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Intermittent Convex Integration in Mathematical Fluid Mechanics: Applications to the Euler Equations and the Chain Rule Problem
No full textThis thesis is concerned with intermittent convex integration and its applications to some equations in fluid mechanics. This technique originated from differential geometry with the proof of the famous Nash-Kuiper theorem on isometric embeddings. It was extended by Gromov and many other authors and is by now considered a powerful tool in the construction of (anomalous) solutions to certain PDEs. One of its most striking applications in the area of fluid mechanics is the proof of the flexible part of Onsager's conjecture.
In this thesis, we consider two concrete examples of intermittent convex integration. The first one concerns the chain rule problem: given scalar functions β and ρ and a divergence-free vector field u, we ask the question whether one can express div(β(ρ)u) only in terms of β'(ρ) and div(ρu). This is clear if β is at least C^1 and u and ρ are Lipschitz continuous.
We prove that in the class of Sobolev vector fields, the answer to that question is negative in general. We even show that for any distribution T which is the divergence of some L^1 function and a given β with suitable growth, there exists a divergence-free, Sobolev regular u and a ρ with div(β(ρ)u)=T and div(ρu) = 0.
The second application deals with the two-dimensional Euler equations. We prove the existence of energy dissipating weak solutions with vorticity in a real Hardy space H^p with p<1. A novel difficulty here compared to previous works in convex integration is that working in real Hardy spaces requires control of higher order moments of the solutions. An additional difficulty is that we work on the full space rather than on a periodic domain
Gamma-ray spectroscopy of neutron-rich scandium isotopes
No full textWith the advances in radioactive isotope science, nuclei far from the valley of beta-stability have become available for nuclear physics experiments. Data on exotic nuclei obtained in the last decades report on the interesting phenomena taking place at the edges of the nuclear chart. The standard magic numbers - 2, 8, 20, 28, 50, 82, and 126, known from the nuclear shell model, appear to not be uniform and can weaken and disappear, while new neutron and proton numbers obtain magic character. An example is the appearance of the neutron N = 32 and N = 34 magic numbers in the calcium isotopes. The establishment of magicity includes a series of experiments such as measurements of excited state energies, reduced transition probabilities, masses and
cross sections. The region around calcium has been extensively investigated in the last decade implementing all mentioned techniques, and others, in order to determine the persistence of the new magic numbers. While the N = 32 subshell closure has been confirmed both below and above calcium, the N = 34 subshell closure seems to disappear when protons are added to ^{54]Ca. The N = 34 isotope of scandium, with one proton more than calcium, makes a perfect ground to test the shell evolution in the pf -shell. Towards the neutron rich side, scandium is approaching the N = 40 island of inversion, IoI, which is characterized by increased deformation and energetically-favoured intruder configurations in the ground states. In light of recent results on neutron-rich N = 36, 38 Ca isotopes, information on the scandium isotones will bring more understanding to the limits of the IoI. The Shell Evolution And Search for Two-plus energies At RIBF project, known as SEASTAR, aims at a systematic investigation of the neutron-rich edge of the nuclear chart, including the nuclei around the new magic numbers N = 32, 34, as well as the N = 40 Island of Inversion. The third SEASTAR campaign took place in 2017 at RIKEN-RIBF and produced the data on the N = 34 isotope of scandium, as well as the first spectroscopy of the ^{57,59}Sc, which will be presented in this work. The primary beam of ^{70}Zn was accelerated to 345 MeV/u and impinged on a ^{9}Be target, producing a beam of fission reaction products. The neutron-rich radioactive isotopes were selected and identified on an event-by-event basis in the BigRIPS fragment separator. A second target of liquid hydrogen was used to induce knockout reactions, while the surrounding Time Projection Chamber allowed for precise reaction vertex determination. In this way a good Doppler correction of the detected gamma-rays was achieved. The DALI2^{+} array was used for the γ-ray detection. The
outgoing fragments were identified using the SAMURAI magnet.
