Entrainment of a spatially extended nonlinear structure under selective forcing

Area of Science:

• Nonlinear dynamics
• Soft condensed matter physics
• Liquid crystal physics

Background:

• Nonlinear systems exhibit complex behaviors when subjected to external forces.
• Liquid crystals are materials with unique properties, sensitive to external stimuli like convection.
• Understanding phase dynamics and defect behavior is crucial in condensed matter physics.

Purpose of the Study:

• To analyze the static and dynamic aspects of entrainment and locking phenomena in a nonlinear liquid crystal system.
• To investigate the role of topological singularities in controlling the phase diffusion dynamics.
• To elucidate the mechanisms by which defects influence spontaneous symmetry breaking in this system.

Main Methods:

• Studied a nonlinear dynamical system modeling a liquid crystal layer driven to convection.
• Analyzed the response to variable, spatially periodic forcing.
• Investigated the dynamics of phase diffusion and defect-mediated evolution.

Main Results:

• Identified entrainment and locking effects in the system's response.
• Demonstrated that topological singularities facilitate phase diffusion.
• Showcased the critical role of defects in systems with spontaneous symmetry breaking.

Conclusions:

• The behavior of nonlinear states in liquid crystals under periodic forcing is governed by defect dynamics.
• Topological defects are key to understanding phase diffusion and symmetry breaking.
• This research provides insights into defect-mediated phenomena in driven soft matter systems.