Comparison of 2D melting criteria in a colloidal system

We use super-paramagnetic spherical particles which are arranged in a two-dimensional monolayer at a water/air interface to investigate the crystal to liquid phase transition. According to the KTHNY theory a crystal melts in thermal equilibrium by two continuous phase transitions into the isotropic liquid state with an intermediate phase, commonly known as hexatic phase. We verify the significance of several criteria based on dynamical and structural properties to identify the crystal - hexatic and hexatic - isotropic liquid phase transition for the same experimental data of the given setup. Those criteria are the bond orientational correlation function, the Larson-Grier criterion, 2D dynamic Lindemann parameter, the bond-orientational susceptibility, the 2D Hansen-Verlet rule, the L\"{o}wen-Palberg-Simon criterion as well as a criterion based on the shape factor of Voronoi cells and Minkowski functionals. For our system with long range repulsion, the bond order correlation function and bond order susceptibility works best to identify the hexatic - isotropic liquid transition and the 2D dynamic Lindemann parameter identifies unambiguously the hexatic - crystalline transition.Comment: 20 pages, 13 figure

DD-α\alphaAMG on QPACE 3

We describe our experience porting the Regensburg implementation of the DD-$\alpha$AMG solver from QPACE 2 to QPACE 3. We first review how the code was ported from the first generation Intel Xeon Phi processor (Knights Corner) to its successor (Knights Landing). We then describe the modifications in the communication library necessitated by the switch from InfiniBand to Omni-Path. Finally, we present the performance of the code on a single processor as well as the scaling on many nodes, where in both cases the speedup factor is close to the theoretical expectations.Comment: 12 pages, 6 figures, Proceedings of Lattice 201

Discontinuous shear modulus determines the glass transition temperature

A solid - amorphous or crystalline - is defined by a finite shear modulus while a fluid lacks such. We thus experimentally investigate the elastic properties of a colloidal glass former near the glass transition: spectroscopy of vibrational excitations yields the dispersion relations of longitudinal and transverse phonons in the glassy state. From the long wavelength limit of the dispersion relation we extract the bulk and the shear modulus. As expected, the latter disappear in a fluid and we measure a clearly resolved discontinuous behaviour of the elastic moduli at the glass transition. This not only determines the transition temperature T_G of the system but also directly addresses recent discussions about elasticity during vitrification. We show that low frequency excitations in our system are plane waves such that continuum elasticity theory can be used to describe the macroscopic behaviour.Comment: 8 pages, 6 figure

Properties of principal component methods for functional and longitudinal data analysis

The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed precisely, in the continuum and without noise. While this has been the traditional setting for functional data analysis, in the context of longitudinal data analysis a random function typically represents a patient, or subject, who is observed at only a small number of randomly distributed points, with nonnegligible measurement error. Nevertheless, essentially the same methods can be used in both these cases, as well as in the vast number of settings that lie between them. How is performance affected by the sampling plan? In this paper we answer that question. We show that if there is a sample of $n$ functions, or subjects, then estimation of eigenvalues is a semiparametric problem, with root-$n$ consistent estimators, even if only a few observations are made of each function, and if each observation is encumbered by noise. However, estimation of eigenfunctions becomes a nonparametric problem when observations are sparse. The optimal convergence rates in this case are those which pertain to more familiar function-estimation settings. We also describe the effects of sampling at regularly spaced points, as opposed to random points. In particular, it is shown that there are often advantages in sampling randomly. However, even in the case of noisy data there is a threshold sampling rate (depending on the number of functions treated) above which the rate of sampling (either randomly or regularly) has negligible impact on estimator performance, no matter whether eigenfunctions or eigenvectors are being estimated.Comment: Published at http://dx.doi.org/10.1214/009053606000000272 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Entanglement and Disentanglement in Circuit QED Architectures

We propose a protocol for creating entanglement within a dissipative circuit QED network architecture that consists of two electromagnetic circuits (cavities) and two superconducting qubits. The system interacts with a quantum environment, giving rise to decoherence and dissipation. We discuss the preparation of two separate entangled cavity-qubit states via Landau-Zener sweeps, after which the cavities interact via a tunable "quantum switch" which is realized with an ancilla qubit. Moreover, we discuss the decay of the resulting entangled two-cavity state due to the influence of the environment, where we focus on the entanglement decay.Comment: 7 pages, 5 figure

Specific heat in two-dimensional melting

We report the specific heat $c_N$ around the melting transition(s) of micrometer-sized superparamagnetic particles confined in two dimensions, calculated from fluctuations of positions and internal energy, and corresponding Monte Carlo simulations. Since colloidal systems provide single particle resolution, they offer the unique possibility to compare the experimental temperatures of peak position of $c_N(T)$ and symmetry breaking, respectively. While order parameter correlation functions confirm the Kosterlitz-Thouless-Halperin-Nelson-Young melting scenario where translational and orientational order symmetries are broken at different temperatures with an intermediate so called hexatic phase, we observe a single peak of the specific heat within the hexatic phase, with excellent agreement between experiment and simulation. Thus, the peak is not associated with broken symmetries but can be explained with the total defect density, which correlates with the maximum increase of isolated dislocations. The absence of a latent heat strongly supports the continuous character of both transitions

Experimental evidence for a partially dissociated water bilayer on Ru{0001}

Core-level photoelectron spectra, in excellent agreement with ab initio calculations, confirm that the stable wetting layer of water on Ru{0001} contains O-H and H2O in roughly 3:5 proportion, for OHx coverages between 0.25 and 0.7 ML, and T<170 K. Proton disorder explains why the wetting structure looks to low energy electron diffraction (LEED) to be an ordered p(root3xroot3)R30degrees adlayer, even though approximate to3/8 of its molecules are dissociated. Complete dissociation to atomic oxygen starts near 190 K. Low photon flux in the synchrotron experiments ensured that the diagnosis of the nature of the wetting structure quantified by LEED is free of beam-induced damage