The Poincare Inequality on Smooth and Bounded Domains in R^d

In this thesis we study for which domain types the Poincare inequality holds for all functions having continuous first derivative. We first consider the classical Poincare inequality, which we prove holds for a very large class of open sets in R^d. We then constructively prove that bounded, open, and connected domains in R^d,...

Eolisch sediment transport

In dit verslag is een eolisch sedimenttransport model geformuleerd en het model van De Vries geïmplementeerd en geanalyseerd. Na de afleiding van de eendimensionale advectie-diffusievergelijking vanuit de driedimensionale continuïteitsvergelijking is eerst het model van De Vries zonder diffusie onderzocht. In het model kan er onderscheid gemaakt...

Developing a second order accurate level-set method for solving the one-dimensional Stefan problem

This work aims at finding a second order accurate level-set method which solves the Stefan problem with non-homogeneous Dirichlet boundary conditions in one dimension. The numerical accuracy of the FTCS-scheme, BTCS-scheme and Crank-Nicolson scheme for the discretization of the heat equation was considered, as well as the accuracy of the first...

Simulation of the Scattering of an Electromagnetic Wave Using Multi-trace Boundary Integral Equations

Metalenz is a spin­off company of Harvard University that works on finding newer and better designs for lenses. To prevent manufacturing designs that might not work, they first want to run computer simulations on their designs. This research focuses on a possible method for these simulations using a test case as design. It turns out that the...

Design and simulation of an invisibility cloak device in Julia

Mankind has always adapted materials to fullfil a need. Recent developments in nano-science allows us to construct objects with varying permittivity and permeability. One possible structure is an invisibility cloak device. This device is put around an object. Any plane wave that enters the cloak should go around this object. The wave exits the...

Reflections of waves induced by a nonlinear spring at the boundary

In this thesis the nonlinear spring system is considered. This system contains a semi-infinite string that is modelled by the wave equation with a pair of inititial conditions and a nonlinear boundary condition. The goal of this thesis is to find a good approximation of this system. Furthermore, the behaviour of the string is studied by plotting...

Extraction of biological parameters of wound-healing processes from time-lapse videos

Experimental data have been extracted from wound-healing time-lapse videos. These data include the detection of the area of the wound and the detection of individual cells. Extracting the area of the wound is done by using a function in Python OpenCV called cv2.findcontours. An improved method to extract the area of the wound is introduced as...

A study into how the relationship between public and private spaces in the built environment influence the social and cultural aspects of the community

Architects have always found it important to understand the interaction between public and private spaces in the context of the built environment. This paper investigates the relationship between public and private spaces, and how it influences the social and cultural aspects of the built environment. Hence, we first explore what a public and...

Analysis of Microscopic Images: Boundary Detection Using a Modified Mumford-Shah Model

Deformable energy-minimizing contours are used in image analysis, particularly to detect boundaries from objects. From the Mumford-Shah model we derive an equation to move such contours towards the boundary, which minimizes the functional. The external force is computed using the mean value of the inside and outside area of the contour. Various...

Optimisation of Propellant Consumption for Power Limited Rockets: What Role do Power Limited Rockets have in Future Spaceflight Missions?

In this thesis we look at the most cost-<br/>effective trajectory for power limited rockets, i.e. the trajectory which costs the least amount of propellant. First some background information as well as the differences between thrust limited and power limited rockets will be discussed. Then the optimal trajectory for thrust limited rockets, the...

Simulation of the effect of atmospheric stratification on the power production of a wind farm

The wind energy industry is growing more than ever before and wind energy as a renewable energy source has shown quite a potential over the years. Unfortunately, the power yield of a wind farm can fluctuate largely over time, which originates from fluctuating wind speed magnitudes. Convection of air, turbulence, humidity and radiation of heat are...

Diffusion in a polymeric environment

Cells of the most common organisms like plants and animals are filled with polymeric networks that fulfil important functions of the cell. There is however no analytically solvable model that describes diffusion in such a cell. This thesis presents a model for diffusion in polymeric environments, and some predictions about the behaviour of the...