Random Organization: A Gift that Keeps on Giving*

Non-Brownian suspensions of spheres periodically sheared at low Reynolds number explore new configurations through collisions in an otherwise reversible flow. Below a critical strain, the particles remain active until they find a configuration with no collisions and fall into an absorbing state. Simulations by Hexner \& Levine show that the system becomes hyperuniform near the critical strain as long length-scale density fluctuations are suppressed. Using a compact rotational shear cell, we explore the effect of collision-induced diffusion on the evolution of the structure factor $S(q)$ using a confocal microscope. From dynamical measurements, we see that the effective diffusion constant is equal to the self-diffusion of the particles below the transition and increases linearly with strain amplitude above. For a 40\% volume fraction suspension, we see low-$q$ long-wavelength fluctuations suppressed near the critical strain of $\gamma=0.9$ with as $S(q)$ exhibits hyperuniform scaling. At short length scales, the nearest neighbor correlations ($S(q\approx 2\pi/a)$) reach a peak at critical.