Because thin systems can deform along the thickness with relative ease, the interplay between surface mechanics and geometry plays a fundamental role in sculpting their three-dimensional shape.... Show moreBecause thin systems can deform along the thickness with relative ease, the interplay between surface mechanics and geometry plays a fundamental role in sculpting their three-dimensional shape. Often, deformations arise as a consequence of elastic pre-stress in the material, for example because of the small-scale geometry of the constituents or their local arrangement. In this thesis, we look at the connection between geometry, local and global, and mechanics in thin closed shells and open sheets which we consider as two-dimensional solids that we study using linear elasticity theory. In particular, we investigate the elasticity-driven shape deformations in the context of three soft matter systems: dense single-layered crystals, oil-in-water emulsions, and biological thin assemblies of tubulin. Show less
A dynamic vortex line traces out a world sheet in spacetime. This thesis shows that the information of all its dynamic behaviour is completely contained in the world sheet. Furthermore a... Show moreA dynamic vortex line traces out a world sheet in spacetime. This thesis shows that the information of all its dynamic behaviour is completely contained in the world sheet. Furthermore a mathematical framework for order–disorder phase transitions in terms of the proliferation of such vortex world sheets is presented, leading to the prediction of quantized vortex lines of electric current in phase-disordered superconductors. Show less
Solitons are non-dissipative, nontrivial solutions of partial differential equations. In many cases their stability is well understood, e.g. there can be topological reasons that prevent a... Show moreSolitons are non-dissipative, nontrivial solutions of partial differential equations. In many cases their stability is well understood, e.g. there can be topological reasons that prevent a localised lump of energy to dissolve and become dissipative. However, there are very persistent, soliton-like objects even when there is no obvious conservation law that would guarantee stability and explain longevity. This thesis considers such solutions, called oscillons, that appear in variety of nonlinear scalar theories. In essence, they are persistent oscillations of the field around the (local) minimum of the potential. A numerical study of oscillons in two spatial dimensions is presented. Use of absorbing boundary conditions in the numerical grid enables the study of radiation losses over a long period of time and permits quantitative approach to the lifetime of oscillons. Furthermore, it is shown that oscillons are emitted by collapsing domains, which way they could come into being in nature, e.g. in the conditions met in the very early Universe. Show less
