| Nucleation and glass formation, both dynamic relaxation processes available to supercooled liquids, are the subjects of this work. We begin by studying the dynamics of nucleation in the three-dimensional Ising model through the analysis of an ensemble of nucleating trajectories. We find that the critical nuclei in the transition state ensemble are rough and anisotropic. We apply these results toward recently obtained neutron scattering data on phase separation in polymer blends. We find that time-dependent structure factors can give a signature of critical nucleus lengthscales during the initial stages of first-order phase transitions.; We then focus on studying the dynamics of glassformers in various models based on the kinetically constrained triangular lattice gas. We find that the two-vacancy and one-vacancy assisted triangular lattice gas, or (2)-TLG and (1)-TLG, show all the salient features of glassformers including dynamic heterogeneity and Stokes-Einstein breakdown, or decoupling. Four-point correlation functions reveal the presence of growing dynamical lengthscales and self-similar structures in space-time indicative of a phase transition in trajectory space.; Motivated by recent single molecule experiments, we study a variation of the (2)-TLG with rotational degrees of freedom. This rotational TLG exhibits features seen in recent single molecule experiments such as stretched exponential decay of rotational correlation functions and broad distributions of exchange times with long time tails.; By interpolating between the (1)-TLG and the (2)-TLG, we create a model which exhibits a fragile-to-strong crossover. The decoupling in this model shows non-monotonic behavior as temperature is lowered through the crossover region.; We add static attractions between particles of the (2)-TLG to create a model of colloids with short-range attractions. Re-entrant melting is observed for this model. That is, the dynamics of the attractive TLG speed up as temperature is lowered.; Finally, we couple the (2)-TLG to a particle reservoir and study non-equilibrium relaxation. Cooling and aging in this model reproduce the features seen in experiment. |
