Absorbing-state transitions in particulate systems under spatially varying driving

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Non-equilibrium transitions into absorbing states are common phenomena.
• Amorphous materials under cyclic shear are key model systems for studying these transitions.
• Real-world flows often involve inhomogeneous conditions, unlike previous homogeneous driving studies.

Purpose of the Study:

• To investigate the absorbing state transition in amorphous materials under inhomogeneous cyclic shear.
• To compare the effects of smoothly varying versus discontinuously varying shear.
• To develop a theoretical model describing the observed phenomenology.

Main Methods:

• Utilized a modified random organization model.
• Simulated amorphous materials subjected to cyclic shear with spatial inhomogeneity.
• Developed and applied a one-dimensional generalized continuum model.

Main Results:

• Smoothly varying inhomogeneous driving yields steady-state results consistent with homogeneous driving, with the absorbing-diffusive boundary position independent of driving wavelength.
• Discontinuously varying driving alters the absorbing phase boundary position and the exponent of the active particle fraction compared to homogeneous driving.
• The observed phenomenology for smoothly varying driving is well-described by the proposed one-dimensional generalized continuum model.

Conclusions:

• The spatial variation of driving significantly impacts absorbing state transitions in amorphous materials.
• A one-dimensional continuum model effectively captures the behavior under smoothly varying inhomogeneous driving.
• Discontinuous driving introduces distinct changes in critical behavior, highlighting the importance of driving heterogeneity.