Coupled Dynamical Phase Transitions in Driven Disk Packings

Akash Ghosh, Jaikumar Radhakrishnan, Paul M. Chaikin, Dov Levine, and Shankar Ghosh

Phys. Rev. Lett. 129, 188002 – Published 25 October 2022

Abstract

Under the influence of oscillatory shear, a monolayer of frictional granular disks exhibits two dynamical phase transitions: a transition from an initially disordered state to an ordered crystalline state and a dynamic active-absorbing phase transition. Although there is no reason a priori for these to be at the same critical point, they are. The transitions may also be characterized by the disk trajectories, which are nontrivial loops breaking time-reversal invariance.

Received 14 March 2022
Revised 5 July 2022
Accepted 20 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.188002

Physics Subject Headings (PhySH)

Granular materials

Granular solids

Polymers & Soft Matter

Authors & Affiliations

Akash Ghosh ¹, Jaikumar Radhakrishnan ², Paul M. Chaikin ³, Dov Levine ⁴, and Shankar Ghosh ¹

¹Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai 400005, India
²School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai 400005, India
³Center for Soft Matter Research and Department of Physics, New York University, New York, New York 10003, USA
⁴Department of Physics, Technion-IIT, 32000 Haifa, Israel

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 129, Iss. 18 — 28 October 2022

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematic of the apparatus. All the walls of the shear cell are about 54 particle diameters long. (b) One cycle: The sequence $(i) \to (ii) \to (iii) \to (iv) \to (i)$ completes one shear cycle. The sequence starts from the “zero position” (i), moving to the rightmost position (ii), returning to the central position (iii), then moving on to the leftmost position (iv) before finally coming back to the zero position.
Reuse & Permissions
Figure 2
(a) Dependence of the activity $α$ on the time (in number $n$ of shear cycles); (c) shows the corresponding dependence of the defect density $ρ_{D}$ . The data in (a) and (c) are fitted with two exponential fits: $α = α_{0} \exp (- n / τ_{A}) + α_{s}$ and $ρ_{D} = ρ_{0} \exp (- n / τ_{D}) + ρ_{D s}$ , which are indicated by the blue lines. (b),(d) We plot the dependence of the characteristic shear cycle numbers $τ_{A}$ and $τ_{D}$ , respectively, as a function of strain $γ$ . In both cases, the characteristic value of shear cycle required to reach a steady state show a divergence of the form $| γ - γ_{c} |^{- ν}$ , with $γ_{c} \sim 0.065$ and $ν \sim 3 / 4$ for both.
Reuse & Permissions
Figure 3
(a) Characteristic configurations of the system showing the positions of defects in the hexagonal packing, for several values of strain $γ$ . The images, which are Voronoi lattices of the disk positions, are from the zero position in the cycle (see Fig. 1). (b) Variation of the defect density $ρ_{D}$ as a function of $γ$ . Solid red circles are for steady states obtained starting from a disordered configuration, for which a cusplike dip in $ρ_{D}$ is seen, suggesting a second-order type transition. The blue lines represent the function $ρ_{D} \sim | γ - γ_{c} |^{β}$ , where $β \sim 1 / 3$ . The hollow blue squares are for runs starting from an ordered state, for which there is no appreciable defect buildup. Inset: $ρ_{D}$ vs $γ$ as measured at different stages of the strain cycle. In all these cases, the initial state was disordered.
Reuse & Permissions
Figure 4
Saturation activity $α_{s}$ of the system as a function of strain $γ$ . We find $α_{s} = 0$ for $γ \leq γ_{c}$ and $α_{s} \sim | γ - γ_{c} |^{0.6}$ for $γ > γ_{c}$ . Typical particle trajectories are shown in the inset for three values of $γ$ , one above, one below, and one equal to $γ_{c}$ . The colors indicate the time as measured in strain cycles.
Reuse & Permissions
Figure 5
(a) Average activity vs depth for several values of strain during a time window spanning 50 cycles. Blue indicates no or small activity; red indicates high activity. For each of the panels, the activity is estimated by subtracting successive strobed images and averaging over slices at each height (see Supplemental Material [30]). Thus, we see that the lower portion of all the systems is recurrent and that the active region at the top increases in size as $γ$ increases above $γ_{c}$ . No activity is observed for $γ < γ_{c}$ . (b) The depth of the active region (in units of disk diameter), plotted as a function of $γ$ . The inclined line in the active region is what might be expected, as discussed in the text. The inset shows the critical strain amplitude $γ_{c}$ vs the disk diameter $D$ for three sizes of disks of the same material, suggesting that $γ_{c}$ corresponds to the strain required to lift the top layer.
Reuse & Permissions

Physical Review Letters