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

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

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 $^{19}$B, $^{22}$C and $^{29}$F as well as that of $^{34}$Na. In addition, the most precise determinations to date for $^{23}$N and $^{31}$Ne are reported. Coupled with recent interaction cross-section measurements, the present results support the occurrence of a two-neutron halo in $^{22}$C, with a dominant $\nu2s_{1/2}^2$ configuration, and a single-neutron halo in $^{31}$Ne with the valence neutron occupying predominantly the 2$p_{3/2}$ orbital. Despite a very low two-neutron separation energy the development of a halo in $^{19}$B is hindered by the 1$d_{5/2}^2$ character of the valence neutrons.Comment: 5 page

On discretization in time in simulations of particulate flows

We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles immersed in the fluid or between a particle and the wall tends to zero. The idea consists in introducing a small threshold for the particle-wall distance below which the real trajectory of the particle is replaced by an approximated one where the distance is kept equal to the threshold value. The error of this approximation is estimated both theoretically and by numerical experiments. Our time marching scheme can be easily incorporated into a full simulation method where the velocity of the fluid is obtained by a numerical solution to Stokes or Navier-Stokes equations. We also provide a derivation of the asymptotic expansion for the lubrication force (used in our numerical experiments) acting on a disk immersed in a Newtonian fluid and approaching the wall. The method of this derivation is new and can be easily adapted to other cases

Regularity issues in the problem of fluid structure interaction

We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier-Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain have H\"older regularity $C^{1, \alpha}$, $0 < \alpha \le 1$. First, we show the existence and uniqueness of strong solutions up to collision. A key ingredient is a BMO bound on the velocity gradient, which substitutes to the standard $H^2$ estimate for smoother domains. Then, we study the asymptotic behaviour of one $C^{1, \alpha}$ body falling over a flat surface. We show that collision is possible in finite time if and only if $\alpha < 1/2$

Transcriptomes of <i>Trypanosoma brucei</i> rhodesiense from sleeping sickness patients, rodents and culture:Effects of strain, growth conditions and RNA preparation methods

All of our current knowledge of African trypanosome metabolism is based on results from trypanosomes grown in culture or in rodents. Drugs against sleeping sickness must however treat trypanosomes in humans. We here compare the transcriptomes of Trypanosoma brucei rhodesiense from the blood and cerebrospinal fluid of human patients with those of trypanosomes from culture and rodents. The data were aligned and analysed using new user-friendly applications designed for Kinetoplastid RNA-Seq data. The transcriptomes of trypanosomes from human blood and cerebrospinal fluid did not predict major metabolic differences that might affect drug susceptibility. Usefully, there were relatively few differences between the transcriptomes of trypanosomes from patients and those of similar trypanosomes grown in rats. Transcriptomes of monomorphic laboratory-adapted parasites grown in in vitro culture closely resembled those of the human parasites, but some differences were seen. In poly(A)-selected mRNA transcriptomes, mRNAs encoding some protein kinases and RNA-binding proteins were under-represented relative to mRNA that had not been poly(A) selected; further investigation revealed that the selection tends to result in loss of longer mRNAs