Negative stiffness and modulated states in active nematics.

Area of Science:

• Soft Matter Physics
• Non-equilibrium Statistical Mechanics
• Liquid Crystal Dynamics

Background:

• Active nematic liquid crystals exhibit complex dynamic behaviors driven by internal stresses.
• Understanding pattern selection in these systems is crucial for both fundamental science and potential applications.

Purpose of the Study:

• To develop a minimal dynamical model for active nematic liquid crystals on frictional substrates.
• To investigate the mechanisms of spatial pattern selection in overdamped active nematics.
• To connect non-equilibrium phenomena to concepts from equilibrium critical phenomena.

Main Methods:

• Formulation of a minimal dynamical model by neglecting flow and focusing on active stresses.
• Renormalization of elastic constants by activity.
• Analysis of linear stability and phase diagrams, identifying a non-equilibrium tricritical point.
• Numerical solutions of nonlinear equations to observe pattern evolution.

Main Results:

• Renormalized elastic constants can become negative, leading to pattern selection.
• A non-equilibrium tricritical point separates ordered, modulated, and disordered phases.
• Increasing activity generates complex structures: kink walls and active turbulence.
• The model successfully reproduces experimental observations and full hydrodynamic simulations.

Conclusions:

• The minimal model provides a framework for understanding pattern selection in active nematics.
• Mechanisms analogous to equilibrium critical phenomena govern non-equilibrium pattern formation.
• This work bridges the gap between active matter dynamics and equilibrium phase transitions.