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Partial differential equations are not always suited to model all physical phenomena, especially, if long-range interactions are involved or if the actual solution might not satisfy the regularity requirements associated with the partial differential equation. One remedy to this problem are nonlocal operators, which typically consist of integrals that incorporate interactions between two separated points in space and the corresponding solutions to nonlocal equations have to satisfy less regularity conditions.
In PDE-constrained shape optimization the goal is to minimize or maximize an objective functional that is dependent on the shape of a certain domain and on the solution to a partial differential equation, which is usually also influenced by the shape of this domain. Moreover, parameters associated with the nonlocal model are oftentimes domain dependent and thus it is a natural next step to now consider shape optimization problems that are governed by nonlocal equations.
Therefore, an interface identification problem constrained by nonlocal equations is thoroughly investigated in this thesis. Here, we focus on rigorously developing the first and second shape derivative of the associated reduced functional. In addition, we study first- and second-order shape optimization algorithms in multiple numerical experiments.
Moreover, we also propose Schwarz methods for nonlocal Dirichlet problems as well as regularized nonlocal Neumann problems. Particularly, we investigate the convergence of the multiplicative Schwarz approach and we conduct a number of numerical experiments, which illustrate various aspects of the Schwarz method applied to nonlocal equations.
Since applying the finite element method to solve nonlocal problems numerically can be quite costly, Local-to-Nonlocal couplings emerged, which combine the accuracy of nonlocal models on one part of the domain with the fast computation of partial differential equations on the remaining area. Therefore, we also examine the interface identification problem governed by an energy-based Local-to-Nonlocal coupling, which can be numerically computed by making use of the Schwarz method. Here, we again present a formula for the shape derivative of the associated reduced functional and investigate a gradient based shape optimization method.
Based on data collected from two surveys conducted in Germany and Taiwan, my first paper (Chapter 2) examines the impact of culture through language priming (Chinese vs. German or English) on individuals’ price fairness perception and attitudes towards government intervention and economic policy involving inequality. We document large cross-language differences: in both surveys, subjects who were asked and answered in Chinese demonstrated significantly higher perceived price fairness in a free market mechanism than their counterparts who completed the survey in German or English language. They were also more inclined to accept a Pareto improvement policy which increases social and economic inequality. In the second survey, Chinese language induced also a lower readiness to accept government intervention in markets with price limits compared to English language. Since language functions as a cultural mindset prime, our findings imply that culture plays an important role in fairness perception and preferences regarding social and economic inequality.
Chapter 3 of this work deals with patriotism priming. By conducting two online experimental studies conducted in Germany and China, we tested three different kinds of priming methods for constructive and blind patriotism respectively. Subjects were randomly distributed to one of three treatments motivated by previous studies in different countries: a constructive patriotism priming treatment, a blind patriotism priming treatment and a non-priming baseline. While the first experiment had a between-subject design, the second one enabled both a between-subject and within-subject comparison, since the level of patriotism of individuals was measured before and after priming respectively. The design of the second survey also enabled a comparison among the three priming methods for constructive and blind patriotism. The results showed that the tested methods, especially the national achievements as a priming mechanism, functioned well overall for constructive patriotism.
Surprisingly, the priming for blind patriotism did not work in either Germany or China and the opposite results were observed. Discussion and implications for future studies are provided at the end of the chapter.
Using data from the same studies as in Chapter 3, Chapter 4 examines the impact of patriotism on individuals’ fairness perception and preferences regarding inequality and on their attitudes toward economic policy involving inequality. Across surveys and countries, a positive and significant effect of blind patriotism on economic individualism was found. For China, we also found a significant relationship between blind patriotism and the agreement to unequal economic policy. In contrast to blind patriotism, we did not find an association of constructive patriotism to economic individualism and to attitudes toward economic policy involving inequality. Political and economic implications based on the results are discussed.
