Computing stable configurations of confined smectic liquid crystals with a deep variational framework

• URL: http://arxiv.org/abs/2609.03389v1
• Date: Thu, 03 Sep 2026 05:45:22 GMT
• Title: Computing stable configurations of confined smectic liquid crystals with a deep variational framework
• Abstract summary: We propose a deep variational framework (DVF) for computing stable smectic configurations in complex geometries.<n>A warmup penalty mitigates the spectral bias of neural networks toward smooth, nonlayered fields, enabling robust recovery of smectic states.<n>Results demonstrate the applicability of the DVF to computing stable smectic configurations across experimentally relevant confinement geometries and anchoring conditions.
• Score: 4.165025214245978
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Learning to Tessellate: Point Cloud Generation via Recursive Spectral Partitioning [58.130498928480456]
  We present PointRSP, an autoregressive framework that reformulates point cloud generation as a topology-preserving tessellation process.<n>PointRSP achieves state-of-the-art performance in generation quality and diversity, demonstrating strong generalization across complex 3D topologies.
  arXiv  Detail & Related papers  (2026-08-03T16:11:43Z)
• A Smooth Phase-Separation Model for Weak-Boundary Segmentation of Homogeneous Structures [10.944941180179223]
  We propose a smooth phase-separation variational model based on the Cahn--Hilliard equation for weak-boundary segmentation of homogeneous-appearance structures.<n>The proposed framework integrates softmax-based region fitting with Cahn--Hilliard phase-field regularization to maintain interface discrimination under weak image-driven forces.<n>For numerical computation, we develop a stabilized auxiliary variable (SAV) scheme that is linear, FFT-based, and satisfies a modified discrete energy dissipation law.
  arXiv  Detail & Related papers  (2026-07-24T07:41:54Z)
• Topological Flow Matching [56.16372813551555]
  Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance.<n>We introduce topological flow matching, a topology-aware generalization of flow matching.<n>We demonstrate its effectiveness on diverse structured datasets, including brain fMRIs, ocean currents, seismic events, and traffic flows.
  arXiv  Detail & Related papers  (2026-06-14T16:29:33Z)
• Exactly Solvable RD Model: RG Cycles Meet Fractality [45.88028371034407]
  We consider the Bethe ansatz integrable Russian Doll (RD) model of superconductivity with time-reversal symmetry breaking.<n>By obtaining an exact solution for the renormalization group flows, we investigate the phase structure in the one-pair sector.<n>We show that the quantum number Q, arising from the Bethe ansatz equations, counts the number of cycles and parametrizes the towers of states.
  arXiv  Detail & Related papers  (2026-03-18T12:54:21Z)
• A Geometry-Adaptive Deep Variational Framework for Phase Discovery in the Landau-Brazovskii Model [4.702925112226925]
  We propose a Geometry-Adaptive Deep Variational Framework (GeoDVF) for pattern-forming systems.<n>By explicitly treating the domain size as trainable variables within the variational formulation, GeoDVF naturally eliminates artificial stress during training.<n>We show that GeoDVF provides a robust and geometry-consistent variational solver capable of identifying both stable and metastable states without prior knowledge.
  arXiv  Detail & Related papers  (2026-03-05T13:32:23Z)
• Scale-Consistent State-Space Dynamics via Fractal of Stationary Transformations [9.983526161001997]
  Recent deep learning models increasingly rely on depth without structural guarantees on the validity of intermediate representations.<n>We address this limitation by formulating a structural requirement for state-space model's scale-consistent latent dynamics.<n>We empirically verify the predicted scale-consistent behavior, showing that adaptive efficiency emerges from the aligned latent geometry.
  arXiv  Detail & Related papers  (2026-01-27T12:44:20Z)
• Smooth embeddings in contracting recurrent networks driven by regular dynamics: A synthesis for neural representation [45.88028371034407]
  Recent empirical work has documented topology-preserving latent organization in trained recurrent models.<n>Recent theoretical results in reservoir computing establish conditions under which the synchronization map is an embedding.<n>Our contribution is an integrated framework that assembles generalized synchronization and embedding guarantees for contracting reservoirs.
  arXiv  Detail & Related papers  (2026-01-26T23:10:39Z)
• Anyon Quasilocalization in a Quasicrystalline Toric Code [0.21410799064827227]
  An exactly solvable model of a quantum spin liquid on a quasicrystal, akin to Kitaev's honeycomb model, was introduced in Kim textitet al.<n>We analyze the strong bond-anisotropic limit of the model and demonstrate that the aperiodic lattice geometry naturally generates a hierarchy of exponentially separated coupling constants.<n>Using numerical studies, we uncover the key mechanisms responsible for this unconventional localization behavior.
  arXiv  Detail & Related papers  (2025-11-21T11:07:02Z)
• CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks [1.2141052067494946]
  We introduce CrystalGRW, a diffusion-based generative model that can predict stable phases validated by density functional theory.<n>CrystalGRW demonstrates the ability to generate realistic crystal structures that are close to their ground states with accuracy comparable to existing models.<n>These features help accelerate materials discovery and inverse design by offering stable, symmetry-consistent crystal candidates for experimental validation.
  arXiv  Detail & Related papers  (2025-01-15T18:26:35Z)
• Real-space detection and manipulation of topological edge modes with ultracold atoms [56.34005280792013]
  We demonstrate an experimental protocol for realizing chiral edge modes in optical lattices. We show how to efficiently prepare particles in these edge modes in three distinct Floquet topological regimes. We study how edge modes emerge at the interface and how the group velocity of the particles is modified as the sharpness of the potential step is varied.
  arXiv  Detail & Related papers  (2023-04-04T17:36:30Z)
• Score-based denoising for atomic structure identification [3.6302902879420302]
  Our method iteratively subtracts thermal noises or perturbations in atomic positions using a denoising score function trained on synthetically noised but otherwise perfect crystal lattices. The resulting denoised structures clearly reveal underlying crystal order while retaining disorder associated with crystal defects.
  arXiv  Detail & Related papers  (2022-12-05T17:18:17Z)
• Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing [58.720142291102135]
  We investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation.
  arXiv  Detail & Related papers  (2022-03-28T14:55:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.