229 research outputs found
Level sets and Composition operators on the Dirichlet space
We consider composition operators in the Dirichlet space of the unit disc in
the plane. Various criteria on boundedness, compactness and Hilbert-Schmidt
class membership are established. Some of these criteria are shown to be
optimal
Dispersion of tracer particles in a compressible flow
The turbulent diffusion of Lagrangian tracer particles has been studied in a
flow on the surface of a large tank of water and in computer simulations. The
effect of flow compressibility is captured in images of particle fields. The
velocity field of floating particles has a divergence, whose probability
density function shows exponential tails. Also studied is the motion of pairs
and triplets of particles. The mean square separation is fitted to
the scaling form ~ t^alpha, and in contrast with the
Richardson-Kolmogorov prediction, an extended range with a reduced scaling
exponent of alpha=1.65 pm 0.1 is found. Clustering is also manifest in strongly
deformed triangles spanned within triplets of tracers.Comment: 6 pages, 4 figure
Emergent states in dense systems of active rods: from swarming to turbulence
Dense suspensions of self-propelled rod-like particles exhibit a fascinating
variety of non-equilibrium phenomena. By means of computer simulations of a
minimal model for rigid self-propelled colloidal rods with variable shape we
explore the generic diagram of emerging states over a large range of rod
densities and aspect ratios. The dynamics is studied using a simple numerical
scheme for the overdamped noiseless frictional dynamics of a many-body system
in which steric forces are dominant over hydrodynamic ones. The different
emergent states are identified by various characteristic correlation functions
and suitable order parameter fields. At low density and aspect ratio, a
disordered phase with no coherent motion precedes a highly-cooperative swarming
state at large aspect ratio. Conversely, at high densities weakly anisometric
particles show a distinct jamming transition whereas slender particles form
dynamic laning patterns. In between there is a large window corresponding to
strongly vortical, turbulent flow. The different dynamical states should be
verifiable in systems of swimming bacteria and artificial rod-like
micro-swimmers.Comment: 14 pages, 8 figure
Structure of velocity distributions in shock waves in granular gases with extension to molecular gases
International audienceVelocity distributions in normal shock waves obtained in dilute granular flows are studied. These distributions cannot be described by a simple functional shape and are believed to be bimodal. Our results show that these distributions are not strictly bimodal but a trimodal distribution is shown to be sufficient. The usual Mott-Smith bimodal description of these distributions, developed for molecular gases, and based on the coexistence of two subpopulations (a supersonic and a subsonic population) in the shock front, can be modified by adding a third subpopulation. Our experiments show that this additional population results from collisions between the supersonic and subsonic subpopulations. We propose a simple approach incorporating the role of this third intermediate population to model the measured probability distributions and apply it to granular shocks as well as shocks in molecular gases
Where surface physics and fluid dynamics meet: rupture of an amphiphile layer by fluid flow
We investigate the fluctuating pattern created by a jet of fluid impingent
upon an amphiphile-covered surface. This microscopically thin layer is
initially covered with 50 m floating particles so that the layer can be
visualized. A vertical jet of water located below the surface and directed
upward drives a hole in this layer. The hole is particle-free and is surrounded
by the particle-laden amphiphile region. The jet ruptures the amphiphile layer
creating a particle-free region that is surrounded by the particle-covered
surface. The aim of the experiment is to understand the (fluctuating) shape of
the ramified interface between the particle-laden and particle-free regions.Comment: published in Journal of Chemical Physic
Macroscopic effects of the spectral structure in turbulent flows
Two aspects of turbulent flows have been the subject of extensive, split
research efforts: macroscopic properties, such as the frictional drag
experienced by a flow past a wall, and the turbulent spectrum. The turbulent
spectrum may be said to represent the fabric of a turbulent state; in practice
it is a power law of exponent \alpha (the "spectral exponent") that gives the
revolving velocity of a turbulent fluctuation (or "eddy") of size s as a
function of s. The link, if any, between macroscopic properties and the
turbulent spectrum remains missing. Might it be found by contrasting the
frictional drag in flows with differing types of spectra? Here we perform
unprecedented measurements of the frictional drag in soap-film flows, where the
spectral exponent \alpha = 3 and compare the results with the frictional drag
in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of
the Reynolds number Re (a measure of the strength of the turbulence), we find
that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in
pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may
be predicted from the attendant value of \alpha by using a new theory, in which
the frictional drag is explicitly linked to the turbulent spectrum. Our work
indicates that in turbulence, as in continuous phase transitions, macroscopic
properties are governed by the spectral structure of the fluctuations.Comment: 6 pages, 3 figure
Vorticity statistics in the two-dimensional enstrophy cascade
We report the first extensive experimental observation of the two-dimensional
enstrophy cascade, along with the determination of the high order vorticity
statistics. The energy spectra we obtain are remarkably close to the Kraichnan
Batchelor expectation. The distributions of the vorticity increments, in the
inertial range, deviate only little from gaussianity and the corresponding
structure functions exponents are indistinguishable from zero. It is thus shown
that there is no sizeable small scale intermittency in the enstrophy cascade,
in agreement with recent theoretical analyses.Comment: 5 pages, 7 Figure
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