Temporal flooding of regular islands by chaotic wave packets

We investigate the time evolution of wave packets in systems with a mixed phase space where regular islands and chaotic motion coexist. For wave packets started in the chaotic sea on average the weight on a quantized torus of the regular island increases due to dynamical tunneling. This flooding weight initially increases linearly and saturates to a value which varies from torus to torus. We demonstrate for the asymptotic flooding weight universal scaling with an effective tunneling coupling for quantum maps and the mushroom billiard. This universality is reproduced by a suitable random matrix model

Flooding of Regular Phase Space Islands by Chaotic States

We investigate systems with a mixed phase space, where regular and chaotic dynamics coexist. Classically, regions with regular motion, the regular islands, are dynamically not connected to regions with chaotic motion, the chaotic sea. Typically, this is also reflected in the quantum properties, where eigenstates either concentrate on the regular or the chaotic regions. However, it was shown that quantum mechanically, due to the tunneling process, a coupling is induced and flooding of regular islands may occur. This happens when the Heisenberg time, the time needed to resolve the discrete spectrum, is larger than the tunneling time from the regular region to the chaotic sea. In this case the regular eigenstates disappear. We study this effect by the time evolution of wave packets initially started in the chaotic sea and find increasing probability in the regular island. Using random matrix models a quantitative prediction is derived. We find excellent agreement with numerical data obtained for quantum maps and billiards systems. For open systems we investigate the phenomenon of flooding and disappearance of regular states, where the escape time occurs as an additional time scale. We discuss the reappearance of regular states in the case of strongly opened systems. This is demonstrated numerically for quantum maps and experimentally for a mushroom shaped microwave resonator. The reappearance of regular states is explained qualitatively by a matrix model.Untersucht werden Systeme mit gemischtem Phasenraum, in denen sowohl reguläre als auch chaotische Dynamik auftritt. In der klassischen Mechanik sind Gebiete regulärer Bewegung, die sogenannten regulären Inseln, dynamisch nicht mit den Gebieten chaotischer Bewegung, der chaotischen See, verbunden. Dieses Verhalten spiegelt sich typischerweise auch in den quantenmechanischen Eigenschaften wider, so dass Eigenfunktionen entweder auf chaotischen oder regulären Gebieten konzentriert sind. Es wurde jedoch gezeigt, dass aufgrund des Tunneleffektes eine Kopplung auftritt und reguläre Inseln geflutet werden können. Dies geschieht wenn die Heisenbergzeit, das heißt die Zeit die das System benötigt, um das diskrete Spektrum aufzulösen, größer als die Tunnelzeit vom Regulären ins Chaotische ist, wobei reguläre Eigenzustände verschwinden. Dieser Effekt wird über eine Zeitentwicklung von Wellenpaketen, die in der chaotischen See gestartet werden, untersucht. Es kommt zu einer ansteigenden Wahrscheinlichkeit in der regulären Insel. Mithilfe von Zufallsmatrixmodellen wird eine quantitative Vorhersage abgeleitet, welche die numerischen Daten von Quantenabbildungen und Billardsystemen hervorragend beschreibt. Der Effekt des Flutens und das Verschwinden regulärer Zustände wird ebenfalls mit offenen Systemen untersucht. Hier tritt die Fluchtzeit als zusätzliche Zeitskala auf. Das Wiederkehren regulärer Zustände im Falle stark geöffneter Systeme wird qualitativ mithilfe eines Matrixmodells erklärt und numerisch für Quantenabbildungen sowie experimentell für einen pilzförmigen Mikrowellenresonator belegt

