active systems.