The aim of this thesis was to test the efficiency in practice of an analytical propagator with collision detection for N-body Keplerian systems. This can be used to simulate the evolution of a protoplanetary disk, which gives insight into how planetary systems form. The analytic propagator calculates collisions one by one, while a numerical propagator would compute each time step. The idea of using the analytic propagator is that collisions are rare in astronomical scales, such that jumping from collision to collision and calculating it, is more efficient than calculating all the time steps that are between collisions. Simplifying the orbits of the planetesimals into perfect Keplerian orbits, analytical solutions exist which are used by the analytic propagator.

In this thesis, the runtimes of simulations were measured as well as other properties directly related to the runtime. The overall efficiency of the algorithm with respect to N seemed to be O(N³), which is one power less than previously predicted. The prediction was that the runtime of the full simulation is O(N²ε + N⁴s³/Ia³). Here ε is the maximum eccentricity, s/a is the ratio of a planetesimal's radius to the semi-major axis of its orbit, and I is the maximum inclination. This was calculated by estimating the total number of collisions to be O(N²s²/Ia²) and the runtime for each collision to be O(N²s/a). But the number of collisions turns from quadratic to linear in N, implying that above a certain N almost all planetesimals collide, which reduces the power of N by one. For comparison, the octree code has an algorithmic efficiency of O(N logN) per time step, and the number of steps for a fixed integration time grows as O(N^4/3 log N).

Nano-carriers have the potential to be an enormous game-changer in medicinal drug delivery systems. The polymeric nano-carriers used in this study are a product of the self-assembly of amphiphilic block copolymers, a complicated process which must be understood completely to finely tune the desired morphology for drug delivery. The goal of this thesis is to gain a better understanding of the self-assembly process of amphiphilic block copolymers. Specifically, it will focus on the ’opaque phase’ observed for poly(1,2-butadiene)-b-poly(ethylene oxide) (PBd-PEO) block copolymers, which seems to occur in the early stages of the self-assembly process. A nano-precipitation method has been developed at the TU Delft, which induces selfassembly and brings forward the opaque phase. The used block copolymer has a hydrophobic PBd block and a hydrophilic PEO block. This block copolymer dissolves well in acetone, but upon water (H2O) addition, it starts to self-assemble into spherical aggregates, useful for drug delivery. At small volumes of H2O, the opaque phase appears and disappears as more H2O is added. In this thesis, multiple samples have been prepared with the so-called Inverse Nanoprecipitation method and different experimental parameters among which the volume percentage of H2O present in the sample, have been varied. The samples have been studied using Visual Inspection, Dynamic Light Scattering and Spin Echo Small Angle Neutron Scattering. The experiments show that the time intervals between H2O addition do not affect the formation of aggregates, but rather the ‘when’ of adding the H2O. If this is added to the acetone before the block copolymer is dissolved, it affects the self-assembly process. A visual experiment showed that the opaque phase occurred 1.2±0.1 vol% H2O earlier than in previous research, which might be a result of the lower room temperature during this thesis. Another significant result might be that the addition of acetone-D6 or D2O affects the self-assembly process, which must be considered for future SESANS measurements. Lastly, during the opaque phase a strong temperature sensitivity is observed (which was already found in previous research at TU Delft, by E. Remmelts and further researched by R. Baaijens), high light scattering intensities are detected with DLS and for SESANS measurements the scattered neutron intensities were low. These observations all strongly point to a theory called ‘pre-micellization’, which gives a better understanding of the opaque phase.

A time of flight MIEZE spectrometer, which employs radio frequency spin flippers with square pole shoes and a magnetic yoke is presented. These flippers can achieve higher fields than conventional resonant RF flippers, which employ an air core. High fields are crucial for the construction of a high resolution and compact MIEZE spectrometer. Setups using conventional and novel flippers are constructed for comparison and a variety of experiments to characterize MIEZE instruments. Evidence is presented which indicates that high field flippers are capable of generating a 100kHz MIEZE signal comparable to that obtained with a conventional setup. Furthermore the need for a fast and thin detector is demonstrated. In addition the shape of the MIEZE focal spot is determined to be Gaussian. Finally the importance of stable timing for time of flight MIEZE is demonstrated. This research is relevant for the implementation of MIEZE on the Larmor instrument at ISIS pulsed neutron source in the UK.