Rigidity Theory and Applications

Abstract

Proceedings of a Conference on Rigidity Theory and Applications held June 14-17, 1998, Traverse City, Michigan. 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. Generic and abstract rigidity / Brigitte Servatius and Herman Servatius -- Rigidity of molecular structures : genric and geometric analysis / Walter Whiteley -- Tensegrity structures : why are they stable? / R. Connelly -- The role of tensegrity in distance geometry / Timothy F. Havel -- Comparison of connectivity and rigidity percolation / Cristian F. Moukarzel and Phillip M. Duxbury -- Rigidity percolation on trees / P.L. Leath and Chen Zeng -- Rigidity as an emergent property of reandom networks : a statistical mechanical view / Paul M. Goldbart -- Granular matter instability : a structural rigidity point of view / Cristian F. Moukarzel -- Rigidity and memory in a simple glass / P. Chandra and L.B. Ioffe -- Constraint theory, stiffness percolation and the rigidity transition in network glasses / J.C. Phillips -- Topologically disordered networks of rigid polytopes : applications to noncrystalline solids and constrained viscous sintering / Prabhat K. Gupta. Rigidity constraints in amorphization of singly- and multiply-polytopic structures / Linn W. Hobbs, C. Esther Jesurum, and Bonnie Berger -- Floppy modes in crystalline and amorphous silicates / Martin T. Dove, Kenton D. Hammonds, and Kostya Trachenko -- Generic rigidity of networks glasses / M.F. Thorpe, D.J. Jacobs, N.V. Chubynsky, and A.J. Rader -- Rigidity transition in chalcogenide glasses / P. Boolchand, Xingwei Feng, D. Selvanathan, and W.J. Bresser -- Rigidity, fragility, bond models and the "energy landscape" for covalentGlassformers / C.A. Angell -- Entropic rigidity / Béla Joós, Michael Plischke, D.C. Vernon, and Z. Zhou -- Molecular dynamics and normal mode analysis of biomolecular rigidity / David A. Case -- Efficient stochastic global optimization for protein structure prediction / Yingyao Zhou and Ruben Abagyan. Flexible and rigid regions in proteins / Donald J. Jacobs, Leslie A. Kuhn, and Michael F. Thorpe -- Flexibly screening for molecules interacting with proteins / Volker Schnecke and Leslie A. Kuhn -- Studying macromolecular motions in a database framework : from structure to sequence / Mark Gerstein [and others].