Quantum Diffusion in Separable d-Dimensional Quasiperiodic Tilings

We study the electronic transport in quasiperiodic separable tight-binding models in one, two, and three dimensions. First, we investigate a one-dimensional quasiperiodic chain, in which the atoms are coupled by weak and strong bonds aligned according to the Fibonacci chain. The associated d-dimensional quasiperiodic tilings are constructed from the product of d such chains, which yields either the square/cubic Fibonacci tiling or the labyrinth tiling. We study the scaling behavior of the mean square displacement and the return probability of wave packets with respect to time. We also discuss results of renormalization group approaches and lower bounds for the scaling exponent of the width of the wave packet.Comment: 6 pages, 4 figures, conference proceedings Aperiodic 2012 (Cairns

Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis

We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most reliable results.Comment: 10 pages, 13 figure

Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings

We study the properties of wave functions and the wave-packet dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider rather large systems numerically. We show that the wave functions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wave packets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wave packet with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wave packet and propose a modified lower bound for the absolute continuous regime.Comment: 25 pages, 13 figure

Microstructure, flow behavior, and bulk texture evolution of cold drawn copper-silver composites

In the last 20 years, several groups used nanostructured composites to produce high strength conductor materials for magnetic applications. The mechanical strength of Cu-Ag composites is strongly influenced by metal forming operations. Within the scope of the paper, the microstructure, the mechanical behavior, and the texture evolution are investigated for two cold drawn Cu-63wt%Ag composite rods. The aim of these investigations is to understand the influence of the microstructure and texture evolution on the mechanical behavior. The investigation is carried out using optical microscopy, scanning electron microscopy (SEM) along with electron backscattered diffraction (EBSD), X-ray diffraction measurements (XRD), and compression testing. The microscopic images show that the drawn samples mainly have a lamellar structure of Cu and Ag phases. However, elliptical shaped regions of primarily solidified copper solid solution are also observed. With increase of plastic deformation, the average lamella thickness of both phases has been decreased. EBSD measurements show that abundant banded regions are observed in the Ag phase while very few banded regions are present in the Cu phase. The bulk XRD measurements reveal that both phases of the drawn samples initially have the same type of texture, and both phases develop the same brass-type [110](112) texture. The texture intensity increases for both phases as the drawing strain increases. Compression tests are performed at constant strain rate of 10-4 s-1 at room temperature. The stress-strain curves under compression are presented for two different drawn samples. The texture measurements after compression reveal that the texture becomes more pronounced

Photogrammetric Analysis of the 2013 El Reno Tornado Combined with Mobile X-Band Polarimetric Radar Data

Abstract This study presents rapid-scanning X-band polarimetric radar data combined with photogrammetry of the El Reno tornado of 31 May 2013. The relationship between the hook echo, weak-echo hole (WEH), weak-echo column (WEC), and the rotational couplet with the visual characteristics of the tornado are shown. For the first time, cross-correlation coefficient (ρhv) and differential reflectivity (ZDR) data are included in the photogrammetric analyses. The tornado was accompanied by a large tornadic debris signature (TDS) with a diameter ~2 km wide during the analysis time. The center of the TDS was not collocated with the WEH and the rotational couplet. Instead, the TDS was displaced ~1 km to the north and within the weak-echo notch of the hook echo. A “debris overhang” was identified in vertical cross sections of the ρhv fields. The overhang was located in a weak-echo trench and a notch of high ρhv, consistent with the position of the tornado updraft. The updraft was hypothesized to be carrying small debris particles to heights that produced the overhang signature. A U-shaped band of high ρhv and ZDR was resolved in a vertical cross section and positioned at the periphery of the WEC during one of the analysis times. It was proposed that the band formed as a result of hydrometeors encircling the WEC while being surrounded on all sides by relatively hydrometeor-free air. The characteristics of the scatterers within the WEC were resolved and believed to be composed of a low concentration of very small, randomly oriented, debris particles, even in the presence of strong centrifuging, and a general absence of hydrometeors

Formen der Kollaboration in Wissensnetzwerken

Gruppenbildung gilt gemeinhin als soziales Phänomen. Doch mit der Evolution sozialer Software im Internet und dem einhergehenden reziproken Interaktionismus von Individuen in Online-Communities werden Kollaborationsstrukturen und Verhaltensmuster innerhalb virtueller Wissensräume sichtbarer denn je. Wie entsteht nun Kollaboration? Und welche Formen der Kollaboration gibt es? Welche Einflussfaktoren sind im Aufbau und Wachstum digitaler Wissensnetzwerke ausschlaggebend, um erfolgreich Information und Wissen verteilen zu können? Diese Fallstudie zeigt erste Einblicke in die Organisationsstruktur virtueller Wissensgemeinschaften anhand der Untersuchung des Wissen- und Lernportals OPAL. Dabei werden Theorien und Modelle aus den Handlungsfeldern der Kommunikationsund Bildungsforschung zu Grunde gelegt und mit dem soziologischen Paradigma der sozialen Netzwerktheorie verbunden