Chaotic dynamics of active topological defects

ABSTRACT

Topological defects are interesting phenomena which can be observed in ordered phases such as oriented active fluids or nematic liquid crystals. Topological defects are determined by the overall structure of the director field in an active fluid in nematic phase and by exerting force to the units of the active particles they can interact or cause motion in the environment. Studying them as particles with dynamical equations, instead of studying the director field of the nematic environment, would provide us the power to study the characteristics of their motion. The equations of motion for multi-defect systems have been previously studied and in this work we focus on the chaotic properties of the dynamics and analyze the effect of activity on the transition of such systems to chaos by numerically estimating their Lyapunov exponents. We show the importance of the $+1/2$ defects for this transition (as they are active in the sense of having self-propulsion) and numerically derive critical activity values for multi-defect systems in which this transition occurs.

KEYWORDS:

• Topological defects
• chaotic dynamics
• active matter

Acknowledgments

We would like to thank Mohammad Fazelzadeh for helpful discussions and his previous studies on this subject in our research group.