We show that the simplest building blocks of origami-based materials-rigid, degree-four vertices-are generically multistable. The existence two distinct branches folding motion emerging from flat state suggests at least bistability, but we how nonlinearities in motions allow generic vertex geometries to have as many five stable states. In special with collinear folds and symmetry, more emerge leading six Tuning fold energy parameters, monostability is also possible. Finally, program...

Networks of rigid bars connected by joints, termed linkages, provide a minimal framework to design robotic arms and mechanical metamaterials built out folding components. Here, we investigate chain-like linkage that, according linear elasticity, behaves like topological insulator whose zero-energy modes are localized at the edge. Simple experiments performed using prototypes chain vividly illustrate how soft motion, initially edge, can in fact propagate unobstructed all way opposite end. We...

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across broad range physical systems. Recently, experimental progress was made in controlling measuring colloidal inclusions liquid crystalline phases. structure these systems quite rich but, at the same time, subtle. Motivated by experiment power reasoning, classification uniaxial nematic crystals reviewed expounded upon. Particular attention paid to ambiguities that arise systems, which have...

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such curvature, Poisson ratio, existence metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is scarcity identify program flexibility fold patterns. We exploit a recent connection between spring networks quantum topological origami with localized folding motions at boundaries study them both experimentally theoretically....

Topological mechanical structures exhibit robust properties protected by topological invariants. In this letter, we study a family of deformed square lattices that display topologically zero-energy bulk modes analogous to the massless fermion Weyl semimetals. Our findings apply sufficiently complex satisfying Maxwell criterion equal numbers constraints and degrees freedom. We demonstrate such systems pairs oppositely charged points, corresponding zero-frequency modes, can appear at origin...

The Hopf fibration is an example of a texture: topologically stable, smooth, global configuration field. Here we demonstrate the controlled sculpting in nematic liquid crystals through control point defects. We how these are related to torons by use topological visualization technique derived from Pontryagin-Thom construction.

Significance As a solid approaches rigidity transition, its failure behavior changes dramatically: cracks become wider and until their width reaches the system size. In this regime, bonds initially break at apparently random positions they produce percolating cluster spanning across sample. Because spatial extent of process zone depends on material toughness, varying can be used as lens to examine nonlinear response that would otherwise observable only microscopic scale in rigid material.

The phase behavior of helical packings thermoresponsive microspheres inside glass capillaries is studied as a function volume fraction. Stable with long-range orientational order appear to evolve abruptly disordered states particle fraction reduced, consistent recent hard sphere simulations. We quantify this transition using correlations and susceptibilities the parameter psi_6. emergence coexisting metastable packings, well ordered states, also observed. These findings support notion...

Many advancements have been made in the field of topological mechanics. The majority works, however, concerns invariant a linear theory. We, this work, present generic prescription defining indices which accommodates non-linear effects mechanical systems without taking any approximation. Invoking tools differential geometry, Z-valued quantity terms Poincare-Hopf index, that features zero modes (ZMs), is predicted. We further identify one type topologically protected solitons are robust to...

ABSTRACT We compared the abilities of media from agar plates surrounding swarming and nonswarming cells Salmonella enterica serovar Typhimurium to wet a nonpolar surface by measuring contact angles small drops. The were wild type for chemotaxis, nonchemotactic mutants with motor biases that counterclockwise ( cheY ) or clockwise cheZ ). latter strains have been shown be defective because remains dry (Q. Wang, A. Suzuki, S. Mariconda, Porwollik, R. M. Harshey, EMBO J. 24:2034-2042, 2005)....

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood terms lack rotational Goldstone modes such and provide an alternate approach correctly accounts for interaction between translations rotations. Dislocations are associated, as usual, branch points a phase field, whereas disclinations arise critical singularities field. introduce three-dimensional model...

Origami structures are characterized by a network of folds and vertices joining unbendable plates. For applications to mechanical design self-folding structures, it is essential understand the interplay between set in unfolded origami possible 3D folded configurations. When deforming structure that has been folded, one can often linearize geometric constraints, but degeneracy state makes linear approach impossible there. We derive theory for second-order infinitesimal rigidity an initially...

We study rigidity percolation transitions in two-dimensional central-force isostatic lattices, including the square and kagome as next-nearest-neighbor bonds ("braces") are randomly added to system. In particular, we focus on differences between regular which perfectly periodic, generic lattices with same topology of but whose sites at random positions space. find that exhibit a transition when number braces is ∼LlnL, where L linear size lattice. This exhibits features both first-order...

Significance The traditional approach to designing origami metamaterials uses particular, highly symmetric crease patterns generate folding motions for reconfigurability. We instead consider sheets with periodic but otherwise generic, asymmetric triangular faces and show they exhibit nonlinear which transform through two-dimensional families of cylindrical configurations, the addition quadrilateral restricting one-dimensional subsets configurations. This leads a topological class mechanical...

We study the dynamical response of a diatomic periodic chain rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In continuum description, we derive nonlinear field theory which admits topological kinks and antikinks as excitations but where boundary term symmetry between two energetically favors kink configuration. Using cobweb plot, develop fixed-point analysis for motion demonstrate that propagate without Peierls-Nabarro potential energy barrier typically...

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases identified. The geometry of equally-spaced layers is highly generic but, at same time, difficult to work with. In this Letter we develop an approach study focal sets in smectics exploits a hidden Poincar\'e symmetry revealed only viewing as projections from one-higher dimension. We use perspective shed light upon several classic textures, including concentric cyclides Dupin, polygonal textures and...

Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern swelling. The stretching bending energies closed strip are frustrated by compatibility constraints between curvatures metric strip. To analyze this frustration, study class ``conical'' with prescribed tensor on their center line. resulting can be...

A topological mechanism is a zero-elastic-energy deformation of mechanical structure that robust against smooth changes in system parameters. Here, we map the nonlinear elasticity paradigmatic class mechanisms onto supersymmetric field theory introduced by Witten and Olive. Heuristically, this approach entails taking square root Hamiltonian. It generalizes standard procedure obtaining two copies Dirac equation linear Klein-Gordon equation. Our real-space formalism goes beyond band...

We utilize total-internal reflection to isolate the two-dimensional `surface foam' formed at planar boundary of a three-dimensional sample. The resulting images surface Plateau borders are consistent with Plateau's laws for truly foam. Samples allowed coarsen into self-similar scaling state where statistical distributions independent time, except an overall scale factor. There we find that measures side number distributions, size-topology correlations, and bubble shapes, all very similar...