H\"older Regularity of Geometric Subdivision Schemes

We present a framework for analyzing non-linear $\mathbb{R}^d$-valued subdivision schemes which are geometric in the sense that they commute with similarities in $\mathbb{R}^d$. It admits to establish $C^{1,\alpha}$-regularity for arbitrary schemes of this type, and $C^{2,\alpha}$-regularity for an important subset thereof, which includes all real-valued schemes. Our results are constructive in the sense that they can be verified explicitly for any scheme and any given set of initial data by a universal procedure. This procedure can be executed automatically and rigorously by a computer when using interval arithmetics.Comment: 31 pages, 1 figur

Trapped ions in Rydberg-dressed atomic gases

We theoretically study trapped ions that are immersed in an ultracold gas of Rydberg-dressed atoms. By off-resonant coupling on a dipole-forbidden transition, the adiabatic atom-ion potential can be made repulsive. We study the energy exchange between the atoms and a single trapped ion and find that Langevin collisions are inhibited in the ultracold regime for these repulsive interactions. Therefore, the proposed system avoids recently observed ion heating in hybrid atom-ion systems caused by coupling to the ion's radio frequency trapping field and retains ultracold temperatures even in the presence of excess micromotion.Comment: 9 pages, 5 figures including appendice

Observation of Interactions between Trapped Ions and Ultracold Rydberg Atoms

We report on the observation of interactions between ultracold Rydberg atoms and ions in a Paul trap. The rate of observed inelastic collisions, which manifest themselves as charge transfer between the Rydberg atoms and ions, exceeds that of Langevin collisions for ground state atoms by about three orders of magnitude. This indicates a huge increase in interaction strength. We study the effect of the vacant Paul trap's electric fields on the Rydberg excitation spectra. To quantitatively describe the exhibited shape of the ion loss spectra, we need to include the ion-induced Stark shift on the Rydberg atoms. Furthermore, we demonstrate Rydberg excitation on a dipole-forbidden transition with the aid of the electric field of a single trapped ion. Our results confirm that interactions between ultracold atoms and trapped ions can be controlled by laser coupling to Rydberg states. Adding dynamic Rydberg dressing may allow for the creation of spin-spin interactions between atoms and ions, and the elimination of collisional heating due to ionic micromotion in atom-ion mixtures.Comment: 7 pages, 5 figures, including appendices. Note that the title has been changed in version

Observation of collisions between cold Li atoms and Yb+^+ ions

We report on the observation of cold collisions between $^6$Li atoms and Yb$^+$ ions. This combination of species has recently been proposed as the most suitable for reaching the quantum limit in hybrid atom-ion systems, due to its large mass ratio. For atoms and ions prepared in the $^2S_{1/2}$ ground state, the charge transfer and association rate is found to be at least~10$^{3}$ times smaller than the Langevin collision rate. These results confirm the excellent prospects of $^6$Li--Yb$^+$ for sympathetic cooling and quantum information applications. For ions prepared in the excited electronic states $^2P_{1/2}$, $^2D_{3/2}$ and $^2F_{7/2}$, we find that the reaction rate is dominated by charge transfer and does not depend on the ionic isotope nor the collision energy in the range $\sim$~1--120~mK. The low charge transfer rate for ground state collisions is corroborated by theory, but the $4f$ shell in the Yb$^+$ ion prevents an accurate prediction for the charge transfer rate of the $^2P_{1/2}$, $^2D_{3/2}$ and $^2F_{7/2}$ states. Using \textit{ab initio} methods of quantum chemistry we calculate the atom-ion interaction potentials up to energies of 30$\times 10^3$~cm$^{-1}$, and use these to give qualitative explanations of the observed rates.Comment: 8 pages, 7 figures (including appendices

Reconstruction of cloud geometry using a scanning cloud radar

Clouds are one of the main reasons of uncertainties in the forecasts of weather and climate. In part, this is due to limitations of remote sensing of cloud microphysics. Present approaches often use passive spectral measurements for the remote sensing of cloud microphysical parameters. Large uncertainties are introduced by three-dimensional (3-D) radiative transfer effects and cloud inhomogeneities. Such effects are largely caused by unknown orientation of cloud sides or by shadowed areas on the cloud. Passive ground-based remote sensing of cloud properties at high spatial resolution could be crucially improved with this kind of additional knowledge of cloud geometry. To this end, a method for the accurate reconstruction of 3-D cloud geometry from cloud radar measurements is developed in this work. Using a radar simulator and simulated passive measurements of model clouds based on a large eddy simulation (LES),the effects of different radar scan resolutions and varying interpolation methods are evaluated. In reality, a trade-off between scan resolution and scan duration has to be found as clouds change quickly. A reasonable choice is a scan resolution of 1 to 2\degree. The most suitable interpolation procedure identified is the barycentric interpolation method. The 3-D reconstruction method is demonstrated using radar scans of convective cloud cases with the Munich miraMACS, a 35 GHz scanning cloud radar. As a successful proof of concept, camera imagery collected at the radar location is reproduced for the observed cloud cases via 3-D volume reconstruction and 3-D radiative transfer simulation. Data sets provided by the presented reconstruction method will aid passive spectral ground-based measurements of cloud sides to retrieve microphysical parameters

