In this thesis the hydrodynamic behaviour of an idealised relatively short tidal estuary is studied using a cross-sectionally averaged model, i.e. a one dimensional model. The geometry of the estuary is simplified and only the hydrodynamic processes are considered. This model is used to gain insight in the behaviour of currents and water levels influenced by a movable barrier situated in the estuary. It is investigated whether shifting the motion of the barrier in time influences the sedimentation in the embayment.

In this thesis, we demonstrate optical trapping of HSP90 proteins in plasmonic nanoapertures to study the HSP90 conformational change. This technique is label-free and non-destructive. The resonance of the bow tie shaped plasmonic nanoaperture is used to create a very strong electric field gradient force able to trap proteins. The resonance phenomenon is also used for detecting the trapping events, using the change in transmission that results from the presence of a protein in the trap. HSP90 can be trapped very stably for upwards of 30 seconds. The signal resulting from trapping HSP90 significantly differs from signals from bead traps, especially in the low-frequency regime. We observe strong evidence for a two level system when HSP90 was incubated with AMP-PNP which should slow down the conformational change (fit with R^2=0.9988). More work is required to demonstrate whether this two level system results from the conformational change. We conclude that there is a need for more advanced statistical methods to more conclusively prove that the HSP90 undergoes conformational change between two main levels and suggest further improvements to the experiments.

Skin grafting is a common technique employed to treat patients after burn injuries. In contrast to the frequency and gravity of contractures following from skin grafts, the phenomenon itself is still poorly understood and subject of studies. The development of an accurate model of skin contractures will allow medical researchers to better understand the healing process compared to current in vitro experiments and thus enable the design of efficient and patient-specific treatments. In this work we provide a mathematical model able to capture both the mechanical and biological processes involved in skin graft healing. Two-dimensional morphoelastic equations are used to model the mechanics of contraction of skin during the healing process. A system of equations describing the cell components (myo-, fibroblasts, collagen density and signalling molecule) is solved separately to derive the forcing terms for the mechanical system. The finite element method with bilinear quadrilateral elements is used to solve the differential equations on a moving time-dependent domain. A flux corrected transport (FCT) algorithm is used to stabilize the biological equations, thus enforcing positivity of the constituents in the dermal layer and nonlinearities are treated using Picard iterations. Time stepping is performed by applying the Euler backward scheme for the mechanical system and the implicit midpoint rule for the biological system. The results are replicated using the IGA (Isogeometric Analysis) library G+Smo in C++. The results of the IGA implementation provide a solid basis for future algorithms using IGA.

Mass-spring systems are commonly used in structural components. Understanding their characteristics and pitfalls is an important issue, combining physics and mathematics to prevent such systems from resonating and causing structures to weaken or collapse. This way, suitable solutions can be found such as the use of dampers with the right characteristics. In this paper we focus on such systems, in particular with a snap-through mechanism. Their dynamical behaviour and the in uence of a small disturbance on the mechanism, such as a wind force, are analyzed. A behavioral model is set up to which Melnikov's Method is applied, in order to analyze the behaviour numerically. The latter is done using the Trapezoidal method.

In dit verslag worden de resultaten van literatuuronderzoek naar de voor- en
nadelen van floats en posits gepresenteerd. Naar aanleiding van de resultaten is de hypothese opgesteld dat posits een goede "drop-in replacement" zouden zijn voor floats vanwege het grotere bereik, de afwezigheid van overflow en underflow en omdat ze enkel één NaN-waarde hebben. Met behulp van Wolfram Mathematica is een omgeving gemaakt welke de prestatiesvan IEEE 754 floating point standard (floats) vergelijkt met Unum Type III posits in 8-bits. De resultaten hiervan bevestigden de hypothese. Als vervolgonderzoek zijn de 32-bits versies van dezelfde
floats en posits vergeleken in Python. Als praktijkvoorbeeld is de methode van Newton-Raphson gekozen met verschillende functies. De resultaten van deze tests lijken de hypothese grotendeels te ontkrachten voor zeer grote en zeer kleine getallen. Gebaseerd op deze onderzoeken lijken posits in de meeste gevallen een geschikte drop-in replacement voor floats, maar zijn ze minder nauwkeurig dan floats wanneer gerekend wordt met zeer grote en kleine getallen. Posits bieden echter meer stabiliteit doordat ze geen overflow en underflow hebben en daarom wel een waarde weergeven. De toepasbaarheid van deze waardes moet nog verder worden onderzocht. Ook kunnen andere numerieke methodes zoals Runge-Kutta gebruikt worden om de hypothese verder te testen.

In this dissertation we look at the seriation problem and the applications of this problem. Given a set of items, we try to find an ordering based on the similarity between the items. We start by explaining the mathematical theory behind the seriation problem. Then we describe a couple of different methods that can be used to find a solution for the problem. After that, we apply these methods to various different datasets. The results of these tests will be analysed.
Solving a seriation problem can be an alternative way to already existing methods when finding a ranking of items for a given dataset. The goal is to find out if is also a viable method to use in practice.

In this report, the rain-wind induced vibrations of cables are studied. This is done by modeling the cable cross-section as a mass-spring system with two time-varying masses. Thereafter, the solution of this model is approximated using a multiple timescale perturbation method. Lastly, for some choices
of the time-varying masses the eigenfrequencies are analyzed, stability properties are derived, and approximations of the solutions are given.