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Explore advanced mathematical analysis of martensitic microstructures in this lecture from the Institute for Advanced Study's Analysis and Mathematical Physics series. Delve into the remarkable microstructural properties observed in the Ti76Nb22Al2 alloy, which undergoes a cubic to orthorhombic transformation featuring six martensitic variants with middle eigenvalues very close to 1. Examine the mathematical framework where assuming λ2(Ui)=1 yields exactly 12 matrices in the energy wells set that are rank-one connected to 1, yet have no rank-one connections among themselves. Investigate gradient Young measures, exact gradients, and TN-configurations supported on these 12 matrices as tools for understanding the observed microstructural phenomena. Learn from collaborative research conducted with Tomonari Inamura and Francesco Della Porta, presented by John Ball from the University of Oxford in this comprehensive mathematical physics seminar.
