Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.

The accretion environment in Vela X-1 during a flaring period using XMM-Newton

We present analysis of 100 ks contiguous XMM-Newton data of the prototypical wind accretor Vela X-1. The observation covered eclipse egress between orbital phases 0.134 and 0.265, during which a giant flare took place, enabling us to study the spectral properties both outside and during the flare. This giant flare with a peak luminosity of 3.92+0.42-0.09 × 1037 erg s-1 allows estimates of the physical parameters of the accreted structure with a mass of ~1021 g. We have been able to model several contributions to the observed spectrum with a phenomenological model formed by three absorbed power laws plus three emission lines. After analysing the variations with orbital phase of the column density of each component, as well as those in the Fe and Ni fluorescence lines, we provide a physical interpretation for each spectral component. Meanwhile, the first two components are two aspects of the principal accretion component from the surface of the neutron star, the third component seems to be the X-ray light echo formed in the stellar wind of the companion.

Water reduction in waste-activated sludge by resettling and filtration in batch. Phase (1): pilot-scale experiments to optimize performance

This article describes an effective procedure for reducing the water content of excess sludge production from a wastewater treatment plant by increasing its concentration and, as a consequence, minimizing the volume of sludge to be managed. It consists of a pre-dewatering sludge process, which is used as a preliminary step or alternative to the thickening. It is made up of two discontinuous sequential stages: the first is resettling and the second, filtration through a porous medium. The process is strictly physical, without any chemical additives or electromechanical equipment intervening. The experiment was carried out in a pilot-scale system, consisting of a column of sedimentation that incorporates a filter medium. Different sludge heights were tested over the filter to verify the influence of hydrostatic pressure on the various final concentrations of each stage. The results show that the initial sludge concentration may increase by more than 570% by the end of the process with the final volume of sludge being reduced in similar proportions and hydrostatic pressure having a limited effect on this final concentration. Moreover, the value of the hydrostatic pressure at which critical specific cake resistance is reached is established.

An XMM-Newton view of FeKα in high-mass X-ray binaries

We present a comprehensive analysis of the whole sample of available XMM-Newton observations of high-mass X-ray binaries (HMXBs) until August 2013, focusing on the FeKα emission line. This line is key to better understanding the physical properties of the material surrounding the X-ray source within a few stellar radii (the circumstellar medium). We collected observations from 46 HMXBs and detected FeKα in 21 of them. We used the standard classification of HMXBs to divide the sample into different groups. We find that (1) different classes of HMXBs display different qualitative behaviours in the FeKα spectral region. This is visible especially in SGXBs (showing ubiquitous Fe fluorescence but not recombination Fe lines) and in γ Cass analogues (showing both fluorescent and recombination Fe lines). (2) FeKα is centred at a mean value of 6.42 keV. Considering the instrumental and fits uncertainties, this value is compatible with ionization states that are lower than Fe xviii. (3) The flux of the continuum is well correlated with the flux of the line, as expected. Eclipse observations show that the Fe fluorescence emission comes from an extended region surrounding the X-ray source. (4) We observe an inverse correlation between the X-ray luminosity and the equivalent width of FeKα (EW). This phenomenon is known as the X-ray Baldwin effect. (5) FeKα is narrow (σline< 0.15 keV), reflecting that the reprocessing material does not move at high speeds. We attempt to explain the broadness of the line in terms of three possible broadening phenomena: line blending, Compton scattering, and Doppler shifts (with velocities of the reprocessing material V ~ 1000 km s-1). (6) The equivalent hydrogen column (NH) directly correlates to the EW of FeKα, displaying clear similarities to numerical simulations. It highlights the strong link between the absorbing and the fluorescent matter. (7) The observed NH in supergiant X-ray binaries (SGXBs) is in general higher than in supergiant fast X-ray transients (SFXTs). We suggest two possible explanations: different orbital configurations or a different interaction compact object – wind. (8) Finally, we analysed the sources IGR J16320-4751 and 4U 1700-37 in more detail, covering several orbital phases. The observed variation in NH between phases is compatible with the absorption produced by the wind of their optical companions. The results clearly point to a very important contribution of the donor’s wind in the FeKα emission and the absorption when the donor is a supergiant massive star.

Influence of sludge retention time on filtration performance and biomass characteristics in a hollow fiber membrane bioreactor

In this study, the filtration process and the biomass characteristics in a laboratory-scale submerged membrane bioreactor (MBR) equipped with a hollow fiber (HF) microfiltration membrane were studied at different solid retention times (SRT). The MBR was fed by synthetic wastewater and the organic loading rate (OLR) was 0.5, 0.2, 0.1, and 0.08 kg COD kg VSS−1 d−1 for 10, 30, 60, and 90 days of SRT, respectively. The hydraulic retention time was 8.4 h and the permeate flux was 6 L m−2 h−1(LMH). Data analysis confirmed that at all the studied SRTs, the HF-MBR operated very good obtaining of high quality permeates. Chemical Oxygen Demand (COD) removal efficiencies were higher than 95%. The best filtration performance was reached at SRT of 30 d. On the other hand, the respirometric analysis showed that biomass was more active and there was more biomass production at low SRTs. The concentration of soluble extracellular polymeric substances (EPS) decreased with increasing SRT. A decrease of soluble EPS caused a decrease of membrane fouling rate, decreasing the frequency of chemical cleanings. The floc size decreased with SRT increasing. At high SRTs, there was more friction among particles due to the increase of the cellular density and the flocs broke decreasing their size.