Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes

We consider the following eigenvalue optimization problem: Given a bounded domain $\Omega\subset\R^n$ and numbers $\alpha\geq 0$, $A\in [0,|\Omega|]$, find a subset $D\subset\Omega$ of area $A$ for which the first Dirichlet eigenvalue of the operator $-\Delta + \alpha \chi_D$ is as small as possible. We prove existence of solutions and investigate their qualitative properties. For example, we show that for some symmetric domains (thin annuli and dumbbells with narrow handle) optimal solutions must possess fewer symmetries than $\Omega$; on the other hand, for convex $\Omega$ reflection symmetries are preserved. Also, we present numerical results and formulate some conjectures suggested by them.Comment: 24 pages; 3 figures (as separate files); (shortened previous version); to appear in Comm. Math. Phy

Hierarchical structuring of Cultural Heritage objects within large aggregations

Huge amounts of cultural content have been digitised and are available through digital libraries and aggregators like Europeana.eu. However, it is not easy for a user to have an overall picture of what is available nor to find related objects. We propose a method for hier- archically structuring cultural objects at different similarity levels. We describe a fast, scalable clustering algorithm with an automated field selection method for finding semantic clusters. We report a qualitative evaluation on the cluster categories based on records from the UK and a quantitative one on the results from the complete Europeana dataset.Comment: The paper has been published in the proceedings of the TPDL conference, see http://tpdl2013.info. For the final version see http://link.springer.com/chapter/10.1007%2F978-3-642-40501-3_2

Absolute rate coefficients for photorecombination and electron-impact ionization of magnesium-like iron ions from measurements at a heavy-ion storage ring

Rate coefficients for photorecombination (PR) and cross sections for electron-impact ionization (EII) of Fe$^{14+}$ forming Fe$^{13+}$ and Fe$^{15+}$, respectively, have been measured by employing the electron-ion merged-beams technique at a heavy-ion storage ring. Rate coefficients for PR and EII of Fe$^{14+}$ ions in a plasma are derived from the experimental measurements. Simple parametrizations of the experimentally derived plasma rate coefficients are provided for use in the modeling of photoionized and collisionally ionized plasmas. In the temperature ranges where Fe$^{14+}$ is expected to form in such plasmas the latest theoretical rate coefficients of Altun et al. [Astron. Astrophys. 474, 1051 (2007)] for PR and of Dere [Astron. Astrophys. 466, 771 (2007)] for EII agree with the experimental results to within the experimental uncertainties. Common features in the PR and EII resonance structures are identified and discussed.Comment: 12 pages, 6 figures, 3 tables, submitted for publication to Physical Review

Absolute rate coefficients for photorecombination of berylliumlike and boronlike silicon ions

We report measured rate coefficients for electron-ion recombination for Si10+ forming Si9+ and for Si9+ forming Si8+, respectively. The measurements were performed using the electron-ion merged-beams technique at a heavy-ion storage ring. Electron-ion collision energies ranged from 0 to 50 eV for Si9+ and from 0 to 2000 eV for Si10+, thus, extending previous measurements for Si10+ [Orban et al. 2010, Astrophys. J. 721, 1603] to much higher energies. Experimentally derived rate coefficients for the recombination of Si9+ and Si10+ ions in a plasma are presented along with simple parameterizations. These rate coefficients are useful for the modeling of the charge balance of silicon in photoionized plasmas (Si9+ and Si10+) and in collisionally ionized plasmas (Si10+ only). In the corresponding temperature ranges, the experimentally derived rate coefficients agree with the latest corresponding theoretical results within the experimental uncertainties.Comment: 17 pages, 7 figures, 3 tables, 66 references, submitted to the J. Phys. B special issue on atomic and molecular data for astrophysicist

Dissociative recombination measurements of HCl+ using an ion storage ring

We have measured dissociative recombination of HCl+ with electrons using a merged beams configuration at the heavy-ion storage ring TSR located at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. We present the measured absolute merged beams recombination rate coefficient for collision energies from 0 to 4.5 eV. We have also developed a new method for deriving the cross section from the measurements. Our approach does not suffer from approximations made by previously used methods. The cross section was transformed to a plasma rate coefficient for the electron temperature range from T=10 to 5000 K. We show that the previously used HCl+ DR data underestimate the plasma rate coefficient by a factor of 1.5 at T=10 K and overestimate it by a factor of 3.0 at T=300 K. We also find that the new data may partly explain existing discrepancies between observed abundances of chlorine-bearing molecules and their astrochemical models.Comment: Accepted for publication in ApJ (July 7, 2013

Ion-lithium collision dynamics studied with an in-ring MOTReMi

We present a novel experimental tool allowing for kinematically complete studies of break-up processes of laser-cooled atoms. This apparatus, the 'MOTReMi', is a combination of a magneto-optical trap (MOT) and a Reaction Microscope (ReMi). Operated in an ion-storage ring, the new setup enables to study the dynamics in swift ion-atom collisions on an unprecedented level of precision and detail. In first experiments on collisions with 1.5 MeV/amu O$^{8+}$-Li the pure ionization of the valence electron as well as ionization-excitation of the lithium target has been investigated