A broader view on jamming: from spring networks to circle packings

Area of Science:

• Physics
• Materials Science
• Network Science

Background:

• Jamming is a collective phenomenon observed in granular materials, leading to phenomena such as traffic jams and earthquakes.
• The mechanical properties of jammed systems are critically dependent on their underlying contact network structure.
• Isostaticity, where degrees of freedom equal constraints, is a key concept in understanding network stability.

Purpose of the Study:

• To highlight the significance of the contact network in jammed systems.
• To define the necessary properties of these networks: one contact in excess of isostaticity and a finite bulk modulus.
• To present a method for constructing such networks without compressive packing.

Main Methods:

• Investigated the role of the contact network in jammed systems.
• Defined network requirements: isostaticity plus one contact and a finite bulk modulus.
• Employed Delaunay triangulation of Poisson disk sampling and edge removal to maximize bulk modulus.

Main Results:

• Demonstrated that jammed systems require specific network properties for stability.
• Developed a construction method for these networks applicable in any dimension.
• Presented 2D results showing the transformation of these networks into disk packs.

Conclusions:

• The contact network's structure is paramount for the behavior of jammed systems.
• A specific network topology (isostaticity + 1) ensures a finite bulk modulus and stability.
• The proposed construction method offers a novel way to create and study jammed systems.