@phdthesis{Novatchev2002,
  author    = {Novatchev, Nikolai},
  title     = {Untersuchung des Verunreinigungsprofils von Aminos{\"a}uren aus fermentativer Herstellung mittels Kapillarelektrophorese},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-4106},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2002},
  abstract  = {Gegenstand der vorliegenden Arbeit war die Untersuchungen von Verunreinigungsprofilen von Aminos{\"a}uren aus biotechnologischer Herstellung. Dazu sollten die Aminos{\"a}uren Arg, His, Ile, Lys, Phe, Pro, Ser und Trp von verschiedenen Herstellern und aus unterschiedlichen Batches genauer unter die Lupe genommen werden. Mit der im Europ{\"a}ischen Arzneibuch beschriebenen d{\"u}nnschichtchromatographischen Methode (DC-Methode) f{\"u}r „mit Ninhydrin nachweisbare Substanzen" k{\"o}nnen ausschließlich Fremdaminos{\"a}uren nachgewiesen werden und dies nur, wenn der jeweilige Gehalt relativ hoch ist. Andere Stoffgruppen, die aus der biotechnologischen Herstellung stammen, werden aufgrund der Trennbedingungen sowie der Detektionsart der DC-Methode nicht erfasst. Deshalb mussten neue Methoden entwickelt werden. Laut Vorschriften der International Conference of Harmonisation (ICH) m{\"u}ssen unbekannte Verunreinigungen in Wirkstoffen f{\"u}r orale Therapeutika auf 0,1 \% w/w begrenzt werden k{\"o}nnen. In die Untersuchungen wurden neben den Fremdaminos{\"a}uren auch Peptide, Aminozucker und Nucleins{\"a}uren als potentielle Verunreinigungen, die aus der Herstellung bzw. aus dem Reinigungsprozess kommen, einbezogen. Diese zus{\"a}tzlichen Stoffgruppen k{\"o}nnen aus den „Nebenaktivit{\"a}ten" der Mikroorganismen entstehen. Aminos{\"a}uren, Peptide und Aminozucker wurden versucht, kapillarelektrophoretisch zu quantifizieren. F{\"u}r die Bestimmung von Nucleins{\"a}uren wurde zus{\"a}tzlich die UV-Spektroskopie eingesetzt.},
  subject      = {Aminos{\"a}uren},
  language  = {de}
}
@phdthesis{Merger2016,
  author    = {Merger, Juri},
  title     = {Optimal Control and Function Identification in Biological Processes},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-138900},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {Mathematical modelling, simulation, and optimisation are core methodologies for future developments in engineering, natural, and life sciences. This work aims at applying these mathematical techniques in the field of biological processes with a focus on the wine fermentation process that is chosen as a representative model. In the literature, basic models for the wine fermentation process consist of a system of ordinary differential equations. They model the evolution of the yeast population number as well as the concentrations of assimilable nitrogen, sugar, and ethanol. In this thesis, the concentration of molecular oxygen is also included in order to model the change of the metabolism of the yeast from an aerobic to an anaerobic one. Further, a more sophisticated toxicity function is used. It provides simulation results that match experimental measurements better than a linear toxicity model. Moreover, a further equation for the temperature plays a crucial role in this work as it opens a way to influence the fermentation process in a desired way by changing the temperature of the system via a cooling mechanism. From the view of the wine industry, it is necessary to cope with large scale fermentation vessels, where spatial inhomogeneities of concentrations and temperature are likely to arise. Therefore, a system of reaction-diffusion equations is formulated in this work, which acts as an approximation for a model including computationally very expensive fluid dynamics. In addition to the modelling issues, an optimal control problem for the proposed reaction-diffusion fermentation model with temperature boundary control is presented and analysed. Variational methods are used to prove the existence of unique weak solutions to this non-linear problem. In this framework, it is possible to exploit the Hilbert space structure of state and control spaces to prove the existence of optimal controls. Additionally, first-order necessary optimality conditions are presented. They characterise controls that minimise an objective functional with the purpose to minimise the final sugar concentration. A numerical experiment shows that the final concentration of sugar can be reduced by a suitably chosen temperature control. The second part of this thesis deals with the identification of an unknown function that participates in a dynamical model. For models with ordinary differential equations, where parts of the dynamic cannot be deduced due to the complexity of the underlying phenomena, a minimisation problem is formulated. By minimising the deviations of simulation results and measurements the best possible function from a trial function space is found. The analysis of this function identification problem covers the proof of the differentiability of the function-to-state operator, the existence of minimisers, and the sensitivity analysis by means of the data-to-function mapping. Moreover, the presented function identification method is extended to stochastic differential equations. Here, the objective functional consists of the difference of measured values and the statistical expected value of the stochastic process solving the stochastic differential equation. Using a Fokker-Planck equation that governs the probability density function of the process, the probabilistic problem of simulating a stochastic process is cast to a deterministic partial differential equation. Proofs of unique solvability of the forward equation, the existence of minimisers, and first-order necessary optimality conditions are presented. The application of the function identification framework to the wine fermentation model aims at finding the shape of the toxicity function and is carried out for the deterministic as well as the stochastic case.},
  subject      = {Optimale Kontrolle},
  language  = {en}
}