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Der vorliegende Band vereint thematisch auf das Essen bezogene Beiträge aus der slavistischen Literatur- und Kulturwissenschaft. Er zeigt das seit einigen Jahren artikulierte Interesse an dem Thema ohne dieses gleich zu einem „culinary turn“ stilisieren zu wollen. Das Essen ist – analysiert man die Präsenz des Themas in Literatur, Film und anderen Medien der Hochkultur – ein Bereich, in und mit dem allgemeinere kulturelle und soziale Prozesse besonders anschaulich gezeigt werden können.
Adopting a minimalist framework, the dissertation provides an analysis for the syntactic structure of comparatives, with special attention paid to the derivation of the subclause. The proposed account explains how the comparative subclause is connected to the matrix clause, how the subclause is formed in the syntax and what additional processes contribute to its final structure. In addition, it casts light upon these problems in cross-linguistic terms and provides a model that allows for synchronic and diachronic differences. This also enables one to give a more adequate explanation for the phenomena found in English comparatives since the properties of English structures can then be linked to general settings of the language and hence need no longer be considered as idiosyncratic features of the grammar of English. First, the dissertation provides a unified analysis of degree expressions, relating the structure of comparatives to that of other degrees. It is shown that gradable adjectives are located within a degree phrase (DegP), which in turn projects a quantifier phrase (QP) and that these two functional layers are always present, irrespectively of whether there is a phonologically visible element in these layers. Second, the dissertation presents a novel analysis of Comparative Deletion by reducing it to an overtness constraint holding on operators: in this way, it is reduced to morphological differences and cross-linguistic variation is not conditioned by way of postulating an arbitrary parameter. Cross-linguistic differences are ultimately dependent on whether a language has overt operators equipped with the relevant – [+compr] and [+rel] – features. Third, the dissertation provides an adequate explanation for the phenomenon of Attributive Comparative Deletion, as attested in English, by way of relating it to the regular mechanism of Comparative Deletion. I assume that Attributive Comparative Deletion is not a universal phenomenon, and its presence in English can be conditioned by independent, more general rules, while the absence of such restrictions leads to its absence in other languages. Fourth, the dissertation accounts for certain phenomena related to diachronic changes, examining how the changes in the status of comparative operators led to changes in whether Comparative Deletion is attested in a given language: I argue that only operators without a lexical XP can be grammaticalised. The underlying mechanisms underlying are essentially general economy principles and hence the processes are not language-specific or exceptional. Fifth, the dissertation accounts for optional ellipsis processes that play a crucial role in the derivation of typical comparative subclauses. These processes are not directly related to the structure of degree expressions and hence the elimination of the quantified expression from the subclause; nevertheless, they are shown to be in interaction with the mechanisms underlying Comparative Deletion or the absence thereof.
Deciphering the functioning of biological networks is one of the central tasks in systems biology. In particular, signal transduction networks are crucial for the understanding of the cellular response to external and internal perturbations. Importantly, in order to cope with the complexity of these networks, mathematical and computational modeling is required. We propose a computational modeling framework in order to achieve more robust discoveries in the context of logical signaling networks. More precisely, we focus on modeling the response of logical signaling networks by means of automated reasoning using Answer Set Programming (ASP). ASP provides a declarative language for modeling various knowledge representation and reasoning problems. Moreover, available ASP solvers provide several reasoning modes for assessing the multitude of answer sets. Therefore, leveraging its rich modeling language and its highly efficient solving capacities, we use ASP to address three challenging problems in the context of logical signaling networks: learning of (Boolean) logical networks, experimental design, and identification of intervention strategies. Overall, the contribution of this thesis is three-fold. Firstly, we introduce a mathematical framework for characterizing and reasoning on the response of logical signaling networks. Secondly, we contribute to a growing list of successful applications of ASP in systems biology. Thirdly, we present a software providing a complete pipeline for automated reasoning on the response of logical signaling networks.
