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The celebrated Schrödinger equation is the key to understanding the dynamics of quantum mechanical particles and comes in a variety of forms. Its numerical solution poses numerous challenges, some of which are addressed in this work. Arguably the most important problem in quantum mechanics is the so-called harmonic oscillator due to its good approximation properties for trapping potentials. In Chapter 2, an algebraic correspondence-technique is introduced and applied to construct efficient splitting algorithms, based solely on fast Fourier transforms, which solve quadratic potentials in any number of dimensions exactly - including the important case of rotating particles and non-autonomous trappings after averaging by Magnus expansions. The results are shown to transfer smoothly to the Gross-Pitaevskii equation in Chapter 3. Additionally, the notion of modified nonlinear potentials is introduced and it is shown how to efficiently compute them using Fourier transforms. It is shown how to apply complex coefficient splittings to this nonlinear equation and numerical results corroborate the findings. In the semiclassical limit, the evolution operator becomes highly oscillatory and standard splitting methods suffer from exponentially increasing complexity when raising the order of the method. Algorithms with only quadratic order-dependence of the computational cost are found using the Zassenhaus algorithm. In contrast to classical splittings, special commutators are allowed to appear in the exponents. By construction, they are rapidly decreasing in size with the semiclassical parameter and can be exponentiated using only a few Lanczos iterations. For completeness, an alternative technique based on Hagedorn wavepackets is revisited and interpreted in the light of Magnus expansions and minor improvements are suggested. In the presence of explicit time-dependencies in the semiclassical Hamiltonian, the Zassenhaus algorithm requires a special initiation step. Distinguishing the case of smooth and fast frequencies, it is shown how to adapt the mechanism to obtain an efficiently computable decomposition of an effective Hamiltonian that has been obtained after Magnus expansion, without having to resolve the oscillations by taking a prohibitively small time-step. Chapter 5 considers the Schrödinger eigenvalue problem which can be formulated as an initial value problem after a Wick-rotating the Schrödinger equation to imaginary time. The elliptic nature of the evolution operator restricts standard splittings to low order, ¿ < 3, because of the unavoidable appearance of negative fractional timesteps that correspond to the ill-posed integration backwards in time. The inclusion of modified potentials lifts the order barrier up to ¿ < 5. Both restrictions can be circumvented using complex fractional time-steps with positive real part and sixthorder methods optimized for near-integrable Hamiltonians are presented. Conclusions and pointers to further research are detailed in Chapter 6, with a special focus on optimal quantum control. / Bader, PK. (2014). Geometric Integrators for Schrödinger Equations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/38716 / Premios Extraordinarios de tesis doctorales

This thesis presents a novel, cost-effective method for mapping the pressure distribution on a rotating cylinder in cross flow, a phenomenon central to the Magnus effect. Utilizing commercial-off-the-shelf (COTS) micro-electromechanical system (MEMS) pressure sensors, a high-resolution data acquisition system was developed and integrated into a rotating cylinder model. Compared to traditional approaches, such as slip rings or one-off designs, this method proved significantly cheaper and faster while achieving comparable or superior resolution. The experimental setup, including a modified continuous rotation technique and adaptable model design, facilitated rapid testing across a broad range of Reynolds numbers and reduced frequencies, exceeding the scope of existing literature. This provided an unprecedentedly detailed view of pressure distributions under both steady and unsteady flow conditions. The validated experimental methodology, applicable to arbitrary bluff body shapes and attitudes, has the potential to significantly accelerate research into unsteady aerodynamics. Moreover, the low-cost, adaptable nature of the setup allows its integration into educational settings, providing students with hands-on experience in experimental fluid mechanics and data acquisition.

