Some problems on nonequilibrium systems

In this thesis, we study the evolution of two nonequilibrium systems: one is of practical significance for present technologies, and the other is of conceptual importance for future theoretical research.In chapter one, we model the $\alpha$-$\delta\sp\prime$ two-phase region in the Al-Li binary alloy system utilizing a coarse-grained phenomenological free energy. Mesoscopic phenomenology provides a natural setting for studying the system at high temperatures and allows for efficient and realistic computer simulations. From general empirical observations, we construct a bulk free energy and identify universal features of the free energy form. We find that our model is able to sufficiently account for both the effects of structural ordering and spinodal decomposition.In chapter two, we investigate the classical XY magnetic spin system subject to time-dependent magnetic fields as an example of a simple but non-trivial system that is far from equilibrium. Infinite-range coupling between the spin systems is assumed. We limit our investigation to elliptical magnetic fields, giving special attention to the limiting cases of AC and rotating fields.Additionally, we investigate the discotic-biaxial phase transition of the homeotropically aligned nematic liquid crystals, since this system has many features in common with the XY magnetic system, and appears to be experimentally accessible.U of I OnlyETDs are only available to UIUC Users without author permissio