@phdthesis{Warnecke2022,
  author    = {Warnecke, Sandra},
  title     = {Numerical schemes for multi-species BGK equations based on a variational procedure applied to multi-species BGK equations with velocity-dependent collision frequency and to quantum multi-species BGK equations},
  edition   = {1. Auflage},
  publisher = {W{\"u}rzburg University Press},
  address   = {W{\"u}rzburg},
  isbn      = {978-3-95826-192-1},
  doi       = {10.25972/WUP-978-3-95826-193-8},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-282378},
  school      = {W{\"u}rzburg University Press},
  pages     = {xiii, 203},
  year      = {2022},
  abstract  = {We consider a multi-species gas mixture described by a kinetic model. More precisely, we are interested in models with BGK interaction operators. Several extensions to the standard BGK model are studied. Firstly, we allow the collision frequency to vary not only in time and space but also with the microscopic velocity. In the standard BGK model, the dependence on the microscopic velocity is neglected for reasons of simplicity. We allow for a more physical description by reintroducing this dependence. But even though the structure of the equations remains the same, the so-called target functions in the relaxation term become more sophisticated being defined by a variational procedure. Secondly, we include quantum effects (for constant collision frequencies). This approach influences again the resulting target functions in the relaxation term depending on the respective type of quantum particles. In this thesis, we present a numerical method for simulating such models. We use implicit-explicit time discretizations in order to take care of the stiff relaxation part due to possibly large collision frequencies. The key new ingredient is an implicit solver which minimizes a certain potential function. This procedure mimics the theoretical derivation in the models. We prove that theoretical properties of the model are preserved at the discrete level such as conservation of mass, total momentum and total energy, positivity of distribution functions and a proper entropy behavior. We provide an array of numerical tests illustrating the numerical scheme as well as its usefulness and effectiveness.},
  subject      = {Kinetische Gastheorie},
  language  = {en}
}
@phdthesis{Pirner2018,
  author    = {Pirner, Marlies},
  title     = {Kinetic modelling of gas mixtures},
  edition   = {1. Auflage},
  publisher = {W{\"u}rzburg University Press},
  address   = {W{\"u}rzburg},
  isbn      = {978-3-95826-080-1 (Print)},
  doi       = {10.25972/WUP-978-3-95826-081-8},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-161077},
  school      = {W{\"u}rzburg University Press},
  pages     = {xi, 222},
  year      = {2018},
  abstract  = {This book deals with the kinetic modelling of gas mixtures. It extends the existing literature in mathematics for one species of gas to the case of gasmixtures. This is more realistic in applications. Thepresentedmodel for gas mixtures is proven to be consistentmeaning it satisfies theconservation laws, it admitsanentropy and an equilibriumstate. Furthermore, we can guarantee the existence, uniqueness and positivity of solutions. Moreover, the model is used for different applications, for example inplasma physics, for fluids with a small deviation from equilibrium and in the case of polyatomic gases.},
  subject      = {Polyatomare Verbindungen},
  language  = {en}
}
@phdthesis{Heinrich2022,
  author    = {Heinrich, Robert},
  title     = {Multi-species gas detection based on an external-cavity quantum cascade laser spectrometer in the mid-infrared fingerprint region},
  doi       = {10.25972/OPUS-26864},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-268640},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Laser spectroscopic gas sensing has been applied for decades for several applications as atmospheric monitoring, industrial combustion gas analysis or fundamental research. The availability of new laser sources in the mid-infrared opens the spectral fingerprint range to the technology where multiple molecules possess their fundamental ro-vibrational absorption features that allow very sensitive detection and accurate discrimination of the species. The increasing maturity of quantum cascade lasers that cover this highly interesting spectral range motivated this research to gain fundamental knowledge about the spectra of hydrocarbon gases in pure composition and in complex mixtures as they occur in the petro-chemical industry. The long-term target of developing accurate and fast hydrocarbon gas analyzers, capable of real-time operation while enabling feedback-loops, would lead to a paradigm change in this industry. This thesis aims to contribute to a higher accuracy and more comprehensive understanding of the sensing of hydrocarbon gas mixtures. This includes the acquisition of yet unavailable high resolution and high accuracy reference spectra of the respective gases, the investigation of their spectral behavior in mixtures due to collisional broadening of their transitions and the verification of the feasibility to quantitatively discriminate the spectra when several overlapping species are simultaneously measured in gas mixtures. To achieve this knowledge a new laboratory environment was planned and built up to allow for the supply of the individual gases and their arbitrary mixing. The main element was the development of a broadly tunable external-cavity quantum cascade laser based spectrometer to record the required spectra. This also included the development of a new measurement method to obtain highly resolved and nearly gap-less spectral coverage as well as a sophisticated signal post-processing that was crucial to achieve the high accuracy of the measurements. The spectroscopic setup was used for a thorough investigation of the spectra of the first seven alkanes as of their mixtures. Measurements were realized that achieved a spectral resolution of 0.001 cm-1 in the range of 6-11 µm while ensuring an accuracy of 0.001 cm-1 of the spectra and attaining a transmission sensitivity of 2.5 x 10-4 for long-time averaging of the acquired spectra. These spectral measurements accomplish a quality that compares to state-of-the art spectral databases and revealed so far undocumented details of several of the investigated gases that have not been measured with this high resolution before at the chosen measurement conditions. The results demonstrate the first laser spectroscopic discrimination of a seven component gas mixture with absolute accuracies below 0.5 vol.\% in the mid-infrared provided that a sufficiently broad spectral range is covered in the measurements. Remaining challenges for obtaining improved spectral models of the gases and limitations of the measurement accuracy and technology are discussed.},
  subject      = {Quantenkaskadenlaser},
  language  = {en}
}