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Recent advances in cell biology and experimental techniques using reconstituted cell extracts have generated significant interest in understanding how geometry and topology influence active fluid dynamics. In this work, we present a comprehensive continuum theory and computational method to explore the dynamics of active nematic fluids on arbitrary surfaces without topological constraints. The fluid velocity and nematic order parameter are represented as the sections of the complex line bundle of a two-manifold. We introduce the Levi–Civita connection and surface curvature form within the framework of complex line bundles. By adopting this geometric approach, we introduce a gauge-invariant discretization method that preserves the continuous local-to-global theorems in differential geometry. We establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. We formulate advection of the nematic field based on a unifying definition of the Lie derivative, resulting in a stable geometric semi-Lagrangian (sL) discretization scheme for transport by the flow. In general, the proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and global topology on the two-dimensional hydrodynamics of active nematic systems.
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This content will become publicly available on July 10, 2026
Self consistent field theory of isotropic–nematic interfaces and disclinations in a semiflexible molecule nematic
We use self-consistent field theory to study the isotropic–nematic interface and topological defects in a compressible nematic of semi-flexible molecules.
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- Award ID(s):
- 2223707
- PAR ID:
- 10639671
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 21
- Issue:
- 27
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 5447 to 5458
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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