Sedimentary environments and climate change: a case study (late Miocene, central Crete)

In this study, conditions of deposition and stratigraphical architecture of Neogene (Tortonian, 11-6,7Ma) sediments of southern central Crete were analysed. In order to improve resolution of paleoclimatic data, new methods were applied to quantify environmental parameters and to increase the chronostratigraphic resolution in shallow water sediments. A relationship between paleoenvironmental change observed on Crete and global processes was established and a depositional model was developed. Based on a detailed analysis of the distribution of non geniculate coralline red algae, index values for water temperature and water depth were established and tested with the distribution patterns of benthic foraminifera and symbiont-bearing corals. Calcite shelled bivalves were sampled from the Algarve coast (southern Portugal) and central Crete and then 87Sr/86Sr was measured. A high resolution chronostratigraphy was developed based on the correlation between fluctuations in Sr ratios in the measured sections and in a late Miocene global seawater Sr isotope reference curve. Applying this method, a time frame was established to compare paleoenvironmental data from southern central Crete with global information on climate change reflected in oxygen isotope data. The comparison between paleotemperature data based on red algae and global oxygen isotope data showed that the employed index values reflect global change in temperature. Data indicate a warm interval during earliest Tortonian, a second short warm interval between 10 and 9,5Ma, a longer climatic optimum between 9 and 8Ma and an interval of increasing temperatures in the latest Tortonian. The distribution of coral reefs and carpets shows that during the warm intervals, the depositional environment became tropical while temperate climates prevailed during the cold interval. Since relative tectonic movements after initial half-graben formation in the early Tortonian were low in southern central Crete, sedimentary successions strongly respond to global sea-level fluctuation. A characteristic sedimentary succession formed during a 3rd order sea-level cycle: It comprises mixed siliciclastic-limestone deposited during sea-level fall and lowstand, homogenous red algal deposits formed during sea-level rise and coral carpets formed during late rise and highstand. Individual beds in the succession reflect glacioeustatic fluctuations that are most prominent in the mixed siliciclastic-limestone interval. These results confirm the fact that sedimentary successions deposited at the critical threshold between temperate and tropical environments develop characteristic changes in depositional systems and biotic associations that can be used to assemble paleoclimatic datasets.

Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the "lab-on-a-chip" paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results.