Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator

Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\epsilon = -\partial_x^2 + x^2 + i\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued function and $\epsilon > 0$ a small parameter. We define $\Sigma(\epsilon)$ as the infimum of the real part of the spectrum of $H_\epsilon$, and $\Psi(\epsilon)^{-1}$ as the supremum of the norm of the resolvent of $H_\epsilon$ along the imaginary axis. Under appropriate conditions on $f$, we show that both quantities $\Sigma(\epsilon)$, $\Psi(\epsilon)$ go to infinity as $\epsilon \to 0$, and we give precise estimates of the growth rate of $\Psi(\epsilon)$. We also provide an example where $\Sigma(\epsilon)$ is much larger than $\Psi(\epsilon)$ if $\epsilon$ is small. Our main results are established using variational "hypocoercive" methods, localization techniques and semiclassical subelliptic estimates.Comment: 38 pages, 4 figure

Fine properties of self-similar solutions of the Navier-Stokes equations

We study the solutions of the nonstationary incompressible Navier--Stokes equations in $\R^d$, $d\ge2$, of self-similar form $u(x,t)=\frac{1}{\sqrt t}U\bigl(\frac{x}{\sqrt t}\bigr)$, obtained from small and homogeneous initial data $a(x)$. We construct an explicit asymptotic formula relating the self-similar profile $U(x)$ of the velocity field to its corresponding initial datum $a(x)$

Orbital stability: analysis meets geometry

We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and the corresponding momentum maps is proposed that allows us to highlight the interplay between (symplectic) geometry and (functional) analysis in the proofs of orbital stability of relative equilibria via the so-called energy-momentum method. The theory is illustrated with examples from finite dimensional systems, as well as from Hamiltonian PDE's, such as solitons, standing and plane waves for the nonlinear Schr{\"o}dinger equation, for the wave equation, and for the Manakov system

Predictors of residual antimalarial drugs in the blood in community surveys in Tanzania.

Understanding pattern of antimalarials use at large scale helps ensuring appropriate use of treatments and preventing the spread of resistant parasites. We estimated the proportion of individuals in community surveys with residual antimalarials in their blood and identified the factors associated with the presence of the most commonly detected drugs, lumefantrine and/or desbutyl-lumefantrine (LF/DLF) or sulfadoxine-pyrimethamine (SP). A cross-sectional survey was conducted in 2015 in three regions of Tanzania with different levels of malaria endemicity. Interviews were conducted and blood samples collected through household surveys for further antimalarial measurements using liquid chromatography coupled to tandem mass spectrometry. In addition, diagnosis and treatment availability was investigated through outlet surveys. Multilevel mixed effects logistic regression models were used to estimate odds ratios for having LF/DLF or SP in the blood. Amongst 6391 participants, 12.4% (792/6391) had LF/DLF and 8.0% (510/6391) SP in the blood. Factors associated with higher odds of detecting LF/DLF in the blood included fever in the previous two weeks (OR = 2.6, p<0.001), living in districts of higher malaria prevalence (OR = 1.5, p<0.001) and living in a ward in which all visited drug stores had artemisinin-based combination therapies in stocks (OR = 2.7, p = 0.020). Participants in older age groups were less likely to have LF/DLF in the blood (OR = 0.9, p<0.001). Factors associated with higher odds of having SP in the blood included being pregnant (OR = 4.6, p<0.001), living in Mwanza (OR = 3.9, p<0.001 compared to Mbeya), fever in the previous two weeks (OR = 1.7, p<0.001) and belonging to older age groups (OR = 1.2, p<0.001). The most significant predictors identified were expected. History of fever in the past two weeks and young age were significant predictors of LF/DLF in the blood, which is encouraging. Antimalarial drug pressure was high and hence the use of recommended first-line drugs in combination with malaria Rapid Diagnostics Tests should be promoted to ensure appropriate treatment

Human papillomavirus (HPV) contamination of gynaecological equipment.

