| In this work, some problems in statistical mechanics related to condensed matter physics and of general interest in materials science, physics, chemistry and polymer science are considered. In chapters 1-4, the work by E.M. Lifshitz on the group-theoretical refinements of the Landau theory of phase transitions is brought to completion. Based on mathematical results obtained by Yamabe, Osgood, Phillips, Sarnak, and Kholodenko analytical results for determinants were developed which allows for prediction of the symmetry of the phase after a phase transition provided that the symmetry prior to the phase transition is known. Numerical results are presented which are in agreement with known phase behavior of actual alloys. In chapters 5-8, the Chern-Simons field theory as well as some known analogies between fluid mechanics and electrodynamics are exploited in order to model suspensions of hard spheres in the presence of a proposed hydrodynamic interaction. In this formalism, a number of rheological phenomena are then explained by screening of hydrodynamic interaction, which is shown to occur in much the same way as the Meisner effect in superconductors. |
