Although broadly admired for its aesthetic qualities, the art of origami is now being recognized also as a framework for mechanical metamaterial design. Working with the Miura-ori tessellation, we find that each unit cell of this crease pattern is mechanically bistable, and by switching between states, the compressive modulus of the overall structure can be rationally and reversibly tuned. By virtue of their interactions, these mechanically stable lattice defects also lead to emergent crystallographic structures such as vacancies, dislocations, and grain boundaries. Each of these structures comes from an arrangement of reversible folds, highlighting a connection between mechanical metamaterials and programmable matter. Given origami's scale-free geometric character, this framework for metamaterial design can be directly transferred to milli-, micro-, and nanometer-size systems.

Origami is used beyond purely aesthetic pursuits to design responsive and customizable mechanical metamaterials. However, a generalized physical understanding of origami remains elusive, owing to the challenge of determining whether local kinematic constraints are globally compatible and to an incomplete understanding of how the folded sheet's material properties contribute to the overall mechanical response. Here, we show that the traditional square twist, whose crease pattern has zero degrees of freedom (DOF) and therefore should not be foldable, can nevertheless be folded by accessing bending deformations that are not explicit in the crease pattern. These hidden bending DOF are separated from the crease DOF by an energy gap that gives rise to a geometrically driven critical bifurcation between mono- and bistability. Noting its potential utility for fabricating mechanical switches, we use a temperature-responsive polymer-gel version of the square twist to demonstrate hysteretic folding dynamics at the sub-millimetre scale.

Human collective behavior can vary from calm to panicked depending on social context. Using videos publicly available online, we study the highly energized collective motion of attendees at heavy metal concerts. We find these extreme social gatherings generate similarly extreme behaviors: a disordered gas-like state called a mosh pit and an ordered vortex-like state called a circle pit. Both phenomena are reproduced in flocking simulations demonstrating that human collective behavior is consistent with the predictions of simplified models. . This variety and magnitude of stimuli are atypical of more moderate settings, and contribute to the collective behaviors studied here ( Fig. 1(A)).Videos filmed by attendees at heavy metal concerts [7] highlight a collective phenomenon consisting of 10 1 − 10 2 participants commonly referred to as a mosh pit. In mosh pits, the participants (moshers) move randomly, colliding with one another in an undirected fashion ( Fig. 1(B)). Qualitatively, this phenomenon resembles the kinetics of gaseous particles, even though moshers are self-propelled agents that experience dissipative collisions. To explore this analogy quantitatively, we obtained video footage, corrected for perspective distortions [8] as well as camera instability, and used PIV analysis [9] to measure the two-dimensional (2D) velocity field on an interpolated grid. From this data, we calculated the velocityvelocity correlation function c vv and noted an absence of the spatial oscillations typically found in liquid-like systems. Additionally, c vv was well fit by a pure exponential (R 2 = 0.97) with a decay length of 0.78 m. Taken together, these findings offer strong support for the analogy between mosh pits and gases. As a further check, we examined the 2D speed distribution; previous observations of human pedestrian traffic and escape panic led us to expect a broad distribution not well described by simple analytic expressions [2,10]. However, the measured speed distribution in mosh pits was well fit by the equilibrium speed distribution of classical 2D gasses (Fig. 1(C)), otherwise known as the Maxwell-Boltzmann distribution [11]. These observations present an interesting question: Why does an inherently non-equilibrium system exhibit equilibrium characteristics?Studies of collective motion in living and complex systems have found notable success within the framework of flocking simulations [12][13][14][15][16]. Thus, we use a Vicsek-like model [17] to simplify the complex behavioral dynamics of each human mosher to that of a simple soft-bodied particle we dub a Mobile Active Simulated Humanoid, or MASHer (SI). Our model includes two species of MASH-

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G(∗)| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G(∗)| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction vc lead to orders-of-magnitude changes in the modulus with |G(∗)| scaling as (vc - v0)(ξ). Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue's surface.

A water bridge refers to an experimental "flexible cable" made up of pure deionized water which can hang across two supports maintained with a sufficiently large voltage difference. The resulting electric fields within the deionized water flexible cable, maintain a tension which sustains the water against the downward force of gravity. A detailed calculation of the water bridge tension will be provided in terms of the Maxwell pressure tensor in a dielectric fluid medium. General properties of the dielectric liquid pressure tensor are discussed along with unusual features of dielectric fluid Bernoulli flows in an electric field. Analogies between dielectric fluid Bernoulli flows in strong electric fields and quantum Bernoulli flows in superfluids are explored.