This thesis studies Lie group methods for inertial navigation. One seeks to find the orientation, position and velocity of a rigid body using measurements of angular velocity and specific force made by an inertial measurement unit (IMU). The orientation and states combining orientation with position and velocity do not live in vector spaces, but in nonlinear spaces like SO(3), SE(3) and SE2(3). These spaces are Lie groups, i.e. both groups and smooth manifolds.

The first part of this thesis develops the mathematical foundations of smooth manifolds and Lie groups. We also explain some important maps on Lie groups, the Lie algebra, how to formulate errors and perturbations on Lie groups, and how to describe a state on a Lie group that evolves with time due to IMU measurements.

In the second part of the thesis we use this foundation to analyze how existing estimation errors propagate and how new errors are introduced by noise. Here we study concepts such as group-affine dynamics, log-linear error behavior and covariance propagation. We also study a technique called preintegration: summarizing the motion implied by high-frequency IMU data in preintegrated increments, which are independent of the initial state. Using these increments, an optimizer can change its estimate of the initial state without having to reintegrate the IMU data to find the final state.

Finally, some numerical experiments on the EuRoC MAV V1_01 easy dataset illustrate that IMU dead reckoning is not reliable as a global estimator and that the accuracy and reliability of preintegrated increments decrease as more IMU data is summarized in them.

Overall, this thesis aims to give a mathematically rigorous but accessible overview of Lie group methods for inertial navigation, connecting the underlying theory with practical implementations while starting from the level of a bachelor’s student in mathematics. ... Read more

The environmental impact of animal agriculture has increased the demand for more sustainable alternatives to conventional meat products. Plant-based meat alternatives offer a promising option, but reproducing the characteristic fibrous structure and texture of meat remains challenging. High-moisture extrusion (HME) is widely used to create fibrous structures in plant-based meat alternatives, yet the mechanisms underlying structure formation across different length scales remain insufficiently understood. The aim of this thesis was to investigate how multiscale structure develops during HME of plant-based proteins, with particular emphasis on nm-to-µm scale structural rearrangements and their role in larger scale structure formation and the final texture of the extrudates. To achieve this aim, SAS techniques were used alongside complementary structural and textural characterisation methods, employing both ex situ and in situ approaches. In Chapter 2, we demonstrated that the complementary use of SANS and (U)SAXS is essential for SPC systems because each method provides different SLD contrasts. Under HME conditions, moderately unfolded yet globular proteins assemble into nano-aggregates that grow in the screw section until reaching a stable size (∼30 nm); these aggregates likely serve as building blocks for protein fibrils. Alignment of protein fibrils is observed at length scales larger than individual nano-aggregates, with greater alignment in the cooling die, especially near the colder walls. In Chapter 3, we confirmed that nm-to-µm scale alignment is already established within the extruder barrel, whereas the development of the lamellar phase-separated structure takes place predominantly in the cooling die. The use of a breaker plate promotes a more homogeneous distribution of structure and temperature in the protein melt. In Chapter 4, we investigated the effect of pH-shifting on multiscale structural anisotropy and texture. pH-shifting was shown to have a pronounced, non-monotonic effect. At the nm scale, SAS indicates that at pH > pI protein nano-aggregates increase in size and a transition from particulate to fibrillar-like aggregation takes place. Aligned lamellar structures emerge at pH > pI and diminish again at pH ≫ pI. In Chapter 5, we clarified mechanisms of structure formation by linking the heat-set gelation behaviour of fractionated 11S and 7S soy globulins to the multiscale structures. 7S globulin promotes deformability and facilitates flow-induced alignment, whereas 11S globulin contributes to network strengthening through covalent crosslinks. In Chapter 6, we developed a custom ‘neutron-transparent’ cooling die to enable direct in situ SANS measurements. The results show that protein aggregation in the extruder barrel is primarily governed by protein charge. Notably, partial relaxation of nanoscale alignment in the cooling die does not eliminate the macroscopic lamellar pattern, demonstrating that the final mm-scale structure reflects the early alignment state established at the cooling die entrance. ... Read more

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). ... Read more

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.
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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. ... Read more