A Stochastic Gradient Method with Mesh Refinement for PDE Constrained Optimization under Uncertainty

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth tracking-type functional subject to a linear partial differential equation with random coefficients and box constraints. The approach we take is based on stochastic approximation where, in place of a true gradient, a stochastic gradient is chosen using one sample from a known probability distribution. Feasibility is maintained by performing a projection at each iteration. In the application of this method to PDE-constrained optimization under uncertainty, new challenges arise. We observe the discretization error made by approximating the stochastic gradient using finite elements. Analyzing the interplay between PDE discretization and stochastic error, we develop a mesh refinement strategy coupled with decreasing step sizes. Additionally, we develop a mesh refinement strategy for the modified algorithm using iterate averaging and larger step sizes. The effectiveness of the approach is demonstrated numerically for different random field choices

A phase-field model for fractures in incompressible solids

Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds on a mixed form of the displacement equation with two unknowns: a displacement field and a hydro-static pressure variable. Corresponding function spaces have to be chosen properly. On the discrete level, stable Taylor-Hood elements are employed for the displacement-pressure system. Two additional variables describe the phase-field solution and the crack irreversibility constraint. Therefore, the final system contains four variables: displacements, pressure, phase-field, and a Lagrange multiplier. The resulting discrete system is nonlinear and solved monolithically with a Newton-type method. Our proposed model is demonstrated by means of several numerical studies based on two numerical tests. First, different finite element choices are compared in order to investigate the influence of higher-order elements in the proposed settings. Further, numerical results including spatial mesh refinement studies and variations in Poisson's ratio approaching the incompressible limit, are presented

Huntingtons Kampf der Kulturen im geschichtsphilosophischen Kontext

In dieser Seminararbeit untersuche ich Huntingtons These vom »Kampf der Kulturen« und stelle sie in einen geschichtsphilosophischen Kontext. Mit Spenglers Idee vom »Untergang des Abendlandes« und Toynbees »Gang der Weltgeschichte« stelle ich zwei solche Ansätze vor, auf die Huntington ganz explizit zurückgreift. Vor allem auf ihren Kulturbegriff greift er zurück, indem er die Kulturen für die Konfliktlinien von morgen hält. Dass er weniger das zyklische Denken berücksichtigt und keine historische Perspektive einnimmt, lässt mich schließen, dass Huntingtons These zwar auf viele geschichtsphilosophische Elemente aufbaut, selbst jedoch keine eigene geschichtsphilosophische Position darstellt. Dies illustrieren auch die von mir angeführten ausgewählten Reaktionen auf Huntington aus unterschiedlichen Perspektiven

Planning Preservation In Pompeii: Revising Wall Painting Conservation Method And Management

The management of Pompeii’s focus on excavation and tourism has caused its wall art to fall into disrepair, but a new focus on efficiency and sustainable practice has the potential to relieve the emergency of Pompeii’s restoration work. Hasty excavations, intermittent and piecemeal conservation, and financial mismanagement have all contributed to the state of decay that has consumed wall painting in this UNESCO World Heritage Site. This article reviews past practices of conservation and management and proposes a step-by-step approach for lasting restoration work on wall paintings

Development of a fabric winding system for the automated manufacture of prefabricated wind turbine blade roots

In the rapidly expanding wind energy market, manufacturing processes of composite components must be continually improved to keep up with high demand and increasing part size. This research focuses on improving the offline production of the root section of wind turbine blades. In this research, a system is developed and tested to replace the two-part manual layup of the prefabricated root with an automated fabric winding machine. The system is designed to wind a limited number of long, stitched plies semi-helically around a male mold at a lower cost and higher quality than current processes. A prototype machine is created that pulls two types of Non-Crimp Fabric from supply rolls onto a rotating mandrel that matches the interior surface of a scaled down blade root. The prototype system proves Non-Crimp Fabric plies can be wound and a male mold can be used as a suitable replacement for a female mold by creating several successful prototype root sections. Process times and labor costs between the current manual layup and the winding method are also compared and show a significant reduction in glass layup, further proving the feasibility of the new system

Understanding the consequences of the loss and damage evidence gap and limiting its adverse effects for developing countries

