Single-pass high-harmonic generation at 20.8 MHz repetition rate

We report on single-pass high-harmonic generation (HHG) with amplified driving laser pulses at a repetition rate of 20.8?MHz. An Yb:YAG Innoslab amplifier system provides 35?fs pulses with 20?W average power at 1030?nm after external pulse compression. Following tight focusing into a xenon gas jet, we observe the generation of high-harmonic radiation of up to the seventeenth order. Our results show that state-of-the-art amplifier systems have become a promising alternative to cavity-assisted HHG for applications that require high repetition rates, such as frequency comb spectroscopy in the extreme UV.     

\mathcal{O}(\alpha ^2 L^2 ) radiative corrections to deep inelasticep scattering for different kinematical variables

The QED radiative corrections are calculated in the leading log approximation up to $\mathcal{O}(\alpha ^2 )$ for different definitions of the kinematical variables using jet measurement, the ‘mixed’ variables, the double angle method, and a measurement based onθ _e andy _JB . Higher order contributions due to exponentiation of soft radiation are included.     

Traveling Salesman Problem with Clustering

In the original traveling salesman problem, the traveling salesman has the task to find the shortest closed tour through a proposed set of nodes, touching each node exactly once and returning to the initial node at the end. For the sake of the tour length to be minimized, nodes close to each other might not be visited one after the other but separated in the tour. However, for some practical applications, it is useful to group nodes to clusters, such that all nodes of a cluster are visited contiguously. Here we present an approach which leads to an automatic clustering with a clustering parameter governing the sizes of the clusters.     

Ideal Mixture Approximation of Cluster Size Distributions at Low Density

We consider an interacting particle system in continuous configuration space. The pair interaction has an attractive part. We show that, at low density, the system behaves approximately like an ideal mixture of clusters (droplets): we prove rigorous bounds (a) for the constrained free energy associated with a given cluster size distribution, considered as an order parameter, (b) for the free energy, obtained by minimising over the order parameter, and (c) for the minimising cluster size distributions. It is known that, under suitable assumptions, the ideal mixture has a transition from a gas phase to a condensed phase as the density is varied; our bounds hold both in the gas phase and in the coexistence region of the ideal mixture. The present paper improves our earlier results by taking into account the mixing entropy.     

Successive coordination of palladium(II)-ions and terpyridine-ligands to a pyridyl-terminated self-assembled monolayer on gold

The deposition of palladium on a novel, reversibly protonatable, pyridyl-terminated self-assembled monolayer on gold substrates has been studied by X-ray photoelectron spectroscopy (XPS), near-edge X-ray absorption fine structure spectroscopy (NEXAFS spectroscopy) and time of flight-secondary ion mass spectrometry (ToF-SIMS). For this purpose, 12-(pyridin-4-yl)dodecane-1-thiol, consisting of a surface-active head group, an unfunctionalized hydrocarbon backbone and a terminal pyridyl group, has been synthesized and deposited on gold surfaces. Coordination of Pd(II) ions to the pyridyl group was examined. Furthermore, a reversible protonation/deprotonation cycle has been applied, and the relation between protonation and the amount of complexed palladium was studied. Investigation of the SAM by angle-resolved NEXAFS spectroscopy revealed the aliphatic backbone to be preferentially upright oriented with the aromatic head group being not preferentially oriented. The palladium layer was further coordinated with a CF₃-labeled terpyridine ligand in order to prove the accessibility of the Pd(II) ions to further complexation and the platform useful for deposition of further layers toward a multi-layered system.     

Measuring the similarity between trajectories using clustering techniques

A clustering method has been developed to group signals that display similar dynamic behavior. The procedure involves using the method of time delay embedding to construct a trajectory in state space from a time series. Certain features that characterize the geometry of the trajectory have been defined. These features were subjected to a series of statistical tests to determine their usefulness in a hierarchical clustering analysis. The latter is aimed at finding groups of similar trajectories. The trajectory-based clustering algorithm has been applied to simulated data, which included both stochastic data generated by a linear AR model, and nonlinear data generated by a Duffing oscillator. The results show that the algorithm works reliably in both cases.     

Threshold effects on renormalization group running of neutrino parameters in the low-scale seesaw model

We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC).