Vortices, rings and pollen grains: Elasticity and statistical physics in soft matter

This thesis examines the effects of defects in three different systems in soft matter physics.;First, we discuss the interaction of vortex filaments in type II superconductors with a curved line defect in thin superconducting slabs. The equilibrium probability density for an isolated fluctuating line and an array of vortices attracted to a particular fixed defect trajectory is derived analytically and finite size effects are discussed.;Next, we explore the zero and finite temperature 2-D physics of hydrostatically pressurized circular rings with non-uniform bending modulus. We perform a stability analysis of rings at zero temperature and determine how weakened segments (low bending modulus) can affect the buckling critical pressure. At finite temperature below the buckling transition, we calculate expectation values and correlation functions of the tangent angle and other thermodynamic quantities. We observe that the ring behavior both at zero and finite temperature is controlled by the average inverse bending modulus and the bending modulus periodicity.;Last, we discuss the deformation of pollen grain walls as the pollen grains dehydrate when released from the flower, and how weakened areas (defects) of the wall affect the folding. Using both experimental and theoretical approaches, we demonstrate that the design of the weakened areas is critical for controlling the folding pattern, and ensures the pollen grain viability. An excellent fit to the experiments is obtained using a discretized version of the theory of thin elastic shells.