Nematic Locking Principle and its Implications for Microtubule-based Active Nematics

Microtubule-based active nematics are active materials composed of rod-like, self-driven units that consume locally available energy to generate large-scale coherent flows. A characteristic feature of this system is the striation pattern formed by density variations of microtubule bundles, which reveals the extended nature of these bundles. The striation pattern also defines the local orientation, i.e., the director field, which can be determined by taking the tangent to the microtubule bundles. We analyze this system from the viewpoint of a "nematic locking" principle: a nematic contour (i.e. an integral curve of the director field) advected forward in the flow remains a nematic contour. We first argue from experimental data that this principle holds for microtubule-based active nematics. Then adopting this as a fundamental principle, we explore some of its physical consequences. Finally, we find that the standard Beris-Edwards equations used to model active nematics need not obey this principle and introduce a modification to these equations that explicitly imposes the constraint of nematic locking.