The jamming transition is a k-core percolation transition.

Area of Science:

• Physics
• Materials Science
• Network Theory

Background:

• Jammed matter exhibits a critical transition point where rigidity emerges.
• Understanding the structural origins of this jamming transition is crucial for materials science.
• Existing theories often relate rigidity to the isostatic point, but this study explores an alternative mechanism.

Purpose of the Study:

• To elucidate the structural origin of the jamming transition in jammed matter.
• To investigate the role of k-cores and k-core percolation theory in rigidity.
• To compare 3D simulation results with mean-field k-core percolation theory.

Main Methods:

• Analysis of k-core structures in jammed matter simulations.
• Application of k-core percolation theory to identify critical coordination numbers.
• Comparison of finite-dimensional simulation data with infinite-dimensional (mean-field) network models.

Main Results:

• The jamming transition is characterized by the sudden appearance of k-cores at specific coordination numbers.
• Rigidity in jammed matter is dominated by the emergence of giant 3- and 4-cores.
• 3D simulation results align with mean-field k-core percolation predictions for random networks.

Conclusions:

• The jamming transition's origin lies in the emergence of k-cores, not the isostatic point.
• K-core percolation theory accurately describes the onset of rigidity in jammed systems.
• Jammed pack structures exhibit properties consistent with random networks, as explained by infinite-dimensional k-core theory.