Research object of this thesis is Magnus the Apostle of the Allgäu area in Germany. Based on the historical background, this thesis analyses Magnus concerning the way and impact of his apostolic ministry to understand and compare it to the ministry of the biblical apostolic ministry and thus describe criteria of apostolic ministry and consequences until today. The originality of this thesis lies, due to a limites written sources concerning the vita of Magnus, in firstly an investigation into historical developments of his context in the Allgäu, secondly evaluates his Iro-Scottish backround and thirdly describes the historical impact. The resulting insights are compared between the apostolic-missionary work of Magnus and the New Testament. The conclusion summarizes the ministry of the apostle into a number of statements Which are in harmony with the life of Magnus and the context of the New Testament. / Forschungsgegenstand dieser Arbeit ist Magnus (699-772 n. Chr.), der Apostel des Allgaus. Aufgabe der Untersuchung ist es, basierend auf dem literarhistorischen Hintergrund des Magnus seine Biographie zu untersuchen, um eine Vorstellung liber die Art und Weise seiner apostolischen Wirksamkeit zu gewinnen. Die Besonderheit dieser Arbeit besteht darin, dass auf Grund des eingeschrankten schriftlichen Quellenbefundes der Magnusvita zum Einen die Erfassung des geschichtlichen Werdens seines Wirkungsfeldes im Allgau, zum Zweiten die Untersuchung seines iroschottischen Hintergrundes und zum Dritten die Darstellung seiner Wirkungsgeschichte unabdingbar sind. Die so gewonnenen Kenntnisse ermoglichen einen thesenhaften Vergleich zwischen dem apostolisch-missionarischen Wirken des Magnus und dem der Apostel des Neuen Testamentes. / Christian Spirituality, Church History & Missiology / M. Th. (Missiology)

Research object of this thesis is Magnus the Apostle of the Allgäu area in Germany. Based on the historical background, this thesis analyses Magnus concerning the way and impact of his apostolic ministry to understand and compare it to the ministry of the biblical apostolic ministry and thus describe criteria of apostolic ministry and consequences until today. The originality of this thesis lies, due to a limites written sources concerning the vita of Magnus, in firstly an investigation into historical developments of his context in the Allgäu, secondly evaluates his Iro-Scottish backround and thirdly describes the historical impact. The resulting insights are compared between the apostolic-missionary work of Magnus and the New Testament. The conclusion summarizes the ministry of the apostle into a number of statements Which are in harmony with the life of Magnus and the context of the New Testament. / Forschungsgegenstand dieser Arbeit ist Magnus (699-772 n. Chr.), der Apostel des Allgaus. Aufgabe der Untersuchung ist es, basierend auf dem literarhistorischen Hintergrund des Magnus seine Biographie zu untersuchen, um eine Vorstellung liber die Art und Weise seiner apostolischen Wirksamkeit zu gewinnen. Die Besonderheit dieser Arbeit besteht darin, dass auf Grund des eingeschrankten schriftlichen Quellenbefundes der Magnusvita zum Einen die Erfassung des geschichtlichen Werdens seines Wirkungsfeldes im Allgau, zum Zweiten die Untersuchung seines iroschottischen Hintergrundes und zum Dritten die Darstellung seiner Wirkungsgeschichte unabdingbar sind. Die so gewonnenen Kenntnisse ermoglichen einen thesenhaften Vergleich zwischen dem apostolisch-missionarischen Wirken des Magnus und dem der Apostel des Neuen Testamentes. / Christian Spirituality, Church History and Missiology / M. Th. (Missiology)

I denna uppsats har jag studerat Konflikten i Antiochia, utifrån två aktuella perspektiv på Paulus - ”Nya Perspektivet på Paulus” och ”Paulus inom judendomen”. Syftet har varit att definiera och klarlägga den huvudsakliga innebörden i de två respektive perspektiven samt att utifrån den förståelsen göra en jämförande analys med hjälp av den valda perikopen. Jag har också sökt analysera vilka konsekvenser perspektiven kan få för vår förståelse av Paulus. För att avgränsa uppgiften har jag utgått från ett urval av forskare inom respektive perspektiv. Dessa är för NPP: E. P. Sanders, James D. G. Dunn och N.T. Wright. För PIJ har jag främst utgått från material av Mark Nanos och Magnus Zetterholm. För att kunna göra perspektiven rättvisa presenterar jag också en kort beskrivning av det ”Traditionella Perspektivet på Paulus” eftersom det är det perspektiv som i lite varierande form har varit det dominerande genom historien. Jag har också gjort några förhoppningsvis förtydligande utvikningar kring hur det gick till när judendom och kristendom skiljdes åt samt ett kort avsnitt kring begreppet bordsgemenskap. Slutsatsen i uppsatsen är att perspektiven förvisso skiljer sig åt på flera punkter men att de till övervägande del ligger nära varandra. Detta är särskilt tydligt vad gäller de vetenskapliga drivkrafterna och metoderna som respektive perspektiv använder sig av.

