Hole-defect chaos in the one-dimensional complex Ginzburg-Landau equation

We study the spatiotemporally chaotic dynamics of holes and defects in the 1D complex Ginzburg--Landau equation (CGLE). We focus particularly on the self--disordering dynamics of holes and on the variation in defect profiles. By enforcing identical defect profiles and/or smooth plane wave backgrounds, we are able to sensitively probe the causes of the spatiotemporal chaos. We show that the coupling of the holes to a self--disordered background is the dominant mechanism. We analyze a lattice model for the 1D CGLE, incorporating this self--disordering. Despite its simplicity, we show that the model retains the essential spatiotemporally chaotic behavior of the full CGLE.Comment: 8 pages, 10 figures; revised and shortened; extra discussion of self-disordering dynamic

Origami building blocks: generic and special 4-vertices

Four rigid panels connected by hinges that meet at a point form a 4-vertex, the fundamental building block of origami metamaterials. Here we show how the geometry of 4-vertices, given by the sector angles of each plate, affects their folding behavior. For generic vertices, we distinguish three vertex types and two subtypes. We establish relationships based on the relative sizes of the sector angles to determine which folds can fully close and the possible mountain-valley assignments. Next, we consider what occurs when sector angles or sums thereof are set equal, which results in 16 special vertex types. One of these, flat-foldable vertices, has been studied extensively, but we show that a wide variety of qualitatively different folding motions exist for the other 15 special and 3 generic types. Our work establishes a straightforward set of rules for understanding the folding motion of both generic and special 4-vertices and serves as a roadmap for designing origami metamaterials.Comment: 8 pages, 9 figure

Nonlocal Granular Rheology: Role of Pressure and Anisotropy

We probe the secondary rheology of granular media, by imposing a main flow and immersing a vane-shaped probe into the slowly flowing granulate. The secondary rheology is then the relation between the exerted torque T and rotation rate \omega of our probe. In the absence of any main flow, the probe experiences a clear yield-stress, whereas for any finite flow rate, the yield stress disappears and the secondary rheology takes on the form of a double exponential relation between \omega and T. This secondary rheology does not only depend on the magnitude of T, but is anisotropic --- which we show by varying the relative orientation of the probe and main flow. By studying the depth dependence of the three characteristic torques that characterize the secondary rheology, we show that for counter flow, the dominant contribution is frictional like --- i.e., T and pressure are proportional for given \omega --- whereas for co flow, the situation is more complex. Our experiments thus reveal the crucial role of anisotropy for the rheology of granular media.Comment: 6 pages, 5 figure

Composite "zigzag" structures in the 1D complex Ginzburg-Landau equation

We study the dynamics of the one-dimensional complex Ginzburg Landau equation (CGLE) in the regime where holes and defects organize themselves into composite superstructures which we call zigzags. Extensive numerical simulations of the CGLE reveal a wide range of dynamical zigzag behavior which we summarize in a `phase diagram'. We have performed a numerical linear stability and bifurcation analysis of regular zigzag structures which reveals that traveling zigzags bifurcate from stationary zigzags via a pitchfork bifurcation. This bifurcation changes from supercritical (forward) to subcritical (backward) as a function of the CGLE coefficients, and we show the relevance of this for the `phase diagram'. Our findings indicate that in the zigzag parameter regime of the CGLE, the transition between defect-rich and defect-poor states is governed by bifurcations of the zigzag structures.Comment: 20 pages, 11 figure

Excess Floppy Modes and Multi-Branched Mechanisms in Metamaterials with Symmetries

Floppy modes --- deformations that cost zero energy --- are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in e.g. mechanical metamaterials, can feature an unlimited number of excess floppy modes that are absent in generic geometries, and in addition can support floppy modes that are multi-branched. We study the number $\Delta$ of excess floppy modes by comparing generic and symmetric geometries with identical topologies, and show that $\Delta$ is extensive, peaks at intermediate connection densities, and exhibits mean field scaling. We then develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, we leverage our insights to design metamaterials with multiple folding mechanisms.Comment: Main text has 4 pages and 5 figures, and is further supported by Supplementary Informatio

Convection in rotating annuli: Ginzburg-Landau equations with tunable coefficients

The coefficients of the complex Ginzburg-Landau equations that describe weakly nonlinear convection in a large rotating annulus are calculated for a range of Prandtl numbers $\sigma$. For fluids with $\sigma \approx 0.15$, we show that the rotation rate can tune the coefficients of the corresponding amplitude equations from regimes where coherent patterns prevail to regimes of spatio-temporal chaos.Comment: 4 pages (latex,multicol,epsf) including 3 figure

Force Mobilization and Generalized Isostaticity in Jammed Packings of Frictional Grains

We show that in slowly generated 2d packings of frictional spheres, a significant fraction of the friction forces lies at the Coulomb threshold - for small pressure p and friction coefficient mu, about half of the contacts. Interpreting these contacts as constrained leads to a generalized concept of isostaticity, which relates the maximal fraction of fully mobilized contacts and contact number. For p->0, our frictional packings approximately satisfy this relation over the full range of mu. This is in agreement with a previous conjecture that gently built packings should be marginal solids at jamming. In addition, the contact numbers and packing densities scale with both p and mu.Comment: 4 pages, 4 figures, submitte