Probing Gardner Physics in an Active Quasithermal Pressure-Controlled Granular System of Noncircular Particles

To search for experimental signals of the Gardner crossover, an active quasithermal granular glass is constructed using a monolayer of air-fluidized star-shaped particles. The pressure of the system is controlled by adjusting the tension exerted on an enclosing boundary. Velocity distributions of the internal particles and the scaling of the pressure, density, effective temperature, and relaxation time are examined, demonstrating that the system has key features of a thermal system. Using a pressure-based quenching protocol that brings the system into deeper glassy states, signals of the Gardner crossover are detected via cage size and separation order parameters for both particle positions and orientations, offering experimental evidence of Gardner physics for a system of anisotropic quasithermal particles in a low spatial dimension.

Figure 1

Photograph of the pressure-controlled experiment with star-shaped particles (inset). Air-fluidized particles are enclosed by a boundary made of a chain of particles on a thin flexible thread. The left end is pulled with a controlled force $G=Mg$, while the right end is anchored. See the Supplemental Material [34] for an example video.

Figure 2

Distributions of (a) the normalized translational speeds, $v_i$, with $i=x$, $y$ and (b) the angular velocity, $\omega$, for internal particles from cases with different number of particles, $N$, under a constant hanging weight of $G=0.58\times {10}^{-3}\mathrm{N}$. The black curves are the standard Gaussian distribution. (c) The translational energies $m⟨v_i^2⟩/2$ (red square for $i=x$, blue circle for $i=y$) vs the average rotational energy $I⟨{\omega }^2⟩/2$. The solid line is a linear fit with a slope of 1.7.

Figure 3

State parameters for the granular system: (a) Dimensionless pressure vs density for the pressure controlled (blue square) and inclined (red circle) experiments, with fitted equation of state (dashed curve). Inset shows the inclined experiment. (b) Dimensionless relaxation time vs dimensionless effective temperature for cases with measurable relaxation times. The blue curve represents a fit to $y=a\exp (b/x^c)$ with $a=0.45$, $b=0.69$, and $c=1/2$. Inset shows the MSD for the pressure-controlled experiments, with the thick green curve being the MSD at the Gardner crossover. The shaded region marks the glass phase and the arrows represent the $T_{\mathrm{eff}}/P{\sigma }^2$ of cases for testing the Gardner physics, with the corresponding density ranging from $\varphi =0.429$ to $\varphi =0.441$.

Figure 4

The transition to the Gardner phase is demonstrated by the onset of a difference between the cage separation ${\mathrm{\Delta }}^{AB}$ (red square) and the cage size $\mathrm{\Delta }$ (blue circle) order parameters with increasing $P_{\mathrm{high}}{\sigma }^2/T_{\mathrm{eff}}$ for (a) positions and (b) orientations. The inset of (a) shows overlapping particle trajectories in the 10 high pressure cycles along with the Voronoi cells for the initial cycle for $P_{\mathrm{high}}{\sigma }^2/T_{\mathrm{eff}}=3732$. The inset of (b) shows the cage order parameters with ${\mathrm{\Delta }}_{\alpha }^{AB}$ calculated only using adjacent cycles. (c) The dynamical susceptibility, $\chi$, and (d) the cage susceptibility, ${\chi }_{AB}$, for the positions (blue circle) and orientations (orange square) for each pressure.