Flooding of Regular Phase Space Islands by Chaotic States

We investigate systems with a mixed phase space, where regular and chaotic dynamics coexist. Classically, regions with regular motion, the regular islands, are dynamically not connected to regions with chaotic motion, the chaotic sea. Typically, this is also reflected in the quantum properties, where eigenstates either concentrate on the regular or the chaotic regions. However, it was shown that quantum mechanically, due to the tunneling process, a coupling is induced and flooding of regular islands may occur. This happens when the Heisenberg time, the time needed to resolve the discrete spectrum, is larger than the tunneling time from the regular region to the chaotic sea. In this case the regular eigenstates disappear. We study this effect by the time evolution of wave packets initially started in the chaotic sea and find increasing probability in the regular island. Using random matrix models a quantitative prediction is derived. We find excellent agreement with numerical data obtained for quantum maps and billiards systems. For open systems we investigate the phenomenon of flooding and disappearance of regular states, where the escape time occurs as an additional time scale. We discuss the reappearance of regular states in the case of strongly opened systems. This is demonstrated numerically for quantum maps and experimentally for a mushroom shaped microwave resonator. The reappearance of regular states is explained qualitatively by a matrix model.Untersucht werden Systeme mit gemischtem Phasenraum, in denen sowohl reguläre als auch chaotische Dynamik auftritt. In der klassischen Mechanik sind Gebiete regulärer Bewegung, die sogenannten regulären Inseln, dynamisch nicht mit den Gebieten chaotischer Bewegung, der chaotischen See, verbunden. Dieses Verhalten spiegelt sich typischerweise auch in den quantenmechanischen Eigenschaften wider, so dass Eigenfunktionen entweder auf chaotischen oder regulären Gebieten konzentriert sind. Es wurde jedoch gezeigt, dass aufgrund des Tunneleffektes eine Kopplung auftritt und reguläre Inseln geflutet werden können. Dies geschieht wenn die Heisenbergzeit, das heißt die Zeit die das System benötigt, um das diskrete Spektrum aufzulösen, größer als die Tunnelzeit vom Regulären ins Chaotische ist, wobei reguläre Eigenzustände verschwinden. Dieser Effekt wird über eine Zeitentwicklung von Wellenpaketen, die in der chaotischen See gestartet werden, untersucht. Es kommt zu einer ansteigenden Wahrscheinlichkeit in der regulären Insel. Mithilfe von Zufallsmatrixmodellen wird eine quantitative Vorhersage abgeleitet, welche die numerischen Daten von Quantenabbildungen und Billardsystemen hervorragend beschreibt. Der Effekt des Flutens und das Verschwinden regulärer Zustände wird ebenfalls mit offenen Systemen untersucht. Hier tritt die Fluchtzeit als zusätzliche Zeitskala auf. Das Wiederkehren regulärer Zustände im Falle stark geöffneter Systeme wird qualitativ mithilfe eines Matrixmodells erklärt und numerisch für Quantenabbildungen sowie experimentell für einen pilzförmigen Mikrowellenresonator belegt

Understanding the Structural and Functional Importance of Early Folding Residues in Protein Structures

Proteins adopt three-dimensional structures which serve as a starting point to understand protein function and their evolutionary ancestry. It is unclear how proteins fold in vivo and how this process can be recreated in silico in order to predict protein structure from sequence. Contact maps are a possibility to describe whether two residues are in spatial proximity and structures can be derived from this simplified representation. Coevolution or supervised machine learning techniques can compute contact maps from sequence: however, these approaches only predict sparse subsets of the actual contact map. It is shown that the composition of these subsets substantially influences the achievable reconstruction quality because most information in a contact map is redundant. No strategy was proposed which identifies unique contacts for which no redundant backup exists. The StructureDistiller algorithm quantifies the structural relevance of individual contacts and identifies crucial contacts in protein structures. It is demonstrated that using this information the reconstruction performance on a sparse subset of a contact map is increased by 0.4 A, which constitutes a substantial performance gain. The set of the most relevant contacts in a map is also more resilient to false positively predicted contacts: up to 6% of false positives are compensated before reconstruction quality matches a naive selection of contacts without any false positive contacts. This information is invaluable for the training to new structure prediction methods and provides insights into how robustness and information content of contact maps can be improved. In literature, the relevance of two types of residues for in vivo folding has been described. Early folding residues initiate the folding process, whereas highly stable residues prevent spontaneous unfolding events. The structural relevance score proposed by this thesis is employed to characterize both types of residues. Early folding residues form pivotal secondary structure elements, but their structural relevance is average. In contrast, highly stable residues exhibit significantly increased structural relevance. This implies that residues crucial for the folding process are not relevant for structural integrity and vice versa. The position of early folding residues is preserved over the course of evolution as demonstrated for two ancient regions shared by all aminoacyl-tRNA synthetases. One arrangement of folding initiation sites resembles an ancient and widely distributed structural packing motif and captures how reverberations of the earliest periods of life can still be observed in contemporary protein structures

