Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions

Area of Science:

• Physics
• Materials Science
• Applied Mathematics

Background:

• Harmonic functions are crucial for solving 2D problems in fields like fluid dynamics and electrostatics.
• Complex analysis offers a powerful framework for analyzing planar nematic director fields.

Purpose of the Study:

• To derive a closed-form solution for quasi-steady state director fields in planar nematics.
• To model the influence of multiple point defects and circular inclusions on director fields.
• To compute forces and torques on these defects and inclusions.

Main Methods:

• Utilizing complex analysis to derive a closed-form solution for the director field.
• Incorporating singularities, defect winding numbers, and spiral textures into the model.
• Accounting for discrete degeneracy and defect braiding for topological free energy minima.

Main Results:

• A comprehensive solution for quasi-steady state director fields with arbitrary defects and inclusions.
• Calculation of forces and torques acting on individual defects and inclusions.
• Demonstration of the impact of singularities on defect equilibrium and dynamics.
• Inclusion of topological degeneracy and defect braiding in the free energy landscape.

Conclusions:

• The derived formalism provides a complete solution for complex nematic director fields.
• The method is applicable to both equilibrium and dynamic scenarios in active or passive nematic fluids.
• Understanding defect interactions and textures is key for controlling nematic material behavior.