319 research outputs found
Chaos and plasticity in superconductor vortices: a low-dimensional dynamics
We present new results of numerical simulations for driven vortex lattices in
presence of random disorder at zero temperature. We show that the plastic
dynamics of vortices display dissipative chaos. Intermittency "routes to chaos"
have been clearly identified below the differential resistance peak. The peak
region is characterized by positive Lyapunov exponents characteristic of chaos,
and low frequency broad-band noise. Furthermore we find a low fractal dimension
of the strange attractor, which suggests that only a few dynamical variables
are sufficient to model the complex plastic dynamics of vortices.Comment: 8 pages, 6 figures, accepted for publication in The Physical Review
Molecular Dynamics Study of Rotating Nanodroplets: Finite-size Effects and Nonequilibrium Deformation
Noneqiuilibrium dynamics of rotating droplets are studied by molecular
dynamics simulations. Small deviations from the theoretical prediction are
observed when the size of a droplet is small, and the deviations become smaller
as the size of the droplet increases. The characteristic timescale of the
deformation is observed, and we find (i) the deformation timescale is almost
independent of the rotating velocity with for small frequency and (ii) the
deformation timescale becomes shorter as temperature increases. A simple model
is proposed to explain the deformation dynamics of droplets.Comment: 14 pages, 8 figure, added references, changed titl
Vortex jamming in superconductors and granular rheology
We demonstrate that a highly frustrated anisotropic Josephson junction
array(JJA) on a square lattice exhibits a zero-temperature jamming transition,
which shares much in common with those in granular systems. Anisotropy of the
Josephson couplings along the horizontal and vertical directions plays roles
similar to normal load or density in granular systems. We studied numerically
static and dynamic response of the system against shear, i. e. injection of
external electric current at zero temperature. Current-voltage curves at
various strength of the anisotropy exhibit universal scaling features around
the jamming point much as do the flow curves in granular rheology, shear-stress
vs shear-rate. It turns out that at zero temperature the jamming transition
occurs right at the isotropic coupling and anisotropic JJA behaves as an exotic
fragile vortex matter : it behaves as superconductor (vortex glass) into one
direction while normal conductor (vortex liquid) into the other direction even
at zero temperature. Furthermore we find a variant of the theoretical model for
the anisotropic JJA quantitatively reproduces universal master flow-curves of
the granular systems. Our results suggest an unexpected common paradigm
stretching over seemingly unrelated fields - the rheology of soft materials and
superconductivity.Comment: 10 pages, 5 figures. To appear in New Journal of Physic
Local Anisotropy of Fluids using Minkowski Tensors
Statistics of the free volume available to individual particles have
previously been studied for simple and complex fluids, granular matter,
amorphous solids, and structural glasses. Minkowski tensors provide a set of
shape measures that are based on strong mathematical theorems and easily
computed for polygonal and polyhedral bodies such as free volume cells (Voronoi
cells). They characterize the local structure beyond the two-point correlation
function and are suitable to define indices of
local anisotropy. Here, we analyze the statistics of Minkowski tensors for
configurations of simple liquid models, including the ideal gas (Poisson point
process), the hard disks and hard spheres ensemble, and the Lennard-Jones
fluid. We show that Minkowski tensors provide a robust characterization of
local anisotropy, which ranges from for vapor
phases to for ordered solids. We find that for fluids,
local anisotropy decreases monotonously with increasing free volume and
randomness of particle positions. Furthermore, the local anisotropy indices
are sensitive to structural transitions in these simple
fluids, as has been previously shown in granular systems for the transition
from loose to jammed bead packs
Geometrically Frustrated Crystals: Elastic Theory and Dislocations
Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the
generation of edge dislocations due to geometrical frustration caused by the
bending is studied. The analogy to superconducting (or superfluid) vortex state
is pointed out and the phase diagram of the ring-crystal, which depends on
radius and thickness, is discussed.Comment: 4 pages, 3 figure
Phase Transition of the Ising model on a Hyperbolic Lattice
The matrix product structure is considered on a regular lattice in the
hyperbolic plane. The phase transition of the Ising model is observed on the
hyperbolic lattice by means of the corner-transfer-matrix
renormalization group (CTMRG) method. Calculated correlation length is always
finite even at the transition temperature, where mean-field like behavior is
observed. The entanglement entropy is also always finite.Comment: 4 pages, 3 figure
Ordinary Percolation with Discontinuous Transitions
Percolation on a one-dimensional lattice and fractals such as the Sierpinski
gasket is typically considered to be trivial because they percolate only at
full bond density. By dressing up such lattices with small-world bonds, a novel
percolation transition with explosive cluster growth can emerge at a nontrivial
critical point. There, the usual order parameter, describing the probability of
any node to be part of the largest cluster, jumps instantly to a finite value.
Here, we provide a simple example of this transition in form of a small-world
network consisting of a one-dimensional lattice combined with a hierarchy of
long-range bonds that reveals many features of the transition in a
mathematically rigorous manner.Comment: RevTex, 5 pages, 4 eps-figs, and Mathematica Notebook as Supplement
included. Final version, with several corrections and improvements. For
related work, see http://www.physics.emory.edu/faculty/boettcher
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