Each violin generates a unique sound with a distinct set of acoustic properties. In particular, the Stradivarius violins are said to have a very unique sound. The ultimate goal of this thesis is to aid in recreating the unique sound of the Stradivarius. Though, the field of research surrounding the violin and its acoustic properties is very broad and many aspects of this research, such as subtle structural differences between violins, fall beyond the scope of this thesis. Rather, the goal of this thesis is to provide the tools to find the differences between different violins. This thesis is split into two parts. In the first part, a literature review, describing the different parts of the violin, is presented along with an overview of different experiments and finite element models, describing the plate dynamics of the violin. In the second part, a model of the violin is devised, with modelling cycles based on consecutive simplification, and implemented in Python using finite difference equations and the method of lines. This model is made with the goal to provide a framework for creating a realistic model of the violin where differences in timbre between violins can shown. In the literature review, four subjects are addressed. First, an explanation on timbre is given with an illustration of its perception. Additionally the timbre of historical and contemporary violins is compared. Second, the radiated sound of the violin is discussed. In specific, the problem with directivity of radiation is brought to attention. Third, an overview of the bridge is given with a strong emphasis on the influence of the bridge admittance on the radiated sound. Last, the corpus is dissected into different parts which are investigated with optical sensors and modelled with the software packages Comsol and Abaqus. The model in the second part of the thesis is based on principle of consecutive simplification. To set the groundwork for further iterations of the model, the most important assumptions are kept track off. The method of lines is then used to simulate the vibrations of a wooden square plate using the flexural wave equation as the governing equation of motion. In this simulation, the forward Euler method is used for the numerical time integration. The steady state solutions of the numerical model are coherent with the analytical solutions to the flexural wave equation. However, the time dependent results diverge from the results shown in the literature study. This is either due numerical time integration method being unstable or due to the physical properties of the wood not being translated by the stiffness matrix in the model.

Hot water pumped out of the ground for purposes of geothermal energy extraction cools down after it is used in a heat exchanger. The now cold water contains minerals that undergo a shift in chemical equilibrium. This may cause the minerals to come out of solution and become sediments. When pumping the cold water back into the porous ground, these sediments can cause cloggings that eventually lead to a net energy loss using this source. It will requiremore mechanical energy to pump up the water, than we gain in geothermal energy. In this reportwe aimto create a simple computer programthat models the creation of these sediments. The goal is to knowwhat minerals cause cloggings, and which do not. The program approximates the underground as a 0-dimensional tank with inflow and outflow called a Continuously Stirred Tank Reactor (CSTR).We derive a set of differential equations for both the inflow and outflow and the chemical reactions that take place. The chemistry used in this model uses data from individual reactions, which gives us differential equations for the concentrations of the minerals. These chemical reactions are very dependent on the temperature in the tank. Because the inflow water may have a different temperature than the tank, we will alsomake a differential equation for the temperature. Using a fourth order Runge-Kutta scheme we can numerically integrate these equations in time. To test the program we use 6 of the most common dissolution reactions in ground water. When using the program we can see that some concentrations change a very insignificant amount and therefore do not contribute to the cloggings. These minerals were Mg 2+ from the dissolution of dolomite and Fe2+ from the dissolution of magnetite. The programworks as desired, but does lack some elements, first and foremost the reactions between acids and bases, such as HCO− 3 and H+.

Geothermal energy can be promising to help the energy transition. Warm water is pumped up from a geothermal well and after it is cooled down, the cold water is reinjected into the hot aquifer underground. The temperature change could cause chemical balances to be disturbed and result in precipitation on the porous medium of the aquifer. This process of clogging of an aquifer is not desirable since it re- duces the efficiency of the production of warm water. This research is a stepping stone for modelling these reactions and clogging of the aquifer. The reactions rates depend on the temperature and the concentration of the reactants in the aquifer. For this reason the temperature distribution of the aquifer was numerically derived with finite difference methods. The velocity field is important for modelling both the temperature and the concentrations. Therefore the pressure and velocity field were modelled with use of mass conservation and the Darcy model. The models were solved numerically with finite difference methods and some results were compared to the analytical solution of the model. It was concluded that the numerical model for the velocity field is accurate when compared to analytical solu- tions of the model equations. In the model used, an increase in porosity resulted in a delay of cooling the aquifer. This is because there was no relation between porosity and permeability implemented in the model. A lower flow rate in the aquifer delays the cooling of the aquifer as well. For further research it is recommended to implement the chemical reactions into the model and use this model to look into how to prevent the clogging in the aquifer.