Design of new responsive materials based on functional polymer brushes

For the development of smart surfaces high attention is focused on stimuli-responsive polymers. Since type and rate of response to environmental stimuli can be regulated by chain length, composition, architecture and topology, polymer films offer a variety of opportunities to develop such stimuli-responsive surfaces. Here polymer brush surfaces designed for a controlled adsorption of proteins and a switchable activity of immobilized enzymes are presented. The work is focused on temperature as well as pH-sensitive binary brushes, consisting of poly(N-isopropylacrylamide) (PNIPAAm) and poly(acrylic acid) (PAA), and their swelling behavior as well as their protein adsorption affinity is compared to the corresponding homopolymer brushes. All polymer brushes are covalently grafted by ester bonds to an anchoring layer of poly(glycidyl methacrylate), that itself is grafted via ether bonds to a silicon surface. Methodical investigations of layer thickness and refractive index of the brushes in the swollen state and after protein adsorption are carried out with in-situ spectroscopic ellipsometry, varying the brush composition and the solution parameters pH, salt concentration and temperature. The ellipsometric findings are correlated to results of contact angle, atomic force microscopy and zeta-potential measurements as well as colorimetric assays of enzyme activities at the brush surface. Furthermore the swelling of PNIPAAm brushes and protein adsorption at PAA Guiselin brushes are investigated in more detail with attenuated total reflexion Fourier-transform infrared spectroscopy and quartz crystal microbalance with dissipation, respectively

Evidence for Scattering of Electroweak Gauge Bosons in the W±Z Channel with the ATLAS Detector at the Large Hadron Collider

The Standard Model (SM) is the fundamental theory describing elementary particles and their main interactions at typical energy scales at collider experiments, the electromagnetic, the weak, and the strong interactions. The more complex underlying structure describing the weak and the strong interactions in the SM compared to the electromagnetic interaction necessitates direct three-point and four-point interactions among the mediators of the weak and strong interactions, called gauge bosons. Such self-interactions do not exist for the gauge boson of the electromagnetic interaction, the photon. While the three-point interaction was studied in detail in earlier collider experiments, the four-point interaction is a fundamental prediction of the SM, which was not observed for the weak interaction when starting this study. One process, where both the three-point as well as the four-point interactions contribute is the scattering of electroweak gauge bosons W, Z, γ also referred to as vector boson scattering (VBS). In the SM, this scattering is mediated by gauge boson self-interactions, or via the exchange of a Higgs boson. The scattering contributions mediated by a Higgs boson are sensitive to the properties of the Higgs boson and the details of the mechanism in which the W and Z bosons acquire their masses, called electroweak symmetry breaking. At hadron colliders such as the Large Hadron Collider (LHC), VBS is observable in a final state with the decay products of two gauge bosons in combination with two jets. These jets have a distinct signature allowing for good suppression of backgrounds and consequently for studies of the complex final state despite the low cross-sections. The first evidence for a VBS process was presented based on the Run 1 dataset alone by the ATLAS collaboration in the WW → WW channel in the fully leptonic final state. The CMS collaboration published the first observation of VBS in the same channel using data from 2015 and 2016 of Run 2, which was later confirmed by the ATLAS collaboration with contributions by the author, e.g. in the modelling of WZ background processes and associated uncertainties. The second boson channel for which VBS was observed was the WZ/γ → WZ boson channel in the fully leptonic final state. This observation was published by the ATLAS collaboration with significant contributions by the author. The studied dataset was collected with the ATLAS detector at a centre-of-mass energy √s = 13 TeV during 2015 and 2016 of Run 2 of the LHC and amounts to an integrated luminosity of 36.1/fb. In this study, the dataset was re-analysed following the same overall approach but with improvements in several key aspects. A comprehensive overview of available setups for reliable simulations of the signal process is presented. In a modelling study of the available setups, modelling issues in the parton shower simulation of SHERPA and earlier versions of PYTHIA observed in earlier studies are confirmed. The best matrix-element accuracies in available setups are leading-order for the full VBS signal process and next-to-leading-order in the VBF approximation. For upcoming analyses, a leading-order calculation of the full process including an additional QCD emission merged with parton shower simulations is found to be most promising, before full next-to-leading order calculations become available for all boson channels in VBS. Additional emphasis is set on the modelling of backgrounds, mainly WZ diboson production in association with additional QCD emissions as well as the experimental background due to misidentified leptons. A data-driven approach is applied and studied in detail for a reliable estimate of the latter background. Significant improvements to the estimate, e.g. in the form of additional corrections, are found via dedicated tests of the self-consistency of the approach using simulations. Machine-learning algorithms in the form of Boosted-Decision-Trees (BDT) are trained and optimized for improved separation of the background and signal processes. Evidence for the signal process is found with a significance of 3.44 σ using the profile likelihood method in a binned maximum-likelihood fit. The fiducial cross-section is measured to be σ= 1.41 + 0.46 - 0.40(stat) + 0.38 - 0.28 (theo) ± 0.13 (sys) fb , which is in good agreement with the leading-order SM prediction of σ = 1.33 + 0.14 -0.15 fb.:1 Introduction 2 Theoretical Framework 3 Simulations and Modelling Studies 4 Experiment 5 Object and Event Selection 6 Background Estimation 7 Multi-variate Event Classification 8 Uncertainties 9 Cross-section Measurement 10 Conclusions & Outloo

