A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

We do magnetohydrodynamic (MHD) simulations of local box models of turbulent Interstellar Medium (ISM) and analyse the process of amplification and saturation of mean magnetic fields with methods of mean field dynamo theory. It is shown that the process of saturation of mean fields can be partially described by the prolonged diffusion time scales in presence of the dynamically significant magnetic fields. However, the outward wind also plays an essential role in the saturation in higher SN rate case. Algebraic expressions for the back reaction of the magnetic field onto the turbulent transport coefficients are derived, which allow a complete description of the nonlinear dynamo. We also present the effects of dynamically significant mean fields on the ISM configuration and pressure distribution. We further add the cosmic ray component in the simulations and investigate the kinematic growth of mean fields with a dynamo perspective.

Galaxies evolve on cosmological timescales and to study this evolution we can either study the stellar populations, tracing the star formation and chemical enrichment, or the dynamics, tracing interactions and mergers of galaxies as well as accretion. In the last decades this field has become one of the most active research areas in modern astrophysics and especially the use of integral field spectrographs furthered our understanding. This work is based on data of NGC 5102 obtained with the panoramic integral field spectrograph MUSE. The data are analysed with two separate and complementary approaches: In the first part, standard methods are used to measure the kinematics and than model the gravitational potential using these exceptionally high-quality data. In the second part I develop the new method of surface brightness fluctuation spectroscopy and quantitatively explore its potential to investigate the bright evolved stellar population. Measuring the kinematics of NGC 5102 I discover that this low-luminosity S0 galaxy hosts two counter rotating discs. The more central stellar component co-rotates with the large amount of HI gas. Investigating the populations I find strong central age and metallicity gradients with a younger and more metal rich central population. The spectral resolution of MUSE does not allow to connect these population gradients with the two counter rotating discs. The kinematic measurements are modelled with Jeans anisotropic models to infer the gravitational potential of NGC 5102. Under the self-consistent mass-follows-light assumption none of the Jeans models is able to reproduce the observed kinematics. To my knowledge this is the strongest evidence evidence for a dark matter dominated system obtained with this approach so far. Including a Navarro, Frenk & White dark matter halo immediately solves the discrepancies. A very robust result is the logarithmic slope of the total matter density. For this low-mass galaxy I find a value of -1.75 +- 0.04, shallower than an isothermal halo and even shallower than published values for more massive galaxies. This confirms a tentative relation between total mass slope and stellar mass of galaxies. The Surface Brightness Fluctuation (SBF) method is a well established distance measure, but due to its sensitive to bright stars also used to study evolved stars in unresolved stellar populations. The wide-field spectrograph MUSE offers the possibility to apply this technique for the first time to spectroscopic data. In this thesis I develop the spectroscopic SBF technique and measure the first SBF spectrum of any galaxy. I discuss the challenges for measuring SBF spectra that rise due to the complexity of integral field spectrographs compared to imaging instruments. Since decades, stellar population models indicate that SBFs in intermediate-to-old stellar systems are dominated by red giant branch and asymptotic giant branch stars. Especially the later carry significant model uncertainties, making these stars a scientifically interesting target. Comparing the NGC 5102 SBF spectrum with stellar spectra I show for the first time that M-type giants cause the fluctuations. Stellar evolution models suggest that also carbon rich thermally pulsating asymptotic giant branch stars should leave a detectable signal in the SBF spectrum. I cannot detect a significant contribution from these stars in the NGC 5102 SBF spectrum. I have written a stellar population synthesis tool that predicts for the first time SBF spectra. I compute two sets of population models: based on observed and on theoretical stellar spectra. In comparing the two models I find that the models based on observed spectra predict weaker molecular features. The comparison with the NGC 5102 spectrum reveals that these models are in better agreement with the data.

We present electrical impedance measurements of amoeboid cells on microelectrodes. The model organism Dictyostelium discoideum shows under starvation conditions a transition to collective behavior when chemotactic cells collect in multicellular aggregates. We show how impedance recordings give a precise picture of the stages of aggregation by tracing the dynamics of cell-substrate adhesion. Furthermore, we present for the first time systematic single cell measurements of wild type cells and four mutant strains that differ in their substrate adhesion strength. We recorded the projected cell area by time lapse microscopy and found a correlation between quasi-periodic oscillations in the kinetics of the projected area - the cell shape oscillation - and the long-term trend in the impedance signal. Typically, amoeboid motility advances via a cycle of membrane protrusion, substrate adhesion, traction of the cell body and tail retraction. This motility cycle results in the quasi-periodic oscillations of the projected cell area and the impedance. In all cell lines measured, similar periods were observed for this cycle, despite the differences in attachment strength. We observed that cell-substrate attachment strength strongly affects the impedance in that the deviations from mean (the magnitude of fluctuations) are enhanced in cells that effectively transmit forces, generated by the cytoskeleton, to the substrate. For example, in talA- cells, which lack the actin anchoring protein talin, the fluctuations are strongly reduced. Single cell force spectroscopy and results from a detachment assay, where adhesion is measured by exposing cells to shear stress, confirm that the magnitude of impedance fluctuations is a correct measure for the strength of substrate adhesion. Finally, we also worked on the integration of cell-substrate impedance sensors into microfluidic devices. A chip-based electrical chemotaxis assay is designed which measures the speed of chemotactic cells migrating over microelectrodes along a chemical concentration gradient.