Edoardo Luna Qualifying Exam

Abstract: 

Active interacting particle systems provide a powerful framework for understanding complex collective dynamics observed in experimental studies of biological systems. In this work, we investigate an active interacting particle system to model the interplay between activity, interactions, and emergent transport properties in non-equilibrium environments. The system is characterized by active forces driving individual particles and repulsive local interaction rules that govern collective behavior, embedded in a periodic domain to simulate infinite systems. Using theoretical and computational tools, we explore how agent interactions influence key features of turbulence, such as energy cascades and vorticity generation. Furthermore, we examine the emergence of superdiffusive transport and the connections to its continuum field theory via the Dean-Kawasaki equation, quantifying the anomalous scaling of mean-squared displacement and identifying regimes long-range order. Our findings are compared with experimental observations of active matter systems and turbulent flows, revealing connections between microscopic dynamics and macroscopic transport phenomena. This study offers new insights into the fundamental mechanisms driving turbulence and superdiffusion in active systems.