Brownian dynamics of active and passive anisotropic colloidal particles

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The description of static equilibrium properties and dynamic behavior of many-particle systems is a longstanding challenge in theoretical physics, relevant across various fields. This work investigates several aspects of this problem, focusing on the Brownian dynamics of interacting anisotropic colloidal particles, both passive (colloidal liquid crystals) and active (self-propelled microswimmers). The main content is divided into three chapters. The first chapter examines the Brownian dynamics of an individual active colloidal particle with arbitrary shape, formulating the Langevin equation and deriving analytical solutions for specific cases, alongside numerical solutions for broader scenarios, including the impact of shear flow on spherical colloidal particles. The second chapter addresses the collective dynamics of a large set of interacting active colloidal particles. It generalizes classical dynamical density functional theory to accommodate arbitrarily shaped particles, demonstrating that this new approach can be reformulated using a dissipation functional, facilitating quicker derivation of dynamic equations for phase field crystal models compared to traditional methods. The third chapter explores the statics and dynamics of colloidal liquid crystals through microscopic, mesoscopic, and macroscopic mean-field theories. It derives phase field crystal models for apolar and polar colloidal liquid crystals and compare