Surface tension has dramatic and well-understood impacts on simple liquids. It forces small droplets to ball up, and drives liquids into narrow channels. At small scales, these interfacial forces influence a wider range of materials and pose a number of open questions.

I will describe microscopic experiments probing the interfaces of soft materials, including polymer networks and lipid bilayers. Here, the interplay of surface tension and elasticity qualitatively changes the phenomena of wetting and adhesion. First, I will describe how we exploit these effects to investigate the surface tension of soft solids. These experiments reveal fundamental differences with familiar liquid surface tension. While the surface tension of simple liquids is a constant scalar quantity, the surface tension of solids is an anisotropic and strain-dependent tensor. It is characterized not only by an interfacial energy, but also by surface shear and dilational moduli. The physical origins of these quantities are essentially unexplored. Second, I will describe new experiments investigating the adhesion of colloidal particles to lipid bilayers. Here, the competition of surface tension, bending rigidity, and interfacial energy can drive the assembly of large scale structures.

Recent progress in additive manufacturing and materials engineering has led to a surge of interest in shape-changing plate and shell-like structures. Such structures are typically manufactured in a planar configuration and, when exposed to an ambient stimulus such as heat or humidity, morph into their desired three-dimensional geometry. Viewed through the lens of differential geometry and elasticity, the application of the physical stimulus can be interpreted as a local change in the metric tensor field of the sheet. In this talk I will present my contributions to the theory and simulation of the sheet's elastic response to such a metric change, considering both the forward and the inverse problem. I will show how these developments have led to the design and experimental realization of a multi-material 4D printed lattice that can undergo complex, predictable 3D shape changes when subjected to a temperature difference.

Biological materials operate far from equilibrium and their dynamic behavior adapts to the surrounding environment as a result of coupling to chemical, mechanical and transport processes and networks of interacting signals that interpret environmental signals and control downstream kinetics. I will describe two model systems we have developed to explore the design principles for these types of responsive materials. Engineered semiflexible filaments, DNA nanotubes, can be used understand how reaction kinetics, diffusion, and chemical reaction networks can regulate growth. Nanotubes can be assembled into structures such as bridges between molecular endpoints or hierarchical networks. DNA polymerization-induced hydrogel shape change can be directed by chemical circuits that interpret upstream signals and produce outputs that initiate a shape change response. These circuits, by amplifying chemical signals, can induce high-energy changes in material shape in response to small amounts of chemical inputs. In these hydrogels the dynamics of shape change are governed by the interplay of DNA polymerization, signal transduction, transport of oligonucleotides and water, and polymer network remodeling, many of which operate on similar time scales. I will conclude by discussing how coupling hydrogel shape change with force sensors could be used for mechanical feedback.

Complex systems are known to exhibit emergent properties that are missing on the constituent level. An example is the appearance of intermittent transitions between distinct dynamical states. Using a levitated, quasi-2D layer of charged microparticles, our recent experiments (Gogia et al., PRL, 2017) showed that a nonequilibrium, many-body system can display intermittent dynamics by switching between an ordered, crystalline state and a gas-like, excited state. The emergent dynamics are a direct consequence of coupling between the inertial dynamics, structural disorder induced by particle size variation, and external noisy forcing. The behavior can be reproduced is a simulation with as little as 50 particles. The key lies in a separation of energy scales. Energy pumped into one degree of freedom will eventually couple non-linearly to other excitable modes and thermalize the system. The behavior bears a striking resemblance to the transition to turbulence in pipe flow, where increasing the flow velocity leads to intermittent "puffs" of turbulence. This transition also depends sensitively on disorder through the roughness of the pipe walls. In analogy to the Reynolds number, we are able to describe our system through a simplified set of equations and a single dimensionless number characterizing the ratio of external forcing to dissipation. This analogy may help identify the minimal ingredients for observing such intermittent, turbulent dynamics in other discrete systems.

Biochemical oscillations are ubiquitous in biology and allow organisms to properly time their biological functions. Two biologically relevant observables in these biochemical oscillator circuits are the coherence and time period of oscillations. In this talk, I will discuss minimal Markov state models of non-equilibrium biochemical networks that support oscillations. In particular, I will discuss how a high energy consumption budget can make these quantities robust in a variety of settings.

For centuries, applying an external pressure difference has remained the only solution to flow a liquid in a pipe. Over the last ten years, by engineering soft materials from self-propelled units, we have learned how to drive fluids from within. In the first part of my talk I will show how to assemble spontaneously flowing liquids from interacting colloidal robots. I will then show how to infer the hydrodynamics of these active fluids from the sole inspection of their fluctuation spectra. In the second part of my talk I will show that the same concepts and tool can be effectively use to account for the flows of pedestrian crowds walking on the streets of a windy city.