One of the most significant current discussions in Astrophysics relates to the origin of high-energy cosmic rays. According to our current knowledge, the abundance distribution of the elements in cosmic rays at their point of origin indicates, within plausible error limits, that they were initially formed by nuclear processes in the interiors of stars. It is also believed that their energy distribution up to 1018 eV has Galactic origins. But even though the knowledge about potential sources of cosmic rays is quite poor above „ 1015 eV, that is the “knee” of the cosmic-ray spectrum, up to the knee there seems to be a wide consensus that supernova remnants are the most likely candidates. Evidence of this comes from observations of non-thermal X-ray radiation, requiring synchrotron electrons with energies up to 1014 eV, exactly in the remnant of supernovae. To date, however, there is not conclusive evidence that they produce nuclei, the dominant component of cosmic rays, in addition to electrons. In light of this dearth of evidence, γ-ray observations from supernova remnants can offer the most promising direct way to confirm whether or not these astrophysical objects are indeed the main source of cosmic-ray nuclei below the knee. Recent observations with space- and ground-based observatories have established shell-type supernova remnants as GeV-to- TeV γ-ray sources. The interpretation of these observations is however complicated by the different radiation processes, leptonic and hadronic, that can produce similar fluxes in this energy band rendering ambiguous the nature of the emission itself. The aim of this work is to develop a deeper understanding of these radiation processes from a particular shell-type supernova remnant, namely RX J1713.7–3946, using observations of the LAT instrument onboard the Fermi Gamma-Ray Space Telescope. Furthermore, to obtain accurate spectra and morphology maps of the emission associated with this supernova remnant, an improved model of the diffuse Galactic γ-ray emission background is developed. The analyses of RX J1713.7–3946 carried out with this improved background show that the hard Fermi-LAT spectrum cannot be ascribed to the hadronic emission, leading thus to the conclusion that the leptonic scenario is instead the most natural picture for the high-energy γ-ray emission of RX J1713.7–3946. The leptonic scenario however does not rule out the possibility that cosmic-ray nuclei are accelerated in this supernova remnant, but it suggests that the ambient density may not be high enough to produce a significant hadronic γ-ray emission. Further investigations involving other supernova remnants using the improved back- ground developed in this work could allow compelling population studies, and hence prove or disprove the origin of Galactic cosmic-ray nuclei in these astrophysical objects. A break- through regarding the identification of the radiation mechanisms could be lastly achieved with a new generation of instruments such as CTA.
Organische Halbleiter besitzen neue, bemerkenswerte Materialeigenschaften, die sie für die grundlegende Forschung wie auch aktuelle technologische Entwicklung (bsw. org. Leuchtdioden, org. Solarzellen) interessant werden lassen. Aufgrund der starken konformative Freiheit der konjugierten Polymerketten führt die Vielzahl der möglichen Anordnungen und die schwache intermolekulare Wechselwirkung für gewöhnlich zu geringer struktureller Ordnung im Festkörper. Die Morphologie hat gleichzeitig direkten Einfluss auf die elektronische Struktur der organischen Halbleiter, welches sich meistens in einer deutlichen Reduktion der Ladungsträgerbeweglichkeit gegenüber den anorganischen Verwandten zeigt. So stellt die Beweglichkeit der Ladungen im Halbleiter einen der limitierenden Faktoren für die Leistungsfähigkeit bzw. den Wirkungsgrad von funktionellen organischen Bauteilen dar. Im Jahr 2009 wurde ein neues auf Naphthalindiimid und Bithiophen basierendes Dornor/Akzeptor Copolymer vorgestellt [P(NDI2OD‑T2)], welches sich durch seine außergewöhnlich hohe Ladungsträgermobilität auszeichnet. In dieser Arbeit wird die Ladungsträgermobilität in P(NDI2OD‑T2) bestimmt, und der Transport durch eine geringe energetischer Unordnung charakterisiert. Obwohl dieses Material zunächst als amorph beschrieben wurde zeigt eine detaillierte Analyse der optischen Eigenschaften von P(NDI2OD‑T2), dass bereits in Lösung geordnete Vorstufen supramolekularer Strukturen (Aggregate) existieren. Quantenchemische Berechnungen belegen die beobachteten