2018/02/10 by Francesco Giglio, Giglio, Francesco, Giovanni De Matteis +3 · 1 citation
Computer Science · Engineering · Materials Science · Physics and Astronomy · #Classical Physics (physics.class-ph) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Material Dynamics and Properties #Nonlinear Dynamics and Pattern Formation #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft #nlin.SI #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1802.07246
13 pages, 6 figures
arxiv created 2018/02/10 · openalex publication_date 2018/02/10 · arxiv updated 2018/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel approach to the solution of nematic Liquid Crystal models based on the derivation of a system of nonlinear wave equations for order parameters such that the occurrence of uniaxial and biaxial phase transitions can be interpreted as the propagation of a two-dimensional shock wave in the space of thermodynamic parameters. We obtain the exact equations of state for an integrable model of biaxial nematic liquid crystals and show that the classical transition from isotropic to uniaxial phase in absence of external fields is the result of a van der Waals type phase transition, where the jump in the order parameters is a classical shock generated from a gradient catastrophe at a non-zero isotropic field. The study of the equations of state provides the first analytical description of the rich structure of nematics phase diagrams in presence of external fields.