Understanding dynamics of colloidal dispersions is important for several applications ranging from coatings such as paints to growing colloidal crystals for photonic bandgap materials. The research outlined in this dissertation describes the use of Monte Carlo and Stokesian Dynamic simulations to model colloidal dispersions, and the development of theoretical expressions to quantify and predict dynamics of colloidal dispersions. The emphasis is on accurately modeling conservative, Brownian, and hydrodynamic forces to model dynamics of colloidal dispersions. In addition, we develop theoretical expressions for quantifying self-diffusion in colloids interacting via different particle-particle and particle-wall potentials. Specifically, we have used simulations to quantitatively explain the observation of anomalous attraction between like-charged colloids, develop a new criterion for percolation in attractive colloidal fluids, and validate the use of analytical expressions for quantifying diffusion in interfacial colloidal fluids. The results of this work contribute to understanding dynamics in interfacial and bulk colloidal fluids.

We consider fast computation methods for simulation of dynamics of a collection of particles dispersed in an unbounded Stokesian suspension. Stokesian suspensions are of great practical interest in the manufacturing and processing of various commercial products. The most popular dynamic simulation method for these kind of suspensions was developed by Brady and Bossis (Brady and Bossis [1988]). This method uses a truncated multipole expansion to represent the fluid traction on particle surfaces. The hydrodynamic interactions in Stoke-sian suspension are long ranged in nature, resulting in strong coupled motion of all particles. For an N particle system, this method imposes an O(N3) computational cost, thus posing limitations to the number of particles that may be simulated. More recent methods (Sierou and Brady [2001], Scintilla, Darve and Shaqfeh [2005]) have attempted to solve this problem using Particle Mesh Ewald summation techniques by distributing the moments on a grid and using Fast Fourier Transform algorithms, resulting in an O(N log N) computational cost. We review these methods and propose a version that we believe is some-what superior. In the course of this study, we have identified and corrected errors in previous studies that maybe of some importance in determining the bulk properties of suspensions. Finally, we show the utility of our method in determining certain properties of suspensions and compare them to existing analytical results for the same.

Molecular simulation is an indispensable tool in many different disciplines such as physics, biology, chemical engineering, materials science, drug design, and others. Performing large-scale molecular simulation is of great interest to biologists and chemists, because many important biological and pharmaceutical phenomena can only be observed in very large molecule systems and after sufficiently long time dynamics. On the other hand, molecular simulation methods usually have very steep computational costs, which limits current molecular simulation studies to relatively small systems. The gap between the scale of molecular simulation that existing techniques can handle and the scale of interest has become a major barrier for applying molecular simulation to study real-world problems. In order to study large-scale molecular systems using molecular simulation, it requires developing highly parallel simulation algorithms and constantly adapting the algorithms to rapidly changing high performance computing architectures. However, many existing algorithms and codes for molecular simulation are from more than a decade ago, which were designed for sequential computers or early parallel architectures. They may not scale efficiently and do not fully exploit features of today's hardware. Given the rapid evolution in computer architectures, the time has come to revisit these molecular simulation algorithms and codes. In this thesis, we demonstrate our approach to addressing the computational challenges of large-scale molecular simulation by presenting both the high-performance algorithms and software for two important molecular simulation applications: Hartree-Fock (HF) calculations and hydrodynamics simulations, on highly parallel computer architectures. The algorithms and software presented in this thesis have been used by biologists and chemists to study some problems that were unable to solve using existing codes. The parallel techniques and methods developed in this work can be also applied to other molecular simulation applications.

At small length scales, low velocities, and high viscosity, the effects of inertia on motion through fluid become insignificant and viscous forces dominate. Microswimmer propulsion, of necessity, is achieved through different means than that achieved by macroscopic organisms. We describe in detail the hydrodynamics of microswimmers consisting of colloidal particles and their interactions. In particular we focus on two-bead swimmers and the effects of asymmetry on collective motion, calculating analytical formulae for time-averaged pair interactions and verifying them with microscopic time-resolved numerical simulation, finding good agreement. We then examine the long-term effects of a swimmer's passing on a passive tracer particle, finding that the force-free nature of these microswimmers leads to loop-shaped tracer trajectories. Even in the presence of Brownian motion, the loop-shaped structures of these trajectories can be recovered by averaging over a large enough sample size. Finally, we explore the phenomenon of synchronisation between microswimmers through hydrodynamic interactions, using the method of constraint forces on a force-based swimmer. We find that the hydrodynamic interactions between swimmers can alter the relative phase between them such that phase-locking can occur over the long term, altering their collective motion.