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This monograph represents an extension of the author's original PhD thesis and includes a more thorough discussion on the concepts and mathematics behind his research works on the foam model, as applied to studying issues of phase stability and elasticity for various non-closed packed structures found in fuzzy and colloidal crystals, as well as on a renormalization-group analysis regarding the critical behavior of loop polymers upon which topological constraints are imposed. The common thread behind these two research works is their demonstration of the importance and effectiveness of utilizing geometrical and topological concepts for modeling and understanding soft systems undergoing phase transitions.
List of contents
The Big Picture: Modern Physics at a Glance; Geometry and Phase Transitions, in General: Phase Transitions and Critical Phenomena; Overview of Density-Functional Theory; Survey of Solid Geometry and Topology; Geometry and Phase Transitions, in Colloidal Crystals: Lattice Free Energy via the Foam Model; Phases of Charged Colloidal Crystals; Elasticity of Colloidal Crystals; Geometry and Phase Transitions, in Topologically Constrained Polymers: Topologically Constrained Polymers in Theta Solution.
