Campuses:

Microstructure

Saturday, October 24, 2015 - 1:45pm - 2:25pm
David Kinderlehrer (Carnegie-Mellon University)
Cellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. The recently discovered grain boundary character distribution (GBCD) is an empirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misorientation and normal.
Monday, June 25, 2012 - 4:10pm - 5:00pm
Kaushik Bhattacharya (California Institute of Technology)
Wednesday, May 21, 2014 - 2:00pm - 2:40pm
Felix Otto (Max-Planck-Institut für Mathematik in den Naturwissenschaften)
In his seminal work on twin splitting (with S. Mueller), Bob Kohn taught us how the presence of an interfacial energy selects certain types of microstructures, i. e. removes the high degree of degeneracy of an unrelaxed non-convex ariational problem. Later, he realized that the same analysis applies to domain branching in ferromagnets (with R. Choksi) and to flux tube branching in superconductors (with S. Conti).
Thursday, May 22, 2014 - 11:10am - 11:50am
David Kinderlehrer (Carnegie-Mellon University)
Cellular networks are ubiquitous in nature. Most technologically useful materials arise as polycrystalline microstructures, composed of a myriad of small crystallites, the grains, separated by interfaces, the grain boundaries. The coarsening of these networks is of obvious concern for applications and has been since pre-history. Any order in the system must be conferred by the evolving boundary network. We discuss how this arises and some implications for future research. We still have much to learn about these very ancient questions.
Monday, July 21, 2008 - 2:45pm - 3:35pm
David Kinderlehrer (Carnegie-Mellon University)
Cellular structures coarsen according to a local evolution law,
a gradient flow or curvature driven growth, for example,
limited by space filling constraints, which give rise to random
changes in configuration. Composed of volumes, facets, their
boundaries, and so forth, they are ensembles of singlular
structures. Among the most challenging and ancient of such
systems are polycrystalline granular networks, especially those
which are anisotropic, ubiquitous among engineered materials.
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