572 research outputs found
Onset of Patterns in an Ocillated Granular Layer: Continuum and Molecular Dynamics Simulations
We study the onset of patterns in vertically oscillated layers of
frictionless dissipative particles. Using both numerical solutions of continuum
equations to Navier-Stokes order and molecular dynamics (MD) simulations, we
find that standing waves form stripe patterns above a critical acceleration of
the cell. Changing the frequency of oscillation of the cell changes the
wavelength of the resulting pattern; MD and continuum simulations both yield
wavelengths in accord with previous experimental results. The value of the
critical acceleration for ordered standing waves is approximately 10% higher in
molecular dynamics simulations than in the continuum simulations, and the
amplitude of the waves differs significantly between the models. The delay in
the onset of order in molecular dynamics simulations and the amplitude of noise
below this onset are consistent with the presence of fluctuations which are
absent in the continuum theory. The strength of the noise obtained by fit to
Swift-Hohenberg theory is orders of magnitude larger than the thermal noise in
fluid convection experiments, and is comparable to the noise found in
experiments with oscillated granular layers and in recent fluid experiments on
fluids near the critical point. Good agreement is found between the mean field
value of onset from the Swift-Hohenberg fit and the onset in continuum
simulations. Patterns are compared in cells oscillated at two different
frequencies in MD; the layer with larger wavelength patterns has less noise
than the layer with smaller wavelength patterns.Comment: Published in Physical Review
Rhombic Patterns: Broken Hexagonal Symmetry
Landau-Ginzburg equations derived to conserve two-dimensional spatial symmetries lead to the prediction that rhombic arrays with characteristic angles slightly differ from 60 degrees should form in many systems. Beyond the bifurcation from the uniform state to patterns, rhombic patterns are linearly stable for a band of angles near the 60 degrees angle of regular hexagons. Experiments conducted on a reaction-diffusion system involving a chlorite-iodide-malonic acid reaction yield rhombic patterns in good accord with the theory.Energy Laboratory of the University of HoustonOffice of Naval ResearchU.S. Department of Energy Office of Basic Energy SciencesRobert A. Welch FoundationCenter for Nonlinear Dynamic
Mach cone in a shallow granular layer
We study the V-shaped wake (Mach cone) formed by a cylindrical rod moving
through a thin, vertically vibrated granular layer. The wake, analogous to a
shock (hydraulic jump) in shallow water, appears for rod velocities v_R greater
than a critical velocity c. We measure the half-angle, theta, of the wake as a
function of v_R and layer depth, h. The angle satisfies the Mach relation,
sin(theta)=c/v_R, where c=sqrt(gh), even for h as small as one particle
diameter.Comment: 4 pages 4 figure
Linear instability and statistical laws of physics
We show that a meaningful statistical description is possible in conservative
and mixing systems with zero Lyapunov exponent in which the dynamical
instability is only linear in time. More specifically, (i) the sensitivity to
initial conditions is given by with
; (ii) the statistical entropy in the infinitely fine graining limit (i.e., {\it
number of cells into which the phase space has been partitioned} ),
increases linearly with time only for ; (iii) a nontrivial,
-generalized, Pesin-like identity is satisfied, namely the . These facts (which are
in analogy to the usual behaviour of strongly chaotic systems with ), seem
to open the door for a statistical description of conservative many-body
nonlinear systems whose Lyapunov spectrum vanishes.Comment: 7 pages including 2 figures. The present version is accepted for
publication in Europhysics Letter
Kink-induced transport and segregation in oscillated granular layers
We use experiments and molecular dynamics simulations of vertically
oscillated granular layers to study horizontal particle segregation induced by
a kink (a boundary between domains oscillating out of phase). Counter-rotating
convection rolls carry the larger particles in a bidisperse layer along the
granular surface to a kink, where they become trapped. The convection
originates from avalanches that occur inside the layer, along the interface
between solidified and fluidized grains. The position of a kink can be
controlled by modulation of the container frequency, making possible systematic
harvesting of the larger particles.Comment: 4 pages, 5 figures. to appear in Phys. Rev. Let
Persistent holes in a fluid
We observe stable holes in a vertically oscillated 0.5 cm deep aqueous
suspension of cornstarch for accelerations a above 10g. Holes appear only if a
finite perturbation is applied to the layer. Holes are circular and
approximately 0.5 cm wide, and can persist for more than 10^5 cycles. Above a =
17g the rim of the hole becomes unstable producing finger-like protrusions or
hole division. At higher acceleration, the hole delocalizes, growing to cover
the entire surface with erratic undulations. We find similar behavior in an
aqueous suspension of glass microspheres.Comment: 4 pages, 6 figure
Extraction of coherent structures in a rotating turbulent flow experiment
The discrete wavelet packet transform (DWPT) and discrete wavelet transform
(DWT) are used to extract and study the dynamics of coherent structures in a
turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by
strong pumping through tubes at the bottom of a rotating tank (48.4 cm high,
39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence
with increasing height in the tank. Particle Image Velocimetry (PIV)
measurements on the quasi-2D flow reveal many long-lived coherent vortices with
a wide range of sizes. The vorticity fields exhibit vortex birth, merger,
scattering, and destruction. We separate the flow into a low-entropy
``coherent'' and a high-entropy ``incoherent'' component by thresholding the
coefficients of the DWPT and DWT of the vorticity fields. Similar thresholdings
using the Fourier transform and JPEG compression together with the Okubo-Weiss
criterion are also tested for comparison. We find that the DWPT and DWT yield
similar results and are much more efficient at representing the total flow than
a Fourier-based method. Only about 3% of the large-amplitude coefficients of
the DWPT and DWT are necessary to represent the coherent component and preserve
the vorticity probability density function, transport properties, and spatial
and temporal correlations. The remaining small amplitude coefficients represent
the incoherent component, which has near Gaussian vorticity PDF, contains no
coherent structures, rapidly loses correlation in time, and does not contribute
significantly to the transport properties of the flow. This suggests that one
can describe and simulate such turbulent flow using a relatively small number
of wavelet or wavelet packet modes.Comment: experimental work aprox 17 pages, 11 figures, accepted to appear in
PRE, last few figures appear at the end. clarifications, added references,
fixed typo
An invariant distribution in static granular media
We have discovered an invariant distribution for local packing configurations
in static granular media. This distribution holds in experiments for packing
fractions covering most of the range from random loose packed to random close
packed, for beads packed both in air and in water. Assuming only that there
exist elementary cells in which the system volume is subdivided, we derive from
statistical mechanics a distribution that is in accord with the observations.
This universal distribution function for granular media is analogous to the
Maxwell-Boltzmann distribution for molecular gasses.Comment: 4 pages 3 figure
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