The neutron-rich ^{55,57,59}Sc isotopes were investigated via in-beam gamma-ray spectroscopy following direct and indirect proton and neutron removal reactions, as well as inelastic scattering. For all three isotopes level schemes were build. In the case of ^{55}Sc the obtained level scheme was compared to the one reported in literature. All level schemes were compared to state-of-the-art shell model calculations. The A3DA and SDPF-MUr interactions were implemented, which have been successfully used for the description of nuclei in the same region
Phenomenological analysis of the electrical behavior of helical gears to identify sensory utilizable effects for condition monitoring approaches
No full textIn this contribution the electrical behavior of helical gear contacts is investigated. The investigation is based on impedance measurements obtained on an industrial gearbox test bench. The results are analyzed to identify the qualitative influence of rotation speed, load, rotation direction, load direction and surface alterations. Furthermore, potentials and limitations of utilizing the electrical behavior of helical gear contacts for condition monitoring applications are discussed. The investigations show that the lubrication condition can be qualitatively identified based on the characteristics of the electrical behavior of the gear contact. Important influencing factors for the lubrication film thickness and consequently the impedance of the gear contact can be determined to be rotation speed and load but also rotation and load direction. Surface alterations like damages but also tooth pitch deviations in the region of single digit micrometers can be seen to have a measurable influence on the impedance signal of the gear contact. These effects can potentially be used for condition monitoring approaches. However, the ambiguity of the impedance signal due to the high number of influencing factors remains a limitation of this new measurement method. Another factor for the ambiguity of the impedance signal is the simultaneous contact of multiple teeth which are not distinguishable in the impedance signal. This contribution shows the potentials and limitations for the sensory utilization of the electrical behavior of helical gear contacts and highlights novel research gaps
Strong coupling spontaneous emission interference near a graphene nanodisk
No full textIn this work, we analyze the spontaneous emission dynamics of a V-type quantum emitter near a graphene nanodisk based on the combination of electromagnetic and quantum dynamical calculations. The presence of the graphene nanodisk gives strong anisotropy to the Purcell factors of the quantum emitter, leading to interference effects in spontaneous emission appearing as coupling between the emitter’s upper levels. This effect is further enhanced by the strong light–matter interaction of the quantum emitter with the modified electromagnetic mode continuum, which induces non-Markovian spontaneous emission dynamics. We have studied the population dynamics of the quantum emitter at a specific distance from the center of the graphene nanodisk for various free-space decay widths and different quantum emitter’s initial conditions and have shown weak coupling results appearing with Markovian decay dynamics, obtained for quantum emitters with small free-space decay widths, and population dynamics that exhibits distinctly non-Markovian features, such as prominent decaying Rabi oscillations in the population evolution of the quantum emitter’s excited states and energy exchange between them during the overall population decay into the photonic mode continuum for largest free-space decay widths. Also, for the largest value of the free-space decay width, we obtain significant population trapping effects in the excited states of the quantum emitter. Furthermore, we find that the population dynamics for specific light–matter interaction strength conditions between the quantum emitter and the graphene nanodisk depend distinctively on the initial state of the quantum emitter, whether it is a single state or a superposition state
An intensity-based LIF measurement technique to quantify film thicknesses in the air gap of an electric motor with direct liquid cooling
No full textThe air gap of an optically accessible model of a directly cooled radial flux electric motor is investigated using laser-induced fluorescence (LIF). The cooling oil enters the air gap and a film forms on the stator surface, which resembles a thin film in a shear flow. The flow phenomena at different rotational speeds (2000 rpm to 10,000 rpm) are described. An intensity-based LIF measurement technique is developed and used to measure the film thickness on the stator in a realistic air gap environment. The rotational speed influences the flow phenomena and the film thickness of the stator film. With increasing rotational speed, i.e., increasing gas Reynolds number, the film thickness probability density functions (PDFs) shift to lower film thicknesses and become narrower, which is in agreement with the characteristic behavior of films in shear flows as reported in the literature. Additionally, the velocities of the wave crests which move across the film surface are evaluated and used to calculate the film Reynolds number ReF, which characterizes the investigated operating points
Safe Trajectory Planning for Autonomous Vehicles Using Motion Primitives: A Moving Horizon Approach
No full textAutonomous systems, from self-driving cars to intelligent manufacturing robots, are increasingly integrated into everyday life, making their safe and reliable interaction with humans and their environments critical. This work addresses the challenges of motion planning and control in dynamic and uncertain environments. It presents a robust, hierarchical planning and control approach based on moving-horizons, which ensures high performance, safety, and robustness in the face of uncertainty while exploiting different operational modes to enhance efficiency.
At the heart of this work is a computational and modeling framework for planning under uncertainty, using the principle of moving-horizon decision making to predict the system’s behavior over a receding horizon. The proposed approach decomposes the system dynamics into a parameterized set of motion primitives, representing different operational modes, and restricts feasible nominal trajectories to sequences of these primitives.
This method results in a mixed-integer mathematical programming problem that explicitly accounts for uncertainty. It is designed to accommodate a wide range of dynamical systems. By integrating interval reachability analysis with set-based robust control, the approach approximates nonlinear system dynamics through the applied primitives. The framework is computationally efficient and suitable for real-time applications.
A key contribution of this work is the decomposition of planning and control through a contract-based interaction between a high-level planner and a low-level controller. This interaction encapsulates the capabilities of the low-level controller within the planner's constraints, simplifying trajectory planning. In addition, integration with optimal control extends safety and performance beyond the planning horizon.
