## Rigidity Theory and ApplicationsAlthough rigidity has been studied since the time of Lagrange (1788) and Maxwell (1864), it is only in the last twenty-five years that it has begun to find applications in the basic sciences. The modern era starts with Laman (1970), who made the subject rigorous in two dimensions, followed by the development of computer algorithms that can test over a million sites in seconds and find the rigid regions, and the associated pivots, leading to many applications. This workshop was organized to bring together leading researchers studying the underlying theory, and to explore the various areas of science where applications of these ideas are being implemented. |

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### Contents

Generic and Abstract Rigidity | 1 |

Why Are They Stable? | 47 |

The Role of Tensegrity in Distance Geometry | 55 |

Comparison of Connectivity and Rigidity Percolation | 69 |

Rigidity Percolation on Trees | 81 |

A Structural Rigidity Point of View | 125 |

Rigidity and Memory in a Simple Glass | 143 |

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### Common terms and phrases

algorithm alpha helix amorphous solid approach atoms average bond-bending Boolchand Cayley tree central-force Chem configuration conformation constraint counting coordination corresponding covalent crosslinks crystalline cycle database defined deformation degrees of freedom density dihedral angles dimension dimensional displacements distance constraints distance geometry Duxbury dynamics edges elastic entropic equation equilibrium example flexible floppy modes framework free energy frequency function geometric glass transition global graph hinge joints hydrogen bonds infinitesimally rigid interaction isostatic lattice Lett ligand linear liquid localisation lengths M.F. Thorpe macromolecules matroid mean field theory molecular molecules motion number of floppy order parameter particles phase transition Phys plane polyhedra polytopes protein random networks redundant rigid cluster rigidity matrix rigidity percolation Rigidity Theory rigidity transition rotation RUMs sample shear sheetwork simulations stress subgraph TD network temperature template tensegrity tetrahedra theorem topological total number triangles triangular underconstrained region vertex vertices wave vectors zero