Abstract: The study of elastic membranes carrying topological defects has a longstanding history, going back at least to the 1950s. When allowed to buckle in three-dimensional space, membranes with defects can totally relieve their in-plane strain, remaining with a bending energy, whose rigidity modulus is small compared to the stretching modulus. It was suggested in the 1980s that a disc endowed with a single edge dislocation can totally relieve its stretching energy on the expense of a bending energy, whose magnitude is independent of the size of the system. In this lecture, I will show that this is not true: the minimum bending energy associated with strain-free configurations diverges logarithmically with the size of the system. PS Despite the possibly obscure terminology, no prior knowledge is needed beyond very elementary differential geometry.
Wed, 13/06/2018 - 12:00 to 13:00
Ross building, room 70