Conference and Research Reports

Groundwater discharge into an open pit lignite mining lake was investigated using radon-222 as a naturally occurring environmental tracer. The chosen study site was a meromictic lake, i.e., a water body that is divided horizontally into two separate layers – the upper mixolimnion (with seasonal mixing) and the lower monimolimnion (without seasonal mixing). For the estimation of groundwater discharge rates into the lake, a simple box model including all radon sinks and sources related to each layer was applied. Two field investigations were performed. During the October campaign, the total groundwater discharge into the lake was found to be 18.9 and 0.7 m³ d^?1 for the mixolimnion and monimolimnion, respectively. During the December campaign, the groundwater discharge into the mixolimnion was 15.0 m³ d^?1, whereas no discharge at all was observed into the monimolimnion. Based on the given water volumes, the residence time of lake water was 5.3 years for the monimolimnion and varies between 0.9 and 1.1 years for the mixolimnion. The investigation confirmed radon to be a useful environmental tracer for groundwater and surface water interactions in meromictic lake environments.     

Perturbative calculation of critical exponents for the Bose–Hubbard model

We develop a strategy for calculating critical exponents for the Mott insulator-to-superfluid transition shown by the Bose–Hubbard model. Our approach is based on the field-theoretic concept of the effective potential, which provides a natural extension of the Landau theory of phase transitions to quantum critical phenomena. The coefficients of the Landau expansion of that effective potential are obtained by high-order perturbation theory. We counteract the divergency of the weak-coupling perturbation series by including the seldom considered Landau coefficient a ₆ into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the two-dimensional Bose–Hubbard model, deviate by less than 1 % from the best known estimates computed so far for the three-dimensional XY universality class.     

On unitary subsectors of polycritical gravities

We study higher-derivative gravity theories in arbitrary space–time dimension $d$ with a cosmological constant at their maximally critical points where the masses of all linearized perturbations vanish. These theories have been conjectured to be dual to logarithmic conformal field theories in the $(d-1)$ -dimensional boundary of an AdS solution. We determine the structure of the linearized perturbations and their boundary fall-off behaviour. The linearized modes exhibit the expected Jordan block structure and their inner products are shown to be those of a non-unitary theory. We demonstrate the existence of consistent unitary truncations of the polycritical gravity theory at the linearized level for odd rank.     

A globalized Newton method for the computation of normalized Nash equilibria

The generalized Nash equilibrium is a Nash game, where not only the players’ cost functions, but also the constraints of a player depend on the rival players decisions. We present a globally convergent algorithm that is suited for the computation of a normalized Nash equilibrium in the generalized Nash game with jointly convex constraints. The main tool is the regularized Nikaido–Isoda function as a basis for a locally convergent nonsmooth Newton method and, in another way, for the definition of a merit function for globalization. We conclude with some numerical results.     

Finding all solutions of affine generalized Nash equilibrium problems with one-dimensional strategy sets

We consider a class of generalized Nash equilibrium problems with quadratic cost functions and common linear constraints for all players. Further we focus on the case where every player has a single strategy variable within a bounded set. For this problem class we present an algorithm that is able to compute all solutions and that terminates finitely. Our method is based on a representation of the solution set as a finite union of polyhedral sets using sign conditions for the derivatives of the cost and constraint functions. The effectiveness of the algorithm is shown in various examples from literature.     

Tricoordinate Coinage Metal Complexes with a Redox-Active Tris-(Ferrocenyl)triazine Backbone Feature Triazine–Metal Interactions

2,4,6-Tris(1-diphenylphosphanyl-1’-ferrocenylene)-1,3,5-triazine ( 1 ) coordinates all three coinage metal(I) ions in a 1:1 tridentate coordination mode. The C₃-symmetric coordination in both solid state and solution is stabilised by an uncommon cation–π interaction between the triazine core and the metal cation. Intramolecular dynamic behaviour was observed by variable-temperature NMR spectroscopy. The borane adduct of 1 , 1BH₃ , displays four accessible oxidation states, suggesting complexes of 1 to be intriguing candidates for redox-switchable catalysis. Complexes 1Cu , 1Ag , and 1Au display a more complicated electrochemical behaviour, and the electrochemical mechanism was studied by temperature-resolved UV/Vis spectroelectrochemistry and chemical oxidation.     

Quantum Interference Line Shifts of Broad Dipole‐Allowed Transitions

High‐resolution laser spectroscopy serves the purpose of determining the energy difference between states of atoms and molecules with the best possible accuracy. Therefore, one may face the problem of finding the center of a symmetric line within a small fraction of the line width, or one needs to extract the energy difference from an asymmetric line without a uniquely defined center. Multiplets of atomic resonance lines are subject to mutual line pullings and give rise to asymmetric line distortions due to quantum interference. This paper reviews the treatment of these distortions for dipole‐allowed one‐photon transitions. Specific examples are given for hydrogen and helium spectroscopy.