The shape of things to come : examining the interplay of elasticity, activity and geometry in soft matter

This dissertation contains within an exploration of the interactions between various soft matter systems and an environmental stimulus. The natural case studies for examining soft matter using the language of thermodynamics and phase transitions are biological constituents, from slender filaments to entire collections of organisms. We first present a brief overview of soft condensed matter, couching the thesis in terms of states of matter and preparing the stage for using continuum mechanics to examine the sensitive balance between competing physical forces in determining the final state of the systems of interest. Following this we present analysis of long-range interactions in a ubiquitous soft matter system, flexible filaments. Adhesion events that occur between attractive filaments can be understood in terms of phase transitions, and herein we present a methodology for describing physical regimes where such transitions take place. Following this we present analyses of slender filaments and flexible membranes interacting with viscous fluids; of primary concern is the transduction of undulatory motion of the surface into propulsive thrust, as a model of microorganism locomotion. We show that slender filaments near walls can be shown to exhibit non-intuitive force characteristics as a fundamental consequence of the flexibility and geometry of the system, for several models of passively actuated and internally active model flagella. We then present two different active models for propulsion using a flexible membrane: the first simplifies the geometry in order to elucidate the direct consequences of internal forcing on macroscopic propulsive thrust, while the second is a proof of principle model for a microscopic vesicular swimmer. Finally, we study collective locomotion of microorganisms and active colloidal dispersions by performing a robust hydrodynamics simulation of a concentrated suspension of microswimmers. We find that global polar order persists throughout the system as a function of various microscopic swimming/ activity parameters, as well as the volume fractio