(4oc) Investigating Lyotropic Liquid Crystals through out-of-Equilibrium Thermodynamics and Numerical Methods

My research interests lie in the mathematical understanding of biological systems and their applications to improve human health. This includes, but is not limited to, modeling the growth of organs and understanding complex signaling processes involved in gene regulation circuits. Currently, I work in the theoretical and computational study of multi-component liquid crystals. Liquid Crystals are a state of matter, in between a solid and a liquid state, highly present in biology. Abundant examples are the cell cytoskeleton, the collective motion of animals and the liver. In addition to this, I have a growing interest in the intersection of natural sciences and humanities and social sciences which has led to undertake diverse scientific projects.

Abstract

Active Lyotropic Liquid Crystals (LCs), partially ordered states of matter depending on their constituents’ concentration, continuously convert energy into mechanical work. Found in living systems like the liver and bacterial suspensions, controlling these dynamic systems poses challenges due to their unclear effective parameters between the ratio of components. This work addresses this problem through cutting-edge computational and theoretical techniques, ensuring reliable simulations for guiding experiments. Here, we introduce LiquidCrystalGLBT.jl, an open-source Julia-based solver designed for managing the nematohydrodynamic equations of active lyotropic liquid crystals. This hybrid solver combines an upwind finite difference scheme with the Galerkin Lattice Boltzmann method. In our acronym, 'G' indicates the use of the out-of-equilibrium GENERIC framework to derive our equations, while 'LB' signifies the implementation of the Lattice Boltzmann Method through the Trixi.jl package, the 'T' in our name. We present three cases stemming from our solutions: 1) A study of a 2D binary mixture, resembling chromonic LC experimental data with +/- ½ topological defects. 2) The introduction of a velocity parabolic profile that distorts an axial LC droplet immersed in an isotropic environment. 3) The addition of biochemical activity, resulting in turbulent simulations flowing naturally, akin to microtubule or actin realizations. In short, these simulations have demonstrated the ability to predict LC experimental data and contribute significantly to our understanding of their dynamic behavior.