A. J. H. Houston | Searcharxiv

arXiv2026

Orienting-Field Effects on Instability and Mode Selection in Active Nematics

We examine the instabilities of a confined active nematic subjected to an orienting field using a low Reynolds number Ericksen-Leslie framework with active stresses and field-induced torques. Linear analysis reveals two distinct modes, with odd and even director symmetry, the instabilities of which depend on the interplay between activity and field strength. We derive exact and approximate analytic forms of the stability boundaries and show that an orienting field that aligns the director perpendicular to the substrate anchoring direction cooperatively lowers activity thresholds and enables a field-driven even symmetry mode instability, while an orienting field that aligns the director parallel to the substrate anchoring tends to stabilise the system. Numerical solutions of the full nonlinear equations show that the linear stability analysis correctly identifies the symmetries of long-time states. These results demonstrate how orienting fields can promote an instability below the classical critical activity and can be used to both tune the instability onset and control the mode selection in confined active nematics.

cond-mat.soft↗

arXiv2026

Geometry and relaxation dynamics of nematic loops

Disclination lines in three-dimensional nematic liquid crystals generically form closed loops whose topology is classified by homotopy theory. While this classification successfully captures global topological features, it does not encode the geometry of the defect profile along the loop, which can strongly influence defect dynamics. Here, we propose a geometric description of nematic disclination loops using the Clifford algebra Cl(3,0). This approach naturally captures the geometry of the local defect profile, as well as changes along the loop, which is mathematically a SU(2) holonomy. Simulations of the dynamics of defect loops with specified geometries embedded in nematic liquid crystals demonstrate that loops nucleate the growth of "topological blobs" of defects, which later dissipate leaving uniform nematic textures. Self-twist of the defect profile leads to nucleation of additional linking disclination lines, with a simple arithmetic relation between total self-twist and linking number. In contrast, loops with an even number of discrete profile transitions generate patterns with threading between loops, but no linking. These results establish a direct connection between the geometric holonomy of a disclination loop and its subsequent evolution, and may be extendable to more complex order parameter manifolds, such as cholesterics or smectics.

cond-mat.soft↗