The methodologies developed are applicable to a broad spectrum of autonomous vehicles. Simulation results demonstrate the practicality and effectiveness of the approach in real-world scenarios
HCC: A Language-Independent Hardening Contract Compiler for Smart Contracts
No full textDeveloping secure smart contracts remains a challenging task. Existing approaches are either impractical or leave the burden to developers for fixing bugs. In this paper, we propose the first practical smart contract compiler, called HCC, which automatically inserts security hardening checks at the source-code level based on a novel and language-independent code property graph (CPG) notation. The high expressiveness of our developed CPG allows us to mitigate all of the most common smart contract vulnerabilities, namely reentrancy, integer bugs, suicidal smart contracts, improper use of this http URL, untrusted delegate-calls, and unchecked low-level call bugs. Our large-scale evaluation on 10k real-world contracts and several sets of vulnerable contracts from related work demonstrates that HCC is highly practical, outperforms state-of-the-art contract hardening techniques, and effectively prevents all verified attack transactions without hampering functional correctness
Yeast complementation assays provide limited informationon functional features of K+ channels
No full textWe investigate to what extent yeast complementation assays, which in principle can provide large amounts of training data for machine learning models, yield quantitative correlations between growth rescue and single channel recordings. If this were the case, yeast complementation results could be used as surrogate data for machine learning-based channel design. Therefore, we mutated position L94 at the cavity entry of the model K channel KcvPBCV1 to all proteinogenic amino acids. The function of the WT channel and its mutants was investigated by reconstituting them in planar lipid bilayers and by their ability to rescue the growth of a yeast strain deficient in K+ uptake. The single channel data show a distinct effect of mutations in this critical position on unitary conductance and open probability, with no apparent causal relationship between the two functional parameters. We also found that even conservative amino acid replacements can alter the unitary conductance and/or open probability and that most functional changes show no systematic relationship with the physicochemical nature of the amino acids. This emphasizes that the functional influence of an amino acid on channel function cannot be reduced to a single chemical property. Mutual comparison of single channel data and yeast complementation results exhibit only a partial correlation between their electrical parameters and their potency of rescuing growth. Hence complementation data alone are not sufficient for enabling functional channel design; they need to be complemented by additional parameters like the number of channels in the plasma membrane
Rolled Wall : Entwicklung eines textilen Wandschalungssystems
No full textGebäudegeometrien werden immer komplexer. Dadurch steigt der Schalungsaufwand mit etablierten Schalungssystemen. Die textile Schalung bietet Lösungsmöglichkeiten, um Zeit-, Arbeits- und Ressourcenaufwand zu reduzieren. Insbesondere die Möglichkeit, einen vollständigen Wandaufbau mit allen notwendigen Schichten vorzufertigen, zeigt das Potenzial der textilen Wandschalung auf. Am Beispiel einer textilen Wandschalung zeigt dieses Buch, welche Auswirkungen Textilien als Schalhaut auf den Baustoff Beton haben. Außerdem erarbeitet es konstruktive Lösungsmöglichkeiten zur Herstellung textiler Wandschalungen. Dabei liegt ein besonderer Schwerpunkt auf dem Einfluss von Textilien auf die Dauerhaftigkeit des Betons und den Frischbetondruck. Darüber hinaus werden die Gestaltungsmöglichkeiten beleuchtet, die der Einsatz verschiedener Textilien und Durchankerungsmöglichkeiten eröffnet
Detailed Analysis of the Raman Vibrational Structure of Vanadia in VOₓ/CeO₂: A Combined Experimental and Theoretical Approach
No full textSupported vanadia is an important catalyst for oxidation reactions but its properties and catalytic activity heavily depend on the support material. Ceria is a promising support due to its reducibility and active participation in many oxidation reactions. To understand these catalysts at work, operando spectroscopy is required, which can be difficult to interpret. To obtain a fundamental, nuclearity-dependent understanding of the vibrational structure of VOₓ/CeO₂, we combined Raman characterization with density functional theory (DFT) by calculating vibrational frequencies and Raman intensities based on established vanadia structures on support structures with (4 × 4) periodicity. Monomeric and oligomeric structures were simulated based on VO and VO₂ clusters, resulting in VₙOₙ (n = 1–3) and VₙO₂ₙ (n = 1–7) oligomers. The latter were combined based on weighting factors determined from the experimental vanadyl fine structure and the thermodynamic stability of the clusters, yielding a simulated spectrum of the nuclearity distribution. Using this approach, vanadium coverage effects could be simulated, resulting in an overall agreement between experimental and theoretical spectra and providing nuclearity-dependent insight into the vibrational spectrum of VOₓ/CeO₂, including the interface region and the vanadyl fine structure. Our study highlights the importance of DFT calculations to facilitate the assignment of spectroscopic features and obtain a detailed understanding of catalytic materials