Reversible to Irreversible Transitions for Cyclically Driven Disks on Periodic Obstacle Arrays

Abstract

We examine the collective dynamics of disks moving through a square array of obstacles under cyclic square wave driving. Below a critical density we find that system organizes into a reversible state in which the disks return to the same positions at the end of every drive cycle. Above this density, the dynamics are irreversible and the disks do not return to the same positions after each cycle. The critical density depends strongly on the angle $\theta$ between the driving direction and a symmetry axis of the obstacle array, with the highest critical densities appearing at commensurate angles such as $\theta =0^{\circ }$ and $\theta =45^{\circ }$ and the lowest critical densities falling at $\theta =\arctan (0.618)$, the inverse of the golden ratio, where the flow is the most frustrated. As the density increases, the number of cycles required to reach a reversible state grows as a power law with an exponent near $\nu =1.36$, similar to what is found in periodically driven colloidal and superconducting vortex systems.

arXiv comment6 pages, 10 postscript figures

References in corpus (30)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Skyrmion Hall Effect Revealed by Direct Time-Resolved X-Ray Microscopy
• Memory formation in matter
• Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review
• Hyperuniformity of critical absorbing states
• The yielding transition in amorphous solids under oscillatory shear deformation
• Onset of Irreversibility and Chaos in Amorphous Solids Under Periodic Shear
• Phase Locking, Devil's Staircases, Farey Trees, and Arnold Tongues in Driven Vortex Lattices with Periodic Pinning
• Mechanical and microscopic properties of the reversible plastic regime in a 2D jammed material
• Persistent memory in athermal systems in deformable energy landscapes
• Hyperuniform density fluctuations and diverging dynamic correlations in periodically driven colloidal suspensions
• Emergent hyperuniformity in periodically-driven emulsions
• Hydrodynamics of Random-Organizing Hyperuniform Fluids
• Multiple transient memories in experiments on sheared non-Brownian suspensions
• Quantized Transport for a Skyrmion Moving on a Two-Dimensional Periodic Substrate
• Networks and Hierarchies: How Amorphous Materials Learn to Remember
• Reversible to Irreversible Flow Transition in Periodically Driven Vortices
• Reversible plastic events during oscillatory deformation of amorphous solids
• The effect of the Magnus force on skyrmion relaxation dynamics
• Controlled motion of skyrmions in a magnetic antidot lattice
• Separation of suspended particles by arrays of obstacles in microfluidic devices
• Multiperiodic orbits from interacting soft spots in cyclically-sheared amorphous solids
• Period proliferation in periodic states in cyclically sheared jammed solids
• Collective Directional Locking of Colloidal Monolayers on a Periodic Substrate
• Classification of the reversible-irreversible transitions in particle trajectories across the jamming transition point
• Colloidal particles driven across periodic optical potential energy landscapes
• Clogging and Jamming Transitions in Periodic Obstacle Arrays
• Reversible to Irreversible Transitions in Periodically Driven Skyrmion Systems
• Directional Clogging and Phase Separation for Disk Flow Through Periodic and Diluted Obstacle Arrays
• Collective Effects and Pattern Formation for Directional Locking of Disks Moving Through Obstacle Arrays

Cited by in corpus (2)

• Perspective on Reversible to Irreversible Transitions in Periodic Driven Many Body Systems and Future Directions For Classical and Quantum Systems
• Coupled dynamical phase transitions in driven disk packings