Magnetostatics play a crucial role in the detection and localisation of naval vessels. Also, minimising a vessel’s magnetic signature is essential to reduce the risk posed by naval mines, which often rely on magnetic detection. This research aims to improve the calculation of magnetic signatures using the Method of Moments (MoM) by implementing it in Julia, a high-performance programming language. A simplified version of TNO’s current MATLAB-based approach is implemented in Julia to establish a baseline for the accuracy and efficiency. Linear basis functions and automatic differentiation (AD) are incorporated into the methodology to explore potential improvements. These extended methods are compared to the baseline to evaluate their performance.
Results show that Julia can be of great value, since it significantly improves the assembly time of the interaction matrix. Point matching is not a suitable approach when using linear basis functions. The Galerkin method shows promising results, though its computational performance remains a significant drawback. Also, using AD shows potential to simplify the implementation of the MoM by eliminating the need for analytical integral expressions. However, AD disappoints in terms of computational performance. Moreover, the AD implementation relies on a mesh-dependent parameter.

After decades of urban growth, mass transport, including buses, will play a significant role in our daily life. Therefore the requirements for buses and their bus door system are increasing. Ventura Systems is a company that is specialized in bus door systems and wishes to gain knowledge on their bus door system using mathematical modeling. This bachelor thesis provides the base for the mathematical models for modeling a bus door system. Multiple models are presented and one model is analyzed in more depth.

About three quarters of our DNA is wrapped into nucleosomes: DNA spools with a protein core. It is well known that the affinity of a given DNA stretch to be incorporated into a nucleosome depends on the geometry and elasticity of the basepair sequence involved, causing the positioning of nucleosomes. Here we show that DNA elasticity can have a much deeper effect on nucleosomes than just their positioning: it affects their "identities". Employing a recently developed computational algorithm, the mutation Monte Carlo method, we design nucleosomes with surprising physical characteristics. Unlike any other nucleosomes studied so far, these nucleosomes are short-lived when put under mechanical tension whereas other physical properties are largely unaffected. This suggests that the nucleosome, the most abundant DNA-protein complex in our cells, might more properly be considered a class of complexes with a wide array of physical properties, and raises the possibility that evolution has shaped various nucleosome species according to their genomic context.

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