Erosion of dust aggregates

Aims: The aim of this work is to gain a deeper insight into how much different aggregate types are affected by erosion. Especially, it is important to study the influence of the velocity of the impacting projectiles. We also want to provide models for dust growth in protoplanetary disks with simple recipes to account for erosion effects. Methods: To study the erosion of dust aggregates we employed a molecular dynamics approach that features a detailed micro-physical model of the interaction of spherical grains. For the first time, the model has been extended by introducing a new visco-elastic damping force which requires a proper calibration. Afterwards, different sample generation methods were used to cover a wide range of aggregate types. Results: The visco-elastic damping force introduced in this work turns out to be crucial to reproduce results obtained from laboratory experiments. After proper calibration, we find that erosion occurs for impact velocities of 5 m/s and above. Though fractal aggregates as formed during the first growth phase are most susceptible to erosion, we observe erosion of aggregates with rather compact surfaces as well. Conclusions: We find that bombarding a larger target aggregate with small projectiles results in erosion for impact velocities as low as a few m/s. More compact aggregates suffer less from erosion. With increasing projectile size the transition from accretion to erosion is shifted to higher velocities. This allows larger bodies to grow through high velocity collisions with smaller aggregates.Comment: accepted for publication in Astronomy & Astrophysic

Tensile & shear strength of porous dust agglomerates

Context.Within the sequential accretion scenario of planet formation, planets are build up through a sequence sticking collisions. The outcome of collisions between porous dust aggregates is very important for the growth from very small dust particles to planetesimals. In this work we determine the necessary material properties of dust aggregates as a function the porosity. Aims: Continuum models such as SPH that are capable of simulating collisions of macroscopic dust aggregates require a set of material parameters. Some of them such as the tensile and shear strength are difficult to obtain from laboratory experiments. The aim of this work is to determine these parameters from ab-initio molecular dynamics simulations. Methods: We simulate the behavior of porous dust aggregates using a detailed micro-physical model of the interaction of spherical grains that includes adhesion forces, rolling, twisting, and sliding. Using different methods of preparing the samples we study the strength behavior of our samples with varying porosity and coordination number of the material. Results: For the tensile strength, we can reproduce data from laboratory experiments very well. For the shear strength, there are no experimental data available. The results from our simulations differ significantly from previous theoretical models, which indicates that the latter might not be sufficient to describe porous dust aggregates. Conclusions: We have provided functional behavior of tensile and shear strength of porous dust aggregates as a function of the porosity that can be directly applied in continuum simulations of these objects in planet formation scenarios.Comment: Accepted for publication in A&

The physics of protoplanetesimal dust agglomerates. VII The low-velocity collision behavior of large dust agglomerates

We performed micro-gravity collision experiments in our laboratory drop-tower using 5-cm-sized dust agglomerates with volume filling factors of 0.3 and 0.4, respectively. This work is an extension of our previous experiments reported in Beitz et al. (2011) to aggregates of more than one order of magnitude higher masses. The dust aggregates consisted of micrometer-sized silica particles and were macroscopically homogeneous. We measured the coefficient of restitution for collision velocities ranging from 1 cm/s to 0.5 m/s, and determined the fragmentation velocity. For low velocities, the coefficient of restitution decreases with increasing impact velocity, in contrast to findings by Beitz et al. (2011). At higher velocities, the value of the coefficient of restitution becomes constant, before the aggregates break at the onset of fragmentation. We interpret the qualitative change in the coefficient of restitution as the transition from a solid-body-dominated to a granular-medium-dominated behavior. We complement our experiments by molecular dynamics simulations of porous aggregates and obtain a reasonable match to the experimental data. We discuss the importance of our experiments for protoplanetary disks, debris disks, and planetary rings. The work is an extensional study to previous work of our group and gives a new insight in the velocity dependency of the coefficient of restitution due to improved measurements, better statistics and a theoretical approach

Funktionelle kardiale Magnet-Resonanz-Tomographie: Einfluss der alternativen Wahl des Narkosemittels Isofluran, Propofol sowie Propofol in Kombination mit Pancuronium auf die kardialen Funktionsparameter im Rattenmodell

