A theoretical phase diagram for an active nematic on a spherical surface

Area of Science:

• Physics
• Soft Matter Physics
• Liquid Crystals

Background:

• Active nematics, liquid crystals with self-generated motion, model systems like microtubule suspensions.
• Spherical confinement of 2D active nematics leads to unique behavior of +1/2 defects.
• Previous models sometimes failed to fully incorporate spherical geometry.

Purpose of the Study:

• To model the behavior of +1/2 nematic defects on a spherical surface.
• To identify and characterize different trajectory states of these defects.
• To explain discrepancies between prior models and experimental/simulated observations.

Main Methods:

• Modeling +1/2 nematic defects as point particles.
• Incorporating elastic forces based on defect position and orientation.
• Including self-propulsion forces due to activity.
• Analyzing trajectory states in different parameter spaces.

Main Results:

• The model predicts four distinct trajectory states for the defects.
• Two states align with existing experimental and simulation data.
• Two novel trajectory states were identified, potentially in unexplored parameter regions.
• The model resolves discrepancies by correctly accounting for spherical geometry.

Conclusions:

• The point-particle model provides a robust framework for understanding active nematic defect dynamics on spheres.
• The identified novel trajectory states warrant further experimental and simulation investigation.
• Accurate incorporation of geometry is crucial for modeling active nematics in confined spaces.