Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

High-resolution Keck I spectroscopy of Galactic halo post-asymptotic giant branch stars

Absolute and differential abundance analyses have been performed from high-resolution, high signal-to-noise ratio optical (Keck I) spectra for three evolved Galactic halo stars, namely PG 1704 + 222, HD 341617 and LSIV -0401. Their derived atmospheric parameters indicate that all three objects are undergoing a post-asymptotic giant branch (post-AGB) phase of evolution. A differential abundance analysis reveals HD 341617 as having a mild carbon deficiency of 0.74 dex, possibly due to the star having evolved off the AGB before the onset of the third dredge-up. Although such carbon underabundances are typical of hot post-AGB objects, the same trend is not observed in PG 1704 + 222, where the carbon abundance is found to be consistent with those derived for nitrogen and oxygen. Hence, a dredge-up scenario need not be invoked to explain the chemical composition of PG 1704 + 222. For LSIV -0401 no iron deficiency is apparent relative to magnesium and silicon, and hence a gas- dust separation event in the AGB progenitor need not be invoked for this star.

High-resolution spectroscopic observations of post-asymptotic giant branch candidates from the Edinburgh-Cape Survey

High spectral resolution ( R similar to 40 000) and signal-to-noise optical spectra, obtained at the Very Large Telescope ( VLT), are presented for three post-asymptotic giant branch ( AGB) candidates selected from the Edinburgh-Cape ( EC) Faint Blue Object Survey. The stellar atmospheric parameters and chemical compositions, derived using sophisticated non-local thermodynamic equilibrium calculations, reveal that EC 14102-1337 and EC 20068-7324 are both in an evolved post-horizontal branch ( HB) evolutionary state. However, EC 11507-2253 is most likely a post-AGB star.

High-resolution spectroscopy of globular cluster post-Asymptotic Giant Branch stars

We present model atmosphere analyses of high resolution Keck and VLT optical spectra for three evolved stars in globular clusters, viz. ZNG-1 in M 10, ZNG-1 in M 15 and ZNG-1 in NGC 6712. The derived atmospheric parameters and chemical compositions confirm the programme stars to be in the post- Asymptotic Giant Branch (post-AGB) evolutionary phase. Differential abundance analyses reveal CNO abundance patterns in M 10 ZNG-1, and possibly M 15 ZNG-1, which Suggest that both objects may have evolved off the AGB before the third dredge-up occurred. The abundance pattern of these stars is similar to the third class of optically, bright post-AGB objects discussed by van Winckel (1997). Furthermore, M 10 ZNG-1 exhibits a large C underabundance (with Delta[C/O] similar to -1.6 dex), typical of other hot post-AGB objects. Differential Delta[alpha/Fe] abundance ratios in both M 10 ZNG-1 and NGC 6712 ZNG-1 are found to be approximately 0.0 dex, with the Fe abundance of the former being in disagreement with the cluster metallicity of M 10. Given that the Fe absorption features in both M 10 ZNG-1 and NGC6712 ZNG-1 are well observed and reliably modelled, we believe that these differential Fe abundance estimates to be secure. However, our Fe abundance is difficult to explain in terms of previous evolutionary processes that Occur oil both the Horizontal Branch and the AGB.

Iron abundances of B-type post-asymptotic giant branch stars in globular clusters: Barnard29 in M13 and ROA5701 in ωCen

High-resolution optical and ultraviolet (UV) spectra of two B-type post-asymptotic giant branch (post-AGB) stars in globular clusters, Barnard29 in M13 and ROA5701 in ?Cen, have been analysed using model atmosphere techniques. The optical spectra have been obtained with FEROS on the ESO 2.2-m telescope and the 2d-Coudé spectrograph on the 2.7-m McDonald telescope, while the UV observations are from the Goddard high-resolution spectrograph on the Hubble Space Telescope (HST). Abundances of light elements (C, N, O, Mg, Al and S) plus Fe have been determined from the optical spectra, while the UV data provide additional Fe abundance estimates from FeIII absorption lines in the 1875-1900 Å wavelength region. A general metal underabundance relative to young B-type stars is found for both Barnard29 and ROA5701. These results are consistent with the metallicities of the respective clusters, as well as with previous studies of the objects. The derived abundance patterns suggest that the stars have not undergone a gas-dust separation, contrary to previous suggestions, although they may have evolved from the AGB before the onset of the third dredge-up. However, the Fe abundances derived from the HST spectra are lower than those expected from the metallicities of the respective clusters, by 0.5 dex for Barnard29 and 0.8 dex for ROA5701. A similar systematic underabundance is also found for other B-type stars in environments of known metallicity, such as the Magellanic Clouds. These results indicate that the FeIII UV lines may yield abundance values which are systematically too low by typically 0.6 dex and hence such estimates should be treated with caution.

