Mathematical Physics and Harmonic Analysis Seminar

Date: February 10, 2017

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: M. Zyskin, Univ. Nottingham, UK

Title: Transformation groups and discrete structures in continuum description of defective crystals

Abstract: Davini description of elasticity and plasticity of defective crystal involves a frame of continuum 'lattice vector' fields, and dislocation density matrix, capturing the structure constants of the Lie bracket of those vector fields. Those fields together describe kinematics of a defective crystal, allowing for elastic and certain plastic deformations. A truncation assumption for the energy functional leads to considering finite dimensional Lie algebras of 'lattice vector' fields and corresponding transformation groups. In low spatial dimensions, such groups may be classified. Discrete crystal structures emerge in such context as discrete subgroups of the corresponding Lie groups. This approach includes the usual crystal lattices as a particular case. In my talk I will focus on cases of non-constant dislocation density, corresponding to 2 dimensional crystals with 3 dimensional algebras of lattice vector fields. (This work is a joint project with Gareth Parry).