Manchester Applied Mathematics and Numerical Analysis Seminars Winter 1998

November 18, 1998, 4.00 pm

Lecture Theatre D13 Material Science

Floppy modes and rigid regions in networks, glasses and proteins

Michael F. Thorpe, Michigan State University and Technical University of Delft.

The simple yet powerful ideas of percolation theory have found their way into many different areas of research. In this talk we show how RIGIDITY PERCOLATION can be studied at a similar level of sophistication, using a powerful new program THE PEBBLE GAME, that uses an integer algorithm. This program can analyse the rigidity of two and three dimensional networks containing more than one million bars and joints. We find the total number of floppy modes, and find the critical behavior as the network goes from floppy to rigid as more bars are added.

We discuss the relevance of this work to network glasses, and how it relates to experiments that involve the mechanical properties like hardness and elasticity of covalent glassy networks like $Ge_{x}As_{y}Se_{1-x-y}$ and dicuss recent experiments that suggest that the rigidity transition may be first order. This approach is also useful in macromolecules and proteins, where detailed information about the rigid domain structure can be obtained.information about the rigid domain structure can be obtained.

For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).