TADA: The Topology-Accommodating Direction Assignment Algorithm for Liquid Crystals.

Area of Science:

• Materials Science
• Computational Physics
• Soft Matter Physics

Background:

• Topological defects are characteristic of liquid crystalline materials.
• Existing computational methods for defect identification in simulations often overlook topological features.
• Current techniques rely on Q-tensor theory, which may not fully capture mesogen-scale topology.

Purpose of the Study:

• To introduce a novel algorithm, topology-accommodating direction assignment (TADA), for identifying topological defects, specifically disclination cores, in liquid crystalline materials.
• To extend the concept of the liquid crystal director field to the mesogen scale.
• To provide a topology-sensitive method for defect analysis in particle-based simulations.

Main Methods:

• The topology-accommodating direction assignment (TADA) algorithm assigns a unique vector to each mesogen.
• It identifies disclination cores by detecting line segments with discontinuous vector fields.
• Defect presence is determined by analyzing regions distant from the defects.

Main Results:

• The TADA algorithm successfully identifies disclination cores in liquid crystalline materials.
• Validation against the scalar order parameter in molecular-dynamics simulations confirms TADA's accuracy.
• The method demonstrates sensitivity to the topological features of the system.

Conclusions:

• The TADA algorithm offers a novel and topology-sensitive approach for identifying disclination cores in liquid crystals.
• It enhances the analysis of topological defects in mesoscale simulations.
• TADA presents several advantages over existing methods for defect identification in liquid crystals.