OBJECTIVE: The gynaecological environment can become contaminated by human papillomavirus (HPV) from healthcare workers' hands and gloves. This study aimed to assess the presence of HPV on frequently used equipment in gynaecological practice. METHODS: In this cross-sectional study, 179 samples were taken from fomites (glove box, lamp of a gynaecological chair, gel tubes for ultrasound, colposcope and speculum) in two university hospitals and in four gynaecological private practices. Samples were collected with phosphate-buffered saline-humidified polyester swabs according to a standardised pattern, and conducted twice per day for 2 days. The samples were analysed by a semiquantitative real-time PCR. Statistical analysis was performed using Pearson's χ(2) test and multivariate regression analysis. RESULTS: Thirty-two (18%) HPV-positive samples were found. When centres were compared, there was a higher risk of HPV contamination in gynaecological private practices compared with hospitals (OR 2.69, 95% CI 1.06 to 6.86). Overall, there was no difference in the risk of contamination with respect to the time of day (OR 1.79, 95% CI 0.68 to 4.69). When objects were compared, the colposcope had the highest risk of contamination (OR 3.02, 95% CI 0.86 to 10.57). CONCLUSIONS: Gynaecological equipment and surfaces are contaminated by HPV despite routine cleaning. While there is no evidence that contaminated surfaces carry infectious viruses, our results demonstrate the need for strategies to prevent HPV contamination. These strategies, based on health providers' education, should lead to well-established cleaning protocols, adapted to gynaecological rooms, aimed at eliminating HPV material

European divertor target concepts for DEMO: Design rationales and high heat flux performance

The divertor target plates are the most thermally loaded in-vessel components in a fusion reactor where high heat fluxes are produced on the plasma-facing components (PFCs) by intense plasma bombardment, radiation and nuclear heating. For reliable exhaust of huge thermal power, robust and durable divertor target PFCs with a sufficiently large heat removal capability and lifetime has to be developed. Since 2014 in the framework of the preconceptual design activities of the EUROfusion DEMO project, integrated R&D efforts have been made in the subproject ‘Target development’ of the work package ‘Divertor’ to develop divertor target PFCs for DEMO. Recently, the first R&D phase was concluded where six (partly novel) target PFC concepts were developed and evaluated by means of non-destructive inspections and high-heat-flux fatigue testing. In this paper, the major achievements of the first phase activities in this subproject are presented focusing on the design rationales of the target PFC concepts, technology options employed for small-scale mock-up fabrication and the results of the first round high-heat-flux qualification test campaign. It is reported that the mock-ups of three PFC concepts survived up to 500 loading cycles at 20 MW/m² (with hot water cooling at 130 °C) without any discernable indication of degradation in performance or structural integrity

The ClpX chaperone controls autolytic splitting of Staphylococcus aureus daughter cells, but is bypassed by β-lactam antibiotics or inhibitors of WTA biosynthesis.

β-lactam antibiotics interfere with cross-linking of the bacterial cell wall, but the killing mechanism of this important class of antibiotics is not fully understood. Serendipitously we found that sub-lethal doses of β-lactams rescue growth and prevent spontaneous lysis of Staphylococcus aureus mutants lacking the widely conserved chaperone ClpX, and we reasoned that a better understanding of the clpX phenotypes could provide novel insights into the downstream effects of β-lactam binding to the PBP targets. Super-resolution imaging revealed that clpX cells display aberrant septum synthesis, and initiate daughter cell separation prior to septum completion at 30°C, but not at 37°C, demonstrating that ClpX becomes critical for coordinating the S. aureus cell cycle as the temperature decreases. FtsZ localization and dynamics were not affected in the absence of ClpX, suggesting that ClpX affects septum formation and autolytic activation downstream of Z-ring formation. Interestingly, oxacillin antagonized the septum progression defects of clpX cells and prevented lysis of prematurely splitting clpX cells. Strikingly, inhibitors of wall teichoic acid (WTA) biosynthesis that work synergistically with β-lactams to kill MRSA synthesis also rescued growth of the clpX mutant, as did genetic inactivation of the gene encoding the septal autolysin, Sle1. Taken together, our data support a model in which Sle1 causes premature splitting and lysis of clpX daughter cells unless Sle1-dependent lysis is antagonized by β-lactams or by inhibiting an early step in WTA biosynthesis. The finding that β-lactams and inhibitors of WTA biosynthesis specifically prevent lysis of a mutant with dysregulated autolytic activity lends support to the idea that PBPs and WTA biosynthesis play an important role in coordinating cell division with autolytic splitting of daughter cells, and that β-lactams do not kill S. aureus simply by weakening the cell wall

Large time existence for 3D water-waves and asymptotics

We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a ``variable'' nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep-water, from small to large surface and bottom variations, and from fully to weakly transverse waves. The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and the energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and remarks added) To appear in Inventione