Nonlinear wave dynamics in the equilibrium thermodynamics of nematics
Francesco Giglio (University of Glasgow)
Thursday 28th November, 2019 14:00-15:00 Maths 311B
Liquid crystals are considered (at least on the Earth) as the forth natural state of matter after gas, liquid and solid states. Nematic liquid crystals, nematics in short, are characterised by the fact that they can appear in two macroscopic phases: an isotropic fluid phase (the isotropic phase) and an anisotropic liquid phase (the nematic phase). While in the former each molecule is oriented randomly in space, in the latter molecules tend to align along specific directions giving rise to a macroscopic anisotropy of the material.
The talk aims at presenting a novel approach to the statistical thermodynamics of nematics based on the theory of nonlinear integrable conservation laws, intended as a set of nonlinear PDEs of hydrodynamic type. In this framework order parameters satisfy suitable nonlinear wave equations and phase transitions are interpreted as the occurrence of classical shocks in the wave dynamics. Exact equations of state for nematics subject to external fields for a discrete version of the Maier-Saupe model are derived and provide the first analytical description of the rich structure of nematics phase diagram in presence of external fields.