212 research outputs found
A Kato type Theorem for the inviscid limit of the Navier-Stokes equations with a moving rigid body
The issue of the inviscid limit for the incompressible Navier-Stokes
equations when a no-slip condition is prescribed on the boundary is a famous
open problem. A result by Tosio Kato says that convergence to the Euler
equations holds true in the energy space if and only if the energy dissipation
rate of the viscous flow in a boundary layer of width proportional to the
viscosity vanishes. Of course, if one considers the motion of a solid body in
an incompressible fluid, with a no-slip condition at the interface, the issue
of the inviscid limit is as least as difficult. However it is not clear if the
additional difficulties linked to the body's dynamic make this issue more
difficult or not. In this paper we consider the motion of a rigid body in an
incompressible fluid occupying the complementary set in the space and we prove
that a Kato type condition implies the convergence of the fluid velocity and of
the body velocity as well, what seems to indicate that an answer in the case of
a fixed boundary could also bring an answer to the case where there is a moving
body in the fluid
Existence of global strong solutions to a beam-fluid interaction system
We study an unsteady non linear fluid-structure interaction problem which is
a simplified model to describe blood flow through viscoleastic arteries. We
consider a Newtonian incompressible two-dimensional flow described by the
Navier-Stokes equations set in an unknown domain depending on the displacement
of a structure, which itself satisfies a linear viscoelastic beam equation. The
fluid and the structure are fully coupled via interface conditions prescribing
the continuity of the velocities at the fluid-structure interface and the
action-reaction principle. We prove that strong solutions to this problem are
global-in-time. We obtain in particular that contact between the viscoleastic
wall and the bottom of the fluid cavity does not occur in finite time. To our
knowledge, this is the first occurrence of a no-contact result, but also of
existence of strong solutions globally in time, in the frame of interactions
between a viscous fluid and a deformable structure
Failure to up-regulate VEGF165b in maternal plasma is a first trimester predictive marker for pre-eclampsia
Pre-eclampsia is a pregnancy-related condition characterized by hypertension,
proteinuria and endothelial dysfunction. VEGF165b, formed by
alternative splicing of VEGF (vascular endothelial growth factor) pre-mRNA,
inhibits VEGF165-mediated vasodilation and angiogenesis, but has not
been quantified in pregnancy. ELISAs were used to measure
means±S.E.M. plasma VEGF165b, sEng (soluble endoglin) and
sFlt-1 (soluble fms-like tyrosine kinase-1). At 12 weeks of
gestation, the plasma VEGF165b concentration was significantly
up-regulated in plasma from women who maintained normal blood pressure
throughout their pregnancy (normotensive group,
4.90±1.6 ng/ml; P<0.01, as
determined using a Mann-Whitney U test) compared with
non-pregnant women (0.40±0.22 ng/ml). In contrast, in
patients who later developed pre-eclampsia, VEGF165b levels were
lower than in the normotensive group (0.467±0.209 ng/ml),
but were no greater than non-pregnant women. At term, plasma VEGF165b
concentrations were greater than normal in both pre-eclamptic
(3.75±2.24 ng/ml) and normotensive
(10.58 ng/ml±3.74 ng/ml;
P>0.1 compared with pre-eclampsia) pregnancies.
Patients with a lower than median plasma VEGF165b at
12 weeks had elevated sFlt-1 and sEng pre-delivery. Concentrations of
sFlt-1 (1.20±0.07 and 1.27±0.18 ng/ml) and sEng
(4.4±0.18 and 4.1±0.5 ng/ml) were similar at
12 weeks of gestation in the normotensive and pre-eclamptic groups
respectively. Plasma VEGF165b levels were elevated in pregnancy, but
this increase is delayed in women that subsequently develop pre-eclampsia. In
conclusion, low VEGF165b may therefore be a clinically useful first
trimester plasma marker for increased risk of pre-eclampsia
Multi-scale analysis of compressible viscous and rotating fluids
We study a singular limit for the compressible Navier-Stokes system when the
Mach and Rossby numbers are proportional to certain powers of a small parameter
\ep. If the Rossby number dominates the Mach number, the limit problem is
represented by the 2-D incompressible Navier-Stokes system describing the
horizontal motion of vertical averages of the velocity field. If they are of
the same order then the limit problem turns out to be a linear, 2-D equation
with a unique radially symmetric solution. The effect of the centrifugal force
is taken into account
On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations
We consider an active scalar equation that is motivated by a model for
magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive
equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast,
the critically diffusive equation is well-posed. In this case we give an
example of a steady state that is nonlinearly unstable, and hence produces a
dynamo effect in the sense of an exponentially growing magnetic field.Comment: We have modified the definition of Lipschitz well-posedness, in order
to allow for a possible loss in regularity of the solution ma
Direct mass measurements of 19B, 22C, 29F, 31Ne, 34Na and other light exotic nuclei
We report on direct time-of-flight based mass measurements of 16 light
neutron-rich nuclei. These include the first determination of the masses of the
Borromean drip-line nuclei B, C and F as well as that of
Na. In addition, the most precise determinations to date for N
and Ne are reported. Coupled with recent interaction cross-section
measurements, the present results support the occurrence of a two-neutron halo
in C, with a dominant configuration, and a
single-neutron halo in Ne with the valence neutron occupying
predominantly the 2 orbital. Despite a very low two-neutron separation
energy the development of a halo in B is hindered by the 1
character of the valence neutrons.Comment: 5 page
Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array
In this paper we investigate the asymptotic validity of boundary layer
theory. For a flow induced by a periodic row of point-vortices, we compare
Prandtl's solution to Navier-Stokes solutions at different numbers. We
show how Prandtl's solution develops a finite time separation singularity. On
the other hand Navier-Stokes solution is characterized by the presence of two
kinds of viscous-inviscid interactions between the boundary layer and the outer
flow. These interactions can be detected by the analysis of the enstrophy and
of the pressure gradient on the wall. Moreover we apply the complex singularity
tracking method to Prandtl and Navier-Stokes solutions and analyze the previous
interactions from a different perspective
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