Auf der 27. Vertragsstaatenkonferenz der Klimarahmenkonvention der Vereinten Nationen (UNFCCC) im Jahr 2022 gelang es den Entwicklungsländern, einen Verlust- und Schadensfonds (engl. „Loss and Damage“ - L&D) einzurichten. L&D, umrissen als die unvermeidbaren Risiken und Auswirkungen des Klimawandels, hat für Entwicklungsländer, deren Vulnerabilität und Exposition gegenüber dem Klimawandel besonders hoch ist, hohe Priorität bei gleichzeitig dünner Beweislage. Die vorliegende Promotion richtet ihr Augenmerk auf diesen Mangel an L&D „Beweisen“ um die Rolle von Evidenzen im Rahmen der L&D Verhandlungen zu verstehen und Ansätze zu entwickeln, die negative Folgen ihres Mangels für Entwicklungsländer begrenzen. Der erste Teil dieser Arbeit zeigt, wie Verhandlungsführerinnen und -führer aus Entwicklungsländern generische Erkenntnisse zu Klimaauswirkungen nutzten, um eine hermeneutische Ungerechtigkeit zu überwinden. Politischer Nutzen von Evidenzen kann Akteuren ein Gefühl der Legitimität zu vermitteln, jedoch ohne Überzeugung der Gegenseite. Der zweite Teil dieser Arbeit hinterfragt die Rolle von Attributionswissenschaften im neuen L&D-Fonds und liefert eine normative Analyse, anhand derer rein qualitativ getroffene Attributionsaussagen einen Anspruch auf Gelder aus dem L&D Fond hinreichend legitimieren. Die Rolle von Vulnerabilität und Exposition sollten demnach keine Rolle bei der Verteilung der Gelder spielen, jedoch bei deren Verwendung in Betracht gezogen werden. Der letzte Teil dieser Promotion befasst sich mit klimatischen Risiken auf die Anpassungsfähigkeit in Entwicklungsländern und deren Konsequenzen im Rahmen von Klimarisikobewertungen. Ein Protokoll wird entworfen, um Annahmen über Anpassungsfähigkeit angesichts erwarteter Klimaschäden, einzugrenzen – was ein verringertes Risiko einer Unterschätzungen zukünftiger L&D in Klimarisikobewertungen zur Folge hätte.At the 27th Conference of the Parties in 2022, developing countries succeeded in establishing a Loss and Damage (L&D) Fund under the United Nations Framework Convention on Climate Change (UNFCCC). L&D, here understood as the residual risks and impacts of climate change that cannot be avoided, has been of high priority to developing countries, who also experience a lack in L&D evidence. This thesis takes the lack of L&D evidence into focus to understand the role of evidence in L&D negotiations and develop approaches to limit adverse consequences of its lack for developing countries. The first part of this thesis shows how developing country negotiators worked to overcome a hermeneutic injustice that had resulted from a lack of L&D evidence. By using publications on climate impacts to claim these risks were “beyond adaptation” negotiators managed to establish L&D as a theme under the UNFCCC. The analysis shows how the political use of evidence can strengthen the resolve of individual negotiators by giving them a sense of legitimacy, although it does not lead to persuasion of political opponents. The second part of this thesis focuses on the role of event attribution in funding decisions under the L&D fund and provides the normative basis for legitimizing claims to the L&D fund with purely qualitative attribution statements. It challenges the view that vulnerability and exposure ought to be considered in L&D funding decisions, and argues that these factors ought to inform spending decisions. Finally, this thesis turns to evidence of climatic risks on adaptive capacity. It develops a protocol for constraining assumptions on adaptive capacity in qualitative climate risk assessments, which, if implemented, could reduce the risk of underestimating future L&D in developing countries

Aktive Arbeitsmarktpolitik im Brennpunkt IV: Evaluierung der Lehrstellenförderung in Wien

Es ist nicht das erste Mal, daß abzwien bzw. einzelne Maßnahmen der Einrichtung einer Evaluation unterzogen wurden. Die Ergebnisse einer ersten - eher qualitativ orientierten - Evaluation, die den Charakter einer wissenschaftlichen Begleitung hat, erschien 1995 als Nr. 2 der Wiener Reihe des AMS Wien.1 Weiterhin gab es in den 90er Jahren eine Overhead-Evaluation. Ganz aktuell liegt die Evaluation einer sehr neuen Maßnahme von abzwien vor, nämlich Karenz Plus. Die Besonderheiten der vorliegenden Studie liegen zum einen darin, daß der Versuch unternommen wird, das gesamte abzwien mit seinen inzwischen sehr vielen und vielfältigen Maßnahmen zu untersuchen. Zum zweiten sind im Design der Studie sowohl qualitative als auch quantitative Methoden integriert

