Department of Mathematics Spring 2026 Colloquium Series - Professor Sir John Ball

Rank-one connections and microstructure in single crystals and polycrystals

Professor Sir John Ball, Heriot-Watt University and Maxwell Institute for Mathematical Sciences, Edinburgh

Abstract: The talk will describe how nonlinear elasticity can be used to predict microstructure arising from solid phase transformations in alloys, and survey some recent results related by the common theme of finding rank-one connections between energy wells, these describing possible planar interfaces between different phases. The results concern (i) slip and twinning in Bravais lattices using the Ericksen energy-well picture, (ii) compatibility of martensitic microstructures across polycrystal grain boundaries and the Taylor set (joint with M. Galanopoulou), and (iii) remarkable martensitic microstructures observed in the alloy Ti₇₆Nb₂₂Al₂, and their interpretation in terms of T_N configurations (joint with T. Inamura & F. Della Porta).

Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).