Physics Colloquium
Friday, December 5th, 2003 4 P.M.

M.E. Glicksman

Rensselaer Polytechnic Institute
Materials Science & Engineering Department

Topological Analysis of 3-d Network Kinetics

The problem of “frustrated” space filling in 3-d network structures is both basic and of long-standing interest. Topology and integral geometry imposes requirements that the total Gaussian curvature for network “cells” is a conserved quantity. Network “cells” may represent physical entities, such as coordination shells in atomic liquids, grains in polycrystals, bubbles in foam, or biological cells in tissues. The kinetic theory to be described is based on representing network cells as average N-hedra that satisfy both space filling and thermodynamic equilibrium on relevant length scales. The analysis yields kinetic laws that predict average volumetric and area growth rates for foams and polyhedral grains comprising isotropic network structures as a function of discrete topological parameters, such as the number of neighbor contacts, quadrajunctions, or triple-lines. The results for area shrinkage rates extend to 3-d the now half-century old von Neumann’s law that provides kinetic predictions for polycrystalline networks in 2-d. The theory yields good correspondence with recent simulations published by A. Kraynik (2002) and S. Cox (2003) for both regular and irregular network cells, and with more approximate theories published by W. Mullins (1989) and S. Hilgenfeldt (2002). Analytically derived relations as discovered here can provide rigorous benchmarks to test numerical simulations, to guide further quantitative experiments on soft matter, and to assist in deriving important statistical measures for glasses, atomic liquids, polyscrystalline materials, foams, and some biological tissues. .

Refreshments 3:30 P.M. Room E200 Math/Science Center