Abstract
Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, B_{mathrm {c}} and d_{mathrm {c}}, the relaxation time tau to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, tau (d) shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, tau (d) exhibits a power-law divergence at the same d_{mathrm {c}} with nearly the same exponent.
Highlights
Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally
The red lines both in the main panel and the inset represent the power-law fits by τ ∝ |B − Bc|−ν, where the best fits are obtained with ν = 1.32 ± 0.10. This value is again close to the value obtained for the shear-driven RIT, ν = 1.38 ± 0.0810, and the predicted one, ν = 1.295 ± 0.006, for the 2D directed percolation (DP) class[1,2]. These results clearly show that the critical behavior of RIT is independent of the parameters, B and d, that drive the transition and that RIT falls into the same universality class as the absorbing phase transition[1,2,40,41] in 2D DP models
This work is the first experimental demonstration of the density-driven RIT with critical behaviors, while the shear-driven RIT has been reported in different many-particle systems
Summary
Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. We measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. This diagram indicates that RIT occurs by increasing a particle density n at fixed d as shown by a rightward arrow. In the same vortex system, we have recently observed the critical behavior of the shear-driven RIT10, which allows a direct comparison of Scientific Reports | (2021) 11:19280
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