Abstract
This thesis investigates how reduced dimensionality, particle interactions, geometric confinement, and external driving forces govern the ordering, fluctuations, and collective dynamics in colloidal and granular matter. Chapter 1 reviews the fundamental principles of colloids and granular systems, details the various theoretical scenarios of two-dimensional (2D) crystal melting, and reports a reentrant crystal-hexatic-liquidsolid transition in a binary mixture of paramagnetic and nonmagnetic particles driven by a magnetic field that tunes the effective sphere diameter to explain anomalous melting behavior. Chapter 2 demonstrates that Mermin-Wagner fluctuations render 2D crystals—conventionally assumed to be trivially hyperuniform—intrinsically antihyperuniform at large scales while maintaining hyperuniformity at small scales across all 2D condensed phases, including crystal, hexatic, liquid, quasicrystal, glass, and supercooled liquid systems, while elucidating the underlying mechanisms and identifying artifacts in conventional structural analyses. Chapter 3 outlines the photolithography fabrication protocols for synthesizing custom-shaped colloidal particles alongside the development of thin sample cells designed for strict 2D geometric confinement.
Chapter 4 examines the complex motion and dynamic pattern formation of multiple granular steel beads immersed in water and driven by a rotating magnetic field, demonstrating strong quantitative agreement between experimental observations and simulation results to clarify the underlying driving mechanisms. Finally, Chapter 5 provides a comprehensive summary of these findings and outlines outlooks for future
research.