Avalanches in active glasses with finite persistence

TL;DR

This study analyzes avalanches in dense active glasses with finite persistence under external shear, bridging active and passive yielding. Using an ABP model with tunable persistence, it shows that stress-drop distributions acquire power-law tails when activity builds correlations, with exponents spanning from around $\tau \approx 1.0$ (passive/strain-dominated) to $\tau \approx 1.2$ (active-dominated), while the persistence length sets the scale for rearrangements. The local structure of plastic events is universal across driving types, evidenced by consistent cluster statistics and fractal dimensions, though activity can reduce the number ofMobile particles needed for a given stress drop. Finite-size scaling confirms a robust, quasi-1D avalanche geometry in 2D and highlights the limitations of the random-stress observable at finite persistence. Overall, the work provides a cohesive framework linking quasistatic yielding in passive systems to active yielding, with implications for mixed active-passive materials and the design of dense active matter systems.

Abstract

We numerically investigate the statistics of avalanches in glassy systems of active particles with finite persistence, with and without an externally applied shear. In departing from the infinite-persistence limit and exploring the interplay of internal activity and external driving, we uncover when and why active and passive systems display similar avalanche statistics and where these analogies fail. We find that power-law distributed stress drops emerge only when activity builds long enough correlations, controlled by the persistence length, with exponents that vary from the purely strain-driven case, to the purely activity-driven case, in a smooth fashion. The local structure and scaling of avalanches of plastic rearrangements remains universal across both limit cases, supporting an interpretation of activity as increasing the typical size of the regions involved in a given avalanche. Our results bridge quasistatic shear strain and finite-persistence active yielding, showing that avalanches driven by self-propulsion retain the characteristic fingerprints of long-range stress propagation.

Figures (7)

• Figure 1: Configuration snapshot of a system composed by $N=10^3$ particles at packing fraction $\phi=0.9$ in a $L\times L$ periodic box. Particles of diameter $d_s=1$ are shown in dark blue while those larger, of diameter $d_b=1.4$, are in lighter blue. The arrow inside each disk show its intrinsic self-propulsion direction. A linear shear profile $\dot{\gamma}y\bm e_x$ is globally applied on the system at a fixed strain-rate $\dot{\gamma}$.
• Figure 2: Example time series of the Irving-Kirkwood stress $\sigma_{xy}(t)$ in the passive sheared system in (a) and the active unsheared system in (b), for $N=10^{3}$ and $\phi=0.9$ in both cases. On the right, the identification of a single avalanche via sign changes in the slope of $\sigma_{xy}(t)$ is illustrated, as described in the text.
• Figure 3: The effect of activity and shearing on avalanche size distributions $p(S)$ of the IK stress $\sigma_{xy}$ for $N=10^3$ particles at $\phi=0.9$ (except in (d), as indicated). (a) Increasing the Péclet number at zero shear suppresses small avalanches and boosts larger ones, until a power-law with exponent $\tau\approx1.2$ emerges at $\mathrm{Pe}\approx30$. (b) Increasing the shear rate $\dot{\gamma}$ also suppresses small avalanches, but the distribution decays more slowly with $\tau\approx1.0$ and the tails of $p(S)$ are not as strongly affected. (c) Applying both active and sheared forcing at $\mathrm{Pe}=30$, the activity dominates for $\dot{\gamma}\leq 10^{-4}$, reflected in the faster decay of $p(S)$ with exponent $\tau\approx1.2$. As $\dot{\gamma}$ increases, the limiting form of decay with $\tau\approx1.0$ is reached at $\dot{\gamma}=10^{-3}$ for dominating shear. (d) The dependence on $\phi$ for high densities $\phi\geq0.8$ is relatively weak and does not strongly affect the power-law scaling, but reduces its range.
• Figure 4: The effect of changing the persistence time $\tau_p$ on purely active avalanches at $\dot{\gamma}=0$ is shown for constant self-propulsion velocity $v_0=0.009$ (corresponding to $\mathrm{Pe}=30$ for $\tau_p=3333$). IK stress drops $S$ in (a) develop a power-law scaling with $\tau\approx1.2$. The drops in the random stress $S_R$ in (b) similarly show a power-law at the highest $\tau_p$, although over a smaller range in $S_R$.
• Figure 5: Finite size scaling of the avalanche size distributions $p(S)$ in the passive, sheared system at $\mathrm{Pe}=0$, $\dot{\gamma}=10^{-3}$ in (a),(b) and the active system at $\mathrm{Pe}=30$, $\dot{\gamma}=0$ in (c),(d).