Nonlinear Collective Dynamics in Active Matter Systems: Studying Self -Propelled Particles and Emergent Phenomena in Complex Systems

One of the most interesting frontiers in the modern nonequilibrium physics concerns active matter systems, i.e. self-propelling entities that constantly convert energy into directed mechanical work. It is a research study on the nonlinear collective behavior of assemblies of active Brownian particles using a hybrid computational and theoretical methodology comprising large-scale agent-based simulations of N = 10,000 self-propelled particles, continuum field theory analysis and machine learning-aided phase classification. Systematic parameter sweeps of Peclet number, noise intensity and area fraction showed that there exist five structurally and dynamically distinct collective phases, viz. disordered gas, polar banded state, polar liquid, motility-induced phase separation cluster phase, and active glass. The polar liquid phase with almost unity orientational order with a 38.6-fold effective diffusivity increase compared to passive Brownian motion, and the super-Poissonian density fluctuation scaling of the motility induced cluster phase with variance 22.7 times the Poisson baseline both indicated the fundamentally nonequilibrium nature of active clustering. Measured transport exponents spanning a vast range (deeply sub diffusive 8 -1 = 0.38) in the active glass to the ballistic (8 -1 = 1.92) in the polar liquid were quantitative traces of mapping the transport landscape of the whole phase diagram. The multi-scale nature of active spatial organization was determined by lengths of spatial correlation ranging almost two orders of magnitude - between 1.2 particle diameters in the disordered gas and 120 particle diameters in the cluster phase. A convolutional neural network classifier had a macro-averaged classification accuracy of 94.7% on all five phases, and the confusion patterns were physically understandable in locations that are true phase boundaries. The presented results contribute to the mechanistic insight into emergent collective behavior in active matter and put in a quantitative perspective applications in biological collective motion, active material engineering, and microfluidic transport design. Keywords: Active matter, Self-propelled Particles, Nonlinear Collective Dynamics, Motility-Induced Phase Separation.