The Formation of Galactic Bulges

We summarise some recent results about nearby galactic bulges that are relevant to their formation. We highlight a number of significant advances in our understanding of the surface brightness profiles, stellar populations, and especially the very centers of spiral galaxies. We also view our own Milky Way as if it were an external galaxy. Our main conclusions are that bulges of early-type spirals (S0 -- Sb) contain central nuclear components, just like late-type spirals and most other types of galaxies. The luminosities of these central components correlate best with total bulge luminosity, and not as well with morphological type. Bulges of early-type spiral galaxies follow the fundamental plane and the colour/line strength vs. luminosity relations of elliptical galaxies. Although we have a reasonable idea about bulges of early-type spirals we know much less about late-type bulges. However, the close resemblance of our Milky Way Bulge to bulges in external disk galaxies makes us suspect that bulges of late-type spirals might be very similar as well.Comment: 10 pages, invited review presented at 'Baryons in Dark Matter', Novigrad Oct 5-9, 2004; eds. R. Dettmar, U. Klein and P. Salucci. On-line publication at http://pos.sissa.i

Small Volume Fraction Limit of the Diblock Copolymer Problem: II. Diffuse-Interface Functional

We present the second of two articles on the small volume fraction limit of a nonlocal Cahn-Hilliard functional introduced to model microphase separation of diblock copolymers. After having established the results for the sharp-interface version of the functional (arXiv:0907.2224), we consider here the full diffuse-interface functional and address the limit in which epsilon and the volume fraction tend to zero but the number of minority phases (called particles) remains O(1). Using the language of Gamma-convergence, we focus on two levels of this convergence, and derive first- and second-order effective energies, whose energy landscapes are simpler and more transparent. These limiting energies are only finite on weighted sums of delta functions, corresponding to the concentration of mass into `point particles'. At the highest level, the effective energy is entirely local and contains information about the size of each particle but no information about their spatial distribution. At the next level we encounter a Coulomb-like interaction between the particles, which is responsible for the pattern formation. We present the results in three dimensions and comment on their two-dimensional analogues

IAU Symposium 241 - Stellar Populations as Building Blocks of Galaxies

Stellar populations, building blocks of galaxies, are direct tracers of the star formation history, the chemical enrichment and the assembly of galaxies in the Universe. They therfore allow us to understand how galaxies formed and evolved. This last decade has witnessed a revolution in our observations of galaxies; with larger telescopes and new instruments we are not only able to look deeper in the Universe, we can also study nearby galaxies with greater detail. The fact that now is becoming possible to resolve stars up to the distance of Virgo Cluster allows us to rigorously compare and calibrate the analysis of the integrated light with resolved stellar populations. These Proceedings report the considerable progress made in recent years in this topic. Theorists and observers, researchers of resolved and unresolved stellar populations, discussed the ingredients of stellar population models, and rigorously compared them to new data, forcing theorists to develop more refined models and methods to derive the physical parameters of the stellar populations. New results from the Milky Way, the Local Group, and nearby and distant galaxies were presented.Comment: This is the table of contents of the upcoming proceedings of IAU Symposium 241. The book will appear in September, from Cambridge University Press, and will also be available electronically at http://www.journals.cambridge.org/action/displayJournal?jid=IA

Small Volume Fraction Limit of the Diblock Copolymer Problem: I. Sharp Interface Functional

We present the first of two articles on the small volume fraction limit of a nonlocal Cahn-Hilliard functional introduced to model microphase separation of diblock copolymers. Here we focus attention on the sharp-interface version of the functional and consider a limit in which the volume fraction tends to zero but the number of minority phases (called particles) remains O(1). Using the language of Gamma-convergence, we focus on two levels of this convergence, and derive first and second order effective energies, whose energy landscapes are simpler and more transparent. These limiting energies are only finite on weighted sums of delta functions, corresponding to the concentration of mass into `point particles'. At the highest level, the effective energy is entirely local and contains information about the structure of each particle but no information about their spatial distribution. At the next level we encounter a Coulomb-like interaction between the particles, which is responsible for the pattern formation. We present the results here in both three and two dimensions.Comment: 37 pages, 1 figur

Near-Infrared Surface Photometry of Bulges and Disks of Spiral Galaxies. The Data

We present optical and near-infrared (NIR) surface brightness and colour profiles,in bands ranging from U to K, for the disk and bulge components of a complete sample of 30 nearby S0 to Sbc galaxies with inclinations larger than 50 degrees. We describe in detail the observations and the determination of colour parameters. Calibrated monochromatic and real-colour images are presented, as well as colour index maps. This data set, tailored for the study of the population characteristics of galaxy bulges, provides useful information on the colours of inner disks as well. In related papers, we have used them to quantify colour gradients in bulges, and age differentials between bulge and inner disk.Comment: 18 pages Latex with 2 postscript figures. Accepted for New Astronomy. This is an electronic paper; a complete preprint, including all of the tables and figures can be found at ftp://www.astro.rug.nl/peletier/newast/newast.htm

Applied Mathematics, the Hans van Duijn way

This is a former PhD student's take on his teacher's scientific philosophy. I describe a set of 'principles' that I believe are conducive to good applied mathematics, and that I have learnt myself from observing Hans van Duijn in action.Comment: 11 page

Non-oriented solutions of the eikonal equation

We study a new formulation for the eikonal equation |grad u| =1 on a bounded subset of R^2. Instead of a vector field grad u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with div P in L^2. We prove existence and uniqueness for solutions of the equation P div P=0. We give a geometric description, comparable with the classical case, and we prove that such solutions exist only if the domain is a tubular neighbourhood of a regular closed curve. The idea of the proof is to apply a generalized method of characteristics introduced in Jabin, Otto, Perthame, "Line-energy Ginzburg-Landau models: zero-energy states", Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002), to a suitable vector field m satisfying P = m \otimes m. This formulation provides a useful approach to the analysis of stripe patterns. It is specifically suited to systems where the physical properties of the pattern are invariant under rotation over 180 degrees, such as systems of block copolymers or liquid crystals.Comment: 14 pages, 4 figures, submitte