Rigidity Theory and Applications

by Thorpe, M. F.; Conference on Rigidity Theory and Applications (1998 : Traverse City, Mich.); Duxbury, P. M.

• ISBN13: 9780306461156
• ISBN10: 0306461153
• Format: Hardcover
• Copyright: 1999-04-01
• Publisher: Kluwer Academic Pub

Summary

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.

Table of Contents

RIGIDITY THEORY
Generic and Abstract Rigidity	1	(20)
Brigitte Servatius
Herman Servatius
Rigidity of Molecular Structures: Generic and Geometric Analysis	21	(26)
Walter Whiteley
Tensegrity Structures: Why Are They Stable?	47	(8)
R. Connelly
The Role of Tensegrity in Distance Geometry	55	(14)
Timothy F. Havel
APPLICATIONS TO NETWORKS
Comparison of Connectivity and Rigidity Percolation	69	(12)
Cristian F. Moukarzel
Phillip M. Duxbury
Rigidity Percolation on Trees	81	(14)
P. L. Leath
Chen Zeng
Rigidity as an Emergent Property of Random Networks: A Statistical Mechanical View	95	(30)
Paul M. Goldbart
Granular Matter Instability: A Structural Rigidity Point of View	125	(18)
Cristian F. Moukarzel
Rigidity and Memory in a Simple Glass	143	(12)
P. Chandra
L. B. Ioffe
APPLICATIONS TO GLASSES
Constraint Theory, Stiffness Percolation and the Rigidity Transition in Network Glasses	155	(18)
J. C. Phillips
Topologically Disordered Networks of Rigid Polytopes: Applications to Noncrystalline Solids and Constrained Viscous Sintering	173	(18)
Prabhat K. Gupta
Rigidity Constraints in Amorphization of Singly-and Multiply-Polytopic Structures	191	(26)
Linn W. Hobbs
C. Esther Jesurum
Bonnie Berger
Floppy Modes in Crystalline and Amorphous Silicates	217	(22)
Martin T. Dove
Kenton D. Hammonds
Kostya Trachenko
Generic Rigidity of Networks Glasses	239	(40)
M. F. Thorpe
D. J. Jacobs
N. V. Chubynsky
A. J. Rader
Rigidity Transition in Chalcogenide Glasses	279	(18)
P. Boolchand
Xingwei Feng
D. Selvanathan
W. J. Bresser
Rigidity, Fragility, Bond Models and the ``Energy Landscape'' for Covalent Glassformers	297	(18)
C. A. Angell
Entropic Rigidity	315	(14)
Bela Joos
Michael Plischke
D. C. Vernon
Z. Zhou
APPLICATIONS TO PROTEINS
Molecular Dynamics and Normal Mode Analysis of Biomolecular Rigidity	329	(16)
David A. Case
Efficient Stochastic Global Optimization for Protein Structure Prediction	345	(12)
Yingyao Zhou
Ruben Abagyan
Flexible and Rigid Regions in Proteins	357	(28)
Donald J. Jacobs
Leslie A. Kuhn
Michael F. Thorpe
Flexibly Screening for Molecules Interacting with Proteins	385	(16)
Volker Schnecke
Leslie A. Kuhn
Studying Macromolecular Motions in a Database Framework: From Structure to Sequence	401	(20)
Mark Gerstein
Ronald Jansen
Ted Johnson
Jerry Tsai
Werner Krebs
List of Participants	421	(8)
Index	429