spektralen Änderungen. Mithilfe der NMR-Spektroskopie kann die Bildung der Aggregate unabhängig von optischer Spektroskopie bestätigt werden. Die Analytische Ultrazentrifugation an P(NDI2OD‑T2) Lösungen legt nahe, dass sich die Aggregation innerhalb der einzelnen Ketten unter Reduktion des hydrodynamischen Radius vollzieht. Die Ausbildung supramolekularen Strukturen nimmt auch eine signifikante Rolle bei der Filmbildung ein und verhindert gleichzeitig die Herstellung amorpher P(NDI2OD‑T2) Filme. Durch chemische Modifikation der P(NDI2OD‑T2)-Kette und verschiedener Prozessierungs-Methoden wurde eine Änderung des Kristallinitätsgrades und gleichzeitig der Orientierung der kristallinen Domänen erreicht und mittels Röntgenbeugung quantifiziert. In hochauflösenden Elektronenmikroskopie-Messungen werden die Netzebenen und deren Einbettung in die semikristallinen Strukturen direkt abgebildet. Aus der Kombination der verschiedenen Methoden erschließt sich ein Gesamtbild der Nah- und Fernordnung in P(NDI2OD‑T2). Über die Messung der Elektronenmobilität dieser Schichten wird die Anisotropie des Ladungstransports in den kristallographischen Raumrichtungen von P(NDI2OD‑T2) charakterisiert und die Bedeutung der intramolekularen Wechselwirkung für effizienten Ladungstransport herausgearbeitet. Gleichzeitig wird deutlich, wie die Verwendung von größeren und planaren funktionellen Gruppen zu höheren Ladungsträgermobilitäten führt, welche im Vergleich zu klassischen semikristallinen Polymeren weniger sensitiv auf die strukturelle Unordnung im Film sind.
In processing and data storage mainly ferromagnetic (FM) materials are being used. Approaching physical limits, new concepts have to be found for faster, smaller switches, for higher data densities and more energy efficiency. Some of the discussed new concepts involve the material classes of correlated oxides and materials with antiferromagnetic coupling. Their applicability depends critically on their switching behavior, i.e., how fast and how energy efficient material properties can be manipulated. This thesis presents investigations of ultrafast non-equilibrium phase transitions on such new materials. In transition metal oxides (TMOs) the coupling of different degrees of freedom and resulting low energy excitation spectrum often result in spectacular changes of macroscopic properties (colossal magneto resistance, superconductivity, metal-to-insulator transitions) often accompanied by nanoscale order of spins, charges, orbital occupation and by lattice distortions, which make these material attractive. Magnetite served as a prototype for functional TMOs showing a metal-to-insulator-transition (MIT) at T = 123 K. By probing the charge and orbital order as well as the structure after an optical excitation we found that the electronic order and the structural distortion, characteristics of the insulating phase in thermal equilibrium, are destroyed within the experimental resolution of 300 fs. The MIT itself occurs on a 1.5 ps timescale. It shows that MITs in functional materials are several thousand times faster than switching processes in semiconductors. Recently ferrimagnetic and antiferromagnetic (AFM) materials have become interesting. It was shown in ferrimagnetic GdFeCo, that the transfer of angular momentum between two opposed FM subsystems with different time constants leads to a switching of the magnetization after laser pulse excitation. In addition it was theoretically predicted that demagnetization dynamics in AFM should occur faster than in FM materials as no net angular momentum has to be transferred out of the spin system. We investigated two different AFM materials in order to learn more about their ultrafast dynamics. In Ho, a metallic AFM below T ≈ 130 K, we found that the AFM Ho can not only be faster but also ten times more energy efficiently destroyed as order in FM comparable metals. In EuTe, an AFM semiconductor below T ≈ 10 K, we compared the loss of magnetization and laser-induced structural distortion in one and the same experiment. Our experiment shows that they are effectively disentangled. An exception is an ultrafast release of lattice dynamics, which we assign to the release of magnetostriction. The results presented here were obtained with time-resolved resonant soft x-ray diffraction at the Femtoslicing source of the Helmholtz-Zentrum Berlin and at the free-electron laser in Stanford (LCLS). In addition the development and setup of a new UHV-diffractometer for these experiments will be reported.
