Rigidity percolation and geometric information in floppy origami

Rigid-floppy percolation threshold.

The mathematical limits for the percolation of rigid and floppy clusters throughout continuous networks are considered. Results are compared to the previous prediction of Thorpe based on the assumption that the threshold condition is the equality of degrees of freedom and the number of constraints. It is demonstrated that, in two-dimensional systems, the thresholds values predicted here and in ...

Lang, Origami and Geometric Constructions Origami and Geometric Constructions 1 Lang, Origami and Geometric Constructions Introduction

By Robert J. Lang Copyright ©1996–2015. All rights reserved. Introduction ................................................................................................................................... 3 Preliminaries and Definitions ...................................................................................................... 3 Binary Divisions ........................................

Lang, Origami and Geometric Constructions Origami and Geometric Constructions Introduction

Comparison of Connectivity and Rigidity Percolation

Generic rigidity percolation in two dimensions.

We study rigidity percolation for random central-force networks on the bondand site-diluted generic triangular lattice. Here, each site location is randomly displaced from the perfect lattice, removing any special symmetries. Using the pebble game algorithm, the total number of floppy modes are counted exactly, and exhibit a cusp singularity in the second derivative at the transition from a rig...