Part I: This research explores the dynamics of polar active particles under varying active stresses, revealing distinct flow fields and self-organizing patterns. A crossover from defect-free to defect-laden active turbulence with increasing stress is observed, leading to the restoration of SO(2) symmetry, indicated by the rapid decay of the two-point correlation function in the polar field. The mechanism of defect pair nucleation is examined, and conducting a stability analysis of the diffusive charge density provides additional insights into the onset of active turbulence laden with topological defects.

Part II: This work examines active turbulence, focusing on the dynamic behavior of topological defects in active nematic fluids. An information-theoretic divergence measure is utilized, which does not require any prior knowledge of the system, to quantify spatiotemporal order. By extracting defect positions and analyzing their dynamics, two key transitions are identified: the onset of defect nucleation and a subsequent hidden spatiotemporal transition marking fully-developed active turbulence, characterized by the optimal spatial and temporal organization of these defects.

Part III: This study unveils a universal feature in the flow patterns of collectively moving cells across diverse biological systems. Experimental evidence demonstrates robust conformal invariance in flows generated by dog kidney cells, human breast cancer cells, and two strains of pathogenic bacteria. Remarkably, these systems exhibit consistent adherence to the Schramm-Loewner Evolution (SLE) and percolation universality class. A continuum model of active matter reproduces the observed conformal invariance and SLE behavior. These findings suggest that living biological matter possesses universal translational, rotational, and scale symmetries, independent of the microscopic properties. The study highlights the conservation of flow patterns among diverse cellular systems, offering unexpected opportunities to test theories for conformally invariant structures in biological contexts.