fluctuations.

![image](PhD.pdf)

In order to study the phase behavior of the model in the $(\mbox{Pe},\, g)$-plane, we integrate the over-damped Langevin equations (\[r\_dot\]), (\[theta\_dot\]) using the Euler method with a time step in the range $\delta t=10^{-3}-10^{-1}$ (depending on the value of the parameters). The white noise term $\eta_i$ eq. (\[theta\_dot\]) is drawn from a flat distribution in the interval $[-1, 1]$ independently for each particle at each time-step. The simulations have been performed for different noise intensities, $\gamma$, and coupling strengths, $K$, while keeping $v_0=0.1$ and $\epsilon=1$ fixed. We explore easily up to four orders of magnitude in the $(\mbox{Pe},\, g)$-plane: $\text{Pe}=[10^{-1},10^{3}]$ and $\text{g}=[10^{-2},10^{1}]$ by varying $\gamma=10^{-4},...,1$ and $K=10^{-4},...,10$. In order to identify the relevance of finite-size corrections, we have explored systems of $N=1000$ up to $10000$ particles with periodic boundary conditions (PBC) both in square $L_x=L_y=L$ and slab $L_x=5L_y$ geometries. We use a slab geometry in order to properly identify bands and lanes, as explained below (see section \[sec:cluster\]).

Phase behaviour {#sec:PhD}
===============

We start our analysis by first discussing the steady states of the model for systems defined on a square $L\times L$ box with PBC. Our systematic analysis resulted in the phase diagram shown in Fig.\[fig:PhD\] 