Random packings of frictionless particles

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Understanding the behavior of granular materials and particle packings is crucial in various scientific fields.
• The concept of jamming, where disordered systems transition to a solid-like state, is a key phenomenon in condensed matter physics.

Purpose of the Study:

• To investigate the jamming threshold and associated properties of frictionless particle packings at zero temperature.
• To analyze the impact of system size on the distribution of jamming thresholds and interparticle forces.

Main Methods:

• Numerical simulations of random packings of frictionless particles were performed.
• The study focused on systems at zero temperature (T = 0).
• Analysis included the calculation of packing fraction, pressure, static shear modulus, and force distributions.

Main Results:

• The packing fraction at which pressure becomes nonzero was found to be identical to the jamming threshold (where static shear modulus becomes nonzero).
• The distribution of threshold packing fractions narrows as system size increases, approaching random close packing.
• Absence of self-averaging within the peak of the threshold distribution leads to an exponential decay in interparticle force distribution.

Conclusions:

• The jamming transition in frictionless particle systems is characterized by a unique packing fraction where both pressure and shear modulus emerge.
• System size plays a critical role in narrowing the jamming threshold distribution and approaching a universal packing fraction.
• Non-self-averaging behavior at the jamming threshold dictates the statistical distribution of forces between particles.