### Tuesday, 12 October 2004 - 2:40 PM

### This presentation is part of : Torquato Symposium

### Co-operative geometric indicators of materials performance

**Phillip M. Duxbury**^{1}, Erin McGarrity, and Elizabeth A. Holm^{2}. (1) Michigan State University, East Lansing, MI 48824, (2) Sandia National Laboratories, Albuquerque, NM 87185
We make a graph representation of the microstructure of a complex material and then use network algorithms to identify co-operative geometric structures in these graphs. One well known co-operative geometric structure is the percolating backbone. We discuss two other structures which are of broader significance: The critical manifold and the optimal path. The definition and significance of these structures will be discussed. Results will be presented for the following problems: the grain boundary engineering of structural materials; the critical current of polycrystalline high temperature superconductors and; the onset voltage of polycrystalline varistors.

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