Publication 26-CNA-016

Spectral Alignment of Mesogens for Three-Dimensional Disclination Localization in Liquid Crystals

Saptarshi Saha
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
saptarshisaha@cmu.edu

Amit Acharya
Department of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

Gerald J. Wang
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
gjwang@cmu.edu

Abstract: Topological defects govern the material properties and dynamics of liquid crystals. Efficiently identifying three-dimensional disclination centerlines from mesogen-resolved datasets remains a fundamental challenge. Traditional diagnostics rely on thresholding local scalar order parameters, which struggle to differentiate between one-dimensional topological defect lines and the three-dimensional volumes within which disorder is present. Herein, we present Spectral Alignment of Mesogens (SPAM) and Discrete Layer Analysis (DLA), a deterministic framework that extracts disclination centerlines directly from unoriented mesogen-scale director fields. This approach casts sign assignment as a continuous spectral relaxation of an Ising-like spin optimization on a distance-weighted interaction graph. We validate this approach on a wide range of molecular-dynamics simulations of calamitic liquid-crystalline assemblies, showing a range of benefits as compared to existing techniques. Together, SPAM and DLA provide a robust framework for three-dimensional topological defect extraction relevant to a wide range of liquid-crystalline media, including passive nematics, active fluids, and nematic elastomers.

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