Large-Scale Chaos and Fluctuations in Active Nematics

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

Figure 1

Hydrodynamic equations: (a) Phase diagram for active nematics. (b) Global order parameter vs system size at different noise values in the chaotic regime (the solid line has slope $-1$). (c),(d) Snapshots of the density field in the chaotic regime for $L=1600$ and ${\rho }_0=1$, (c) localized chaos ($\sigma =0.26$), (d) fully developed chaos ($\sigma =0.28$).

Figure 2

Microscopic dynamics: (a),(c) Rescaled distribution of $S$ at various system sizes in the homogeneous ordered (a) and inhomogeneous (c) phases. Insets of (a),(c): Log log plots of $⟨S⟩\times L^{-\zeta }$ vs $L$, where $\zeta$ is estimated from a fit of the initial decay of $⟨S⟩$. (b) Phase diagram in the $(\eta ,{\rho }_0)$ plane. (d) Variance $\mathrm{\Delta }{n}^2$ as a function of the mean number of particle $⟨n⟩$, in the homogeneous ordered phase. Dashed lines: Power laws with exponents 2 (magenta or dark gray in black and white) and 1.6 (cyan or light gray in black and white). (e),(f) Snapshots of coarse-grained density in the chaotic phase of panel (c) for system sizes $L=8192$ (e) and $L=16384$ (f). Parameters: In all cases $v_0=0.3$, for (a),(d): ${\rho }_0=2$, $\eta =0.1$, $\zeta =0.007$ and for (c),(e),(f): ${\rho }_0=1/8$, $\eta =0.038$, $\zeta =0.103$. In (a),(c),(d), the arrow indicates increasing system sizes.