Existence of weak solutions up to collision for viscous fluid-solid systems with slip

We study in this paper the movement of a rigid solid inside an incompressible Navier-Stokes flow, within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface, through a Navier condition. Taking into account slip at the interface is very natural within this model, as classical no-slip conditions lead to unrealistic collisional behavior between the solid and the domain boundary. We prove for this model existence of weak solutions of Leray type, up to collision, in three dimensions. The key point is that, due to the slip condition, the velocity field is discontinuous across the fluid/solid interface. This prevents from obtaining global H1 bounds on the velocity, which makes many aspects of the theory of weak solutions for Dirichlet conditions unadapted.Comment: 45 page

Computation of the drag force on a rough sphere close to a wall

We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force. In this way, we recover and clarify the various expressions that can be found in the litterature

Finite Decomposition Semigroup

In this paper, we explain the importance of finite decomposition semigroups and present two theorems related to their structure

Independence of hyperlogarithms over function fields via algebraic combinatorics

We obtain a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms. The key fact is that the multiplier (i.e. the factor $M$ in the differential equation $dS=MS$) has only singularities of first order (Fuchsian-type equations) and this implies that they freely span a space which contains no primitive. We give direct applications where we extend the property of linear independence to the largest known ring of coefficients

Interspecies Exchange of a Hoxd Enhancer in Vivo Induces Premature Transcription and Anterior Shift of the Sacrum

AbstractThe precise activation, in space and time, of vertebrateHoxgenes is an essential requirement for normal morphogenesis. In order to assess for the functional potential of evolutionary conservedHoxregulatory sequences, a phylogenetically conserved bipartite regulatory element necessary for proper spatial and temporal activation of theHoxd-11gene was replaced by its fish counterpart in theHoxDcomplex of mice, using an ES cell-based targeted exchange. Fetuses carrying this replacement activatedHoxd-11transcription prematurely, which led to a rostral shift of its expression boundary and a consequent anterior transposition of the sacrum. These results demonstrate the high phylogenetic conservation of regulatory mechanisms acting over vertebrateHoxcomplexes and suggest that minor time difference (heterochronies) inHoxgene activation may have contributed to important morphological variations in the course of evolution

The influence of boundary conditions on the contact problem in a 3D Navier-Stokes Flow

34 p.We consider the free fall of a sphere above a wall in a viscous incompressible fluid. We investigate the influence of boundary conditions on the finite-time occurrence of contact between the sphere and the wall. We prove that slip boundary conditions enable to circumvent the "no-collision" paradox associated with no-slip boundary conditions. We also examine the case of mixed boundary conditions

Modélisation du déroulement d'activités humaines en mer côtière, scénarios appliqués à la mer d'Iroise.

http://letg.univ-nantes.fr/colloque/actes.htm#54c2International audienceCoastal seas, marine part of the coastal zone, are particulary attractive for human society. Human activities involve interactions that can lead to conflicts and to ressources degradation. In order to analyse the coastal system, the Geomer laboratory has developed a modelling platform of Human Activities Dynamic (DAHU) which contains a specific module adapted to the human marine activities (DAHU-MAM). This paper presents applications developed on the Iroise Sea (France). Three scenarios are proposed in an operational coastal management objective : (1) highlighting potential conflicts of use, (2) impact of a shipwrek (3) or impact of a substructure installation.Les mers côtières, franges marines des zones côtières, sont particulièrement concernées par les activités humaines qui interagissent entre elles et avec leur environnement. Afin d'analyser ces interactions, le laboratoire Géomer (LETG - UMR 6554 CNRS) a développé une plate-forme de modélisation de la Dynamique des Activités Humaines (DAHU) qui comporte un module adapté au déroulement d'activités humaines en milieu marin. Cet article présente les applications développées en mer d'Iroise. Elles sont fondées sur l'élaboration de scénarios plausibles visant à fournir des éléments relatifs aux activités humaines (1) dans leur déroulement quotidien, (2) en cas d'événement accidentel (3) ou dans le cas d'aménagement d'infrastructures

Sweet Clovers, a Source of Fibers Adapted for Growth on Wet and Saline Soils

Sweet clovers are legumes able to grow on most soils, and two sweet clover species, Melilotus albus and Melilotus officinalis have been introduced and are now cultivated on estuary land. We characterized the composition and morphology of sweet clover stems collected after the seeds had reached maturity. We also carried out histochemical analyses on transverse sections. The two species had similar morphological structures, which two fiber fractions: flexible long fibers and stiff, dense shives, accounting for about 12% and 88% of stem dry matter, respectively. Histological analysis revealed the presence of bundles of highly cellulosic bast fibers (lignocellulosic material: 71–78% of dry matter). The shives are a natural mesoporous material composed of 85–90% lignocellulosic fibers. Both fiber fractions displayed good thermal resistance to temperatures up to 225°C and a moderate affinity for water. These two types of fibers are similar to those of flax and hemp, suggesting their possible use for the same types of applications. Sweet clovers therefore constitute a new source of fibers that can be cultivated on wet and saline soils not otherwise suitable for agriculture