Turbulent Dynamics in Active Solids

Abstract

We investigate numerically the polar ordering dynamics in the active elastic solid model (AES) and find classic signatures of turbulent dynamics: power-law scaling for the energy spectrum and non-Gaussian statistics of velocity increments. However, there is no energy cascade, in line with previous findings for active turbulence in fluids. The results extend the concept of active turbulence to solid systems and are expected to be important for understanding active biological solids, such as bacterial colonies and migrating epithelial monolayers.

Figures (4)

• Figure 1: (a) Elastic deformations, at start of simulation (left) and during ordering process (right). (b) Magnitude of the velocity field at start (left) and during ordering (right). (c) Direction of the velocity field. Parameters: $N=128000.0$, $K=20$, $\xi=6$. The left column corresponds to the early stage with no net polar order $\Pi = 0.0$. In the right column, the system has a global polar order of $\Pi = 0.25$.
• Figure 2: (a) Energy-spectra (at $\Pi = 0.7$) show broad distribution over length-scales. (b) At very early stages injection spectrum and dissipation spectrum are different, however (c) shows that the system evolve towards a situation where dissipation and injection of energy is balanced on all scales. (d) Velocity increment at $\Pi = 0.1$ shows some Gaussian-like behavior on short scales. (e) As the systems evolve to $\Pi = 0.7$ there is a strong non-Gaussian velocity fluctuation on intermediate scales. Parameters for (a)--(e): $N=128000.0$, $K=20$, $\xi=4$. Figures (a)--(e) are ensemble average results.
• Figure 3: (a) Vorticity map of a snapshot of the velocity field in a system with parameters $N=128000.0$, $K=20$, $\xi=6$, and an ordering $\Pi = 0.25$. (b) Velocity of domain walls $V_F$ for different turning rates $\xi$. The markers are individual measurements from systems the systems, green originating from systems of $N = 64000.0$ particles, while blue markers are from systems of $N =128.0 000$ particles. (c) Direction of velocity field with cutout displaying a domain wall. (d) Angular velocity of the velocity direction displaying high angular velocity at the domain wall.
• Figure 4: (a) Ensemble results for the time to order $\tau_{0.9}$ against the system size $L$, for different turning rates $\xi$. Data points are accompanied by lines fitted using the least squares method. (b)--(e) Ensemble results for the time to order $\tau_{0.9}$ against the velocity of domain walls $V_F$. Data points are accompanied by inverse linear, least squares fitted functions, fitted to $\tau_{0.9}^{-1}$.