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 bachelor thesis we propose a spatial Markov Chain Cellular Automata model for the spread of the COVID-19 virus as well as two methods for parameter estimation. Network topologies are used to model the progression of the epidemic by considering each individual on a grid and using stochastic principles to determine the transition between different states. The model is able to predict the time-evolution of outbreaks under different lockdown policies. Additionally, the impact of variation in infection probability and recovery rates on the amount of active cases, deaths as well as the length of the epidemic is investigated. These results can provide us with insights and predictions of the spread of the virus under different scenarios. Parameter estimation is done by using both Maximum likelihood estimation and Bayesian estimation based on simulated data. The produced estimates were relatively accurate, suggesting that these methods can be applied in order to estimate the parameters of the proposed model based on actual data.

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.

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.

The present thesis discusses two modelling endeavours that serve to provide insights into both the magnetic and structural dynamics associated with a first order magnetic phase transition. Firstly, density functional theory has been used to model the lithiation of a supercell of 2x2x2 the conventional unit cell of the ferromagnet Fe2P. Subsequently, the magnetic moments in the resulting structure were set to proxy a paramagnetic state and compute the energy difference between the ferromagnetic and paramagnetic state. It has been found that non-magnetic Li-atoms substitute for magnetic Fe-atoms at 3g-positions in the a,b-plane. Moreover, since these are the positions of Fe-atoms that carry a high magnetic moment and induce a magnetic moment on the Fe-atoms in the 3f-layer, the lithiation of the respective positions leads to a reduction of the magnetic moment per formula unit. The energy difference between the ferromagnetic state and the selected proxy of a paramagnetic state showed to decrease linearly in the fraction of lithiated 3g-positions. This deviates from experimental findings suggesting an increase of Tc of the structure upon lithiation. This difference can stem from the fact that the lithiation fractions considered here were higher than those achieved experimentally or that the selected proxy of a paramagnetic state was incorrect. Secondly, the finite element method has been applied to approximate the displacement field of a 2D structure consisting of grains distributed over two structural phases with different associated lattice parameters. The development of shear stress discontinuities across grain boundaries has been studied in relation to the degree of porosity in a domain. The replacement of grain boundaries by voids appears, after correction for the orientation of edges at these grain boundaries, to lead to a reduction in the values for these discontinuities. More delicate development of the grid to correspond to physically realistic orientations of grain boundaries is needed to gain more robust quantitative measures for this relation. Moreover, the relation between the orientation of grain boundaries and shearing stresses at these boundaries forms an interesting venue for further research to which the present FEM-model can be readily applied.

With increasing attention to climate change,renewable energy generation has become a major topic for research anddevelopment. Wind and solar energy are generated on land, whereas wave, windand tidal energy generators are getting attention in the offshore domain. Anovel extension of onshore solar energy is the concept of offshore solar energyusing floating platforms. As little research has been performed on the conceptof offshore solar energy generations, main challenges in the field are relatedto consequences to the marine ecology, economics and production and structuraldesign of the platforms. In this thesis, a numerical model to assess wrinklingbehaviour of thin, floating sheets with application to the structural design ofoffshore solar platforms is developed. Since wrinkling of thin sheets, in general, isinitiated by a structural instability (i.e. buckling), the developed modelconsists of an arc-length method that is capable to deal with bifurcationpoints and to switch to bifurcation branches. In this way, buckling andpost-buckling behaviour of thin sheets are modelled and wrinkled shapes can beassessed without imposing a priori definition of unbalancingimperfections or loads. The computational model is developed using a shelldiscretization with Isogeometric rotation-free Kirchhoff-Love elements, whichare higher-order elements with a B-spline or NURBS basis with global supportand global higher-order continuity of the solution. For the illustrativepurpose and future use, a similar Euler-Bernoulli beam model was developed andnumerical solvers for static, dynamic, modal and linear buckling analysis wereimplemented. The model was verified using various benchmarkstudies for static, modal, (post-)buckling and dynamic analysis. In particular,the post-buckling solver was assessed by modelling the collapse of a sphericalroof and using buckling (post-)bucking of a cantilever strip. Both benchmarkshave shown excellent agreement with previous publications. Additionalverification was done on the approaching accuracy and prediction of bifurcationpoints. It was found that this accuracy showed the accurate prediction of thebifurcation point, although slightly underpredicted for finer meshes and higherorders. Additionally, the model wasapplied to three cases where wrinkling is involved. In these cases, sheets withlow bending stiffness were modelled such that their post-buckling shapes showmultiple half-waves and thus wrinkles. Based on the model of a floating sheetsubject to surface traction (e.g. wind or current), design parameters werevaried. From this case, it follows a decrease in foundation stiffness or anincrease in flexural rigidity (either by varying Young's modulus or thickness)implies the number of wrinkles to decrease and the wrinkling instability tooccur for lower loads. Thirdly, based on the wrinkling geometries of a quarterdisk, design consideration for VLFTSs for offshore solar energy generation weregiven. These are: (i) adding reinforcement to arrest wrinkles and to introducestructural hierarchy for structural reliability; (ii) consider the effect ofdifferent mooring system connections to the (reinforced) platform; and (iii)investigate the effect of holes and point loads on local wrinkling behaviour. Basedon the results of the study, it is concluded that the isogeometric thin shellformulation is suitable for different structural analyses and that in particularthat robustness and accuracy on a per-degree of freedom basis is observed inthe isogeometric post-buckling analysis. This adds post-buckling analysis tothe seamless integration of Computer Aided Design (CAD) and Analysis ofIsogeometric Analysis. Suggestions for further studies include severalimprovements of the current implementation (patch coupling, boundary conditionimplementation), utilization of nonlinear material models for modelling ofrubber-like materials, adaptive re-meshing using THB-splines to capture localwrinkling phenomena and Fluid-Structure Interaction computations with anonlinear structural and fluid description of VLTFSs in large waves.

This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, implementation and analysis of numerical algorithms, as well as their applications to relevant societal problems.ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).@en

Superconductivity was discovered in 1911 and since then it has become indispensable in a wide range of fields. It is often accompanied by strong magnetic fields which can do away with the superconducting properties of the material. This process is described by the Ginzburg-Landau theory of superconductivity. In this report, this theory is discussed at length. The result is a system of two coupled, time-dependent partial differential equations that can be solved using numerical methods. A nite element method is constructed using standard Lagrangian and curl-conforming Nedelec elements. Numerical simulations were performed with Lagrangian and Nedelec elements in COMSOL and MATLAB respectively. Using Lagrangian elements delivers flawed results. Using Nedelec elements should improve these results but so far only parts of the problem have successfully been solved using these elements.

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, a model for modeling passenger flows on a platform with obstacles is presented. The report incorporates situations with one exit, benches as obstacles and an additional train and compares those to a basic model in which the platform has two exits and no obstacles. The present study considers the Particle Model as a basis for passenger flows on a platform. The parts of the Particle Model that are integrated are chemotaxis, random walk, repulsive forces and mechanotaxis. Therefore the model is based on both deterministic and stochastic principles. Simulation results are discussed concerning the time needed for a certain amount of passengers to leave the platform, the average number of encounters between individuals and of individuals with benches.