Granular collapse as a percolation transition

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Inelastic collapse is a phenomenon observed in granular systems where particles lose energy during collisions.
• Understanding the behavior of granular materials under confinement and energy input is crucial for various applications.

Purpose of the Study:

• To investigate the phenomenon of inelastic collapse in a two-dimensional system of hard disks.
• To analyze the transition in system behavior as the coefficient of restitution is altered.
• To characterize the scaling of cluster size distribution during the transition.

Main Methods:

• Simulated a two-dimensional system of inelastic hard disks.
• Confined the disks between two walls acting as an energy source.
• Varied the coefficient of restitution to observe changes in system dynamics.
• Analyzed the size distribution of collapsed clusters.

Main Results:

• Observed inelastic collapse in the simulated system.
• Identified a transition from small collapsed clusters to a single large cluster as the coefficient of restitution decreased.
• Found the transition to be analogous to a percolation transition.
• Determined that the number of clusters n(s) of size s scales as n(s) ~ s^(-tau) with tau ≈ 2.7 at the transition.

Conclusions:

• The study demonstrates a clear transition in inelastic collapse behavior driven by energy input and inter-particle restitution.
• The observed transition and scaling laws suggest a deep connection between granular collapse and percolation theory.
• The findings provide insights into the collective behavior and self-organization in dissipative granular systems.