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This paper deals with the electrical conductivity problem in geophysics. It is formulated as an elliptic boundary value problem of second order for a large class of bounded and unbounded domains. A special boundary condition, the so called "Complete Electrode Model", is used. Poincaré inequalities are formulated and proved in the context of weighted Sobolev spaces, leading to existence and uniqueness statements for the boundary value problem. In addition, a parameter-to-solution operator arising from the inverse conductivity problem in medicine (EIT) and geophysics is investigated mathematically and is shown to be smooth and analytic.
The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.
Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}
We present results of full 3D hydrodynamical and radiative transfer simulations of the colliding stellar winds in the massive binary system η Carinae. We accomplish this by applying the SimpleX algorithm for 3D radiative transfer on an unstructured Voronoi-Delaunay grid to recent 3D smoothed particle hydrodynamics (SPH) simulations of the binary colliding winds. We use SimpleX to obtain detailed ionization fractions of hydrogen and helium, in 3D, at the resolution of the original SPH simulations. We investigate several computational domain sizes and Luminous Blue Variable primary star mass-loss rates. We furthermore present new methods of visualizing and interacting with output from complex 3D numerical simulations, including 3D interactive graphics and 3D printing. While we initially focus on η Car, the methods employed can be applied to numerous other colliding wind (WR 140, WR 137, WR 19) and dusty `pinwheel' (WR 104, WR 98a) binary systems. Coupled with 3D hydrodynamical simulations, SimpleX simulations have the potential to help determine the regions where various observed time-variable emission and absorption lines form in these unique objects.
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T−h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
The total population of Wolf-Rayet (WR) stars in the Galaxy is predicted by models to be as many as ~6000 stars, and yet the number of catalogued WR stars as a result of optical surveys was far lower than this (~200) at the turn of this century. When beginning our WR searches using infrared techniques it was not clear whether WR number predictions were too optimistic or whether there was more hidden behind interstellar and circumstellar extinction. During the last decade we pioneered a technique of exploiting the near- and mid-infrared continuum colours for individual point sources provided by large-format surveys of the Galaxy, including 2MASS and Spitzer/GLIMPSE, to pierce through the dust and reveal newly discovered WR stars throughout the Galactic Plane. The key item to the colour discrimination is via the characteristic infrared spectral index produced by the strong winds of the WR stars, combined with dust extinction, which place WR stars in a relatively depopulated area of infrared colour-colour diagrams. The use of the Spitzer/GLIMPSE 8µm and, more recently, WISE 22µm fluxes together with cross-referencing with X-ray measurements in selected Galactic regions have enabled improved candidate lists that increased our confirmation success rate, achieved via follow-up infrared and optical spectroscopy. To date a total of 102 new WR stars have been found with many more
candidates still available for follow-up. This constitutes an addition of ~16% to the current
inventory of 642 Galactic WR stars. In this talk we review our methods and provide some
new results and a preliminary review of their stellar and interstellar medium environments. We provide a roadmap for the future of this search, including statistical modeling, and what we can add to star formation and high mass star evolution studies.
We present results of investigation of spectral variability of one of the most interesting massive stars, Romano's star (M33/V532 or GR290), located in the M33 galaxy. Brightness of the star changes together with its spectral class, which varies from WN11 to WN8. Using CMFGEN code we estimated parameters of stellar atmosphere and found that during last ten years bolometric luminosity of the star changed synchronously with stellar magnitude. Our calculations argue in favor of the hypothesis of a post-LBV status of GR290.
We summarize past and current surveys for WRs among the Local Group galaxies, empha- sizing both the why and how. Such studies are invaluable for helping us learn about massive star evolution, and for providing sensitive tests of the stellar evolution models. But for such surveys to be useful, the completeness limits must be well understood. We illustrate that point by following the “evolution” of the observed WC/WN ratio in nearby galaxies. We end by examining our new survey for WR stars in the Magellanic Clouds, which has revealed a new type of WN star, never before seen.
Helium stars
(2015)
There are outstanding problems in trying to reproduce the observed nature of Wolf–Rayet stars from theoretical stellar models. We have investigated the effects of uncertainties, such as composition and mass-loss rate, on the evolution and structure of Wolf–Rayet stars and their lower mass brethren. We find that the normal Conti scenario needs to be altered, with different WR types being due to different initial masses as well as different stages of evolution.
Ring Nebulae
(2015)
Preliminary results are presented from spectroscopic data in the optical range of the Galactic ring nebulae NGC 6888, G2:4+1:4, RCW 58 and Sh2-308. Deep observations with long exposure times were carried out at the 6.5m Clay Telescope and at the 10.4m Gran Telescopio Canarias. In NGC 6888, recombination lines of C ii, O ii and N ii are detected with signal-to-noise ratios higher than 8. The chemical content of NGC 6888 is discussed within the chemical enrichment predicted by evolution models of massive stars. For all nebulae, a forthcoming work will content in-depth details about observations, analysis and final results (Esteban et al. 2015, in prep.).