194 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
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
Conformal invariance in two-dimensional turbulence
Simplicity of fundamental physical laws manifests itself in fundamental
symmetries. While systems with an infinity of strongly interacting degrees of
freedom (in particle physics and critical phenomena) are hard to describe, they
often demonstrate symmetries, in particular scale invariance. In two dimensions
(2d) locality often promotes scale invariance to a wider class of conformal
transformations which allow for nonuniform re-scaling. Conformal invariance
allows a thorough classification of universality classes of critical phenomena
in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example
of strongly-interacting non-equilibrium system? Here, using numerical
experiment, we show that some features of 2d inverse turbulent cascade display
conformal invariance. We observe that the statistics of vorticity clusters is
remarkably close to that of critical percolation, one of the simplest
universality classes of critical phenomena. These results represent a new step
in the unification of 2d physics within the framework of conformal symmetry.Comment: 10 pages, 5 figures, 1 tabl
Wetting of a symmetrical binary fluid mixture on a wall
We study the wetting behaviour of a symmetrical binary fluid below the
demixing temperature at a non-selective attractive wall. Although it demixes in
the bulk, a sufficiently thin liquid film remains mixed. On approaching
liquid/vapour coexistence, however, the thickness of the liquid film increases
and it may demix and then wet the substrate. We show that the wetting
properties are determined by an interplay of the two length scales related to
the density and the composition fluctuations. The problem is analysed within
the framework of a generic two component Ginzburg-Landau functional
(appropriate for systems with short-ranged interactions). This functional is
minimized both numerically and analytically within a piecewise parabolic
potential approximation. A number of novel surface transitions are found,
including first order demixing and prewetting, continuous demixing, a
tricritical point connecting the two regimes, or a critical end point beyond
which the prewetting line separates a strongly and a weakly demixed film. Our
results are supported by detailed Monte Carlo simulations of a symmetrical
binary Lennard-Jones fluid at an attractive wall.Comment: submitted to Phys. Rev.
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