Random organization criticality with long-range hydrodynamic interactions

Area of Science:

• Soft Matter Physics
• Statistical Mechanics
• Complex Systems

Background:

• Driven soft athermal systems can transition between arrested and active states.
• Cyclically sheared suspensions provide a model system for studying these transitions.
• Existing models like the random organization model (ROM) simplify particle interactions.

Purpose of the Study:

• To investigate the impact of long-range hydrodynamic interactions on the reversible-irreversible transition in driven soft athermal systems.
• To generalize the random organization model (ROM) by incorporating these interactions.
• To understand how critical properties change with interaction range.

Main Methods:

• Generalizing the random organization model (ROM) to include long-range interactions with power-law decay.
• Analyzing critical properties as a function of the interaction decay exponent.
• Employing a local mean-field model to rationalize the observed critical behavior.

Main Results:

• Critical properties continuously depend on the decay exponent for exponents smaller than the space dimension.
• Increasing interaction range leads to a convex transition ($\beta >1$ ), vanishing fluctuations, and loss of hyperuniformity.
• Diffusive motion induced by long-range interactions dominates for slowly decaying interactions.

Conclusions:

• Long-range interactions significantly alter the critical behavior of driven soft athermal systems.
• The generalized ROM provides a more realistic description by including hydrodynamic effects.
• The transition's nature is sensitive to the range and nature of inter-particle forces.