Jamming graphs: A local approach to global mechanical rigidity

Jorge H. Lopez, L. Cao, Jennifer M Schwarz

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We revisit the concept of minimal rigidity as applied to frictionless, repulsive soft sphere packings in two dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's theorem in two dimensions. It constrains the global, average coordination number of the graph, for example. However, minimal rigidity does not address the geometry of local mechanical stability. The jamming graph contains both properties of global mechanical stability at the onset of jamming and local mechanical stability. We demonstrate how jamming graphs can be constructed using local moves via the Henneberg construction such that these graphs fall under the jurisdiction of correlated percolation. We then probe how jamming graphs destabilize, or become unjammed, by deleting a bond and computing the resulting rigid cluster distribution. We also study how the system restabilizes with the addition of new contacts and how a jamming graph with extra (redundant) contacts destabilizes. The latter endeavor allows us to probe a disk packing in the rigid phase and uncover a potentially new diverging length scale associated with the random deletion of contacts as compared to the study of cut-out (or frozen-in) subsystems.

Original languageEnglish (US)
Article number062130
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume88
Issue number6
DOIs
StatePublished - Dec 16 2013

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jamming
Jamming
rigidity
Rigidity
Graph in graph theory
Contact
Two Dimensions
Probe
deletion
probes
Sphere packing
coordination number
Length Scale
Deletion
Packing
theorems
Subsystem
geometry
Computing
Theorem

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Jamming graphs : A local approach to global mechanical rigidity. / Lopez, Jorge H.; Cao, L.; Schwarz, Jennifer M.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 88, No. 6, 062130, 16.12.2013.

Research output: Contribution to journalArticle

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