interactions, an Active Brownian Particle has a diffusivity $D\propto \text{Pe}^2$; so the higher $\text{Pe}$, the shorter is $\tau$ and the easiest is for a particle to leave a lane. This can be heuristically described in terms of an effective temperature, as put forward in the context of co-fluent tissue models in [@Giavazzi2017]. Following [@Giavazzi2017], if one considers the macroscopic coherent structures as a solid - where particles inside are caged by their neighbors - then, one can argue that fluctuations are well captured by an effective temperature $T^K_{\text{eff}}\propto \text{Pe}^2/\text{g}$. This explains why lanes have a tendency to become less stable as $\text{Pe}$ increases. Still, this does not explain why the typical band structures of the Vicsek model take over as $\text{Pe}$ increases.

At high $\text{Pe}$, fluctuations in the orientations are large, so the orientational degrees of freedom of the particles in the macro-cluster cannot be considered as frozen anymore. In this regime, we observe bands and lanes structures. As illustrated in Fig. \[fig:laneband\], it is harder for a particle in the surface of a band to leave the cluster than for a particle in the surface of a lane. If a particle in the surface of a lane picks a 