Shapes and Dynamics of Blood Cells in Poiseuille and Shear Flows

The dynamics, shape, deformation, and orientation of red blood cells in microcirculation affect the rheology, flow resistance and transport properties of whole blood. This leads to important correlations of cellular and continuum scales. Furthermore, the dynamics of RBCs subject to different flow conditions and vessel geometries is relevant for both fundamental research and biomedical applications (e.g drug delivery). In this thesis, the behaviour of RBCs is investigated for different flow conditions via computer simulations. We use a combination of two mesoscopic particle-based simulation techniques, dissipative particle dynamics and smoothed dissipative particle dynamics. We focus on the microcapillary scale of several μm. At this scale, blood cannot be considered at the continuum but has to be studied at the cellular level. The connection between cellular motion and overall blood rheology will be investigated. Red blood cells are modelled as viscoelastic objects interacting hydrodynamically with a viscous fluid environment. The properties of the membrane, such as resistance against bending or shearing, are set to correspond to experimental values. Furthermore, thermal fluctuations are considered via random forces. Analyses corresponding to light scattering measurements are performed in order to compare to experiments and suggest for which situations this method is suitable. Static light scattering by red blood cells characterises their shape and allows comparison to objects such as spheres or cylinders, whose scattering signals have analytical solutions, in contrast to those of red blood cells. Dynamic light scattering by red blood cells is studied concerning its suitability to detect and analyse motion, deformation and membrane fluctuations. Dynamic light scattering analysis is performed for both diffusing and flowing cells. We find that scattering signals depend on various cell properties, thus allowing to distinguish different cells. The scattering of diffusing cells allows to draw conclusions on their bending rigidity via the effective diffusion coefficient. The scattering of flowing cells allows to draw conclusions on the shear rate via the scattering amplitude correlation. In flow, a RBC shows different shapes and dynamic states, depending on conditions such as confinement, physiological/pathological state and cell age. Here, two essential flow conditions are studied: simple shear flow and tube flow. Simple shear flow as a basic flow condition is part of any more complex flow. The velocity profile is linear and shear stress is homogeneous. In simple shear flow, we find a sequence of different cell shapes by increasing the shear rate. With increasing shear rate, we find rolling cells with cup shapes, trilobe shapes and quadrulobe shapes. This agrees with recent experiments. Furthermore, the impact of the initial orientation on the dynamics is studied. To study crowding and collective effects, systems with higher haematocrit are set up. Tube flow is an idealised model for the flow through cylindric microvessels. Without cell, a parabolic flow profile prevails. A single red blood cell is placed into the tube and subject to a Poiseuille profile. In tube flow, we find different cell shapes and dynamics depending on confinement, shear rate and cell properties. For strong confinements and high shear rates, we find parachute-like shapes. Although not perfectly symmetric, they are adjusted to the flow profile and maintain a stationary shape and orientation. For weak confinements and low shear rates, we find tumbling slippers that rotate and moderately change their shape. For weak confinements and high shear rates, we find tank-treading slippers that oscillate in a limited range of inclination angles and strongly change their shape. For the lowest shear rates, we find cells performing a snaking motion. Due to cell properties and resultant deformations, all shapes differ from hitherto descriptions, such as steady tank-treading or symmetric parachutes. We introduce phase diagrams to identify flow regimes for the different shapes and dynamics. Changing cell properties, the regime borders in the phase diagrams change. In both flow types, both the viscosity contrast and the choice of stress-free shape are important. For in vitro experiments, the solvent viscosity has often been higher than the cytosol viscosity, leading to a different pattern of dynamics, such as steady tank-treading. The stress-free state of a RBC, which is the state at zero shear stress, is still controversial, and computer simulations enable direct comparisons of possible candidates in equivalent flow conditions.

