The Isostatic Conjecture

We show that a jammed packing of disks with generic radii, in a generic container, is such that the minimal number of contacts occurs and there is only one dimension of equilibrium stresses, which have been observed with numerical Monte Carlo simulations. We also point out some connections to packin...

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Bibliographic Details
Published inDiscrete & computational geometry Vol. 64; no. 3; pp. 734 - 758
Main Authors Connelly, Robert, Gortler, Steven J., Solomonides, Evan, Yampolskaya, Maria
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2020
Springer Nature B.V
Subjects
Combinatorics
Computational Mathematics and Numerical Analysis
Computer simulation
Contact stresses
Disks
Mathematics
Mathematics and Statistics
Monte Carlo simulation
Ricky Pollack Memorial Issue
Triangulation
Koebe
Stress distribution
Packings
Square torus
Granular materials
Andreev
Density
Thurston
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Summary:We show that a jammed packing of disks with generic radii, in a generic container, is such that the minimal number of contacts occurs and there is only one dimension of equilibrium stresses, which have been observed with numerical Monte Carlo simulations. We also point out some connections to packings with different radii and results in the theory of circle packings whose graph forms a triangulation of a given topological surface.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-018-00051-0