Aus dem Inhalt: - Die Bildungsartikel und ihre praktische Umsetzung in der Frauenrechtskonvention, der Kinderrechtskonvention und der Behindertenrechtskonvention der Vereinten Nationen - Binnenvertreibung als Angelegenheit des Völkerrechts - Die Durchsetzung von Menschenrechten vor US-Gerichten nach dem Kiobel-Urteil
Wood is used for many applications because of its excellent mechanical properties, relative abundance and as it is a renewable resource. However, its wider utilization as an engineering material is limited because it swells and shrinks upon moisture changes and is susceptible to degradation by microorganisms and/or insects. Chemical modifications of wood have been shown to improve dimensional stability, water repellence and/or durability, thus increasing potential service-life of wood materials. However current treatments are limited because it is difficult to introduce and fix such modifications deep inside the tissue and cell wall. Within the scope of this thesis, novel chemical modification methods of wood cell walls were developed to improve both dimensional stability and water repellence of wood material. These methods were partly inspired by the heartwood formation in living trees, a process, that for some species results in an insertion of hydrophobic chemical substances into the cell walls of already dead wood cells, In the first part of this thesis a chemistry to modify wood cell walls was used, which was inspired by the natural process of heartwood formation. Commercially available hydrophobic flavonoid molecules were effectively inserted in the cell walls of spruce, a softwood species with low natural durability, after a tosylation treatment to obtain “artificial heartwood”. Flavonoid inserted cell walls show a reduced moisture absorption, resulting in better dimensional stability, water repellency and increased hardness. This approach was quite different compared to established modifications which mainly address hydroxyl groups of cell wall polymers with hydrophilic substances. In the second part of the work in-situ styrene polymerization inside the tosylated cell walls was studied. It is known that there is a weak adhesion between hydrophobic polymers and hydrophilic cell wall components. The hydrophobic styrene monomers were inserted into the tosylated wood cell walls for further polymerization to form polystyrene in the cell walls, which increased the dimensional stability of the bulk wood material and reduced water uptake of the cell walls considerably when compared to controls. In the third part of the work, grafting of another hydrophobic and also biodegradable polymer, poly(ɛ-caprolactone) in the wood cell walls by ring opening polymerization of ɛ-caprolactone was studied at mild temperatures. Results indicated that polycaprolactone attached into the cell walls, caused permanent swelling of the cell walls up to 5%. Dimensional stability of the bulk wood material increased 40% and water absorption reduced more than 35%. A fully biodegradable and hydrophobized wood material was obtained with this method which reduces disposal problem of the modified wood materials and has improved properties to extend the material’s service-life. Starting from a bio-inspired approach which showed great promise as an alternative to standard cell wall modifications we showed the possibility of inserting hydrophobic molecules in the cell walls and supported this fact with in-situ styrene and ɛ-caprolactone polymerization into the cell walls. It was shown in this thesis that despite the extensive knowledge and long history of using wood as a material there is still room for novel chemical modifications which could have a high impact on improving wood properties.
