5,657 research outputs found
Comment on "Minimal size of a barchan dune"
It is now an accepted fact that the size at which dunes form from a flat sand
bed as well as their `minimal size' scales on the flux saturation length. This
length is by definition the relaxation length of the slowest mode toward
equilibrium transport. The model presented by Parteli, Duran and Herrmann
[Phys. Rev. E 75, 011301 (2007)] predicts that the saturation length decreases
to zero as the inverse of the wind shear stress far from the threshold. We
first show that their model is not self-consistent: even under large wind, the
relaxation rate is limited by grain inertia and thus can not decrease to zero.
A key argument presented by these authors comes from the discussion of the
typical dune wavelength on Mars (650 m) on the basis of which they refute the
scaling of the dune size with the drag length evidenced by Claudin and
Andreotti [Earth Pla. Sci. Lett. 252, 30 (2006)]. They instead propose that
Martian dunes, composed of large grains (500 micrometers), were formed in the
past under very strong winds. We show that this saltating grain size, estimated
from thermal diffusion measurements, is not reliable. Moreover, the microscopic
photographs taken by the rovers on Martian aeolian bedforms show a grain size
of 87 plus or minus 25 micrometers together with hematite spherules at
millimetre scale. As those so-called ``blueberries'' can not be entrained by
reasonable winds, we conclude that the saltating grains on Mars are the small
ones, which gives a second strong argument against the model of Parteli et al.Comment: A six page comment on ``Minimal size of a barchan dune'' by Parteli,
Duran and Herrmann [Phys. Rev. E 75, 011301 (2007) arXiv:0705.1778
Dynamic and instability of submarine avalanches
We perform a laboratory-scale experiment of submarine avalanches on a rough
inclined plane. A sediment layer is prepared and thereafter tilted up to an
angle lower than the spontaneous avalanche angle. The sediment is scrapped
until an avalanche is triggered. Based on the stability diagram of the sediment
layer, we investigate different structures for the avalanche front dynamics.
First we see a straight front descending the slope, and then a transverse
instability occurs. Eventually, a fingering instability shows up similar to
rivulets appearing for a viscous fluid flowing down an incline. The mechanisms
leading to this new instability and the wavelength selection are discussed.Comment: 4 pages, 6 figures, to appear in the proceedings of Powders and
Grains 200
Droplets move over viscoelastic substrates by surfing a ridge
Liquid drops on soft solids generate strong deformations below the contact
line, resulting from a balance of capillary and elastic forces. The movement of
these drops may cause strong, potentially singular dissipation in the soft
solid. Here we show that a drop on a soft substrate moves by surfing a ridge:
the initially flat solid surface is deformed into a sharp ridge whose
orientation angle depends on the contact line velocity. We measure this angle
for water on a silicone gel and develop a theory based on the substrate
rheology. We quantitatively recover the dynamic contact angle and provide a
mechanism for stick-slip motion when a drop is forced strongly: the contact
line depins and slides down the wetting ridge, forming a new one after a
transient. We anticipate that our theory will have implications in problems
such as self-organization of cell tissues or the design of capillarity-based
microrheometers.Comment: 9 pages, 5 figure
Origin of line tension for a Lennard-Jones nanodroplet
The existence and origin of line tension has remained controversial in
literature. To address this issue we compute the shape of Lennard-Jones
nanodrops using molecular dynamics and compare them to density functional
theory in the approximation of the sharp kink interface. We show that the
deviation from Young's law is very small and would correspond to a typical line
tension length scale (defined as line tension divided by surface tension)
similar to the molecular size and decreasing with Young's angle. We propose an
alternative interpretation based on the geometry of the interface at the
molecular scale
Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds
We consider an abstract compact orientable Cauchy-Riemann manifold endowed
with a Cauchy-Riemann complex line bundle. We assume that the manifold
satisfies condition Y(q) everywhere. In this paper we obtain a scaling
upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high
tensor powers of the line bundle. This gives after integration weak Morse
inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a
refined spectral analysis we obtain also strong Morse inequalities which we
apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a
multiplicative constant 1/2 ; v.2 is a final updat
Erosion waves: transverse instabilities and fingering
Two laboratory scale experiments of dry and under-water avalanches of
non-cohesive granular materials are investigated. We trigger solitary waves and
study the conditions under which the front is transversally stable. We show the
existence of a linear instability followed by a coarsening dynamics and finally
the onset of a fingering pattern. Due to the different operating conditions,
both experiments strongly differ by the spatial and time scales involved.
Nevertheless, the quantitative agreement between the stability diagram, the
wavelengths selected and the avalanche morphology reveals a common scenario for
an erosion/deposition process.Comment: 4 pages, 6 figures, submitted to PR
Twistor theory of symplectic manifolds
This article is a contribution to the understanding of the geometry of the
twistor space of a symplectic manifold. We consider the bundle with fibre
the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic 2n-manifold
M. Then, after recalling the construction of the almost complex structure
induced on by a symplectic connection on M, we study and find some specific
properties of both. We show a few examples of twistor spaces, develop the
interplay with the symplectomorphisms of M, find some results about a natural
almost Hermitian structure on and finally prove its n+1-holomorphic
completeness. We end by proving a vanishing theorem about the Penrose
transform.Comment: 34 page
Linear stability analysis of transverse dunes
Sand-moving winds blowing from a constant direction in an area of high sand
availability form transverse dunes, which have a fixed profile in the direction
orthogonal to the wind. Here we show, by means of a linear stability analysis,
that transverse dunes are intrinsically unstable. Any along-axis perturbation
on a transverse dune amplify in the course of dune migration due to the
combined effect of two main factors, namely: the lateral transport through
avalanches along the dune's slip-face, and the scaling of dune migration
velocity with the inverse of the dune height. Our calculations provide a
quantitative explanation for recent observations from experiments and numerical
simulations, which showed that transverse dunes moving on the bedrock cannot
exist in a stable form and decay into a chain of crescent-shaped barchans.Comment: 8 pages, 4 figure
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