Cloning and Phylogenetic Analysis of NMDA Receptor Subunits NR1, NR2A and NR2B in Xenopus laevis Tadpoles

N-methyl-d-aspartate receptors (NMDARs) play an important role in many aspects of nervous system function such as synaptic plasticity and neuronal development. NMDARs are heteromers consisting of an obligate NR1 and most commonly one or two kinds of NR2 subunits. While the receptors have been well characterized in some vertebrate and invertebrate systems, information about NMDARs in Xenopus laevis brain is incomplete. Here we provide biochemical evidence that the NR1, NR2A and NR2B subunits of NMDARs are expressed in the central nervous system of X. laevis tadpoles. The NR1-4a/b splice variants appear to be the predominant isoforms while the NR1-3a/b variants appear to be expressed at low levels. We cloned the X. laevis NR2A and NR2B subunits and provide a detailed annotation of their functional domains in comparison with NR2A and NR2B proteins from 10 and 13 other species, respectively. Both NR2A and NR2B proteins are remarkably well conserved between species, consistent with the importance of NMDARs in nervous system function

Reconstruction of cloud geometry using a scanning cloud radar

Clouds are one of the main reasons of uncertainties in the forecasts of weather and climate. In part, this is due to limitations of remote sensing of cloud microphysics. Present approaches often use passive spectral measurements for the remote sensing of cloud microphysical parameters. Large uncertainties are introduced by three-dimensional (3-D) radiative transfer effects and cloud inhomogeneities. Such effects are largely caused by unknown orientation of cloud sides or by shadowed areas on the cloud. Passive ground-based remote sensing of cloud properties at high spatial resolution could be crucially improved with this kind of additional knowledge of cloud geometry. To this end, a method for the accurate reconstruction of 3-D cloud geometry from cloud radar measurements is developed in this work. Using a radar simulator and simulated passive measurements of model clouds based on a large eddy simulation (LES),the effects of different radar scan resolutions and varying interpolation methods are evaluated. In reality, a trade-off between scan resolution and scan duration has to be found as clouds change quickly. A reasonable choice is a scan resolution of 1 to 2\degree. The most suitable interpolation procedure identified is the barycentric interpolation method. The 3-D reconstruction method is demonstrated using radar scans of convective cloud cases with the Munich miraMACS, a 35 GHz scanning cloud radar. As a successful proof of concept, camera imagery collected at the radar location is reproduced for the observed cloud cases via 3-D volume reconstruction and 3-D radiative transfer simulation. Data sets provided by the presented reconstruction method will aid passive spectral ground-based measurements of cloud sides to retrieve microphysical parameters

Gravitational waves from relativistic rotational core collapse

We present results from simulations of axisymmetric relativistic rotational core collapse. The general relativistic hydrodynamic equations are formulated in flux-conservative form and solved using a high-resolution shock-capturing scheme. The Einstein equations are approximated with a conformally flat 3-metric. We use the quadrupole formula to extract waveforms of the gravitational radiation emitted during the collapse. A comparison of our results with those of Newtonian simulations shows that the wave amplitudes agree within 30%. Surprisingly, in some cases, relativistic effects actually diminish the amplitude of the gravitational wave signal. We further find that the parameter range of models suffering multiple coherent bounces due to centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure

Low temperature specific heat and possible gap to magnetic excitations in the Heisenberg pyrochlore antiferromagnet Gd2Sn207

The Gd2Sn2O7 pyrochlore Heisenberg antiferromagnet displays a phase transition to a four sublattice Neel ordered state at a temperature near 1 K. Despite the seemingly conventional nature of the ordered state, the specific heat has been found to be described in the temperature range 350-800 mK by an anomalous T-squared power law. A similar temperature dependence has also been reported for Gd2Ti2O7, another pyrochlore Heisenberg material. Such anomalous T-squared behavior in Cv has been argued to be correlated to an unusual energy-dependence of the density of states which also seemingly manifests itself in low-temperature spin fluctuations found in muon spin relaxation experiments. In this paper, we report calculations of Cv that consider spin wave like excitations out of the Neel order observed in Gd2Sn2O7 and argue that the parametric T-squared behavior does not reflect the true low-energy excitations of Gd2Sn2O7. Rather, we find that the low-energy excitations of this material are antiferromagnetic magnons gapped by single-ion and dipolar anisotropy effects, and that the lowest temperature of 350 mK considered in previous specific heat measurements accidentally happens to coincide with a crossover temperature below which magnons become thermally activated and Cv takes an exponential form. We argue that further specific heat measurements that extend down to at least 100 mK are required in order to ascribe an unconventional description of magnetic excitations out of the ground state of Gd2Sn2O7 or to invalidate the standard picture of gapped excitations proposed herein.Comment: 12 pages, 13 figures; shortened introduction and added 1 figur