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Life sciences · Preprint
arXiv · September 3, 2026
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This is an unreviewed computational methods paper proposing a deep variational framework (DVF) to compute stable smectic liquid crystal configurations in confined geometries. The authors demonstrate that their method recovers known defect structures and predicts new layered states, but the work is methodological in nature and lacks independent experimental validation or quantitative performance benchmarks.
Computational methods development with retrospective comparison to reference methods. Theoretical smectic liquid crystal systems in various confinement geometries; no human, animal, or clinical population.. Intervention: Deep variational framework with warmup penalty for computing stable smectic configurations under the modified Landau–de Gennes model. Compared with: Neural-network baseline and finite-difference relaxation methods.
DVF successfully reproduces experimentally established smectic-A defect structures and layer morphologies across diverse confinement geometries A warmup penalty mitigates spectral bias of neural networks toward smooth fields, enabling recovery of oscillatory smectic states DVF predicts a chevron-like smectic-C state in a tangent-anchored sphere
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A proof-of-concept computational method for modelling liquid crystal configurations, demonstrated against limited comparators and without experimental validation beyond qualitative morphology matching.
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Smectic liquid crystals are layered liquid-crystalline phases characterized by orientational order and periodic density modulation. Although their structures can be modeled using continuum theories, computing stable configurations remains challenging in complex geometries, particularly when the high-frequency density modulations associated with smectic layering should be resolved. We propose a deep variational framework (DVF) for computing these configurations within the modified Landau--de Gennes model, in which the coupled orientational and positional order parameters are represented on a regular reference domain while physical confinement is incorporated through coordinate mappings. A warmup penalty mitigates the spectral bias of neural networks toward smooth, nonlayered fields, enabling robust recovery of oscillatory smectic states. Comparisons with a neural-network baseline and finite-difference relaxation demonstrate the essential role of this penalty and the numerical stability of the resulting layered states. The DVF reproduces experimentally established smectic-A defect structures and layer morphologies across diverse confinement geometries and further predicts a chevron-like smectic-C state in a tangent-anchored sphere. Together, these results demonstrate the applicability of the DVF to computing stable smectic configurations across experimentally relevant confinement geometries and anchoring conditions.
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