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My research focuses on multiscale modeling and analysis with a stochastic flavor. In particular I'm interested in stochastic particle systems and stochastic homogenization. Applications comprise catalytic surface reactions, neural networks, and chemical engineering.
Catalytic surface reactions In my diploma and PhD thesis work I have been concerned with the modelling of the oxidation of carbon monoxide on platinum single crystal surfaces. This particular surface reaction has been studied extensively in experiments not only for its importance in the design of the automotive catalytic converter, where the oxidation of poisonous carbon monoxide is a major task, but also because of its role as model system for the study of self-organization and pattern formation far from thermodynamic equilibrium. Since the platinum surface constitutes a truly two-dimensional chemical reactor and thus fluctuations can play a significant role for the dynamical behavior, we have modelled the reaction both with a stochastic many-particle system and a macroscopic deterministic model in the form of partial differential equations (reaction-diffusion equations). The stochastic model can be shown to converge to the deterministic one in the limit of large particle numbers. In simulations of the stochastic model for CO oxidation we could reproduce an experimentally observed phenomenon of spatiotemporal pattern formation (`raindrop patterns') that is initiated by internal fluctuations and therefore cannot be captured in a deterministic model. (The modelling work is done in collaboration with J. Starke, DTU Copenhagen, and M. Eiswirth, FHI Berlin.)
Olfactory dynamics Since the end of my PhD I mainly deal with the modeling of the neural network in the olfactory bulb, which constitutes the first processing unit for electrical signals evoked by odour molecules in the receptor neurons in the nose. The aim of this project is to understand the collective dynamics of the bulbar neurons on the macroscopic level starting from a microscopic model. This work is carried out in the framework of the interdisciplinary WIN group on olfactory dynamics of the Heidelberg Academy of Sciences.
Modelling of a catalytic converter The main part of an automotive catalytic converter consists of a periodic array of tubes the walls of which are covered by a layer of catalytic material. We propose to derive an effective model for a catalytic converter by combining homogenization and singular perturbation techniques. This work is done in collaboration with S. Lacharme (PhD student).
|Last revised: 06/12/2007 · Christian Reichert|