Sensitivity analysis of a parabolic-elliptic problem

We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative L-infinity-capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous justification for modeling a small thermal capacity by setting it to zero. We also characterize weak directional derivatives of the temperature with respect to capacity as solutions of related parabolic-elliptic problems.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Survival of the fittest: Herausforderungen an den Fremdenverkehr im Zeichen des global change

Der Globale Wandel ist im Begriff, den Tourismus zu verändern. Die Wechselwirkung von Tourismus und Klimawandel sind beidseitiger Art. Die vorliegende Arbeit zeigt Möglichkeiten der Adaption und einen wandelbaren Fremdenverkehr. Eine Übersicht der gängigen Tourismusmodelle stellt den Stand der Forschung dar. Der Fremdenverkehr ist durch drei Faktoren massiv geprägt: Die Nachfrage und Motivation, die Reisemittler und Veranstalter sowie das Destinationsangebot. Bei der Motivation wirken Motiv und Anreiz Motivationspsychologisch betrachtet auf die Reiseentscheidung deren Grundlage verarbeitete Informationen sind. Reisemittler und Veranstalter haben einen großen Einfluss auf Entscheidungsprozesse. Neue IuK Technologien haben deren Arbeit grundlegend verändert. Das Tourismusangebot wird stark durch die naturräumlichen Gegebenheiten sowie das politische System bestimmt. Überlebenswichtig für die Destination ist die evolutionstheoretisch etrachtete Fitnessmaximierung also Adaption und Wandel, um sich an geänderte Rahmenbedingungen anpassen zu können. Gerade im Bereich des Klimawandels müssen Maßnahmen ergriffen werden. Aber auch die Marktsättigung gerade in Verbindung mit der aktuellen Finanzkrise wirkt besonders schwer auf die Destination. Eine hohes Innovationsvermögen, Trendscanning und der Zusammenschluss in flexiblen Netzwerkclustern können einen Kundenmehrwert erzeugen. Die Fitnessmaximierung ist somit Überlebensziel der Destination und führt zur Kundenzufriedenheit die im Sättigungsmarkt alleinig Wachstum generieren kann.

Global simulated soil biogenic nitric oxide (NO) emissions: Impact, improvement and innovation

rnNitric oxide (NO) is important for several chemical processes in the atmosphere. Together with nitrogen dioxide (NO2 ) it is better known as nitrogen oxide (NOx ). NOx is crucial for the production and destruction of ozone. In several reactions it catalyzes the oxidation of methane and volatile organic compounds (VOCs) and in this context it is involved in the cycling of the hydroxyl radical (OH). OH is a reactive radical, capable of oxidizing most organic species. Therefore, OH is also called the “detergent” of the atmosphere. Nitric oxide originates from several sources: fossil fuel combustion, biomass burning, lightning and soils. Fossil fuel combustion is the largest source. The others are, depending on the reviewed literature, generally comparable to each other. The individual sources show a different temporal and spatial pattern in their magnitude of emission. Fossil fuel combustion is important in densely populated places, where NO from other sources is less important. In contrast NO emissions from soils (hereafter SNOx) or biomass burning are the dominant source of NOx in remote regions.rnBy applying an atmospheric chemistry global climate model (AC-GCM) I demonstrate that SNOx is responsible for a significant part of NOx in the atmosphere. Furthermore, it increases the O3 and OH mixing ratio substantially, leading to a ∼10% increase in the oxidizing efficiency of the atmosphere. Interestingly, through reduced O3 and OH mixing ratios in simulations without SNOx, the lifetime of NOx increases in regions with other dominating sources of NOx

Global modeling of pollutant transport and deposition from anthropogenic emission hot spots on global scale

Urban centers significantly contribute to anthropogenic air pollution, although they cover only a minor fraction of the Earth's land surface. Since the worldwide degree of urbanization is steadily increasing, the anthropogenic contribution to air pollution from urban centers is expected to become more substantial in future air quality assessments. The main objective of this thesis was to obtain a more profound insight in the dispersion and the deposition of aerosol particles from 46 individual major population centers (MPCs) as well as the regional and global influence on the atmospheric distribution of several aerosol types. For the first time, this was assessed in one model framework, for which the global model EMAC was applied with different representations of aerosol particles. First, in an approach with passive tracers and a setup in which the results depend only on the source location and the size and the solubility of the tracers, several metrics and a regional climate classification were used to quantify the major outflow pathways, both vertically and horizontally, and to compare the balance between pollution export away from and pollution build-up around the source points. Then in a more comprehensive approach, the anthropogenic emissions of key trace species were changed at the MPC locations to determine the cumulative impact of the MPC emissions on the atmospheric aerosol burdens of black carbon, particulate organic matter, sulfate, and nitrate. Ten different mono-modal passive aerosol tracers were continuously released at the same constant rate at each emission point. The results clearly showed that on average about five times more mass is advected quasi-horizontally at low levels than exported into the upper troposphere. The strength of the low-level export is mainly determined by the location of the source, while the vertical transport is mainly governed by the lifting potential and the solubility of the tracers. Similar to insoluble gas phase tracers, the low-level export of aerosol tracers is strongest at middle and high latitudes, while the regions of strongest vertical export differ between aerosol (temperate winter dry) and gas phase (tropics) tracers. The emitted mass fraction that is kept around MPCs is largest in regions where aerosol tracers have short lifetimes; this mass is also critical for assessing the impact on humans. However, the number of people who live in a strongly polluted region around urban centers depends more on the population density than on the size of the area which is affected by strong air pollution. Another major result was that fine aerosol particles (diameters smaller than 2.5 micrometer) from MPCs undergo substantial long-range transport, with about half of the emitted mass being deposited beyond 1000 km away from the source. In contrast to this diluted remote deposition, there are areas around the MPCs which experience high deposition rates, especially in regions which are frequently affected by heavy precipitation or are situated in poorly ventilated locations. Moreover, most MPC aerosol emissions are removed over land surfaces. In particular, forests experience more deposition from MPC pollutants than other land ecosystems. In addition, it was found that the generic treatment of aerosols has no substantial influence on the major conclusions drawn in this thesis. Moreover, in the more comprehensive approach, it was found that emissions of black carbon, particulate organic matter, sulfur dioxide, and nitrogen oxides from MPCs influence the atmospheric burden of various aerosol types very differently, with impacts generally being larger for secondary species, sulfate and nitrate, than for primary species, black carbon and particulate organic matter. While the changes in the burdens of sulfate, black carbon, and particulate organic matter show an almost linear response for changes in the emission strength, the formation of nitrate was found to be contingent upon many more factors, e.g., the abundance of sulfuric acid, than only upon the strength of the nitrogen oxide emissions. The generic tracer experiments were further extended to conduct the first risk assessment to obtain the cumulative risk of contamination from multiple nuclear reactor accidents on the global scale. For this, many factors had to be taken into account: the probability of major accidents, the cumulative deposition field of the radionuclide cesium-137, and a threshold value that defines contamination. By collecting the necessary data and after accounting for uncertainties, it was found that the risk is highest in western Europe, the eastern US, and in Japan, where on average contamination by major accidents is expected about every 50 years.