The gradient flow of microstructure
speaker: David Kinderlehrer (Department of Mathematical Sciences, Carnegie Mellon University)abstract: A central problem of microstructure is to develop technologies capable of producing an arrangement, or ordering, of the material, in terms of mesoscopic parameters like geometry and crystallography, appropriate for a given application. Is there such an order in the fi place? We describe the emergence of the grain boundary character distribution (GBCD), a statistic that details texture evolution, and illustrate why it should be considered a material property. The theory relies on mass transport and entropy methods, that is De Giorgi’s minimizing movement scheme, and as a consequence we seek to identify it as a gradient fl w in the sense of Ambrosio, Gigli, and Savar´e. In this way, the empirical texture statistic is revealed as a solution of a Fokker-Planck type equation whose limit behavior is a Boltzmann distribution. The development exposes the question of how to understand the circumstances under which a harvested empirical statistic is a property of the underlying process. (joint work with P. Bardsley, K. Barmak, E. Eggeling, M. Emelianenko, Y. Epshteyn, X.-Y. Lu and S. Ta’asan)
timetable:
Thu 22 Sep, 14:30 - 15:25, Palazzo dei Congressi
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