Chemistry in anisotropic asymptotic giant branch winds

We have constructed a model for chemistry in the outflow of an asymptotic giant branch (AGB) star, using a spheroidal anisotropy in density, after that used by Jura. The predicted distributions of a selection of representative species are shown, and it is suggested that the abundance distributions observed by interferometry in IRC + 10216 may be the result of directional variation in outflow velocity.

Ruling out a massive asymptotic giant-branch star as the progenitor of supernova 2005cs

We calculate the predicted UBVRIJHK absolute magnitudes for models of supernova progenitors and apply the result to the case of supernova 2005cs. We agree with previous results that the initial mass of the star was low, around 6 to 8 M-circle dot. However, such stars are thought to go through a second dredge-up to become asymptotic giant branch (AGB) stars. We show that had this occurred to the progenitor of 2005cs it would have been observed in JHK pre-explosion images. The progenitor was not detected in these bands and therefore we conclude that it was not an AGB star. Furthermore, if some AGB stars do produce supernovae they will have a clear signature in pre-explosion near-infrared images. Electron-capture supernovae are thought to occur in AGB stars, hence the implication is that 2005cs was not an electron-capture supernova but was the collapse of an iron core.

Asymptotic layer-type model of high pressure direct current glow discharge in electronegative gases

Here a self-consistent one-dimensional continuum model is presented for a narrow gap plane-parallel dc glow discharge. The governing equations consist of continuity and momentum equations for positive and negative ions and electrons coupled with Poisson's equation. A singular perturbation method is developed for the analysis of high pressure dc glow discharge. The kinetic processes of the ionization, electron attachment, and ion-ion recombination are included in the model. Explicit results are obtained for the asymptotic limits: delta=(r(D)/L)(2)--> 0, omega=(r(S)/L)(2)--> 0, where r(D) is the Debye radius, r(S) is recombination length, and L is the gap length. The discharge gap divides naturally into four layers with multiple space scales: anode fall region, positive column, transitional region, cathode fall region and diffusion layer adjacent to the cathode surface, its formation is discussed. The effects of the gas pressure, gap spacing and dc voltage on the electrical properties of the layers and its dimension are investigated. (C) 2000 American Institute of Physics. [S0021-8979(00)00813-6].

Asymptotic modeling of short plane-parallel high-pressure glow discharge

Here a self-consistent continuum model is presented for a narrow gap plane-parallel dc glow discharge. The set of governing equations consisting of continuity and momentum equations for positive ions, fast (emitted by the cathode) and slow electrons (generated by fast electron impact ionization) coupled with Poisson's equation is treated by the technique of matched asymptotic expansions. Explicit results are obtained in the asymptotic limit: (chi delta) much less than 1, where chi = e Phi(a)/kT, delta = (r(D)/L)(2) (Phi(a) is the applied voltage, r(D) is the Debye radius) and pL much greater than 1(Hg mm cm), where p is the gas pressure and L is the gap length. In the case of high pressure, the electron energy relaxation length is much smaller than the gap length, and so the local field approximation is valid. The discharge space divides naturally into a cathode fall sheath, a quasineutral plasma region, and an anode fall sheath. The electric potential distribution obtained for each region in a (semi)analytical form is asymptotically matched to the adjoining regions in the region of overlap. The effects of the gas pressure, gap length, and applied voltage on the length of each region are investigated. (C) 2000 American Institute of Physics. [S1070-664X(00)01302-1].

Detection of sensor decalibration using the asymptotic local approach

A novel method for the detection of linear decalibration of sensors is proposed. The presence of a fault is indicated as a change in the mean of a white noise sequence. A simulation example is described which shows the success of the technique.