Averaging lemmas with a force term in the transport equation

We obtain several averaging lemmas for transport operator with a force term. These lemmas improve the regularity yet known by not considering the force term as part of an arbitrary right-hand side. Two methods are used: local variable changes or stationary phase. These new results are subjected to two non degeneracy assumptions. We characterize the optimal conditions of these assumptions to compare the obtained regularities according to the space and velocity variables. Our results are mainly in $L^2$, and for constant force, in $L^p$ for $1<p \leq 2$

A model for the formation and evolution of traffic jams

In this paper, we establish and analyze a traffic flow model which describes the formation and dynamics of traffic jams. It consists of a pressureless gas dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. From this analysis, we deduce the particular dynamical behavior of clusters (or traffic jams), defined as intervals where the density limit is reached. An existence result for a generic class of initial data is proved by means of an approximation of the solution by a sequence of clusters. Finally, numerical simulations are produced

L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method

We consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L^2 perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L^2 norm of a perturbed solution relative to the shock wave is bounded above by the L^2 norm of the initial perturbation.Comment: 17 page

Two-way multi-lane traffic model for pedestrians in corridors

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian density cannot exceed a maximal density corresponding to contact between pedestrians. In a first step, we propose a singularly perturbed pressure relation which models the fact that the pedestrian velocity is considerably reduced, if not blocked, at congestion. In a second step, we carry over the singular limit into the model and show that abrupt transitions between compressible flow (in the uncongested regions) to incompressible flow (in congested regions) occur. We also investigate the hyperbolicity of the two-way models and show that they can lose their hyperbolicity in some cases. We study a diffusive correction of these models and discuss the characteristic time and length scales of the instability

Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non BV perturbations

We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of large amplitude) among bounded entropic weak solutions having an additional trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness condition. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.Comment: 29 page

Congestion in a macroscopic model of self-driven particles modeling gregariousness

International audienceWe analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper investigates the transition between the compressible and incompressible regions. To capture this transition, we study a one-dimensional Riemann problem and introduce a perturbation problem which regularizes the compressible-incompressible transition. Specific difficulties related to the non-conservativity of the problem are discussed

Weak-strong uniqueness for the isentropic compressible Navier-Stokes system

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong uniqueness results are improved. Classical uniqueness results for this equation follow naturally.Comment: 12 page

Gametogenesis in the Pacific Oyster Crassostrea gigas: A Microarrays-Based Analysis Identifies Sex and Stage Specific Genes

Background: The Pacific oyster Crassostrea gigas (Mollusca, Lophotrochozoa) is an alternative and irregular protandrous hermaphrodite: most individuals mature first as males and then change sex several times. Little is known about genetic and phenotypic basis of sex differentiation in oysters, and little more about the molecular pathways regulating reproduction. We have recently developed and validated a microarray containing 31,918 oligomers (Dheilly et al., 2011) representing the oyster transcriptome. The application of this microarray to the study of mollusk gametogenesis should provide a better understanding of the key factors involved in sex differentiation and the regulation of oyster reproduction. Methodology/Principal Findings: Gene expression was studied in gonads of oysters cultured over a yearly reproductive cycle. Principal component analysis and hierarchical clustering showed a significant divergence in gene expression patterns of males and females coinciding with the start of gonial mitosis. ANOVA analysis of the data revealed 2,482 genes differentially expressed during the course of males and/or females gametogenesis. The expression of 434 genes could be localized in either germ cells or somatic cells of the gonad by comparing the transcriptome of female gonads to the transcriptome of stripped oocytes and somatic tissues. Analysis of the annotated genes revealed conserved molecular mechanisms between mollusks and mammals: genes involved in chromatin condensation, DNA replication and repair, mitosis and meiosis regulation, transcription, translation and apoptosis were expressed in both male and female gonads. Most interestingly, early expressed male-specific genes included bindin and a dpy-30 homolog and female-specific genes included foxL2, nanos homolog 3, a pancreatic lipase related protein, cd63 and vitellogenin. Further functional analyses are now required in order to investigate their role in sex differentiation in oysters. Conclusions/Significance: This study allowed us to identify potential markers of early sex differentiation in the oyster C. gigas, an alternative hermaphrodite mollusk. We also provided new highly valuable information on genes specifically expressed by mature spermatozoids and mature oocytes