Thermal Tightrope: Trajectory Dynamics of Levitating Droplet Clusters under Variable Temperature Conditions.

We introduce a comprehensive computational framework for quantifying the dynamics of levitating droplets in a cluster during controlled cooling from 50 to 46 °C. This framework integrates state-of-the-art Computer Vision and Machine Learning techniques such as YOLO-based detection and robust multiobject tracking, to extract kinematic and energetic metrics: estimated velocity, acceleration, kinetic energy, and spatial uniformity. Directional statistics of droplet motion are analyzed through circular statistics, specifically, Mean Resultant Length (MRL) and the Hermans-Rasson (HR) test, to explain temperature-driven changes in trajectory orientation. In addition, we study the efficiency of trajectories defined as the ratio of the straight-line Euclidean displacement to the actual path length. This metric enables objective classification of droplets into high- and low-efficiency groups. Our analysis reveals a dynamical transition at 47 °C. Below this critical temperature, the angular distributions evolve from multimodal to isotropic (uniform/random) behavior, accompanied by a marked reorganization of both MRL and HR values. These findings establish a quantitative link between thermal conditions and collective droplet motion, providing fundamental insights into the stability and self-organization of levitated liquid ensembles.