Stability with respect to domain of the low Mach number limit of compressible viscous fluids

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter \ep \to 0 and the fluid is confined to an exterior spatial domain \Omega_\ep that may vary with \ep. As $\epsilon \rightarrow 0$, it is shown that the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier-Stokes equations on a limit domain. The velocities approach the limit strongly (a.a.) on any compact set, uniformly with respect to a certain class of domains. The proof is based on spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.Comment: 32 page

Time quasi-periodic gravity water waves in finite depth

We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions\u2014namely periodic and even in the space variable x\u2014of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the fully nonlinear nature of the gravity water waves equations\u2014the highest order x-derivative appears in the nonlinear term but not in the linearization at the origin\u2014and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators, obtained at each approximate quasi-periodic solution along a Nash\u2013Moser iterative scheme, to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions which lose derivatives both in time and space. Despite the fact that the depth parameter moves the linear frequencies by just exponentially small quantities, we are able to verify such non-resonance conditions for most values of the depth, extending degenerate KAM theory

Flexible Mode Modelling of the InSight Lander and Consequences for the SEIS Instrument

We present an updated model for estimating the lander mechanical noise on the InSight seismometer SEIS, taking into account the flexible modes of the InSight lander. This new flexible mode model uses the Satellite Dynamics Toolbox to compute the direct and the inverse dynamic model of a satellite composed of a main body fitted with one or several dynamic appendages. Through a detailed study of the sensitivity of our results to key environment parameters we find that the frequencies of the six dominant lander resonant modes increase logarithmically with increasing ground stiffness. On the other hand, the wind strength and the incoming wind angle modify only the signal amplitude but not the frequencies of the resonances. For the baseline parameters chosen for this study, the lander mechanical noise on the SEIS instrument is not expected to exceed the instrument total noise requirements. However, in the case that the lander mechanical noise is observable in the seismic data acquired by SEIS, this may provide a complementary method for studying the ground and wind properties on Mars

Economic activity and congenital anomalies: An ecologic study in Argentina

In this study, we analyze the association between industrial activity and the occurrence of 34 congenital anomalies. We selected 21 counties in Argentina during 1982-1994 and examined a total of 614,796 births in these counties in consecutive series. We used the International Standard Industrial Classification of All Economic Activities as an indicator of exposure to 80 specific industrial activities. Incidence rate ratios for each congenital anomaly were adjusted by the socioeconomic level of the county according to a census index of social deprivation. For a given exposure/anomaly association to be considered as significant and relevant, the exposure had to be a statistically significant risk for the occurrence of the anomaly and an increase in the birth prevalence rate of the congenital anomaly type involved had to be observed in those counties where the putative causal activity was being performed. Significant associations (p < 0.01) were identified between textile industry and anencephaly, and between the manufacture of engines and turbines and microcephaly. These observations are consistent with previous reports on occupational exposure, and their further investigation by means of case-control studies is recommended.Instituto Multidisciplinario de Biología Celula

Economic activity and congenital anomalies: An ecologic study in Argentina

In this study, we analyze the association between industrial activity and the occurrence of 34 congenital anomalies. We selected 21 counties in Argentina during 1982-1994 and examined a total of 614,796 births in these counties in consecutive series. We used the International Standard Industrial Classification of All Economic Activities as an indicator of exposure to 80 specific industrial activities. Incidence rate ratios for each congenital anomaly were adjusted by the socioeconomic level of the county according to a census index of social deprivation. For a given exposure/anomaly association to be considered as significant and relevant, the exposure had to be a statistically significant risk for the occurrence of the anomaly and an increase in the birth prevalence rate of the congenital anomaly type involved had to be observed in those counties where the putative causal activity was being performed. Significant associations (p < 0.01) were identified between textile industry and anencephaly, and between the manufacture of engines and turbines and microcephaly. These observations are consistent with previous reports on occupational exposure, and their further investigation by means of case-control studies is recommended.Instituto Multidisciplinario de Biología Celula

RNA polymerase II stalling promotes nucleosome occlusion and pTEFb recruitment to drive immortalization by Epstein-Barr virus

Epstein-Barr virus (EBV) immortalizes resting B-cells and is a key etiologic agent in the development of numerous cancers. The essential EBV-encoded protein EBNA 2 activates the viral C promoter (Cp) producing a message of ~120 kb that is differentially spliced to encode all EBNAs required for immortalization. We have previously shown that EBNA 2-activated transcription is dependent on the activity of the RNA polymerase II (pol II) C-terminal domain (CTD) kinase pTEFb (CDK9/cyclin T1). We now demonstrate that Cp, in contrast to two shorter EBNA 2-activated viral genes (LMP 1 and 2A), displays high levels of promoter-proximally stalled pol II despite being constitutively active. Consistent with pol II stalling, we detect considerable pausing complex (NELF/DSIF) association with Cp. Significantly, we observe substantial Cp-specific pTEFb recruitment that stimulates high-level pol II CTD serine 2 phosphorylation at distal regions (up to +75 kb), promoting elongation. We reveal that Cp-specific pol II accumulation is directed by DNA sequences unfavourable for nucleosome assembly that increase TBP access and pol II recruitment. Stalled pol II then maintains Cp nucleosome depletion. Our data indicate that pTEFb is recruited to Cp by the bromodomain protein Brd4, with polymerase stalling facilitating stable association of pTEFb. The Brd4 inhibitor JQ1 and the pTEFb inhibitors DRB and Flavopiridol significantly reduce Cp, but not LMP1 transcript production indicating that Brd4 and pTEFb are required for Cp transcription. Taken together our data indicate that pol II stalling at Cp promotes transcription of essential immortalizing genes during EBV infection by (i) preventing promoter-proximal nucleosome assembly and ii) necessitating the recruitment of pTEFb thereby maintaining serine 2 CTD phosphorylation at distal regions

Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems

A rigorous justification of several well-known mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled Navier-Stokes-Fourier system, where some of the characteristic numbers become small or large enough. We discuss the problem in the framework of global-in-time solutions for both the primitive and the target system. © 2010 Springer Basel AG

On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media

We consider the zero-electron-mass limit for the Navier-Stokes-Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier-Stokes system