The isostatic conjecture. (English) Zbl 1472.52033
Authors’ abstract: 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.
Reviewer: A. E. Litvak (Edmonton)
MSC:
| 52C26 | Circle packings and discrete conformal geometry |
| 52C15 | Packing and covering in \(2\) dimensions (aspects of discrete geometry) |
| 70C20 | Statics |
| 74E20 | Granularity |
Keywords:
packings; square torus; density; granular materials; stress distribution; Koebe; Andreev; ThurstonSoftware:
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