Die Magnetresonanztomographie stellt den Goldstandard zur kardialen Funktionsdiagnostik dar und ermöglicht die nicht-invasive Analyse der Herzfunktion mit valider Bestimmung von Volumina, Flüssen sowie der Ejektionsfraktion in vivo. In unserer Arbeitsgruppe erfolgt eine stetige Weiterentwicklung der Methode am Rattenmodell, wobei regelhaft eine Narkose des Versuchtstiers notwendig ist. Im Rahmen meiner Arbeit wurde der Effekt verschiedener Narkoseformen auf die Herzfunktion untersucht. Dabei wurde eine Isoflurannarkose einer Narkose mittels Propofol sowie Propofol in Kombination mit Pancuronium gegenübergestellt. Hierbei zeigen sich teilweise deutliche Unterschiede in den kardialen Funktionsparametern während der Untersuchung. Hieraus ist zu folgern, dass ein sinnvoller Vergleich der Herzfunktion von Versuchsreihen mit unterschiedlicher Narkosetechnik problematisch ist. Dies unterstreicht die Wichtigkeit einer Festlegung der Narkosetechnik vor Beginn einer Versuchsreihe in der kardiovaskulären Forschung und deren Konstanthaltung über die gesamte Versuchsdauer.Cardiac magnetic resonance imaging (MRI) is considered the current gold standard for in vivo-analysis of cardiac structure and function. Our workgroup is concentrating on developing cardiac MRI techniques in small animal models, which generally requires anaesthesia of the animal. In the current study, the effects of the narcotics Isoflurane vs. Propofol vs. Propofol in combination with Pancuronium on functional cardiac parameters measured by cardiac MRI were analyzed. The results reveal major differences of the acquired functional cardiac parameters in animals anaesthetized with Isoflurane, Propofol, or Propofol in combination with Pancuronium, respectively. This highlights the importance of establishing a specific anaesthesia technique and keeping it unchanged during an entire MRI study

Embedded Software Development with Digital Twins: Specific Requirements for Small and Medium-Sized Enterprises

The transformation to Industry 4.0 changes the way embedded software systems are developed. Digital twins have the potential for cost-effective software development and maintenance strategies. With reduced costs and faster development cycles, small and medium-sized enterprises (SME) have the chance to grow with new smart products. We interviewed SMEs about their current development processes. In this paper, we present the first results of these interviews. First results show that real-time requirements prevent, to date, a Software-in-the-Loop development approach, due to a lack of proper tooling. Security/safety concerns, and the accessibility of hardware are the main impediments. Only temporary access to the hardware leads to Software-in-the-Loop development approaches based on simulations/emulators. Yet, this is not in all use cases possible. All interviewees see the potential of Software-in-the-Loop approaches and digital twins with regard to quality and customization. One reason it will take some effort to convince engineers, is the conservative nature of the embedded community, particularly in SMEs.Comment: 6 pages, 1 figure, 2 tables, conference, In Proceedings Of The 2023 IEEE International Conference on Digital Twin (Digital Twin 2023

A Phase-Field Approach to Diffusion-Driven Fracture

In recent years applied mathematicians have used modern analysis to develop variational phase-field models of fracture based on Griffith\u27s theory. These variational phase-field models of fracture have gained popularity due to their ability to predict the crack path and handle crack nucleation and branching. In this work, we are interested in coupled problems where a diffusion process drives the crack propagation. We extend the variational phase-field model of fracture to account for diffusion-driving fracture and study the convergence of minimizers using gamma-convergence. We will introduce Newton\u27s method for the constrained optimization problem and present an algorithm to solve the diffusion-driven fracture problem numerically. For the implementation of this method, we use a finite difference scheme

From Hubbard bands to spin-polaron excitations in the doped Mott material Nax_xCoO2_2

We investigate the excitation spectrum of strongly correlated sodium cobaltate within a realistic many-body description beyond dynamical mean-field theory (DMFT). At lower doping around $x$=0.3, rather close to Mott-critical half-filling, the single-particle spectral function of Na$_x$CoO$_2$ displays an upper Hubbard band which is captured within DMFT. Momentum-dependent self-energy effects beyond DMFT become dominant at higher doping. Around a doping level of $x\sim 0.67$, the incoherent excitations give way to finite-energy spin-polaron excitations in close agreement with optics experiments. These excitations are a direct consequence of the formation of bound states between quasiparticles and paramagnons in the proximity to in-plane ferromagnetic ordering.Comment: 5 pages, 3 figures; supplementary materia

From Hagedorn to Lee-Yang: Partition functions of N=4\mathcal{N}=4 SYM theory at finite NN

We study the thermodynamics of the maximally supersymmetric Yang-Mills theory with gauge group U(N) on R x S^3, dual to type IIB superstring theory on AdS_5 x S^5. While both theories are well-known to exhibit Hagedorn behavior at infinite N, we find evidence that this is replaced by Lee-Yang behavior at large but finite N: the zeros of the partition function condense into two arcs in the complex temperature plane that pinch the real axis at the temperature of the confinement-deconfinement transition. Concretely, we demonstrate this for the free theory via exact calculations of the (unrefined and refined) partition functions at N<=7 for the su(2) sector containing two complex scalars, as well as at N<=5 for the su(2|3) sector containing 3 complex scalars and 2 fermions. In order to obtain these explicit results, we use a Molien-Weyl formula for arbitrary field content, utilizing the equivalence of the partition function with what is known to mathematicians as the Poincare series of trace algebras of generic matrices. Via this Molien-Weyl formula, we also generate exact results for larger sectors.Comment: 34 pages, 3 figures, 2 ancillary files; v2: some references and clarifications added, matches published versio

