WorkshopsEvolution of networks in the plane by curvature
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A regular network is a union of planar arcs meeting at 120 degrees. We study the evolution by curvature of such networks. This was proposed by Mullins to study grain boundaries in annealing processes. All kinds of interesting singularities can form and then resolve. Regions disappear, arcs re-arrange themelves and re-emerge. We will show some pictures and discuss a rough classification of singularity types. Theorem: For a given initial network, there exists a flow gamma_t for all time (past singularities). There are only countably many singular points in space-time.
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Tom Ilmanen
2011-07-06
14:00:00 - 15:00:00
R101 , Astronomy and Mathematics Building
A regular network is a union of planar arcs meeting at 120 degrees. We study the evolution by curvature of such networks. This was proposed by Mullins to study grain boundaries in annealing processes. All kinds of interesting singularities can form and then resolve. Regions disappear, arcs re-arrange themelves and re-emerge. We will show some pictures and discuss a rough classification of singularity types. Theorem: For a given initial network, there exists a flow gamma_t for all time (past singularities). There are only countably many singular points in space-time.