Fluctuations, disorder, and geometry in soft matter

Abstract

Soft matter refers to a broad category of materials, united by the characteristic that their shape or internal structure is easily deformable. Such materials are typically made up of individual constituents on the mesoscopic length scale, with collective excitation energies on the room temperature thermal energy scale. These systems make up the world around us (e.g. a crushed soda can, the liquid crystal display of a TV screen, a spoonful of mayonnaise, or the cells inside our bodies) and can display a variety of interesting phenomena due to the interplay of their geometry, thermodynamic fluctuations, and environmental disorder. This thesis studies a breadth of soft matter systems, namely (1) the effect of biophysical stochasticity on the dynamical states of neural networks, (2) the consequences of thermal fluctuations on defect assemblies in crystalline solids, (3) the implication of geometry-induced inhomogeneity on phonon localization in colloidal crystals, and (4) the influence of surface curvature and boundary conditions on the ground state of liquid crystals. These studies demonstrate the non-negligible and intriguing effects that fluctuations and disorder can have on the geometrical properties of soft materials.