@phdthesis{Hannes2022,
  author    = {Hannes, Sebastian},
  title     = {Boundary Value Problems for the Lorentzian Dirac Operator},
  doi       = {10.25932/publishup-54839},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-548391},
  school      = {Universit{\"a}t Potsdam},
  pages     = {67},
  year      = {2022},
  abstract  = {The index theorem for elliptic operators on a closed Riemannian manifold by Atiyah and Singer has many applications in analysis, geometry and topology, but it is not suitable for a generalization to a Lorentzian setting. In the case where a boundary is present Atiyah, Patodi and Singer provide an index theorem for compact Riemannian manifolds by introducing non-local boundary conditions obtained via the spectral decomposition of an induced boundary operator, so called APS boundary conditions. B{\"a}r and Strohmaier prove a Lorentzian version of this index theorem for the Dirac operator on a manifold with boundary by utilizing results from APS and the characterization of the spectral flow by Phillips. In their case the Lorentzian manifold is assumed to be globally hyperbolic and spatially compact, and the induced boundary operator is given by the Riemannian Dirac operator on a spacelike Cauchy hypersurface. Their results show that imposing APS boundary conditions for these boundary operator will yield a Fredholm operator with a smooth kernel and its index can be calculated by a formula similar to the Riemannian case. Back in the Riemannian setting, B{\"a}r and Ballmann provide an analysis of the most general kind of boundary conditions that can be imposed on a first order elliptic differential operator that will still yield regularity for solutions as well as Fredholm property for the resulting operator. These boundary conditions can be thought of as deformations to the graph of a suitable operator mapping APS boundary conditions to their orthogonal complement. This thesis aims at applying the boundary conditions found by B{\"a}r and Ballmann to a Lorentzian setting to understand more general types of boundary conditions for the Dirac operator, conserving Fredholm property as well as providing regularity results and relative index formulas for the resulting operators. As it turns out, there are some differences in applying these graph-type boundary conditions to the Lorentzian Dirac operator when compared to the Riemannian setting. It will be shown that in contrast to the Riemannian case, going from a Fredholm boundary condition to its orthogonal complement works out fine in the Lorentzian setting. On the other hand, in order to deduce Fredholm property and regularity of solutions for graph-type boundary conditions, additional assumptions for the deformation maps need to be made. The thesis is organized as follows. In chapter 1 basic facts about Lorentzian and Riemannian spin manifolds, their spinor bundles and the Dirac operator are listed. These will serve as a foundation to define the setting and prove the results of later chapters. Chapter 2 defines the general notion of boundary conditions for the Dirac operator used in this thesis and introduces the APS boundary conditions as well as their graph type deformations. Also the role of the wave evolution operator in finding Fredholm boundary conditions is analyzed and these boundary conditions are connected to notion of Fredholm pairs in a given Hilbert space. Chapter 3 focuses on the principal symbol calculation of the wave evolution operator and the results are used to proof Fredholm property as well as regularity of solutions for suitable graph-type boundary conditions. Also sufficient conditions are derived for (pseudo-)local boundary conditions imposed on the Dirac operator to yield a Fredholm operator with a smooth solution space. In the last chapter 4, a few examples of boundary conditions are calculated applying the results of previous chapters. Restricting to special geometries and/or boundary conditions, results can be obtained that are not covered by the more general statements, and it is shown that so-called transmission conditions behave very differently than in the Riemannian setting.},
  language  = {en}
}
@article{LauKubiakBurchertetal.2014,
  author    = {Lau, Stephan and Kubiak, Thomas and Burchert, Sebastian and Goering, Mark and Oberlaender, Nils and von Mauschwitz, Hannes and von Sass, Sarah and Selle, Mareen and Hiemisch, Anette},
  title     = {Disentangling the effects of optimism and attributions on feelings of success},
  series = {Personality and individual differences : an international journal of research into the structure and development of personality, and the causation of individual differences},
  volume    = {56},
  journal   = {Personality and individual differences : an international journal of research into the structure and development of personality, and the causation of individual differences},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0191-8869},
  doi       = {10.1016/j.paid.2013.08.030},
  pages     = {78 -- 82},
  year      = {2014},