This work introduces concepts and corresponding tool support to enable a complementary approach in dealing with recovery. Programmers need to recover a development state, or a part thereof, when previously made changes reveal undesired implications. However, when the need arises suddenly and unexpectedly, recovery often involves expensive and tedious work. To avoid tedious work, literature recommends keeping away from unexpected recovery demands by following a structured and disciplined approach, which consists of the application of various best practices including working only on one thing at a time, performing small steps, as well as making proper use of versioning and testing tools. However, the attempt to avoid unexpected recovery is both time-consuming and error-prone. On the one hand, it requires disproportionate effort to minimize the risk of unexpected situations. On the other hand, applying recommended practices selectively, which saves time, can hardly avoid recovery. In addition, the constant need for foresight and self-control has unfavorable implications. It is exhaustive and impedes creative problem solving. This work proposes to make recovery fast and easy and introduces corresponding support called CoExist. Such dedicated support turns situations of unanticipated recovery from tedious experiences into pleasant ones. It makes recovery fast and easy to accomplish, even if explicit commits are unavailable or tests have been ignored for some time. When mistakes and unexpected insights are no longer associated with tedious corrective actions, programmers are encouraged to change source code as a means to reason about it, as opposed to making changes only after structuring and evaluating them mentally. This work further reports on an implementation of the proposed tool support in the Squeak/Smalltalk development environment. The development of the tools has been accompanied by regular performance and usability tests. In addition, this work investigates whether the proposed tools affect programmers’ performance. In a controlled lab study, 22 participants improved the design of two different applications. Using a repeated measurement setup, the study examined the effect of providing CoExist on programming performance. The result of analyzing 88 hours of programming suggests that built-in recovery support as provided with CoExist positively has a positive effect on programming performance in explorative programming tasks.
Der vorliegende Text gibt eine Bestandserhebung der bisher stattgefundenen Aktivitäten im E-Learning an der Universität Potsdam wieder, andererseits dient er auch dazu, Potenziale zu sichten und in einem nächstem Schritt daraus Ideen und Vorschläge für eine hochschulweite E-Learning-Strategie abzuleiten. Zielsetzung der Bestandsaufnahme ist es, die relevanten Informationen darzustellen, über den Platz der Universität Potsdam in der hochschulischen E-Learning-Landschaft zu orientieren und den Stand der Entwicklung zu bewerten.
The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift.
This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.
Genossenschaften wirken auf manche wie ein angestaubtes Relikt aus der Vergangenheit. Das eingetrübte Image überrascht. Denn Genossenschaften haben sich immer wieder als besonders krisenfest erwiesen und längst auch als erfolgreiches Zukunftsmodell entpuppt. Der stetige Zuwachs an Neugründungen, die steigenden Mitgliederzahlen und die ständige Ausweitung der Aktionsfelder bestätigen die hohe Attraktivität. Dem entspricht eine enorme Einsatzbreite der Genossenschaftsidee. Sie reicht von Agrargenossenschaften über Produktionsgenossenschaften in Handel, Handwerk und Gewerbe bis hin zu sehr modernen Bereichen etwa der neuen Informations- und Kommunikationstechnologien. In all diesen und vielen anderen Segmenten finden sich variantenreiche genossenschaftliche Gestaltungsoptionen nach Maximen wie Selbsthilfe, Solidarität, Bürgerengagement, Partizipation, Mitglieder- und Gemeinwohlorientierung. Inzwischen lockt die hohe Anziehungskraft der Genossenschaftsidee auch die Kommunen. Angestoßen durch gesetzgeberische Impulse erleben die Genossenschaften auf der kommunalen Ebene derzeit bundesweit einen richtigen Aufschwung. Die Aufwertung erweitert die Überlegungen zur Gewährleistung und Optimierung kommunaler Leistungserbringung um eine wichtige Gestaltungsvariante, nimmt aber den Kommunen die Auswahlentscheidung nicht ab. Denn wie bei allen Organisationsentscheidungen ist vor dem Rückgriff auf genossenschaftliche Organisationsformen in jedem Einzelfall eine nüchterne aufgaben-, sach- und situationsbezogene Vergleichsanalyse geboten, die den Entscheidungsträgern spezifische Kenntnisse und detaillierte Fachkompetenz abverlangt. Die 19. Fachtagung des KWI diskutiert rechtliche Rahmenbedingungen und normative Direktiven, praktische Erfahrungen, Einsatzfelder, Erfolgsbedingungen und Fallstricke in der Praxis.
