Feedback cooling of a single neutral atom

We demonstrate feedback cooling of the motion of a single rubidium atom trapped in a high-finesse optical resonator to a temperature of about 160 μK. Time-dependent transmission and intensity-correlation measurements prove the reduction of the atomic position uncertainty. The feedback increases the 1/e storage time into the 1 s regime, 30 times longer than without feedback. Feedback cooling therefore rivals state-of-the-art laser cooling, but with the advantages that it requires less optical access and exhibits less optical pumping.     

Reversible bond formation in a gold-atom-organic-molecule complex as a molecular switch

We report on the formation of a metal-molecule complex that can be used as a molecular switch. Using a cryogenic scanning tunneling microscope, a covalent bond was formed reversibly between a gold atom and a perylene-3,4,9,10-tetracarboxylic dianhydride molecule supported by a thin insulating film. The bonded and the nonbonded state of the complex were found to be associated with different charge states, and the switching between the two states was accompanied by a considerable change in the tunneling current. Atomic force microscopy molecular imaging was employed to determine precisely the atomic structure of the complex, and the experimental results were corroborated by density functional theory calculations.     

Sectorial extensions for ultraholomorphic classes defined by weight functions

We prove an extension theorem for ultraholomorphic classes defined by so-called Braun–Meise–Taylor weight functions ω and transfer the proofs from the single weight sequence case from V. Thilliez to the weight function setting. We are following a different approach than the results obtained in a recent paper by the authors, more precisely we are working with real methods by applying the ultradifferentiable Whitney-extension theorem. We are treating both the Roumieu and the Beurling case, the latter one is obtained by a reduction from the Roumieu case.     

Many-body hydrodynamic interactions in charge-stabilized suspensions

In this joint experimental-theoretical work we study hydrodynamic interaction effects in dense suspensions of charged colloidal spheres. Using x-ray photon correlation spectroscopy we have determined the hydrodynamic function H(q), for a varying range of electrosteric repulsion. We show that H(q) can be quantitatively described by means of a novel Stokesian dynamics simulation method for charged Brownian spheres, and by a modification of a many-body theory developed originally by Beenakker and Mazur. Very importantly, we can explain the behavior of H(q) for strongly correlated particles without resorting to the controversial concept of hydrodynamic screening, as was attempted in earlier work by Riese [Phys. Rev. Lett. 85, 5460 (2000)].     

Modal-based fluid structure coupling in room acoustics considering non-deterministic properties

Nowadays fluid structure interaction methods gain more and more importance. For room acoustical problems the coupling to realistic boundary conditions, absorbers and reflectors, is still a remaining challenge in the optimization process for the frequency response of the acoustic volume. The following work will present a coupling method based on the Component Mode Synthesis and Hamilton's Principle for the steady state response of linear room acoustic problems. Therein realistic boundaries like absorbers are coupled with the help of their related frequency dependent impedances. For a more physical interpretation uncertain parameters are considered within the input data. Basic possibilistic and probabilistic concepts are applied on benchmark configurations to estimate the variation in frequency response functions from uncertain input data. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Complete reducibility and separable field extensions

Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility under separable field extensions. Part of our proof relies on the recently established Tits Centre Conjecture for the spherical building of the reductive group G.     

Non-empirical CI potential curves for the ground and excited states of PH and its positive ion

A series of calculated potential curves is reported for the low lying valence and (selected) Rydberg states of the PH molecule by employing the multi-reference (single- and) double-excitation CI method. A large AO basis including f functions on phosphorous is chosen for this study and up to twenty main configurations are used to generate a given MRD-CI space in the accompanying theoretical treatment. Very good agreement is obtained between calculation and experiment for a variety of spectroscopic constants and a number of predictions for electronically excited states of PH are made for cases in which no comparable empirical data are yet available. The repulsive ⁵∑^- state is shown to be responsible for the predissociation of several states of the neutral system and is also thought to explain the failure to detect a number of low lying Rydberg states experimentally. Analogous calculations for the PH⁺ molecular ion have also been carried out and spectroscopic constants for this system are reported. In this case the ⁴Π state plays much the same role as the neutral ⁵∑^- species in bringing about predissociation in its electronic spectrum. Finally a comparison is made throughout between the results for PH and PH⁺ and a number of isovalent systems, especially NH and NH⁺ and also SiH.     

Control of the Discotic to Isotropic Transition in Alkoxy-Substituted Silicondihydroxo-Phthalocyanines by Axial Substituents

The synthesis of a homologous series of octaalkoxy-substituted silicondihydroxo-phthalocyanines is described. The mesomorphic properties of these new materials were studied by DSC, optical microscopy and X-ray investigations. Compounds with n ≤ 4 (n is the number of carbon atoms in a single alkoxy side chain) show a discotic mesophase transition. A transition to the isotropic state is only observed when n ≤ 8. X-ray diffraction patterns of the mesophases confirm that all compounds form a hexagonal columnar mesophase of the type D_hd.     

The impact of taking a college pre-calculus course on students’ college calculus performance

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.