DFG-Abschlussberichte

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    Final Report of the DFG Project "Drawing Graphs: Geometric Aspects Beyond Planarity" (project number 654838)
    (Hannover : Technische Informationsbibliothek, 2025-04) Wolff, Alexander
    The aim of our project was to get a better understanding of the mathematical structures that correspond to the different ways of measuring the visual complexity of a drawing of a graph. Examples for such measures are the local crossing number, that is, the maximum number of crossings per edge, the slope number, that is, the number of different slopes in a crossing-free straight-line drawing, the segment number or the line cover number, that is, the number of straight-line segments or straight lines needed to cover a crossing-free straight-line drawing. For a graph, the measures are defined as the minimum over all drawings (of the corresponding type). The center of our studies became the measure segment number, which is known to be NP-hard to compute. In particular, we showed that there is a parameterized algorithm for computing the segment number of a given graph with respect to the several parameters; the natural parameter, the line cover number, and the vertex cover number. The latter proof was the technically most challenging. In a different work, we showed that it is ETR-complete to compute the segment number of a given graph, that is, the segment number of a graph can be expressed in terms of the existential theory of the reals, but its computation is at least as hard as every problem in the complexity class ETR. Moreover, we extended a result concerning the segment number of triconnected cu- bic planar graphs by showing that the segment number of every triconnected 4-regular planar graph with n vertices is at most n + 3, which is tight up to the additive constant. We have proved the first linear universal lower bounds for the segment number of out- erpaths, maximal outerplanar graphs, 2-trees, and planar 3-trees. This shows that the existing algorithms for these graph classes are in fact constant-factor approximation algorithms. For maximal outerpaths, our universal lower bound is best possible.
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    Berechnung, Messung und Kontrolle der Energiebarrieren und der lichtinduzierten Kinetik des ASi-Sii-Defektes
    (Hannover : Technische Informationsbibliothek, 2025-04-09) Lauer, Kevin
    Die Siliziumtechnologie hat umfangreiche Anwendungsmöglichkeiten, die sich im gegenwärtigen Alltag überall wiederfinden. Anwendungen wie Computer, Smartphones, Sensoren, Detektoren, Solarzellen und viele mehr sind nur möglich geworden durch jahrzehntelange Erforschung des Siliziums und der nötigen technologischen Prozesse. Nichtsdestotrotz gibt es noch immer unverstandene Phänomene und Mechanismen, speziell im Bereich der Defekte und der Degradation. Ein besseres Verständnis ist notwendig, da Defekte zum einen notwendig für die Funktionsweise von Bauelementen sind, sich aber auch negativ auswirken können. Das Projekt untersuchte eine besondere Kategorie von Defekten, die einen Akzeptor und interstitielles Silizium involvieren, so genannte ASi-Sii-Defekte. Sie tragen vermutlich maßgeblich zur licht-induzierten Degradation von Solarzellen und Detektorbauelemente bei. Konkret wurden in diesem Projekt die Energiebarrieren zwischen verschiedenen Defektzuständen der ASi-Sii-Defekte, die teilweise erst identifiziert werden mussten, in enger Zusammenarbeit von Experiment und Theorie erforscht und bestimmt. Die Barrierenhöhen haben einen direkten Einfluss auf die Defektkinetik und -stabilität, weshalb ihre Kenntnis essentiell ist. Gelingt es, die Barrierenhöhen gezielt zu beeinflussen (z.B. durch Wahl des Akzeptors), so können Bauelementeigenschaften ggf. gezielt eingestellt werden, z.B. zur Effizienzsteigerung oder Lebenszeitverlängerung von Solarzellen. Zudem erscheint es reizvoll künftig zu untersuchen, inwieweit Defekte aus dieser Kategorie als Qubit Verwendung finden können und somit für die Silizium-basierte Quantentechnologie interessant sind. Das Projekt hat erfolgreich einen Beitrag zum grundlegenden Verständnis der ASi-Sii-Defekte geleistet und legt den Grundstein für die weitere Erforschung dieser interessanten Defektkategorie.
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    Collaborative Research Center 917 : Resistively Switching Chalcogenides for Future Electronics : Structure, Kinetics, and Device Scalability : Final report : 2019/2-2020-2021-2022-2023/1
    (Hannover : Technische Informationsbibliothek, 2025-03-25) Wuttig, Matthias; Waser, Rainer; Dronskowski, Richard; Dittmann, Regina; Simon, Ulrich; Mayer, Joachim
    The goal of SFB 917 has been the development of novel nanoswitches that can be reproducibly and reversibly changed between two states on very short time and length scales. Such nanoswitches can enable new storage and memory devices as well as neuro-inspired architectures for information technology. In the third and final funding period of SFB 917 we have witnessed and contributed to three major trends. The exponential growth in the demand for data storage and processing has continued. Hardware improvements are therefore urgently needed to meet the increased demands for data storage and processing as well as the related increase in energy consumption. SFB 917 strives to realize novel storage devices by exploiting the full potential of chalcogenide-based nanoswitches. Yet, it has become increasingly clear in the last few years, that improvements in device performance alone are insufficient to deal with the exponential growth mentioned above. The advance of Large Language Models (LLMs) like ChatGPT and related software has produced a further increase in data processing related energy consumption. This is a major challenge considering the expected further increase of professional and private usage of such machine learning tools. To minimize the related energy consumption, particularly energy-efficient software and hardware developments are mandatory. Within SFB9917, we have this intensified our efforts to work on effects related to a reduction in energy consumption. While energy-efficient devices can help, an improvement in hardware architecture offers significantly more leverage. We have thus explored the potential of chalcogenide based nano-switches in neuro-inspired computer architectures. To this end, several new large-scale research projects have been initiated (NeuroSys and NeuroTec), which extend our research on these devices in increasingly more complex architectures, offering new opportunities to harvest the findings of SFB 917 in new applications. To tailor chalcogenide-based nano-switches, major advances in instrumentation as well as an in-depth understanding of the origin of underlying phenomena and unconventional properties in these materials have been mandatory. Challenges included the characterization of switching in these materials on nanosecond time and nanometer length scales. Sophisticated tools have been built and utilized. Understanding unconventional properties are required building a bridge between concepts of inorganic chemistry and material properties leading to novel treasure maps which help to identify and tailor chalcogenides for specific applications. These successes are described in detail in the present report. To demonstrate that these findings are also relevant for industry, close cooperation with industrial partners has been established to ensure that the findings made within SFB 917 can also be implemented on the shortest possible time scales.
