Odd Elasticity, Excitable Interfaces, and Spontaneous Wrinkling of Atomically Thin Films

This thesis explores three distinct topics, each requiring a generalization of a classical continuum theory in order to capture a striking phenomenon from a coarsegrained perspective. Chapter 2 revisits the time-honored subject of elasticity theory, which describes how solids exert stresses in response to deformation. Classical elasticity is strongly constrained by the assumption that stress is related to strain through gradients of a potential energy. This assumption is not generally valid for systems with internal sources of energy or that are governed by non-energetic effective interactions. In this chapter, I formulate a continuum theory known as odd elasticity, which generalizes classical elasticity to include nonconservative forces. Phenomenological consequences and experimental implications are discussed. Chapter 3 visits the topic of reaction-diffusion equations. In homogeneous media, it is known that adversarial forces (present everywhere in space) can give rise to local bistabilities, resulting in spikes and wave propagation. In this chapter, I show how global bistability can emerge and cause spikes and wave propagation in the presence of heterogeneities, e.g. boundaries and interfaces, that segregate competing forces. These surprisingly robust interfacial excitations arise in models of chemical reactions and predator-prey dynamics, as well as in recent experiments wherein localized action potentials are created at the interface of distinct, nonspiking bioelectric tissues. Finally, Chapter 4 studies the emergence of spontaneous wrinkles recently observed in novel confinement-free measurements of atomically thin films. I show that a classic thin sheet model with a minimal twist, disordered strain, is sufficient to recreate these wrinkles. Using continuum theory, I derive scaling predictions for the wrinkle morphology that are consistent with experimental observations. A theoretical analysis of indentation experiments reveals that these wrinkles have dramatic implications for the effective strength and heterogeneity of unconfined atomically thin films.