Generic rigidity percolation: The pebble game

D. J. Jacobs; M. F. Thorpe

doi:10.1103/PhysRevLett.75.4051

Generic rigidity percolation: The pebble game

D. J. Jacobs, M. F. Thorpe

Arizona State University

Research output: Contribution to journal › Article › peer-review

378 Scopus citations

Abstract

The percolation of rigidity in 2D central-force networks with no special symmetries (generic networks) has been studied using a new combinatorial algorithm. We count the exact number of floppy modes, uniquely decompose the network into rigid clusters, and determine all overconstrained regions. With this information we have found that, for the generic triangular lattice with random bond dilution, the transition from rigid to floppy occurs at pcen=0.66020.0003 and the critical exponents include =1.210.06 and =0.180.02.

Original language	English (US)
Pages (from-to)	4051-4054
Number of pages	4
Journal	Physical Review Letters
Volume	75
Issue number	22
DOIs	https://doi.org/10.1103/PhysRevLett.75.4051
State	Published - Jan 1 1995

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General Physics and Astronomy

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10.1103/PhysRevLett.75.4051

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title = "Generic rigidity percolation: The pebble game",

abstract = "The percolation of rigidity in 2D central-force networks with no special symmetries (generic networks) has been studied using a new combinatorial algorithm. We count the exact number of floppy modes, uniquely decompose the network into rigid clusters, and determine all overconstrained regions. With this information we have found that, for the generic triangular lattice with random bond dilution, the transition from rigid to floppy occurs at pcen=0.66020.0003 and the critical exponents include =1.210.06 and =0.180.02.",

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AB - The percolation of rigidity in 2D central-force networks with no special symmetries (generic networks) has been studied using a new combinatorial algorithm. We count the exact number of floppy modes, uniquely decompose the network into rigid clusters, and determine all overconstrained regions. With this information we have found that, for the generic triangular lattice with random bond dilution, the transition from rigid to floppy occurs at pcen=0.66020.0003 and the critical exponents include =1.210.06 and =0.180.02.

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Generic rigidity percolation: The pebble game

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