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    Sedimentation of binary mixtures: Phase stacking and Nonequilibrium dynamics
    (Hannover : Technische Informationsbibliothek, 2024-12-30) Schmidt, Matthias; de las Heras, Daniel
    Based on equilibrium sedimentation path theory and the local density functional approximation, we investigated the effects of gravity on several relevant types of binary colloidal mixtures. Settled systems are represented by so-called sedimentation paths, which determine the variation of the species-resolved chemical potentials with altitude. Analysing the resulting line segments in the plane of chemical potentials of the bulk phase diagram allows one to rationalize the full equilibrium stacking phenomenology for a given system under gravity. The approach predicts theoretically the stacking sequences of colloidal rod-plate mixtures that were observed in iconic experiments by van der Kooij and Lekkerkerker. Thereby the occurrence of up to five simultaneous phase layers emerges naturally from the mere interplay of gravity and two-phase bulk coexistence, without invoking particle polydispersity. We studied the effects on equilibrium phase stacking upon varying the buoyant mass ratio of both components and our predictions are testable in experiments by systematic variation of the height of sedimentation columns. We have carried out similar sedimentation studies for: plate-spheres mixtures, mass-polydisperse systems, and hard spherocylinders. We suggest that microscopic particle properties, such as the buoyant mass, can be inferred from macroscopic measurements of layer thicknesses in phase stacking sequences. We addressed gravity-induced nonequilibrium flow and structure formation on the basis of power functional theory, adaptive Brownian dynamics computer simulations, and functional machine learning. Power functional theory allows one to rationalize and to model the nonequilibrium behaviour of many-body systems based on the one-body density and velocity field. We have used the approach to categorize systematically the different types of relevant nonequilibrium force contributions and have developed corresponding analytical gradient approximations. Neural functionals, as trained on the basis of both equilibrium and nonequilibrium computer simulation data, were shown to yield accurate predictions for structure formation and design of nonequilibrium flow. We have formulated force-based density functional theory and have demonstrated that neural density functionals outperform the best available hard sphere fundamental measure functionals. We have developed adaptive Brownian dynamics as a performant and highly stable numerical integration scheme for the temporal integration of overdamped many-body Langevin equations of motion, as demonstrated for a particle gel subject to convective sedimentation flow. We have put forward general frameworks for fluctuations of general hyperobservables, for their associated hyperforce correlation functions, and for the gauge invariance of statistical mechanics, where Noether's theorem yields exact sum rules that constrain correlations, as exemplified for ideal and for active sedimentation.
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    DFG Abschlussbericht : Neuer Ansatz für eine optische Biopsie in der Melanomdiagnostik
    (Hannover : Technische Informationsbibliothek, 2025) Roth, Bernhard; Fedorov Kukk, Anatoly; Emmert, Steffen
    Das Forschungsprojekt hatte die Entwicklung eines multimodalen Systems für die optische Biopsie der Haut mit der Anwendung in der Melanomdiagnostik zum Ziel. Es wurde erfolgreich ein neuartiges multimodales Bildgebungssystem entwickelt und validiert, das Ultraschall, photoakustische Tomographie, optische Kohärenztomographie, Raman-Spektroskopie und Kameramodalitäten in einer einzigen Scaneinheit zur nicht-invasiven optischen Biopsie von Hautläsionen integriert. Ein solches in seiner Konstruktion neuartiges System, das diese Modalitäten kombiniert, existierte in der Literatur bisher nicht. Das entwickelte System wurde erfolgreich in einer (prä)klinischen Studie validiert. Der Aufbau, der einen Wassertank mit einem akustischen Spiegel und einer flexiblen Membran umfasst, ermöglicht 3D-US/PAT-Bildgebung mit hoher räumlicher Auflösung und Tiefenkapazität, validiert durch umfangreiche Phantomtests und klinische Messungen. Das System zeigte eine starke Korrelation mit histopathologischen Standards, insbesondere bei dünnen Läsionen, und erhielt positives Feedback von Dermatologen für seine 3D-Bildgebungsfähigkeiten. Die Arbeit hebt das Potenzial dieses integrierten Systems hervor, die Diagnose und Behandlung von Hautkrebs zu verbessern, indem detaillierte, schnelle und nicht-invasive Messungen bereitgestellt werden, und schlägt weitere Verbesserungen zur Steigerung der diagnostischen Genauigkeit und Benutzerfreundlichkeit vor.