(Quantum-) critical dynamics of magnetoelectric materials

In this thesis the critical dynamics of several magnetoelectric compounds at their phase transition were examined. Mostly measurements of the dielectric properties in the frequency range of below 1 Hz up to 5 GHz were employed to evaluate the critical exponents for both magnetic field and temperature-dependent measurements. Most of the materials that are part of this work show anomalous behavior, especially at very low temperatures where quantum fluctuations are of the order of or even dominate those induced thermally. This anomalous behavior manifests in different forms. In Dy2Ti2O7 we demonstrate the existence of electric dipoles on magnetic monopoles. Here the dynamics at the critical endpoint located at 0.36K and in a magnetic field of 1T parallel to the [111] direction are of special interest. At this critical endpoint the expected critical slowing down of the dynamics could not only not be observed but instead the opposite, critical speeding-up by several orders of magnitude, could be demonstrated. Furthermore, we show that the phase diagram of Dy2Ti2O7 in this field direction can be reproduced solely from the dynamical properties, for example the resonance frequency of the observed relaxation that is connected to the monopole movement. Away from this point of the phase diagram the dynamics are slowing-down with reduction of temperature as one would expect. Additional measurements on Y2Ti2O7, a structurally identical but non-magnetic material, show only slowing down with reduction of temperature and no additional features. A possible explanation for the observed critical speeding-up is a coherent movement of magnetic monopoles close to the critical field that increases the resonance frequency by reducing the damping of the process. LiCuVO4 on the other hand behaves normally at its phase transition as long as the temperature is higher than 0.4 K. In this temperature regime the dynamics show critical slowing-down analogous to classical ferroelectric materials. This analogy extends also towards higher frequencies where the permittivity displays a ‘dispersion’ minimum that is temperature-dependent but of the order of 2 GHz. Below 0.4K the observed behavior changes drastically. Here we found no longer relaxational behavior but instead an excitation with very low energy. This low energy excitation was predicted by theory and is caused by nearly gapless soliton excitations within the 1D Cu2+ chains of LiCuVO4. Finally, in TbMnO3 the dynamics of the phase transition into the multiferroic phase was observed at roughly 27 K, a much higher temperature compared to the other materials. Here the expected critical slowing-down was observed, even though in low-frequency measurements this transition into the ferroelectric phase is overshadowed by the so-called c-axis relaxation. Therefore, only frequencies above 1MHz could be used to determine the critical exponents for both temperatureand magnetic-field-dependent measurements. This was done for both the peak frequency as well as the relaxation strength. In TbMnO3 an electromagnetic soft-mode with small optical weight causes the observed fluctuations, similar to the case of multiferroic MnWO4.

Diversity and Stability in Food Webs : Impacts of Non-Equilibrium Dynamics, Topology and Variation

With progressive climate change, the preservation of biodiversity is becoming increasingly important. Only if the gene pool is large enough and requirements of species are diverse, there will be species that can adapt to the changing circumstances. To maintain biodiversity, we must understand the consequences of the various strategies. Mathematical models of population dynamics could provide prognoses. However, a model that would reproduce and explain the mechanisms behind the diversity of species that we observe experimentally and in nature is still needed. A combination of theoretical models with detailed experiments is needed to test biological processes in models and compare predictions with outcomes in reality. In this thesis, several food webs are modeled and analyzed. Among others, models are formulated of laboratory experiments performed in the Zoological Institute of the University of Cologne. Numerical data of the simulations is in good agreement with the real experimental results. Via numerical simulations it can be demonstrated that few assumptions are necessary to reproduce in a model the sustained oscillations of the population size that experiments show. However, analysis indicates that species "thrown together by chance" are not very likely to survive together over long periods. Even larger food nets do not show significantly different outcomes and prove how extraordinary and complicated natural diversity is. In order to produce such a coexistence of randomly selected species—as the experiment does—models require additional information about biological processes or restrictions on the assumptions. Another explanation for the observed coexistence is a slow extinction that takes longer than the observation time. Simulated species survive a comparable period of time before they die out eventually. Interestingly, it can be stated that the same models allow the survival of several species in equilibrium and thus do not follow the so-called competitive exclusion principle. This state of equilibrium is more fragile, however, to changes in nutrient supply than the oscillating coexistence. Overall, the studies show, that having a diverse system means that population numbers are probably oscillating, and on the other hand oscillating population numbers stabilize a food web both against demographic noise as well as against changes of the habitat. Model predictions can certainly not be converted at their face value into policies for real ecosystems. But the stabilizing character of fluctuations should be considered in the regulations of animal populations.