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In the thesis there are constructed new quantizations for pseudo-differential boundary value problems (BVPs) on manifolds with edge. The shape of operators comes from Boutet de Monvel’s calculus which exists on smooth manifolds with boundary. The singular case, here with edge and boundary, is much more complicated. The present approach simplifies the operator-valued symbolic structures by using suitable Mellin quantizations on infinite stretched model cones of wedges with boundary. The Mellin symbols themselves are, modulo smoothing ones, with asymptotics, holomorphic in the complex Mellin covariable. One of the main results is the construction of parametrices of elliptic elements in the corresponding operator algebra, including elliptic edge conditions.
In a changing world facing several direct or indirect anthropogenic challenges the freshwater resources are endangered in quantity and quality. An excessive supply of nutrients, for example, can cause disproportional phytoplankton development and oxygen deficits in large rivers, leading to failure of the aims requested by the Water Framework Directive (WFD). Such problems can be observed in many European river catchments including the Elbe basin, and effective measures for improving water quality status are highly appreciated.
In water resources management and protection, modelling tools can help to understand the dominant nutrient processes and to identify the main sources of nutrient pollution in a watershed. They can be effective instruments for impact assessments investigating the effects of changing climate or socio-economic conditions on the status of surface water bodies, and for testing the usefulness of possible protection measures. Due to the high number of interrelated processes, ecohydrological model approaches containing water quality components are more complex than the pure hydrological ones, and their setup and calibration require more efforts. Such models, including the Soil and Water Integrated Model (SWIM), still need some further development and improvement.
Therefore, this cumulative dissertation focuses on two main objectives: 1) the approach-related objectives aiming in the SWIM model improvement and further development regarding nutrient (nitrogen and phosphorus) process description, and 2) the application-related objectives in meso- to large-scale Elbe river basins to support adaptive river basin management in view of possible future changes. The dissertation is based on five scientific papers published in international journals and dealing with these research questions.
Several adaptations were implemented in the model code to improve the representation of nutrient processes including a simple wetland approach, an extended by ammonium nitrogen cycle in the soils, as well as a detailed in-stream module, simulating algal growth, nutrient transformation processes and oxygen conditions in the river reaches, mainly driven by water temperature and light. Although this new approaches created a highly complex ecohydrological model with a large number of additional calibration parameters and rising uncertainty, the calibration and validation of the SWIM model enhanced by the new approaches in selected subcatchment and the entire Elbe river basin delivered satisfactory to good model results in terms of criteria of fit. Thus, the calibrated and validated model provided a sound base for the assessment of possible future changes and impacts in climate, land use and management in the Elbe river (sub)basin(s).
The new enhanced modelling approach improved the applicability of the SWIM model for the WFD related research questions, where the ability to consider biological water quality components (such as phytoplankton) is important. It additionally enhanced its ability to simulate the behaviour of nutrients coming mainly from point sources (e.g. phosphate phosphorus). Scenario results can be used by decision makers and stakeholders to find and understand future challenges and possible adaptation measures in the Elbe river basin.
Gamma-ray astronomy has proven to provide unique insights into cosmic-ray accelerators in the past few decades. By combining information at the highest photon energies with the entire electromagnetic spectrum in multi-wavelength studies, detailed knowledge of non-thermal particle populations in astronomical objects and systems has been gained: Many individual classes of gamma-ray sources could be identified inside our galaxy and outside of it. Different sources were found to exhibit a wide range of temporal evolution, ranging from seconds to stable behaviours over many years of observations. With the dawn of both neutrino- and gravitational wave astronomy, additional messengers have come into play over the last years. This development presents the advent of multi-messenger astronomy: a novel approach not only to search for sources of cosmic rays, but for astronomy in general.
In this thesis, both traditional multi-wavelength studies and multi-messenger studies will be presented. They were carried out with the H.E.S.S. experiment, an imaging air Cherenkov telescope array located in the Khomas Highland of Namibia. H.E.S.S. has entered its second phase in 2012 with the addition of a large, fifth telescope. While the initial array was limited to the study of gamma-rays with energies above 100 GeV, the new instrument allows to access gamma-rays with energies down to a few tens of GeV. Strengths of the multi-wavelength approach will be demonstrated at the example of the galaxy NGC253, which is undergoing an episode of enhanced star-formation. The gamma-ray emission will be discussed in light of all the information on this system available from radio, infrared and X-rays. These wavelengths reveal detailed information on the population of supernova remnants, which are suspected cosmic-ray accelerators. A broad-band gamma-ray spectrum is derived from H.E.S.S. and Fermi-LAT data. The improved analysis of H.E.S.S. data provides a measurement which is no longer dominated by systematic uncertainties. The long-term behaviour of cosmic rays in the starburst galaxy NGC253 is finally characterised.
In contrast to the long time-scale evolution of a starburst galaxy, multi-messenger studies are especially intriguing when shorter time-scales are being probed. A prime example of a short time-scale transient are Gamma Ray Bursts. The efforts to understand this phenomenon effectively founded the branch of gamma-ray astronomy. The multi-messenger approach allows for the study of illusive phenomena such as Gamma Ray Bursts and other transients using electromagnetic radiation, neutrinos, cosmic rays and gravitational waves contemporaneously. With contemporaneous observations getting more important just recently, the execution of such observation campaigns still presents a big challenge due to the different limitations and strengths of the infrastructures.
An alert system for transient phenomena has been developed over the course of this thesis for H.E.S.S. It aims to address many follow-up challenges in order to maximise the science return of the new large telescope, which is able to repoint much faster than the initial four telescopes. The system allows for fully automated observations based on scientific alerts from any wavelength or messenger and allows H.E.S.S. to participate in multi-messenger campaigns. Utilising this new system, many interesting multi-messenger observation campaigns have been performed. Several highlight observations with H.E.S.S. are analysed, presented and discussed in this work. Among them are observations of Gamma Ray Bursts with low latency and low energy threshold, the follow-up of a neutrino candidate in spatial coincidence with a flaring active galactic nucleus and of the merger of two neutron stars, which was revealed by the coincidence of gravitational waves and a Gamma-Ray Burst.
Modern gamma-ray telescopes, provide the main stream of data for astrophysicists in quest of detecting the sources of gamma rays such as active galactic nuclei (AGN). Many blazars have been detected with gamma-ray telescopes such as HESS, VERITAS, MAGIC and Fermi satellite as sources of gamma-rays with the energy E ≥ 100 GeV. These very-high-energy photons interact with extragalactic background light (EBL) producing ultra-relativistic electron-positron pairs. Observations with Fermi-LAT indicate that the GeV gamma-ray flux from some blazars is lower than that predicted from the full electromagnetic cascade. The pairs can induce electrostatic and electromagnetic instabilities. In this case, wave-particle interactions can reduce the energy of the pairs. Therefore, the collective plasma effects can also substantially suppress the GeV-band gamma-ray emission affecting as well the IGMF constraints. Using Particle in cell (PIC) simulations, we have revisited the issue of plasma instabilities induced by electron-positron beams in the fully ionized intergalactic medium. This problem is related to pair beams produced by TeV radiation of blazars. The main objective of our study is to clarify the feedback of the beam-driven instabilities on the pairs. The present dissertation provides new results regarding the plasma instabilities from blazar induced pair beams interacting with intergalactic medium. This clarifies the relevance of plasma instabilities and improves our understanding of blazars.