Topological Entropy in Simulations of Active Nematics

Microtubule-kinesin-based active nematic is a non-equilibrium system composed of rod-like subunits that can generate self-driven flows. The spontaneous emergence of the topological defects occurs due to the active flow, and the movement of defects generate a complex braiding pattern. Experimental observation suggests that the local fluid stretching, and global mixing can be quantified by Lyapunov exponent, and topological entropy. However, there has been no systematic study to verify experimental observations using theory. In this study, we simulate nematohydrodynamics equation with periodic boundary conditions. Using the simulation data, we compute topological entropy from defect braiding as well as curve extension rates. Then from the microtubule velocity field, we compute Lyapunov exponent to quantify local fluid stretching. This study represents theoretical verification of topological chaos in active nematics.