Rigidity Theory and Applications

Although 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.

Rigidity Theory. - Generic and Abstract Rigidity. - Rigidity of Molecular Structures: Generic and Geometric Analysis. - Tensegrity Structures: Why are They Stable? . - The Role of Tensegrity in Distance Geometry. - Applications to Networks. - Comparison of Connectivity and Rigidity Percolation. - Rigidity Percolation on Trees. - Rigidity as an Emergent Property of Random Networks: A Statistical Mechanical View. - Granular Matter Instability: A Structural Rigidity Point of View. - Rigidity and Memory in a Simple Glass. - Constraint Theory, Stiffness Percolation and the Rigidity Transition in Network Glasses. - Topologically Disordered Networks of Rigid Polytopes: Applications to Noncrystalline Solids and Constrained Viscous Sintering. - Rigidity Constraints in Amorphization of Singly- and Multiply-Polytopic Structures. - Floppy Modes in Crystalline and Amorphous Silicates. - Generic Rigidity of Network Glasses. - Rigidity Transition in Chalcogenide Glasses. - Rigidity, Fragility, Bond Models and the Energy Landscape for Covalent Glassformers. - Entropic Rigidity. - Applications to Proteins. - Molecular Dynamics and Normal Mode Analysis of Biomolecular Rigidity. - Efficient Stochastic Global Optimization for Protein Structure Prediction. - Flexible and Rigid Regions in Proteins. - Flexibly Screening for Molecules Interacting with Proteins. - Studying Macromolecular Motions in a Database Framework: From Structure to Sequence.