The last chapter (Chapter 5) studies the self-serving bias (when an individual’s perception about fairness is biased by self-interest) in the context of price setting and profit distribution. By analyzing data from four surveys conducted in six countries, we found that the stated appropriate product price and the fair allocation of profit was significantly higher, when the outcome was favorable to oneself. This self-serving bias in price fairness perception, however, differed across countries significantly and was significantly higher in Germany, Taiwan and China than in Vietnam, Estonia and Japan.
Although economic individualism and masculinity were found to have a significant negative effect on self-interest bias in price fairness judgment, they did not sufficiently explain the differences in self-interest bias between countries. Furthermore, we also observed an increase of self-interest bias in profit allocation over time in time-series data for one country (Germany) with data from 2011 to 2023.
The four papers are all co-authored with Prof. Marc Oliver Rieger, and the first paper has been accepted for publications in Review of Behavioral Economics.
Veterinärantibiotika werden weltweit in großem Umfang zur Behandlung von Tierkrankheiten eingesetzt. Aufgrund der schlechten Resorption der Mittel im Darm der Tiere gelangen sie zum Großteil unverändert über Ausscheidungen auf landwirtschaftliche Nutzflächen. Dort können sie von Nichtzielorganismen, wie Gefäßpflanzen, aufgenommen werden und deren frühe Entwicklung bedrohen. In diesem Kontext wurde bisher vor allem der Einfluss auf Kulturpflanzen untersucht, während Wildpflanzenarten des ökologisch bedeutsamen Kulturgraslandes, die vor allem durch Gülleausbringung in Kontakt mit Antibiotikastoffen kommen, deutlich weniger fokussiert wurden. Deshalb wurde in dieser Arbeit der Einfluss realistischer Konzentrationen (0,1 - 20 mg/L) zweier häufig verwendeter Veterinärantibiotika, Tetracyclin und Sulfamethazin, auf die Keimung und das frühe Wachstum von typischen Arten des temperaten Kulturgraslandes untersucht. Da in der Natur oft mehrere Stressoren gleichzeitig auf einen Organismus einwirken, wurden auch zwei Multistressszenarien, nämlich Pharmazeutikamischungen und das Zusammenspiel von pharmazeutischem Wirkstoff mit abiotischen Bedingungen (Trockenstress) untersucht. In vier Themenblöcken wurden sowohl standardisierte Laborversuche als auch naturnähere Topf- und Feldversuche durchgeführt.
Die Ergebnisse zeigten, dass sowohl die Keimung als auch das frühe Wachstum durch beide Wirkstoffe, jedoch häufiger durch Tetracyclin, beeinträchtigt wurden. Während die Keimung uneinheitlich in Bezug auf die Effektrichtung beeinflusst wurde, zeigte sich eine starke, antibiotika- und konzentrationsabhängige Reduktion der Wurzellänge vor allem durch Tetracyclin, in den Petrischalenversuchen (20 mg/L bis 96 %, bei Dactylis glomerata). Das oberirdische Wachstum (Blattlänge, Wuchshöhe, Biomasse) wurde geringer beinflusst, und dabei oft wachstumsfördernd. In der gesamten Arbeit zeigten sich immer wieder Hormesis- Effekte, d.h. geringe Konzentrationen, die stimulierend wirkten, während höhere Konzentrationen toxisch wirkten. Die betrachteten Kombinationen verschiedener Faktoren führten entgegen der Erwartung nicht eindeutig zu stärkeren oder alleinigen Einflüssen. In einzelnen Fällen zeigten sich solche Muster, jedoch wurden auch Verluste von Einzeleffekten bei den Kombinationen beobachtet oder Einzeleffekte, die sich dort erneut abbildeten.
Es zeigten sich, wenn auch uneinheitlich, signifikante Einflüsse auf die frühen Entwicklungsstadien von typischen Wildpflanzenarten, die bereits durch andere Faktoren einen Rückgang erfahren. Gerade im Hinblick auf die wiederholte Ausbringung von Gülle und die potenzielle Akkumulation dieser hoch persistenten Stoffe stellen Veterinärantibiotika einen weiteren wichtigen Einflussfaktor dar, der die Biodiversität und Artzusammensetzung gefährdet, weshalb zu einem umweltbewussten Umgang mit ihnen geraten wird.
