Signatures of Elastic Anisotropy Across Non-Equilibrium Nematic Textures

One limitation in applying liquid crystal theories to active matter experiments is that the interplay of active and elastic forces makes it challenging to measure the elastic constants independently. What is an efficient way to measure the effective liquid crystal elastic ratios, quantified by elastic anisotropy in non-equilibrium systems? We propose a robust and computationally efficient measure of effective elastic anisotropy from director fields around +1/2 topological defect cores, which captures equilibrium elastic constant ratios for passive systems and reveals the interplay between activity and liquid crystal distortions for active ones. We offer a theoretical explanation for why +1/2 defect profiles are uniquely suited to deduce elastic anisotropy and show that our measure is related to the unique Fourier mode of defect director fields that can reveal splay or bend preference in 2D nematic textures. We apply our method of extracting elastic anisotropy in semi-flexible filament simulations, fibroblast cell experiments, and Beris-Edwards nematohydrodynamics to reveal the scaling relations between active forcing and bending rigidity on elastic anisotropy. Our results also provide a meaningful way to characterize and quantify the defect core regions in complex nematic textures such as cell networks, where coherence lengths are typically difficult to measure.