The aim of this thesis is to explore work as an idea and a practice for the construction and maintenance of differences and power relations, and to examine what the consequences were for the individual and society in early modern Sweden. The period saw an expansion of the state apparatus which created numerous new opportunities for employment. There also exists a body of literature from this period, in the form of instructions relating to work and households. The thesis draws both on these instructions and descriptions and on sources produced by the crown. The thesis shows that gender was a crucial factor for the organisation of work. Operating The service of the crown was characterised by two principal organisational forms: the household, and a precursor of a bureaucratic system. The household had its basis in the couple, and had a clear gendered division of power, the couple together constituted the management of the household, at the same time there was an element of male superordination. The other form was exclusively male and based on delegation of power within the organisation and on an attempt to formalise relations by written instructions. The majority of the jobs created were held by men. In crafts and administration, men took over a number of female areas of competence. In this process was occupational positions created for these men. Women’s opportunities to work were heavily affected by an idea of a female area of expertise, ‘womenfolk’s work’ which never become specialiced, but the investigation also shows that work created in the crowns households in positions of leadership created livelihoods for married adult women. Among employees that were young and unmarried the similarities between the genders were often more striking than the differences. Greater differences emerge from a comparison of the entire workforce of the crown, which shows women’s annual wages to be 75 per cent of those of men. Overall women had few opportunities to make careers and get well paid employments.

Thesis (Ph. D.)--Ohio State University, 2007.

A revision of the author's thesis, Heidelberg. / Includes bibliographical references.

This dissertation examines how transgender feelings and gender variation emerged as a vital motivator for scientific and aesthetic explorations of human personhood and social experiences of marginality in German-speaking culture in the early twentieth century. My research illustrates how concepts of gender variation served as a generative problem for modernist practitioners of sexual science and as a creative impulse and figural resource for modernist literary and artistic innovations. The feedback between these fields allowed for novel social categories to develop in a period where designations like “transgender” or “transsexual” were not yet in use as stable public identities or diagnoses, but nevertheless circulated in response to experiences of embodied difference and social alienation. By reading for “transgender feeling” as a heuristic that unites multiple historical categories of gender and sexual variation, I argue that transgender phenomena were instrumental for the development of German modernist movements at large. Building on affect studies, trans and queer studies, and German literary and cultural studies, my project intervenes in limited contemporary understandings of transgender history and identity as a minority political and diagnostic discourse. Instead, I argue for a more expansive, “democratized” notion of transgender feeling that encompasses diverse historical forms of gender variation, some of which have disappeared or become “obsolete,” and show how narratives of gender intermediacy and incongruence are essential to modernist aesthetic practices. Chapter One examines theories of sexual intermediacy in the sexological work of Magnus Hirschfeld and Otto Weininger, who both suggested that a transgender condition underlies “normal” human sexual development. I show that trans feelings cut across Hirschfeld’s sexological categories and, in particular, his deployment of the case genre, troubling stable taxonomies of sexual affect and allowing for promising forms of coauthorship and “trans genre writing” to emerge in sexology. Chapter Two takes up Rainer Maria Rilke’s writing in The Notebooks of Malte Laurids Brigge and Das Stunden-Buch, as well as his early childhood experience, to argue that dysphoria and intermediacy are key to understanding the social alienation that Rilke expressed in his modernist work alongside personal attachments to femininity and a feminine poetic voice. Chapter Three on Else Lasker-Schüler illustrates how trans feelings, the masculine persona of Jussuf and appropriations of racial and ethnic difference significantly frame the novel Mein Herz and become enduring features of Lasker-Schüler’s literary and artistic production. I highlight how scholarly reception of Rilke and Lasker-Schüler’s work have intentionally disavowed these expressions as transgender and argue for a reassessment of trans feeling as a creative impulse in German modernism through their texts and images. My last chapter explores how modernist periodical media served as a vital tool for crafting trans intimate publics in the Weimar period and for negotiating the shared norms of gender and social participation for a novel class of gender-variant people under the category of transvestism. In my conclusion, I turn to the unfinished business of sexual and gender definition that continues to frame LGBTQ politics in Germany and abroad today, and I link contemporary questions of trans aesthetics to modernist dynamics of gender and sexual multiplicity.