Speaker: John Ball, Heriot-Watt University, Edinburgh
Title: "Highly irregular microstructures and TN configurations."
Abstract:
Remarkable martensitic microstructures are observed in the alloy Ti76Nb22Al2, which undergoes a cubic to orthorhombic transformation with six martensitic variants Ui = UiT > 0 having middle eigenvalue λ2(Ui) = 1, thus allowing exact interfaces be-tween the high temperature cubic austenite phase and the low temperature orthorhombic martensite phase. The unusual microstructure arises from the fact that the 12 matrices in the set of martensitic energy wells U6i=1SO(3)Ui which are compatible with the undistorted austentite, i.e. which are rank-one connected to 1, are pairwise incompati-ble. The talk will explain the underlying theory and describe attempts to understand the observed microstructures by studying gradient Young measures, exact gradients and TN -configurations supported on these 12 incompatible matrices. This is joint work with Tomonari Inamura and Francesco Della Porta.
Bio:
John Ball is Professor of Mathematics at Heriot-Watt University, Edinburgh. His research is focused on nonlinear analysis and its applications to materials science, liquid crystals and computer vision. He is a former President of the International Mathematical Union and from 2021-25 served as President of the Royal Society of Edinburgh, Scotland’s national academy.
In person attendance at this seminar is only open to Columbia University affiliates. External guests are welcome to attend remotely. Please contact [email protected] if you need the Zoom link for this seminar.
