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.

Rod-shaped plasmonic sensors

Plasmonic nanoparticles exhibit strong light scattering efficiency due to the oscillations of their conductive electrons (plasmon), which are excited by light. For rod-shaped nanoparticles, the resonance position is highly tunable by the aspect ratio (length/width) and the sensitivity to changes in the refractive index in the local environment depends on their diameter, hence, their volume. Therefore, rod-shaped nanoparticles are highly suitable as plasmonic sensors.rnWithin this thesis, I study the formation of gold nanorods and nanorods from a gold-copper alloy using a combination of small-angle X-ray scattering and optical extinction spectroscopy. The latter represents one of the first metal alloy nanoparticle synthesis protocols for producing rod-shaped single crystalline gold-copper (AuxCu(1-x)) alloyed nanoparticles. I find that both length and width independently follow an exponential growth behavior with different time-constants, which intrinsically leads to a switch between positive and negative aspect ratio growth during the course of the synthesis. In a parameter study, I find linear relations for the rate constants as a function of [HAuCl4]/[CTAB] ratio and [HAuCl4]/[seed] ratio. Furthermore, I find a correlation of final aspect ratio and ratio of rate constants for length and width growth rate for different [AgNO3]/[HAuCl4] ratios. I identify ascorbic acid as the yield limiting species in the reaction by the use of spectroscopic monitoring and TEM. Finally, I present the use of plasmonic nanorods that absorb light at 1064nm as contrast agents for photoacoustic imaging (BMBF project Polysound). rnIn the physics part, I present my automated dark-field microscope that is capable of collecting spectra in the range of 450nm to 1750 nm. I show the characteristics of that setup for the spectra acquisition in the UV-VIS range and how I use this information to simulate measurements. I show the major noise sources of the measurements and ways to reduce the noise and how the combination of setup charactersitics and simulations of sensitivity and sensing volume can be used to select appropriate gold rods for single unlabeled protein detection. Using my setup, I show how to estimate the size of gold nano-rods directly from the plasmon linewidth measured from optical single particle spectra. Then, I use this information to reduce the distribution (between particles) of the measured plasmonic sensitivity S by 30% by correcting for the systematic error introduced from the variation in particle size. I investigate the single particle scattering of bowtie structures — structures consisting of two (mostly) equilateral triangles pointing one tip at each other. I simulate the spectra of the structures considering the oblique illumination angle in my setup, which leads to additional plasmon modes in the spectra. The simulations agree well with the measurements form a qualitative point of view.rn