Flocking through a sea of rods

Abstract

We investigate the collective behavior of motile rods immersed in a monolayer of apolar rods confined between vertically vibrating plates using numerical simulations. We uncover an antidiffusive instability whereby motile rods segregate from the apolar medium and form flocks whose size increases with the medium concentration. Remarkably, enhanced segregation leads to a reduction of the global polar order. The flock structure is strongly influenced by the anisotropy of the medium rods. For small aspect ratios, the flocks are elongated perpendicular to the mean direction of motion, whereas for larger aspect ratios, they elongate along the direction of motility. We rationalize the emergence of segregation-induced disorder using a minimal mean-field model.

Figures (14)

• Figure 1: Effect of the area fraction $\phi_{\mathrm{a}}$ of apolar rods at $D_{\mathrm{r}} = 0~\mathrm{rad}^2\,\mathrm{s}^{-1}$. (a,b) Steady-state configurations at $\phi_{\mathrm{p}} = 0.05$ for (a) $\phi_{\mathrm{a}} = 0.05$ and (b) $\phi_{\mathrm{a}} = 0.80$. (c) Polar order parameter $P$ of the motile rods vs $\phi_{\mathrm{a}}$ for different $\phi_{\mathrm{p}}$. Effect of the intrinsic angular noise $D_{\mathrm{r}}$ of the polar rods at $\phi_{\mathrm{a}} = 0.50$. (d,e) Steady-state configurations at $\phi_{\mathrm{p}} = 0.05$ for (d) $D_{\mathrm{r}} = 0~\mathrm{rad}^2\,\mathrm{s}^{-1}$ and (e) $D_{\mathrm{r}} = 0.026~\mathrm{rad}^2\,\mathrm{s}^{-1}$ (corresponding to the maximum value of $P$ in (f)). (f) $P$ vs $D_{\mathrm{r}}$ for different $\phi_{\mathrm{p}}$. Inset: $D_{\mathrm{r}}^{\mathrm{m}}$ (where $P$ is maximal) vs $\phi_{\mathrm{p}}$. Here $\sigma=0.3125$ ($\ell_{\mathrm{a}} = 2.5\,\mathrm{mm}$). The apolar-rod medium remains in the isotropic phase.
• Figure 2: (a) Schematic illustrating the mechanism of segregation-induced disorder. As segregation between motile and apolar rods increases with $\phi_{\mathrm{a}}$, the interfacial length decreases, leading to a reduction of the coupling constant $\alpha$ in Eq. \ref{['eq:v_eom']}. (b) Average speed $|\mathbf{v}|$ of the medium rods measured at a distance of $100\,\mathrm{mm}$ from a polar rod in its comoving frame, averaged over rods and time, as a function of $\phi_{\mathrm{a}}$ for $D_{\mathrm{r}} = 0~\mathrm{rad}^2\,\mathrm{s}^{-1}$. Consistent with the mechanism shown in (a), $|\mathbf{v}|$ decreases with increasing $\phi_{\mathrm{a}}$. Inset: $|\mathbf{v}|$ as a function of $D_{\mathrm{r}}$ at $\phi_{\mathrm{a}} = 0.50$, showing an increase at small $D_{\mathrm{r}}$. Here, $\sigma = 3.125$ ($\ell_{\mathrm{a}} = 2.5\,\mathrm{mm}$) and $\phi_{\mathrm{p}} = 0.05$.
• Figure 3: (a) $P$ vs $\phi_{\mathrm{a}}$ for different $D_{\mathrm{r}}$. (b) Phase diagram in the $D_{\mathrm{r}}$--$\phi_{\mathrm{a}}$ plane. Hollow and solid circles denote states with $P < 0.5$ and $P > 0.5$, respectively. Here, $\sigma = 0.3125$ ($\ell_{\mathrm{a}} = 2.5\,\mathrm{mm}$) and $\phi_{\mathrm{p}} = 0.05$.
• Figure 4: (a) Segregation order parameter $\Sigma$ vs $\phi_{\mathrm{a}}$; the inset shows $\sigma_{\mathrm{f}}$, quantifying the flock aspect ratio, as a function of $\phi_{\mathrm{a}}$. Polar heat maps of $g(r,\theta)$ at (b) $\phi_{\mathrm{a}} = 0.05$ and (c) $\phi_{\mathrm{a}} = 0.80$. Here, $\sigma = 0.3125$ ($\ell_{\mathrm{a}} = 2.5\,\mathrm{mm}$), $D_{\mathrm{r}} = 0~\mathrm{rad}^2\,\mathrm{s}^{-1}$, and $\phi_{\mathrm{p}} = 0.05$.
• Figure 5: (a) $P$ vs $\phi_{\mathrm{a}}$ for different values of $\sigma$. Also, see Fig. \ref{['fig06']} illustrating the phase diagram in the $\sigma-\phi_\mathrm{a}$ plane. (b)--(d) Steady-state configurations for (b) $\sigma = 1.0$, (c) $\sigma = 1.25$, and (d) $\sigma = 5.62$. Here, $D_{\mathrm{r}} = 0~\mathrm{rad}^2\,\mathrm{s}^{-1}$ and $\phi_{\mathrm{p}} = 0.05$. Inset of (d): $P$ vs $D_{\mathrm{r}}$ for $\phi_{\mathrm{p}} = 0.05$.