Multistable sheets with rewritable patterns for switchable shape-morphing

Flat sheets patterned with folds, cuts or swelling regions can deform into complex three-dimensional shapes under external stimuli1-24. However, current strategies require prepatterning and lack intrinsic shape selection5-24. Moreover, they either rely on permanent deformations6,12-14,17,18, preventing corrections or erasure of a shape, or sustained stimulation5,7-11,25, thus yielding shapes that are unstable. Here we show that shape-morphing strategies based on mechanical multistability can overcome these limitations. We focus on undulating metasheets that store memories of mechanical stimuli in patterns of self-stabilizing scars. After removing external stimuli, scars persist and force the sheet to switch to sharply selected curved, curled and twisted shapes. These stable shapes can be erased by appropriate forcing, allowing rewritable patterns and repeated and robust actuation. Our strategy is material agnostic, extendable to other undulation patterns and instabilities, and scale-free, allowing applications from miniature to architectural scales.

Jamming of soft particles: geometry, mechanics, scaling and isostaticity

Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can jam into a rigid, disordered state where they withstand finite shear stresses before yielding. Here we review the current understanding of the transition to jamming and the nature of the jammed state for disordered packings of particles that act through repulsive contact interactions and are at zero temperature and zero shear stress. We first discuss the breakdown of affine assumptions that underlies the rich mechanics near jamming. We then extensively discuss jamming of frictionless soft spheres. At the jamming point, these systems are marginally stable (isostatic) in the sense of constraint counting, and many geometric and mechanical properties scale with distance to this jamming point. Finally, we discuss current explorations of jamming of frictional and non-spherical (ellipsoidal) particles. Both friction and asphericity tune the contact number at jamming away from the isostatic limit, but in opposite directions. This allows one to disentangle the distance to jamming and the distance to isostaticity. The picture that emerges is that most quantities are governed by the contact number and scale with the distance to isostaticity, while the contact number itself scales with the distance to jamming.

Stability balloon for two-dimensional vortex ripple patterns

Patterns of vortex ripples form when a sand bed is subjected to an oscillatory fluid flow. Here we describe experiments on the response of regular vortex ripple patterns to sudden changes of the driving amplitude a or frequency f. A sufficient decrease of f leads to a "freezing" of the pattern, while a sufficient increase of f leads to a supercritical secondary "pearling" instability. Sufficient changes in the amplitude a lead to subcritical secondary "doubling" and "bulging" instabilities. Our findings are summarized in a "stability balloon" for vortex ripple pattern formation.

Breakdown of universality in transitions to spatiotemporal chaos

We show that the transition from laminar to active behavior in extended chaotic systems can vary from a continuous transition in the universality class of directed percolation with infinitely many absorbing states to what appears as a first-order transition. The latter occurs when finite lifetime nonchaotic structures, called "solitons," dominate the dynamics. We illustrate this scenario in an extension of the deterministic Chaté-Manneville coupled map lattice model and in a soliton including variant of the stochastic Domany-Kinzel cellular automaton.

Dynamical models for sand ripples beneath surface waves

We introduce order parameter models for describing the dynamics of sand ripple patterns under oscillatory flow. A crucial ingredient of these models is the mass transport between adjacent ripples, which we obtain from detailed numerical simulations for a range of ripple sizes. Using this mass transport function, our models predict the existence of a stable band of wave numbers limited by secondary instabilities. Small ripples coarsen in our models and this process leads to a sharply selected final wave number, in agreement with experimental observations.

Ordered and self-disordered dynamics of holes and defects in the one-dimensional complex Ginzburg-Landau equation

We study the dynamics of holes and defects in the 1D complex Ginzburg-Landau equation in ordered and chaotic cases. Ordered hole-defect dynamics occurs when an unstable hole invades a plane wave state and periodically nucleates defects from which new holes are born. The results of a detailed numerical study of these periodic states are incorporated into a simple analytic description of isolated "edge" holes. Extending this description, we obtain a minimal model for general hole-defect dynamics. We show that interactions between the holes and a self-disordered background are essential for the occurrence of spatiotemporal chaos in hole-defect states.