Active nematic liquid crystals under a quenched random field

Coupling between flow and orientation is a central issue in understanding the collective dynamics of active biofilaments and cells. Active stresses generated by motor activity destroy (quasi-)long-range orientational order and induce chaotic flows with many vortices. In cellular and subcellular environment, alignment is also hindered by heterogeneous filamentous structures in extracellular matrix and various intracellular organelles. Here we address the effects of a quenched random field on the flow patterns and orientational order in two-dimensional active nematic liquid crystals. We find that the director dynamics becomes frozen above a critical disorder strength. For sufficiently strong randomness, the orientational correlation function decays exponentially with distance, reproducing the behavior of passive random-field nematics. In contrast, the flow velocity decreases only gradually with increasing disorder, and exhibits a logarithmic spatial correlation under strong randomness. We identify the threshold between the activity- and disorder-dominated regimes and examine its dependence on the activity parameter.