Active Brownian particles in quenched matrices

Active particles convert stored energy into directed motion and can display complex emergent behavior arising from non-equilibrium effects. In many cases, e.g., living cells, the environment is complex and heterogeneous. In this work, we investigate a two-dimensional system of soft active Brownian particles (ABPs) in quenched matrices. The matrix induces a clustering of the particles even at low density and activity. However, the nature of clustering is different in regimes of low and high activity. For low activity (Peclet number less than 10), the number of clusters increases with increasing activity and the size of the clusters decreases. The opposite is true for high activity (Peclet number greater than 50). We perform a percolation analysis using a Voronoi construction where the connectedness of empty space depends on the activity. As expected, the percolation threshold is higher for active particles (compared to passive counterparts) because they can push through the matrix. For a fixed time slice, a fraction of particles satisfy all four diagnostic criteria consistent with genuine fractional Brownian motion (FBM), including scale-free velocity correlations. Analysis of long trajectories shows that single particles display FBM-like dynamics for some stretches. Such a behavior is absent for passive particles in a matrix and for active particles without a matrix and suggests a possible physical origin for the particle-to-particle variability observed in single-particle tracking experiments in cellular environments. Polydispersity in the matrix particle size has a quantitative but not qualitative effect on the properties of the ABPs.