On the Dependence of the Pressure on the Time Step in Incompressible Flow Simulations on Varying Spatial Meshes

Subject of this paper is an analysis of the behavior of the pressure on dynamically changing spatial meshes during the computation of nonstationary incompressible flows. In particular, we are concerned with discontinuous Galerkin finite element discretizations in time. Here it is observed that whenever the spatial mesh is changed between two time steps the pressure in the next time step will diverge with order $k^{-1}$. We will proof that this behavior is due to the fact, that discrete solenoidal fields lose this property under changes of the spatial discretization. In addition we will numerically study the fractional-step-$theta$ scheme, and discuss why the divergence is not observed when using this time discretization. Finally we will derive a possible way to circumvent this problem

A posteriori estimator for the adaptive solution of a quasi-static fracture phase-field model with irreversibility constraints

Within this article, we develop a residual type a posteriori error estimator for a time discrete quasi-static phase-field fracture model. Particular emphasize is given to the robustness of the error estimator for the variational inequality governing the phase-field evolution with respect to the phase-field regularization parameter $\epsilon$. The article concludes with numerical examples highlighting the performance of the proposed a posteriori error estimators on three standard test cases; the single edge notched tension and shear test as well as the L-shaped panel test

From Theory to Practice I: Passing Judgments of Exploitation

In an earlier work, we offered a view on how trade should be treated within a theory of global justice. We proposed an account of exploitation to spell out the nature of the obligations that arise from trading. That account greatly benefits from a detailed development for concrete cases. The goal of this study and its close companion is to explore how our philosophical views help formulate judgments on a range of moral problems that arise from trading and to identify responsibilities of various actors and inform policy responses to instances of exploitation in trade. To that end we use a well-known episode in the recent history of activism against a multinational corporation—the protests against Nike. We use Harvard Business School Case No. 9-700-047 (the Case), written up by Debora Spar. The title is Hitting the Wall: Nike and International Labor Practices. This is a thirteen-page discussion (plus several pages of exhibits) describing Nike’s success story and subsequent plights with labor activists through the ‘90s. Even though the Case has been used for teaching purposes since 2002, it has lost none of its systematic interest. It draws on a range of contexts where judgments of exploitation continue to be made and refers to ongoing businesses practices. The case has the additional advantage that it tells the story of one company (a well-known one, making it likely many of our readers own its products), which allows us to assess a number of judgments as part of an interconnected story, rather than deal with a laundry list of scenarios. In some instances, the Case itself uses the terminology of exploitation, but in others, it does not. Our aim in discussing this Case is twofold. On the one hand, we show that the notion of exploitation can fruitfully be applied to thinking about justice in trade. On the other hand, we cast judgment on central aspects of Nike’s activity in Southeast Asia. One downside of our strategy of expounding judgments of exploitation in terms of this Case is that there are too many questions that need careful treatment. We have therefore broken this discussion into two pieces, narrating the Case in both. Section 2 summarizes our account of exploitation and elaborates on the distinction between moral problems that arise in the context of trade and those that arise from trading. Section 3 presents the Case and develops six questions for discussion in this piece and its companion. The first of three addressed in this study is the following: What moral questions arise in the context of relocating or outsourcing a business? In response we formulate conditions under which relocation is or is not morally problematic. One important result is that moral and political outrage at relocating companies to wealthier countries should often be redirected at the political community for not doing enough to soften the blow that some people suffer from such a move. The second question is the following: How should a company deal with an authoritarian regime in a country where it does business? In response we offer some thoughts on the circumstances under which states of exploitation could be justified as stepping stones towards a just world. The third question is the following: Under what conditions is compliance with existing regulation—such as labor protection legislation—required, and under what conditions are violations acceptable? We argue that absent special circumstances, a company ought to comply even if its competitors do not. The remaining three questions, addressed in the companion piece, are these: How should one think about a just wage: is it a matter of productivity, should it reflect needs, or does it amount to an appropriate share in profits?; Is Nike responsible for actions of its subcontractors and thus perhaps guilty of indirect exploitation if, for instance, those subcontractors pay unjust wages?; Finally, do safety and health standards generate particular problems from the standpoint of exploitation? Our focus on a company in this study and its companion should not deflect from the fact that our approach can account for exploitation among a range of actors—individuals, states, companies, international organizations. Nor should this focus be taken as an indication that efforts at ending exploitation should target companies rather than governments. Our project here is to think through a number of normative judgments, and we use Nike as a case study for that purpose