We explore the surprisingly rich energy landscape of origami-like folding planar structures. We show that the configuration space of rigid-paneled degree-4 vertices, the simplest building blocks of such systems, consists of at least two distinct bran
ches meeting at the flat state. This suggests that generic vertices are at least bistable, but we find that the nonlinear nature of these branches allows for vertices with as many as five distinct stable states. In vertices with collinear folds and/or symmetry, more branches emerge leading to up to six stable states. Finally, we introduce a procedure to tile arbitrary 4-vertices while preserving their stable states, thus allowing the design and creation of multistable origami metasheets.
Observations of flowing granular matter have suggested that same-material tribocharging de- pends on particle size, rendering large grains positive and small ones negative. Models assuming the transfer of trapped electrons can explain this, but so fa
r have not been validated. Tracking individual grains in an electric field, we show quantitatively that charge is transferred based on size between materially identical grains. However, the surface density of trapped electrons, measured independently by thermoluminescence techniques, is orders of magnitude too small to account for the scale of charge transferred. This suggests that another negatively charged species, such as ions, is responsible.
Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent
experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the streams macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gas-like jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams.
