1,377 research outputs found
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 of excess floppy modes by comparing generic and symmetric
geometries with identical topologies, and show that 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 . For fluids with , 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
- …