What makes issuers happy? Testing the Prospect Theory of IPO Underpricing

We derive a behavioral measure of the IPO decision-maker's satisfaction with the underwriter's performance based on Loughran and Ritter's (2002) prospect theory of IPO underpricing. We assess the plausibility of this measure by studying its power to explain the decision-maker’s subsequent choices. Controlling for other known factors, IPO firms are less likely to switch underwriters for their first seasoned equity offering when our behavioral measure indicates they were satisfied with the IPO underwriter’s performance. Underwriters also appear to benefit from behavioral biases in the sense that they extract higher fees for subsequent transactions involving satisfied decision-makers. Although our tests suggest there is explanatory power in the behavioral model, they do not speak directly to whether deviations from expected utility maximization determine patterns in IPO initial returns

Finite Element Methods for Geometric Problems

In the herewith presented work we numerically treat geometric partial differential equations using finite element methods. Problems of this type appear in many applications from physics, biology and engineering use. We may partition the work in two blocks. The first one, including the chapters two to five, is about the approximation of stationary points of conformally invariant, nonlinear, elliptic energy functionals. Main interest is a compactness result for accumulation points of their discrete counterparts. The corresponding Euler-Lagrange equations are nonlinear, elliptic and of second order. They contain critical nonlinearities that are quadratic in the first derivatives. Thus, accumulation points of solutions to the discrete problem are not solutions of the continuous problem in general. We deduce a weak formulation in a mixed form and chose appropriate spaces for the discretization. First we show existence of discrete solutions and then, by the use of compensated compactness and standard finite element arguments, we establish convergence. Finally we introduce an iterative algorithm for the numerical realization and run different simulations. Hereby we confirm theoretical predictions derived in the stability analysis. The second part is about the derivation of gradient flows for shape functionals and their discretization with parametric finite elements. First, we consider the Willmore energy of a twodimensional surface in the threedimensional ambient space and deduce its first variation. Afterwards we phrase the corresponding gradient flow in a weak form and discuss possible discretizations. During the further progress of the work we modell cell membranes and the effects of surface active agents on the shape of these cells. Numerical simulations with closed surface give promising results and a reason to intensify the research in this field.Finite Elemente Methoden für Geometrische Probleme In der vorliegenden Dissertationsschrift geht es um die numerische Behandlung geometrischer partieller Differentialgleichungen unter Verwendung von Finite Elemente Methoden. Probleme dieser Art treten in einer Vielzahl von physikalischen, technischen und biologischen Anwendungen auf. Thematisch lässt sich die Arbeit in zwei Blöcke aufteilen. In den Kapiteln zwei bis fünf geht es um die Approximation stationärer Punkte konform invarianter, nichtlinearer, elliptischer Energiefunktionale. Das Hauptaugenmerk liegt dabei auf einem Kompaktheitsresultat für Häufungspunkte der diskretisierten Energiefunktionale. Die Euler Lagrange Gleichungen sind elliptisch und von zweiter Ordnung. Sie beinhalten kritische Nichtlinearitäten welche quadratisch von den ersten Ableitungen abhängen. Dies f¨hrt dazu, dass Häufungspunkte von Lösungen der diskretisierten Gleichung nicht zwangsläufig Lösungen der ursprünglichen Gleichung sind. Wir leiten eine schwache Formulierung der Gleichung in gemischter Form her und wählen stabile Finite Elemente Paare für die Diskretisierung. Zunächst zeigen wir, dass Lösungen der diskreten gemischten Formulierung Sattelpunkte eines erweiterten diskreten Energiefunktionals sind und schließen daraus auf die Existenz diskreter Löosungen. Um zu beweisen, dass Häufungspunkte der diskreten Sattelpunkte tatsächlich Lösungen der schwachen Formulierung sind bedienen wir uns einigen Resultaten der kompensierten Kompaktheit sowie bekannten Techniken aus dem Bereich der Finiten Elemente. Schließlich stellen wir einen iterativen Algorithmus für die numerische Realisierung auf und föhren mehrere Simulationen durch. Theoretische Stabilitätsergebnisse für den Algorithmus werden dabei numerisch bestätigt. Im zweiten Teil stehen die Herleitung von Gradientenflüssen von Flächenfunktionalen (shape functional) sowie deren Diskretisierung unter Verwendung von Parametrischen Finite Elemente Methoden im Mittelpunkt. Wir betrachten zunächst die sogenannte Willmore Energie einer zweidimensionalen Fläche im dreidimensionalen Raum und bestimmen deren erste Variation. Anschließend formulieren wir den zugehörigen Gradientenfluss in schwacher Form und diskutieren eine Diskretisierung mittels parametrischer Finite Elemente. Im weiteren Verlauf diskutieren wir die Modellierung von Zellmembranen und die Wirkung von oberflächenaktiven Substanzen (surfactants) auf die Form von Zellen. Numerische Simulationen mit geschlossenen Flächen liefern viel versprechende Resultate und geben Anlass zu weiteren Forschungsarbeiten in diesem Bereich