Modeling density variations in microtubule-based active nematics

Microtubule-based active nematics are a common model system for studying the emergent motion of topological defects from purely local interactions between individual agents with an internal power source. This canonical system is typically modeled using a continuum theory for the Q-tensor (describing the order and orientation of the nematic phase) and the fluid velocity u. Critically, the microtubule density is almost always assumed to be constant. However, experimental images of these systems clearly show strong fractal density variations. In fact, these density variations are what reveal the nematic structure itself. We present a new approach to modeling this system that explicitly incorporates density variations, producing simulations that strongly resemble the experimental movies, including the characteristic striation patterns typically observed. Interestingly, we abandon the usual Landau-deGennes free energy functional, replacing it with a simpler density-dependent elastic free energy.