Effectiveness of Aid: Panel Data Analysis of Foreign Aid in Africa

This paper investigates the effectiveness of international foreign aid flows into the continent of Africa. The study incorporates economic information into an econometric model to examine the influence of variables including natural resources, types of government, corruption, and education. The influence of gender equality and rule of law in relation to developed countries is factored in through a dependent variable. These findings provide an analysis on the efficiency of foreign aid and its effects on economic development in the region

Extending Tomas Kulka\u27s Aesthetic Dualism: Value, Not Meaning, in the Case of Absolute Music

Within the past few decades the topic of musical meaning in the case of absolute music has received increasingly greater attention in the philosophical communities. One discussion is a debate between Constantijn Koopman and Stephen Davies, on the one side, and Peter Kivy, on the other. In this paper, I argue that many of the features of the musical encounter captured in terms of meaning by Koopman & Davies’ position are better addressed in terms of value. On Kivy’s suggestions, I contend we avoid use of the term ‘meaning’. To wit, I extend a conceptual framework for aesthetic value, advocated elsewhere by Thomas Kulka, to make the case that absolute music has the kinds of value that explain our tendency to ascribe ‘meaning’ to it, and that absolute music is valuable in multiple philosophically relevant ways, even if not meaningful in any

Trade-offs between manure management with and without biogas production

Introduction: In rural developing countries with a traditional manure management, animal manure is a value-added agricultural commodity being utilized as a source of fuel and plant nutrients. The sustainable environmental management of this resource has to consider the whole upstream and downstream activities of current management systems. Methods & Materials: In line with this requirement, this study has integrated the Intergovernmental Panel on Climate Change (IPCC) method on manure managements into the life-cycle assessment of two different manure management systems: the traditional system without biogas production and the alternative system with biogas production. Special attention is given to compare the GHG emissions as well as Nitrogen (N), Phosphorous (P), and Potassium (K) Fertilizing Nutrients (NPK) from the two systems. Results: The great advantage of manure conversion to biogas is mainly due to the avoided wood (18 kg/animal.yr), crop-residues (12 kg/ animal.yr) and dung (8 kg/ animal.yr) used as cooking fuels in the region. If methane leakage is over 38% then this will offset the GHG emission reduction of manure-to-biogas system

Evaluation of optical data gained by ARAMIS-measurement of abdominal wall movements for an anisotropic pattern design of stress-adapted hernia meshes produced by embroidery technology

For the sustainable repair of abdominal wall hernia the application of hernia meshes is required. One reason for the relapse of hernia after surgery is seen in an inadequate adaption of the mechanical properties of the mesh to the movements of the abdominal wall. Differences in the stiffness of the mesh and the abdominal tissue cause tension, friction and stress resulting in a deficient tissue response and subsequently in a recurrence of a hernia, preferentially in the marginal area of the mesh. Embroidery technology enables a targeted influence on the mechanical properties of the generated textile structure by a directed thread deposition. Textile parameters like stitch density, alignment and angle can be changed easily and locally in the embroidery pattern to generate a space-resolved mesh with mechanical properties adapted to the requirement of the surrounding tissue. To determine those requirements the movements of the abdominal wall and the resulting distortions need to be known. This study was conducted to gain optical data of the abdominal wall movements by non-invasive ARAMIS-measurement on 39 test persons to estimate direction and value of the major strains