Dynamics of compressible active nematic fluids

Active nematics are bioinspired fluids with nematic ordering that exhibit chaotic dynamics and self-mixing.  We study a canonical example consisting of a two-dimensional (2D) layer of microtubule bundles and kinesin molecular motors driven by ATP.  Previous work showed that density variations in this system exhibit fractal structure due to the chaotic stretching and folding dynamics, but only when the system is compressible.  Most theoretical models in current use, however, assume incompressibility.  Here, we propose a new set of 2D nematohydrodynamic equations that incorporate compressibility and density variations.  We show how these equations reproduce the fractal density variations discovered in the earlier study, thereby capturing an essential feature of this material in a realistic model.