High precision swept volume approximation with conservative error bounds

In technical design processes in the automotive industry, digital prototypes rapidly gain importance, because they allow for a detection of design errors in early development stages. The technical design process includes the computation of swept volumes for maintainability analysis and clearance checks. The swept volume is very useful, for example, to identify problem areas where a safety distance might not be kept. With the explicit construction of the swept volume an engineer gets evidence on how the shape of components that come too close have to be modified.rnIn this thesis a concept for the approximation of the outer boundary of a swept volume is developed. For safety reasons, it is essential that the approximation is conservative, i.e., that the swept volume is completely enclosed by the approximation. On the other hand, one wishes to approximate the swept volume as precisely as possible. In this work, we will show, that the one-sided Hausdorff distance is the adequate measure for the error of the approximation, when the intended usage is clearance checks, continuous collision detection and maintainability analysis in CAD. We present two implementations that apply the concept and generate a manifold triangle mesh that approximates the outer boundary of a swept volume. Both algorithms are two-phased: a sweeping phase which generates a conservative voxelization of the swept volume, and the actual mesh generation which is based on restricted Delaunay refinement. This approach ensures a high precision of the approximation while respecting conservativeness.rnThe benchmarks for our test are amongst others real world scenarios that come from the automotive industry.rnFurther, we introduce a method to relate parts of an already computed swept volume boundary to those triangles of the generator, that come closest during the sweep. We use this to verify as well as to colorize meshes resulting from our implementations.

Complex tracer mobilities in polymer networks revealed by fluorescence correlation spectroscopy

Gels are elastic porous polymer networks that are accompanied by pronounced mechanical properties. Due to their biocompatibility, ‘responsive hydrogels’ (HG) have many biomedical applications ranging from biosensors and drug delivery to tissue engineering. They respond to external stimuli such as temperature and salt by changing their dimensions. Of paramount importance is the ability to engineer penetrability and diffusion of interacting molecules in the crowded HG environment, as this would enable one to optimize a specific functionality. Even though the conditions under which biomedical devices operate are rather complex, a bottom-up approach could reduce the complexity of mutually coupled parameters influencing tracer mobility. The present thesis focuses on the interaction-induced tracer diffusion in polymer solutions and their homologous gels, probed by means of Fluorescence Correlation Spectroscopy (FCS). This is a single-molecule-sensitive technique having the advantage of optimal performance under ultralow tracer concentrations, typically employed in biosensors. Two different types of hydrogels have been investigated, a conventional one with broad polydispersity in the distance between crosslink points and a so-called ‘ideal’, with uniform mesh size distribution. The former is based on a thermoresponsive polymer, exhibiting phase separation in water at temperatures close to the human body temperature. The latter represents an optimal platform to study tracer diffusion. Mobilities of different tracers have been investigated in each network, varying in size, geometry and in terms of tracer-polymer attractive strength, as perturbed by different stimuli. The thesis constitutes a systematic effort towards elucidating the role of the strength and nature of different tracer-polymer interactions, on tracer mobilities; it outlines that interactions can still be very important even in the simplified case of dilute polymer solutions; it also demonstrates that the presence of permanent crosslinks exerts distinct tracer slowdown, depending on the tracer type and the nature of the tracer-polymer interactions, expressed differently by each tracer with regard to the selected stimulus. In aqueous polymer solutions, the tracer slowdown is found to be system-dependent and no universal trend seems to hold, in contrast to predictions from scaling theory for non-interacting nanoparticle mobility and empirical relations concerning the mesh size in polymer solutions. Complex tracer dynamics in polymer networks may be distinctly expressed by FCS, depending on the specific synergy among-at least some of - the following parameters: nature of interactions, external stimuli employed, tracer size and type, crosslink density and swelling ratio.