Daphnias: from the individual based model to the large population equation

The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and throught their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approximated by the delay equation featured in (Diekmann et al., l.c.)

Inverse design of artificial few-level schemes with Mössbauer nuclei in thin-film cavities

In this thesis, an inverse design approach to the engineering of quantum optical few-level schemes at hard x-ray energies is introduced. Such quantum systems can be realized with layers of Mössbauer nuclei embedded in thin-film cavities and probed with low-intensity x-rays. The approach pursued in the thesis allows to comprehensively study the realizable quantum optical setups and gives immediate access to the geometries they are realized in. This feature alleviates the need for trial-and-error methods and – due to its systematic nature – enables general and partly unexpected insights that might impact x-ray cavities beyond the system under study. The approach is introduced using the example of an artificial twolevel scheme and its generalization to more complex level schemes is illustrated with the design of quantum optical effects in an artificial three-level system. Finally, the inverse design is applied to directly shape the observable spectrum of the joint nuclei-cavity system. The results of the thesis promise to enlarge the performance of existing applications and will likely help to extend the scope of x-ray quantum optics towards novel ideas