Dynamics and Self-organization of Crowded Active Systems

Abstract

The perplexing and intriguing world of biological systems has inaugurated a new research field in statistical physics: out-of-equilibrium systems, known as active matter that mimic systems in the biological world around us from a statistical mechanical point of view. These systems exhibit captivating collective dynamics such as self-sustained pattern formation. Self-organization of motors and microtubules within the cell, swarming colonies of bacteria, and starling murmuration are some fascinating patterns in nature that organize themselves independently, without external control. Numerous computational, theoretical, and experimental models have been developed to unravel the physics of active matter systems. In this thesis, we employ several agent-based minimal models to study self-propelled particles to explore the key parameters that play a significant role in their dynamics and self-organization. We develop a hexagonal lattice model to study the dynamics of passive "tracers" in the presence of active crowders where the tracer is pushed by the active particles, which leads to enhanced diffusion. We show that the degree to which this diffusion is enhanced depends crucially on the activity and the density of the crowders. Furthermore, we show that a decrease in the diffusion coefficient of passive particles is an explicit consequence of the local accumulation of active crowders in the system. We employ Brownian dynamics simulation for spherical particles in continuous space to explore the strong velocity correlation in a mixture of active and passive particles in the absence of explicit alignment interaction. We decouple the effect caused by a high density of the medium from the one caused by the persistent activity of the self-propelled particles and show that a dopant of active particles can produce a strong velocity correlation in a sufficiently dense system of passive particles. We extend Brownian dynamics simulation to long, semiflexible active filaments to explore the various dynamical states in the system. We show that the self-propulsion force and the bending stiffness are two indispensable parameters in the systems that control the size and shape of the emergent clusters and the dynamical steady states in the system. Moreover, we add a direction reversal mechanism to the polymers to mimic the stochastic direction switching motion of filaments. The stochastic direction reversal rate is the third crucial parameter that controls the emergence of clusters and spirals in the system and provides an additional mechanism to either unwind spirals or to resolve clusters. We employ our overdamped Brownian dynamic simulation to study the self-buckling of an individual active filament to infer essential parameters for studying the pattern formation of colonies of filamentous Cyanobacteria in the next chapter. We confirm that a critical length of Cyanobacteria is required for self-buckling which is in perfect agreement with the theoretical model that was developed recently in Dr. S. Karpitschka's lab. Finally, by using inferred parameters from our self-buckling simulation, we investigate the pattern formation of filamentous Cyanobacteria at high density. Using the critical length from the self-buckling study as well as a length below and above this critical length, the polar and nematic long-range order in the system is investigated. The active filaments without stochastic direction reversal show a longer-range polar and nematic order in the system. We then incorporate the direction reversal mechanism: Increasing the reversal rate decreases the polar order in the system, but simultaneously increases the nematic order. Remarkably, the critical aspect ratio for the given reversal rates exhibits the strongest polar order in the tangential direction of the filament and the strongest nematic order in both the normal and tangential directions of the filaments.