The jamming transition is a k-core percolation transition

• Published in: Physica A 2019-02, Vol.516, p.172-177
• Main Authors: Morone, Flaviano, Burleson-Lesser, Kate, Vinutha, H.A., Sastry, Srikanth, Makse, Hernán A.
• Format: Article
• Language: English
• Subjects: Frictional packings; Granular materials; Jamming transition; k-core; Random network theory
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2018.10.035

We explain the structural origin of the jamming transition in jammed matter as the sudden appearance of k-cores at precise coordination numbers which are related not to the isostatic point, but to the emergence of the giant 3- and 4-cores as given by k-core percolation theory. At the transition, the k-core variables freeze and the k-core dominates the appearance of rigidity. Surprisingly, the 3-D simulation results can be explained with the result of mean-field k-core percolation in the Erdös–Rényi network. That is, the finite-dimensional transition seems to be explained by the infinite-dimensional k-core, implying that the structure of the jammed pack is compatible with a fully random network. •Jamming has precursor in emergence of giant 3- and 4-cores in same-size ER networks.•Shear stress begins to increase near giant 3-core emergence in ER networks.•Shear stress has density-independent discontinuous jump at isostatic point.•ER networks’ 3- and 4-cores jump in size around same coord. numbers as packings.•Applications include constraint satisfaction, computer science, math, soft materials.