Detection of small buried objects: asymptotic factorization and MUSIC

In this work, we consider a simple model problem for the electromagnetic exploration of small perfectly conducting objects buried within the lower halfspace of an unbounded two–layered background medium. In possible applications, such as, e.g., humanitarian demining, the two layers would correspond to air and soil. Moving a set of electric devices parallel to the surface of ground to generate a time–harmonic field, the induced field is measured within the same devices. The goal is to retrieve information about buried scatterers from these data. In mathematical terms, we are concerned with the analysis and numerical solution of the inverse scattering problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two–layered background medium from near field measurements of time–harmonic electromagnetic waves. For this purpose, we first study the corresponding direct scattering problem in detail and derive an asymptotic expansion of the scattered field as the size of the scatterers tends to zero. Then, we use this expansion to justify a noniterative MUSIC–type reconstruction method for the solution of the inverse scattering problem. We propose a numerical implementation of this reconstruction method and provide a series of numerical experiments.

A sampling method for detecting buried objects using electromagnetic scattering

We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scattering theory for this particular set-up.

Neuronale Netzwerke des Zentralkomplexes und ein räumliches Arbeitsgedächtnis von Drosophila melanogaster

Zielgerichtete Orientierung ermöglicht es Lebewesen, überlebenswichtige Aufgaben, wie die Suche nach Ressourcen, Fortpflanzungspartnern und sicheren Plätzen zu bewältigen. Dafür ist es essentiell, die Umgebung sensorisch wahrzunehmen, frühere Erfahrungen zu speichern und wiederabzurufen und diese Informationen zu integrieren und in motorische Aktionen umzusetzen.rnWelche Neuronengruppen vermitteln zielgerichtete Orientierung im Gehirn einer Fliege? Welche sensorischen Informationen sind in einem gegebenen Kontext relevant und wie werden diese Informationen sowie gespeichertes Vorwissen in motorische Aktionen übersetzt? Wo findet im Gehirn der Übergang von der sensorischen Verarbeitung zur motorischen Kontrolle statt? rnDer Zentralkomplex, ein Verbund von vier Neuropilen des Zentralhirns von Drosophila melanogaster, fungiert als Übergang zwischen in den optischen Loben vorverarbeiteten visuellen Informationen und prämotorischem Ausgang. Die Neuropile sind die Protocerebralbrücke, der Fächerförmige Körper, der Ellipsoidkörper und die Noduli. rnIn der vorliegenden Arbeit konnte gezeigt werden, dass Fruchtfliegen ein räumliches Arbeitsgedächtnis besitzen. Dieses Gedächtnis kann aktuelle visuelle Information ersetzen, wenn die Sicht auf das Zielobjekt verloren geht. Dies erfordert die sensorische Wahrnehmung von Zielobjekten, die Speicherung der Position, die kontinuierliche Integration von Eigen-und Objektposition, sowie die Umsetzung der sensorischen Information in zielgerichtete Bewegung. Durch konditionale Expression von Tetanus Toxin mittels des GAL4/UAS/GAL80ts Systems konnte gezeigt werden, dass die Ringneurone, welche in den Ellipsoidkörper projizieren, für das Orientierungsgedächtnis notwendig sind. Außerdem konnte gezeigt werden, dass Fliegen, denen die ribosomale Serinkinase S6KII fehlt, die Richtung verlieren, sobald keine Objekte mehr sichtbar sind und, dass die partielle Rettung dieser Kinase ausschließlich in den Ringneuronenklassen R3 und R4d hinreichend ist, um das Gedächtnis wieder herzustellen. Bei dieser Gedächtnisleistung scheint es sich um eine idiothetische Form der Orientierung zu handeln. rn Während das räumliche Arbeitsgedächtnis nach Verschwinden von Objekten relevant ist, wurde in der vorliegende Arbeit auch die Vermittlung zielgerichteter Bewegung auf sichtbare Objekte untersucht. Dabei wurde die zentrale Frage bearbeitet, welche Neuronengruppen visuelle Orientierung vermitteln. Anhand von Gehirnstrukturmutanten konnte gezeigt werden, dass eine intakte Protocerebralbrücke notwendig ist, um Laufgeschwindigkeit, Laufaktivität und Zielgenauigkeit bei der Ansteuerung visueller Stimuli korrekt zu vermitteln. Dabei scheint das Horizontale Fasersystem, welches von der Protocerebralbrücke über den Fächerförmigen Körper auf den Zentralkomplex assoziierte Neuropile, die Ventralkörper, projiziert, notwendig für die lokomotorische Kontrolle und die zielgenaue Bewegung zu sein. Letzeres konnte zum einen durch Blockade der synaptischen Transmission anhand konditionaler Tetanus Toxin Expression mittels des GAL4/UAS/GAL80ts Systems im Horizontalen Fasersystem gezeigt werden;. zum anderen auch durch partielle Rettung der in den Strukturmutanten betroffenen Gene. rn Den aktuellen Ergebnissen und früheren Studien folgend, ergibt sich dabei ein Modell, wie zielgerichtete Bewegung auf visuelle Stimuli neuronal vermittelt werden könnte. Nach diesem Modell bildet die Protocerebralbrücke die Azimuthpositionen von Objekten ab und das Horizontale Fasersystem vermittelt die entsprechende lokomotorische Wo-Information für zielgerichtete Bewegungen. Die Eigenposition in Relation zum Zielobjekt wird über die Ringneurone und den Ellipsoidkörper vermittelt. Wenn das Objekt aus der Sicht verschwindet, kann die Relativposition ideothetisch ermittelt werden und integriert werden mit Vorinformation über das Zielobjekt, die im Fächerförmigen Körper abgelegt ist (Was-Information). Die resultierenden Informationen könnten dann über das Horizontale Fasersystem in den Ventralkörpern auf absteigende Neurone gelangen und in den Thorax zu den motorischen Zentren weitergeleitet werden.rn

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.