Population difference between L4 and L5 Trojans due to Jupiter's outward migration: A numerical analysis using actual Trojan data

Ever since their discovery, the Trojans have raised many questions among astrophysicists. In 1989 it was found that there were more L4 than L5 Trojans and the current L4:L5 ratio value is estimated to be 1.6. However, this asymmetry could not be explained by Jupiter’s current orbit and must therefore have arisen during the early development of...

Analysis of Runge-Kutta methods using Butcher tableaus

This Bachelor thesis provides an analysis of Runge-Kutta methods using Butcher tableaus. Runge-Kutta method are numerical methods used for approximating initial value problems. A Runge-Kutta method can be classified as either an explicit or an implicit method. A special kind of implicit methods are diagonally implicit methods. The type of method...

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...

Cross diffusion in single-step enzymatic reactions

In several experiments, enzymes have shown an in increase in diffusivity in the presence of their substrate. The enhancement in diffusivity ranged from as low as 28% for urease to 80% in the case of alkaline phosphatase. There are two main competing theories. One asserts that catalytically driven boosts propel the enzyme forward in ‘leaps’,...

An exploration of the Kuramoto model: Mathematical background, links with physics and numerical analysis

This work is a bachelor thesis featuring a collection of explorations of the Kuramoto model in the presence of noise in one and two dimensions. The model was explored analytically and numerically. It contains a study of literature and new analytical derivations. An attempt to link the fraction of oscillators to the order parameter resulted in...

Unbeatable cooperative strategies under noise

This paper combines the concepts of noise and stability in the iterated prisoner's dilemma. The purpose is to find strategies that score well (have a high cooperation percentage) in a homogeneous noisy environment, but are also robust to invasions. Generally, strategies that perform best under noise are maximally forgiving, however,...

On the positive stabilizability and contollability of linear discrete-time systems

This paper is a research in positive controllability and stabilizability for discrete-time linear systems. Several conditions are given and explained for both single input as multiple input systems. Also the connection between controllability and reachability will be mentioned. Furthermore, a method for multiple input positive controllability is...

Response of an oscillator with a Duffing parameter of the fifth power

Quintic Duffing oscillator is considered. Amplitude-phase relations are derived using averaging theorem and perturbation methods. First The forced quintic system is studied. Stability regions are com-pared to the general case with quintic-qubic non-linearity. Numerical results show that Perturbationmethod and averaging are in agreement with each...

A Geotechnical Working Plan for a Thorough but Quick Assessment of Existing Slopes in Clay Mines

In the Westerwald area clay quarries are in production. In order to assess the stability of the slopes the geotechnical characterisation of these quarries needs to be improved. This report provides the justification for a working plan for a thorough but quick assessment of existing slopes in clay mines. Literature is consulted for the...

Analysis of Tidal Inlet Stability

The main goal of this project is to predict the in uence of non-uniform basin depths on the stability of single inlet systems. This is achieved by making use of Escoffier's principle, which poses a relationship between the relative water flow velocity in an inlet and the rate of change of its cross-sectional area. To this end, a thorough...

Bepalen van het massatraagheidsmoment met behulp van een bifilar pendulum: Determining the moments of inertia using a bifilar pendulum

The aim of this thesis is to investigate the use of a bifilar pendulum for determining the moments of inertia of the TU Delft solar boat and to quantitatively predict the estimates. In the first part, several methods are discussed which can be applied in deriving the equations of motion of the pendulum. A new method, Kane's method, will be...

The stabilization and destabilization of Brouwer's Rotating Vessel

We beschouwen Brouwers roterende lichaam, een voorbeeld van een mechanisch systeem met het volgende paradoxale gedrag; zonder demping is er stabiliteit, met demping is er sprake van instabiliteit. Met modulatie van de hoeksnelheid wordt er een model afgeleid waarbij we pogen de instabiele gevallen te stabiliseren, hierbij is het meenemen van de...

Stability analysis in a model of the human inner ear

In this thesis a special kind of differential equation will be analysed, namely the delay differential equation. For test equations the stability behaviour is analysed and there's checked whether there is a method to prove stability. Also, a full description is given, for the model submitted by INCAS3.

Linear Stability Analysis of a Supercritical Water Loop driven by Natural Convection

The HPLWR (High Performance Light Water Reactor) is the European version of the SCWR (Supercritical Water Reactor) and is one of the Generation IV concepts that have enhanced safety, improved efficiency and less nuclear waste compared to current nuclear reactors. A possible way to enhance the safety is by using natural convection as the driving...

Oscillations and stability of a mass-varying system

In this paper the stability properties of the vibrations of a singular degree of freedom oscillator with a periodically and multi-stepwise time-varying mass are studied. The free vibrations and the vibrations due to two types of forcing are investigated.