Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits. We also propose a kinetic formulation for the Hall-MHD equations which contains as fluid closure different variants of the Hall-MHD model. Then, we prove the existence of global weak solutions for the incompressible viscous resistive Hall-MHD model. We use the particular structure of the Hall term which has zero contribution to the energy identity. Finally, we discuss particular solutions in the form of axisymmetric purely swirling magnetic fields and propose some regularization of the Hall equation

An effective mass theorem for the bidimensional electron gas in a strong magnetic field

We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr\"odinger equations in the plane $(x,y)$, coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator

PDE4 as a target in preterm labour

Cyclic nucleotide phosphodiesterases (PDE) are the enzymes catalyzing the hydrolysis and inactivation of the second messengers, cAMP and cGMP. Eleven PDE families are described to date, and selective inhibitors of some PDEs families are currently used in clinic for treating cardiovascular disorders, erectile dysfunction, and pulmonary hypertension. Isoforms of the PDE4 family are involved in smooth muscle contraction and inflammation. PDE4 selective inhibitors are currently in clinical trials for the treatment of diseases related to inflammatory disorders. Because of their myorelaxant properties, we first examined their expression in human myometrium and uncover an increased expression of one specific isoform, PDE4B2, in the near-term myometrium as compared to myometrium in the nonpregnant state. Using human myometrial cells in culture, we demonstrated that PDE4B2 can be induced by its own substrate, under the control of one of the major utero-contractile agonists, PGE2, itself upregulated by the proinflammatory cytokine IL-1β. Functionally, augmentation of global PDE4 activity decreases the ability of β-adrenergic agonists (the most commonly used tocolytic drugs) to inhibit myometrial contraction at the end of pregnancy and during pathophysiological situations, such as persistent intrauterine inflammation which is a major cause of very preterm delivery. Currently exploring the anti-inflammatory properties of PDE4 inhibitors in gestational tissues, we recently demonstrated the ability of these drugs to block a persistent inflammatory response of the foetal membranes in Humans and to prevent inflammation-driven preterm delivery and foetal demise in mice. These data open up a new therapeutical strategy to prevent inflammation-induced preterm delivery and its sequelae in very preterm infants

Pan-Genomic Regulation of Gene Expression in Normal and Pathological Human Placentas.

In this study, we attempted to find genetic variants affecting gene expression (eQTL = expression Quantitative Trait Loci) in the human placenta in normal and pathological situations. The analysis of gene expression in placental diseases (Pre-eclampsia and Intra-Uterine Growth Restriction) is hindered by the fact that diseased placental tissue samples are generally taken at earlier gestations compared to control samples. The difference in gestational age is considered a major confounding factor in the transcriptome regulation of the placenta. To alleviate this significant problem, we propose here a novel approach to pinpoint disease-specific cis-eQTLs. By statistical correction for gestational age at sampling as well as other confounding/surrogate variables systematically searched and identified, we found 43 e-genes for which proximal SNPs influence expression level. Then, we performed the analysis again, removing the disease status from the covariates, and we identified 54 e-genes, 16 of which are identified de novo and, thus, possibly related to placental disease. We found a highly significant overlap with previous studies for the list of 43 e-genes, validating our methodology and findings. Among the 16 disease-specific e-genes, several are intrinsic to trophoblast biology and, therefore, constitute novel targets of interest to better characterize placental pathology and its varied clinical consequences. The approach that we used may also be applied to the study of other human diseases where confounding factors have hampered a better understanding of the pathology

A new variational approach to the stability of gravitational systems

We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system subject to its own gravity. A well-known conjecture in astrophysics is that the steady state solutions which are nonincreasing functions of their microscopic energy are nonlinearly stable by the flow. This was proved at the linear level by several authors based on the pioneering work by Antonov in 1961. Since then, standard variational techniques based on concentration compactness methods as introduced by P.-L. Lions in 1983 have led to the nonlinear stability of subclasses of stationary solutions of ground state type. In this paper, inspired by pioneering works from the physics litterature (Lynden-Bell 94, Wiechen-Ziegler-Schindler MNRAS 88, Aly MNRAS 89), we use the monotonicity of the Hamiltonian under generalized symmetric rearrangement transformations to prove that non increasing steady solutions are local minimizer of the Hamiltonian under equimeasurable constraints, and extract compactness from suitable minimizing sequences. This implies the nonlinear stability of nonincreasing anisotropic steady states under radially symmetric perturbations

Orbital stability of spherical galactic models

International audienceWe consider the three dimensional gravitational Vlasov Poisson system which is a canonical model in astrophysics to describe the dynamics of galactic clusters. A well known conjecture is the stability of spherical models which are nonincreasing radially symmetric steady states solutions. This conjecture was proved at the linear level by several authors in the continuation of the breakthrough work by Antonov in 1961. In a previous work, we derived the stability of anisotropic models under {\it spherically symmetric perturbations} using fundamental monotonicity properties of the Hamiltonian under suitable generalized symmetric rearrangements first observed in the physics litterature. In this work, we show how this approach combined with a {\it new generalized} Antonov type coercivity property implies the orbital stability of spherical models under general perturbations

