Standard map-like models for single and multiple walkers in an annular cavity

Area of Science:

• Fluid dynamics
• Nonlinear dynamics
• Complex systems

Background:

• Walking droplets in annular cavities exhibit complex dynamics, including chaotic velocity fluctuations.
• Existing models may not fully capture the intricate behaviors observed in these systems.

Purpose of the Study:

• To develop and validate models for single and multiple walking droplets in annular cavities.
• To investigate the complex dynamics and chaotic behaviors of these droplet systems.
• To predict previously unobserved phenomena in droplet motion.

Main Methods:

• Development of models inspired by the kicked rotator and standard map.
• Comparison of model predictions with experimental data for qualitative and quantitative agreement.
• Application of dynamical systems techniques and bifurcation theory for theoretical analysis.

Main Results:

• Models demonstrate strong qualitative and quantitative agreement with experimental observations.
• The models successfully replicate the complex and chaotic velocity changes of walking droplets.
• Predictions for novel behaviors in droplet dynamics were generated.

Conclusions:

• The proposed models provide a robust framework for understanding walking droplet dynamics.
• Dynamical systems analysis confirms the chaotic nature of single droplet motion.
• The models offer a powerful tool for exploring and predicting droplet behavior in confined geometries.