a $2D$ system [@Barci_2DNematic]) $$\label{eq:lmbdaMtrx}
Q_{hk}(t)=\frac{1}{N}\sum_{i=1}^{N}\left(2 e_{ih}(t)e_{ik}(t)-\delta_{hk}\right),$$ (being $h$ and $k$ equal to ${x,y}$ and $N$ the total number of squirmers) and the nematic order parameter $\lambda(t)$ being the largest eigenvalue of $Q_{hk}$ [@Eppenga1984].

We have also computed both global nematic and global polar order parameters, substituting $s$ with $N$ in the global polar order parameter (Eq. \[eq:PolarOrderCluster\]). Therefore, the polar order in steady-state is $P_{\infty} = P(t>>0)$ while the nematic order in steady-state is $\lambda_{\infty} = \lambda(t>>0)$.

\[sec:Results\] Results
=======================

Mean cluster size
-----------------

We start with computing the mean cluster size $\langle  s \rangle$ as a function of time for different values of $\beta $ and $\xi$. This allows us to distinguish coarsening from clustering, establishing, in the latter case, when the system reaches a steady state.

![\[fig:nct\_xi0\_1\]Time evolutions of the mean cluster size for squirmers when $\xi=0.1$ (pullers: red [squares]{} and black [circles]{}; neutral: blue [up triangles]{}; pushers: pink [down-triangles]{} and grey [diamonds]{}). (a) AP squirmers with $r_c=2.5\sigma$ and (b) $r_c=1.5\sigma$, (c) WP squirmers with $r_c=2.5\sigma$ and (d) $r_c=1.5\sigma$. Note the different scale on the y-axis.](ntxi01rc25ttbis.pdf "fig:"){width="0.48\columnwidth"} ![\[fig:nct\_xi0\_1\]Time evolutions of the mean cluster size for squirmers when $\xi=0.1$ (pullers: red [squares]{} and black [circles]{}; neutral: blue [up 