Second order averaging for the nonlinear Schroedinger equation with strongly anisotropic potential

International audienceWe consider the three dimensional Gross-Pitaevskii equation (GPE) describing a Bose-Einstein Condensate (BEC) which is highly confi ned in vertical z direction. The highly confi ned potential induces high oscillations in time. If the confi nement in the z direction is a harmonic trap (which is widely used in physical experiments), the very special structure of the spectrum of the confi nement operator will imply that the oscillations are periodic in time. Based on this observation, it can be proved that the GPE can be averaged out with an error of order of epsilon, which is the typical period of the oscillations. In this article, we construct a more accurate averaged model, which approximates the GPE up to errors of order epsilon squared. Then, expansions of this model over the eigenfunctions (modes) of the vertical Hamiltonian Hz are given in convenience of numerical application. Effi cient numerical methods are constructed for solving the GPE with cylindrical symmetry in 3D and the approximation model with radial symmetry in 2D, and numerical results are presented for various kinds of initial data

Effects of Phosphodiesterase 4 Inhibition on Alveolarization and Hyperoxia Toxicity in Newborn Rats

International audienceBACKGROUND: Prolonged neonatal exposure to hyperoxia is associated with high mortality, leukocyte influx in airspaces, and impaired alveolarization. Inhibitors of type 4 phosphodiesterases are potent anti-inflammatory drugs now proposed for lung disorders. The current study was undertaken to determine the effects of the prototypal phosphodiesterase-4 inhibitor rolipram on alveolar development and on hyperoxia-induced lung injury. METHODOLOGY/FINDINGS: Rat pups were placed under hyperoxia (FiO2>95%) or room air from birth, and received rolipram or its diluent daily until sacrifice. Mortality rate, weight gain and parameters of lung morphometry were recorded on day 10. Differential cell count and cytokine levels in bronchoalveolar lavage and cytokine mRNA levels in whole lung were recorded on day 6. Rolipram diminished weight gain either under air or hyperoxia. Hyperoxia induced huge mortality rate reaching 70% at day 10, which was prevented by rolipram. Leukocyte influx in bronchoalveolar lavage under hyperoxia was significantly diminished by rolipram. Hyperoxia increased transcript and protein levels of IL-6, MCP1, and osteopontin; rolipram inhibited the increase of these proteins. Alveolarization was impaired by hyperoxia and was not restored by rolipram. Under room air, rolipram-treated pups had significant decrease of Radial Alveolar Count. CONCLUSIONS: Although inhibition of phosphodiesterases 4 prevented mortality and lung inflammation induced by hyperoxia, it had no effect on alveolarization impairment, which might be accounted for by the aggressiveness of the model. The less complex structure of immature lungs of rolipram-treated pups as compared with diluent-treated pups under room air may be explained by the profound effect of PDE4 inhibition on weight gain that interfered with normal alveolarization

On quantum extensions to classical Spherical Harmonics Expansion / Fokker-Planck models

By following a strategy introduced in previous works, quantum extensions of the classical electron-phonon scattering operator are deduced from first principles. These quantum collision operators satisfy a quantum H-theorem and relax towards quantum equilibria. Then, under an assumption of dominant elastic interactions, a hierarchy of quantum Spherical Harmonic Expansion (SHE) models is derived by a diffusive approximation of collisional Wigner equations. These models are proven entropic and their expansions into powers of the reduced Planck constant ℏ are calculated, leading to ℏ 2 corrections for the classical SHE model.

Antenatal Phosphodiesterase 4 Inhibition Restores Postnatal Growth and Pulmonary Development in a Model of Chorioamnionitis in Rabbits

International audienceChorioamnionitis is implicated in the pathophysiology of bronchopulmonary disease, and the associated inflammatory response is responsible for adverse effects on alveolar development. The aim of this work was to analyze the effects of a phosphodiesterase 4 (PDE4)-selective inhibitor, rolipram (a modulator of the inflammatory response), in an experimental model of chorioamnionitis on pulmonary development and on the processes of infection and inflammation. Rabbit mothers were assigned to four groups: 1) saline serum inoculation (controls); 2) Escherichia coli intrauterine inoculation (C+); 3) rolipram infusion (R+); and 4) E. coli inoculation + rolipram infusion (C+R+). High rates of morbility and mortality were noticed in mothers and pups (5 of 13 pregnant rabbits in groups with rolipram). Alveolar development, inflammation, and infection were analyzed in pups at day 0 and day 5. At day 0, in the context of chorioamnionitis, rolipram significantly decreased birth weight (p < 0.01) relative to that of controls (p < 0.05). At day 5, weight normalized in group C+R+ but not in group C+ relative to controls (p < 0.001); moreover, alveolar airspace volume was preserved in group C+R+ but not in group C+ (p < 0.05). Interstitial volume decreased in group C+ versus controls (p < 0.05) but was preserved in group C+R+. Specific alveolar area was not significantly modified by rolipram. No significant difference was found concerning bronchoalveolar lavage cellularity, and all blood cultures remained sterile. In this model of impaired alveologenesis, rolipram significantly preserved specific alveolar density. However, PDE4 inhibition induced antenatal fetal demise and growth retardation