Die vorliegende Studie untersucht die gesellschaftliche Rolle des gegenwärtigen Mathematikunterrichts an deutschen allgemeinbildenden Schulen aus einer soziologisch-kritischen Perspektive. In Zentrum des Interesses steht die durch den Mathematikunterricht erfahrene Sozialisation. Die Studie umfasst unter anderem eine Literaturdiskussion, die Ausarbeitung eines soziologischen Rahmens auf der Grundlage des Werks von Michel Foucault und zwei Teilstudien zur Soziologie der Logik und des Rechnens. Abschließend werden Dispositive des Mathematischen beschrieben, die darlegen, in welcher Art und mit welcher persönlichen und gesellschaftlichen Folgen der gegenwärtige Mathematikunterricht eine spezielle Geisteshaltung etabliert.
Donor-acceptor (D-A) copolymers have revolutionized the field of organic electronics over the last decade. Comprised of a electron rich and an electron deficient molecular unit, these copolymers facilitate the systematic modification of the material's optoelectronic properties. The ability to tune the optical band gap and to optimize the molecular frontier orbitals as well as the manifold of structural sites that enable chemical modifications has created a tremendous variety of copolymer structures. Today, these materials reach or even exceed the performance of amorphous inorganic semiconductors. Most impressively, the charge carrier mobility of D-A copolymers has been pushed to the technologically important value of 10 cm^{2}V^{-1}s^{-1}. Furthermore, owed to their enormous variability they are the material of choice for the donor component in organic solar cells, which have recently surpassed the efficiency threshold of 10%. Because of the great number of available D-A copolymers and due to their fast chemical evolution, there is a significant lack of understanding of the fundamental physical properties of these materials. Furthermore, the complex chemical and electronic structure of D-A copolymers in combination with their semi-crystalline morphology impede a straightforward identification of the microscopic origin of their superior performance. In this thesis, two aspects of prototype D-A copolymers were analysed. These are the investigation of electron transport in several copolymers and the application of low band gap copolymers as acceptor component in organic solar cells. In the first part, the investigation of a series of chemically modified fluorene-based copolymers is presented. The charge carrier mobility varies strongly between the different derivatives, although only moderate structural changes on the copolymers structure were made. Furthermore, rather unusual photocurrent transients were observed for one of the copolymers. Numerical simulations of the experimental results reveal that this behavior arises from a severe trapping of electrons in an exponential distribution of trap states. Based on the comparison of simulation and experiment, the general impact of charge carrier trapping on the shape of photo-CELIV and time-of-flight transients is discussed. In addition, the high performance naphthalenediimide (NDI)-based copolymer P(NDI2OD-T2) was characterized. It is shown that the copolymer posses one of the highest electron mobilities reported so far, which makes it attractive to be used as the electron accepting component in organic photovoltaic cells.\par Solar cells were prepared from two NDI-containing copolymers, blended with the hole transporting polymer P3HT. I demonstrate that the use of appropriate, high boiling point solvents can significantly increase the power conversion efficiency of these devices. Spectroscopic studies reveal that the pre-aggregation of the copolymers is suppressed in these solvents, which has a strong impact on the blend morphology. Finally, a systematic study of P3HT:P(NDI2OD-T2) blends is presented, which quantifies the processes that limit the efficiency of devices. The major loss channel for excited states was determined by transient and steady state spectroscopic investigations: the majority of initially generated electron-hole pairs is annihilated by an ultrafast geminate recombination process. Furthermore, exciton self-trapping in P(NDI2OD-T2) domains account for an additional reduction of the efficiency. The correlation of the photocurrent to microscopic morphology parameters was used to disclose the factors that limit the charge generation efficiency. Our results suggest that the orientation of the donor and acceptor crystallites relative to each other represents the main factor that determines the free charge carrier yield in this material system. This provides an explanation for the overall low efficiencies that are generally observed in all-polymer solar cells.