  abstract  = {Two experiments examined the effects of dispositional optimism and attributions on feelings of success in a performance setting. In Experiment 1, participants successfully solved three cognitive tasks and attributed the success either internally (i.e., to themselves) or externally (i.e., to a teammate). We found no effect of optimism, but a significant effect of the attribution: Internal attribution predicted an increase in feelings of success. In Experiment 2, we replicated the design and adopted an extreme groups approach in order to include the extremes of the optimism dimension. Only optimism affected feelings of success in this sample: Pessimistic participants showed higher increases in feelings of success than optimistic participants. We conclude that optimism, if disentangled from attribution, may have an effect on affect, with pessimism showing potential affective benefits. However, this association may be concealed if samples with a restricted range of the optimism dimension are studied.},
  language  = {en}
}
@article{HeimannVasyuraBathkeSudhausetal.2019,
  author    = {Heimann, Sebastian and Vasyura-Bathke, Hannes and Sudhaus, Henriette and Isken, Marius Paul and Kriegerowski, Marius and Steinberg, Andreas and Dahm, Torsten},
  title     = {A Python framework for efficient use of pre-computed Green's functions in seismological and other physical forward and inverse source problems},
  series = {Solid earth},
  volume    = {10},
  journal   = {Solid earth},
  number    = {6},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1869-9510},
  doi       = {10.5194/se-10-1921-2019},
  pages     = {1921 -- 1935},
  year      = {2019},
  abstract  = {The computation of such synthetic GFs is computationally and operationally demanding. As a consequence, the onthe-fly recalculation of synthetic GFs in each iteration of an optimisation is time-consuming and impractical. Therefore, the pre-calculation and efficient storage of synthetic GFs on a dense grid of source to receiver combinations enables the efficient lookup and utilisation of GFs in time-critical scenarios. We present a Python-based framework and toolkit - Pyrocko-GF - that enables the pre-calculation of synthetic GF stores, which are independent of their numerical calculation method and GF transfer function. The framework aids in the creation of such GF stores by interfacing a suite of established numerical forward modelling codes in seismology (computational back ends). So far, interfaces to back ends for layered Earth model cases have been provided; however, the architecture of Pyrocko-GF is designed to cover back ends for other geometries (e.g. full 3-D heterogeneous media) and other physical quantities (e.g. gravity, pressure, tilt). Therefore, Pyrocko-GF defines an extensible GF storage format suitable for a wide range of GF types, especially handling elasticity and wave propagation problems. The framework assists with visualisations, quality control, and the exchange of GF stores, which is supported through an online platform that provides many pre-calculated GF stores for local, regional, and global studies. The Pyrocko-GF toolkit comes with a well-documented application programming interface (API) for the Python programming language to efficiently facilitate forward modelling of geophysical processes, e.g. synthetic waveforms or static displacements for a wide range of source models.},
  language  = {en}
}
@article{IskenVasyuraBathkeDahmetal.2022,
  author    = {Isken, Marius Paul and Vasyura-Bathke, Hannes and Dahm, Torsten and Heimann, Sebastian},
  title     = {De-noising distributed acoustic sensing data using an adaptive frequency-wavenumber filter},
  series = {Geophysical journal international},
  volume    = {231},
  journal   = {Geophysical journal international},
  number    = {2},
  publisher = {Oxford University Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggac229},
  pages     = {944 -- 949},
  year      = {2022},
  abstract  = {Data recorded by distributed acoustic sensing (DAS) along an optical fibre sample the spatial and temporal properties of seismic wavefields at high spatial density. Often leading to massive amount of data when collected for seismic monitoring along many kilometre long cables. The spatially coherent signals from weak seismic arrivals within the data are often obscured by incoherent noise. We present a flexible and computationally efficient filtering technique, which makes use of the dense spatial and temporal sampling of the data and that can handle the large amount of data. The presented adaptive frequency-wavenumber filter suppresses the incoherent seismic noise while amplifying the coherent wavefield. We analyse the response of the filter in time and spectral domain, and we demonstrate its performance on a noisy data set that was recorded in a vertical borehole observatory showing active and passive seismic phase arrivals. Lastly, we present a performant open-source software implementation enabling real-time filtering of large DAS data sets.},
  language  = {en}
}