In this report, we have taken a look at three different types of trebuchets: the seesaw, the traction trebuchet or mangonel, and the counterweight trebuchet. We have created models to describe their motion by making use of Lagrangian mechanics and have compared them based on their maximum ranges. Moreover, we have also calculated a lower bound for the dimensions of themain beam needed to prevent it from breaking based on a static state. We have seen that the mangonel and trebuchet improved on the seesaw by increasing the range roughly sixfold which was expected. The maximum range of the trebuchet, however, slightly decreased compared to the mangonel. This was something we did not expect but think is due to the fact that the dimensions of the catapults were not optimised. Lastly, we found that the beam needed to be at least 18.7 cm to prevent it from breaking. However, for the real catapults, the beam would most likely need to be thicker to prevent it from breaking.

In this thesis, we present a study to obtain a clear and accurate overview of the progress and behaviour of COVID-19 in the Netherlands. We distinguish two parts for this study. The first part is to estimate the total number of infected people as a function of time by combining data from hospital admissions, daily reported cases and serological data. Using these data sets, we found that our estimation for the number of infected people was comparable to the estimations provided by the RIVM and Sanquin. Furthermore, we found that on average only 39.3% of the total number of cases were detected. 1.2% of the total number of infected people is admitted to the hospital and 18.6% of the hospitalized patients is admitted to the ICU. The second part is to develop a representative model that reproduces the estimated total number of infections using a modified SEIR model. These modifications include modelling the infection rate β(t) as a function of time using a simple linear ODE, a system of ODEs inspired by the Lotka-Volterra equations, the implementation of gamma distributed exposed and infected stages and lastly the incorporation of spatial heterogeneity. We found that our Lotka-Volterra inspired model was able to model multiple consecutive waves, which differs from the standard compartmental models. The other modifications however seemed to have only minor effects on the model and had some difficulties with matching historical data. We conclude that our Lotka-Volterra inspired model should be used to model consecutive waves for a longer period of time. The other modifications can be used to optimize the model.

In dit project worden vier vereenvoudigingen van de trebuchet onderzocht. Er wordt gekeken naar het rendement met betrekking tot de energie overdracht van het zware tegengewicht op het afgeschoten voorwerp. De invloed van het toevoegen van extra armen en wielen wordt onderzocht. Bij meer energie overdracht kan het voorwerp verder weg geschoten worden en zal het voorwerp meer impact hebben als het op de grond terecht komt.

Due to an increase of precipitation reactions in water by temperature changes, cloggings canoccur in a geothermal doublet. A consequence of the cloggings is that the process of generatinggeothermal energy becomes inefficient eventually. Our goal is to determine which minerals playan important role in the clogging process in each part of the geothermal doublet. First, we havedivided the geothermal doublet into four tanks. Then we have derived a general model for ageneral chemical reaction. Afterwards, we have used this model for 5 kinds of mineralisationreactions. This led to first-order differential equations, which we have solved analytically ornumerically with the Forward Euler method. Finally, we have concluded that the mineralsbarite, calcite, dolomite and goethite play an important role in the clogging process in tank 3and tank 4.

The counterweight trebuchet is a type of catapult from the late middle ages. This siege engine uses a swinging arm with a sling attached to throw a projectile. After lifting the heavy counterweight with manpower, all that potential energy can be released within a second. This made it possible to fire a projectile with enormous force. In figure 1 we see a drawing of a counterweight trebuchet.

In dit project is onderzoek gedaan naar de stabiliteit van de fiets. Hiervoor is het model gebruikt van een fiets van Herfkens. In dit model kan de berijder niet sturen en zit vast verbonden aan de fiets. Dit model bestaat uit 25 parameters. De stabiliteit is onderzocht aan de hand van de stuurhoek en de kanteling van de fiets. Er is gekeken naar wat er gebeurt bij kleine verstoringen in deze twee componenten. Vervolgens is onderzocht welke parameters een grotere of kleinere rol spelen bij de stabiliteit van de fiets.

Calibration of groundwater models can be done manually by comparing the measured and computed groundwater heads or automatically using algorithms which do the work for you. Modules for this purpose are included in or linked externally to traditional groundwater modelling software and used. One such module PEST (Parameter ESTimation) uses the Levenburg Marquardt algorithm which is a combination of Gauss Newton and Gradient Descent methods to find the minima of a function. However, PEST is capable of finding only a local minimum for the objective function. A possibility exists that there is a global minimum that better fits our function and could give even better results for the optimization problem in, in our case, parameter estimation in groundwater models. A performance assessment has been done with a Genetic algorithm on a groundwater modelling problem in this study.