Active transport and cluster formation on 2D networks.

We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment which is motivated by vesicular transport on actin filaments. In the presence of a hard-core interaction, particle clusters are observed that exhibit an algebraically decaying distribution in a large parameter regime, indicating the existence of clusters on all scales. The scale-free behavior can be understood by a mechanism promoting preferential attachment of particles to large clusters. The results are compared with a diffusion-limited aggregation model and active transport on a regular network. For both models we observe aggregation of particles to clusters which are characterized by a finite size scale if the relevant time scales and particle densities are considered.