Analytical model for the motion and interaction of two-dimensional active nematic defects

Area of Science:

• Soft Matter Physics
• Active Matter Systems
• Liquid Crystal Dynamics

Background:

• Topological defects in nematics exhibit complex motion.
• Active nematics generate flows influencing defect dynamics.
• Understanding defect interactions is crucial for active matter research.

Purpose of the Study:

• To develop an approximate analytical model for defect velocity in active nematics.
• To incorporate long-range hydrodynamic interactions and orientational coupling between defects.
• To provide a predictive framework for defect behavior in active nematic systems.

Main Methods:

• Combining existing models for topological defect velocity in liquid crystals.
• Integrating the flow field generated by individual defects in active nematics.
• Employing a linear approximation for two-body defect interactions and hydrodynamic screening.

Main Results:

• Analytical prediction of bound states for +1/2 defects and effective attraction for -1/2 defects.
• Determination of critical unbinding length scaling with activity for ±1/2 defects.
• Prediction of defect trajectories, including scattering and braiding motions under confinement.

Conclusions:

• The developed model accurately captures key aspects of defect motion in active nematics.
• The model offers insights into defect interactions, stability, and collective behaviors.
• This work provides a valuable tool for studying and predicting active nematic phenomena.