Decoding Complex Structures in Medical Physics, Plasma Physics and Astrophysics

Kurzfassung

Emergent, complex structures which detract from a pure linear description are ubiquitous in science. A necessary prerequisite for understanding those structures and for modelling the underlying (physical) processes is a quantitative characterization of them, where one naturally has to put an emphasis on extracting the information contained in the nonlinearities. First, methods and strategies to quantitatively assess nonlinearities or higher order correlations in data sets are presented. The methods being discussed comprise the assessment of (local) scaling properties of point sets, morphological measures, prediction errors in artificial embedding spaces and statistics of Fourier phases. The method of surrogate data represents one of the key strategies to detect (weak) nonlinearities in data sets. Pitfalls as well as extensions and new fields of applications of this approach are outlined. Next, applications of the methodologies introduced above to a number of interdisciplinary research topics are reported: It is demonstrated how the inner bone structures and their disease-induced changes can effectively be characterized in in vitro studies as well as in clinical in vivo studies. One thus obtains refined insights on the changes of bone structures in the context of osteoporosis like e.g. universal mass-structure scaling relations, which may lead - among others - to a better diagnostic performance in discriminating osteoporotic and healthy patients. A number of self-organization processes and phase transitions in complex plasmas are investigated on the microcanonical level. The kinetics of fluid demixing in a binary complex plasma is systematically studied using the evolving domain size and it is shown that the demixing dynamics depends crucially on the interaction range of the potential. The dynamics of lane formation in driven binary complex plasmas as well as the transition from normal fluids to string fluids in electrorheological (ER) plasmas are quantitatively described by newly developed order parameters. The observed time-resolved lane-formation process is in good agreement with computer simulations of a binary Yukawa model with Langevin dynamics. Microgravity experiments with ER plasmas as well as molecular dynamics simulations show a second order phase transition from an isotropic to an anisotropic (string) plasma state as the electric field is increased. Signatures of nonlinearities are identified in the x-ray light curve of active galactic nuclei (AGN) and galactic black holes (GBH). These findings lead to the exclusion of linear models like e.g. the traditional shot noise model or the global disk oscillation model for explaining the variability of AGNs and GBHs. In-depth analyses of maps of the cosmic microwave background (CMB) as obtained with the WMAP and Planck satellite consistently yield significant signatures for large scale Fourier phase correlations and for anisotropies in the maps of the CMB. These detected anomalies question the Copernican principle, i.e. the isotropy and homogeneity of the universe, which is a basic assumption of standard cosmological models. Finally, it is demonstrated how to generate data sets with tailored nonlinearities by imposing a few constraints on the distribution of Fourier phases. It is found that the power law character of leptokurtic probability distributions being typical for intermittent signals found in turbulence and financial data can thus be explained in terms of linear phase correlations. These findings point towards new research directions on deciphering the meaning of Fourier phases, which is of eminent importance for better understanding complex structures.