Eine Folge positiver interpolationsoperatoren

Ohne Zusammenfassung     

Structural phase transitions in multipole traps

A small number of laser-cooled ions trapped in a linear radiofrequency multipole trap forms a hollow tube structure. We have studied, by means of molecular dynamics simulations, the structural transition from a double ring to a single ring of ions. We show that the single-ring configuration has the advantage to inhibit the thermal transfer from the rf-excited radial components of the motion to the axial component, allowing ions to reach the Doppler limit temperature along the direction of the trap axis. Once cooled in this particular configuration, the ions experience an angular dependency of the confinement if the local adiabaticity parameter exceeds the empirical limit. Bunching of the ion structures can then be observed and an analytic expression is proposed to take into account for this behavior.     

Neural Networks for Optimal Approximation of Continuous Functions on the Unit Sphere

We prove that, to approximate continuous target functions defined on the unit sphere of ${\mathbb{R}^d}$ , neural networks are at least as good as algebraic polynomials.     

Entropic Separations of Mixtures of Aromatics by Selective Face‐to‐Face Molecular Stacking in One‐Dimensional Channels of Metal–Organic Frameworks and Zeolites

Separation of challenging mixtures using metal–organic frameworks can be achieved by an entropy‐driven mechanism, where one of the components can arrange into a “face‐to‐face” stacking, thus reducing its “footprint” and reaching a higher saturation loading.     

Star polymers by cross‐linking of linear poly(benzyl‐L‐glutamate) macromonomers via free‐radical and RAFT polymerization. A simple route toward peptide‐stabilized nanoparticles

Poly(benzyl‐L ‐glutamate) (PBLG) macromonomers were synthesized by N‐carboxyanhydride (NCA) polymerization initiated with 4‐vinyl benzylamine. MALDI‐ToF analysis confirmed the presence of styrenic end‐groups in the PBLG. Free‐radical and RAFT polymerization of the macromonomer in the presence of divinyl benzene produced star polymers of various molecular weights, polydispersity, and yield depending on the reaction conditions applied. The highest molecular weight (M_w) of 10,170,000 g/mol was obtained in a free‐radical multibatch approach. It was shown that the PBLG star polymers can be deprotected to obtain poly(glutamic acid) star polymers, which form water soluble pH responsive nanoparticles. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Dark resonances as a probe for the motional state of a single ion

Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second-order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. In this paper the motional state of a confined three-level ion is probed, taking advantage of the high sensitivity of observed dark resonances to the trapped ion’s velocity. Excess micromotion is controlled by monitoring the dark-resonance contrast with varying laser-beam geometry. The influence of different parameters such as the cooling laser intensity has been investigated experimentally and numerically.     

Terahertz frequency standard based on three-photon coherent population trapping

A scheme for a terahertz frequency standard based on three-photon coherent population trapping in stored ions is proposed. Assuming the propagation directions of the three lasers obey the phase matching condition, we show that stability of few 10(-14) at 1 s can be reached with a precision limited by power broadening to 10(-11) in the less favorable case. The referenced terahertz signal can be propagated over long distances, the useful information being carried by the relative frequency of the three optical photons.     

Characterization of a miniature Paul-Straubel trap

Frequency standard applications and ultra-high resolution spectroscopy of a confined single ion require traps of drastically reduced dimensions (about or below 1 mm). These small dimensions increase the sensitivity of the trapping behavior to imperfections in the trap geometry and to patch potentials. For the aim of the metrological laser interrogation of a single Ca⁺ ion, a miniature cylindrical ring trap was built. In order to optimize the laser cooling process and to reach strong binding conditions, the boundaries of the stability diagram and the zones of low confinement as well as the ion motion properties were characterized. Received 14 November 2000 and Received in final form 1st February 2001