Forest-Based Binary Phylogenetic Networks: Finding Optimal Base Forests with Integer Linear Programming

Phylogenetic trees are commonly utilised in evolutionary biology. These trees represent the evolution of a set of species. In case of gene transfer however, a phylogenetic tree is insufficient. In such cases, tree-based phylogenetic networks are more suitable as they can depict reticulate evolution.<br/>Nonetheless, tree-based phylogenetic...

Stability of four-body kite central configurations

Central configurations provide the only closed-form analytical solutions of the n-body problem. All possible central configurations of three bodies have been extensively studied along with the stability of the associated periodic orbits. Stable cases have been found for the Lagrangian triangle configuration, which we see occurring with the...

A semi-group approach to the thin-film equation with general mobility

This thesis treats the thin-film equation which models the film height $h$ for a viscous film in the complete wetting regime. We show existence and uniqueness to the thin-film equation with mobility m(h) = hⁿ and mobility exponent n∈ (1,3/2)∪ (3/2,3). The thin-film equation is rewritten as an abstract Cauchy problem and usage of semi...

On the Application of the Competitive Modes Conjecture

Modelling natural phenomena via Dynamical System Theory has become commonplace amongst mathematicians, physicists, engineers, and the like. As such, research in this field is currently underway, with a notable focus on chaos. The Competitive Modes Conjecture is a relatively new approach in the field of chaotic Dynamical Systems, aiming to...

Mathematical spatial compartmental epidemic models for the infectious disease cholera

Cholera is an infectious disease caused by the bacterium Vibrio cholerae. Infections can occur directly via contact with infected people, but also indirectly via infected water. Because of these direct, but especially indirect infections, it is useful to investigate the spread of the disease using mathematical epidemic models. In this report a...

Nonlinear dynamics of graphene membranes: Quality factor limits of membranes caused by mode interaction

Graphene is expected to open up a world of new possibilities in the field of micro and nano sensors, due to its outstanding properties. However, graphene membranes suffer from high damping which limit their performance. The physical mechanism behind this damping is still unknown. Therefore, in this work, it is investigated how coupling between...

The influence of spring-neap cycles on sediment trapping in tide-dominated estuaries

Using an idealized width-averaged model, the influence of spring-neap cycles on the transport and trapping of suspended fine sediment in tide-dominated estuaries is investigated. To this end we introduce a multiple time scale expansion. This provides a mathematically sound argument for treating the fast ebb-flood cycle and the slow spring-neap...

Velocity Enhancement Models for Polymer Flooding in Reservoir Simulation

In the past decades, several EOR (Enhanced Oil Recovery) techniques have been developed to increase the amount of oil recoverable from a reservoir. Among these techniques, polymer flooding consists in the injection of a solution of water and polymer into the reservoir, and it is performed in order to lower the mobility of injected water. A...