Die Tränen des Henri Quatre
(2014)
Der vorliegende zweite Band mit Texten aus dem Nachlass von Dieter Adelmann (1936–2008) macht eine der letzten Arbeiten, die ihr Verfasser anlässlich seines 70. Geburtstags aus der Hand gegeben hat, für ein breites Publikum zugänglich. Der Essay bildet dabei einen Abschluss von Adelmanns ersten, im weitesten Sinne philosophischen Publikationen, die nach der Doktorarbeit (Bd. 1 der Nachlasspublikationen) entstanden sind. Ausgehend von einer Beobachtung in Heinrich Manns epochaler Doppelromanbiografie des navarresisch-französischen protestantischen Königs Henri IV. untersucht Adelmann die Tränen- und Todesmetaphorik in dem Romanwerk aus den 1930er Jahren. Von hier aus wird eine Brücke zur literaturwissenschaftlichen Ästhetik und Erkenntnistheorie Walter Benjamins geschlagen, mit der sich Adelmann bereits in seinen Arbeiten zur Politkunst Klaus Staecks beschäftigt hatte. Dabei deckt der Verfasser Fehlinterpretationen der Benjaminschen Theorien durch dessen Freund und Nachlassverwalter Theodor W. Adorno auf.
Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set A in R^d. We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of A plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.
Unstetige Galerkin-Diskretisierung niedriger Ordnung in einem atmosphärischen Multiskalenmodell
(2014)
Die Dynamik der Atmosphäre der Erde umfasst einen Bereich von mikrophysikalischer Turbulenz über konvektive Prozesse und Wolkenbildung bis zu planetaren Wellenmustern. Für Wettervorhersage und zur Betrachtung des Klimas über Jahrzehnte und Jahrhunderte ist diese Gegenstand der Modellierung mit numerischen Verfahren. Mit voranschreitender Entwicklung der Rechentechnik sind Neuentwicklungen der dynamischen Kerne von Klimamodellen, die mit der feiner werdenden Auflösung auch entsprechende Prozesse auflösen können, notwendig. Der dynamische Kern eines Modells besteht in der Umsetzung (Diskretisierung) der grundlegenden dynamischen Gleichungen für die Entwicklung von Masse, Energie und Impuls, so dass sie mit Computern numerisch gelöst werden können. Die vorliegende Arbeit untersucht die Eignung eines unstetigen Galerkin-Verfahrens niedriger Ordnung für atmosphärische Anwendungen. Diese Eignung für Gleichungen mit Wirkungen von externen Kräften wie Erdanziehungskraft und Corioliskraft ist aus der Theorie nicht selbstverständlich. Es werden nötige Anpassungen beschrieben, die das Verfahren stabilisieren, ohne sogenannte „slope limiter” einzusetzen. Für das unmodifizierte Verfahren wird belegt, dass es nicht geeignet ist, atmosphärische Gleichgewichte stabil darzustellen. Das entwickelte stabilisierte Modell reproduziert eine Reihe von Standard-Testfällen der atmosphärischen Dynamik mit Euler- und Flachwassergleichungen in einem weiten Bereich von räumlichen und zeitlichen Skalen. Die Lösung der thermischen Windgleichung entlang der mit den Isobaren identischen charakteristischen Kurven liefert atmosphärische Gleichgewichtszustände mit durch vorgegebenem Grundstrom einstellbarer Neigung zu(barotropen und baroklinen)Instabilitäten, die für die Entwicklung von Zyklonen wesentlich sind. Im Gegensatz zu früheren Arbeiten sind diese Zustände direkt im z-System(Höhe in Metern)definiert und müssen nicht aus Druckkoordinaten übertragen werden.Mit diesen Zuständen, sowohl als Referenzzustand, von dem lediglich die Abweichungen numerisch betrachtet werden, und insbesondere auch als Startzustand, der einer kleinen Störung unterliegt, werden verschiedene Studien der Simulation von barotroper und barokliner Instabilität durchgeführt. Hervorzuheben ist dabei die durch die Formulierung von Grundströmen mit einstellbarer Baroklinität ermöglichte simulationsgestützte Studie des Grades der baroklinen Instabilität verschiedener Wellenlängen in Abhängigkeit von statischer Stabilität und vertikalem Windgradient als Entsprechung zu Stabilitätskarten aus theoretischen Betrachtungen in der Literatur.