An Investigation into the Stabilization of Electrical Power Grids Using a Second Order Kuramoto Model

In this thesis different mechanisms of stabilizing a power grid are tested. The grid dynamics are modelled by a second order extension of the Kuramoto coupled oscillator model, also known as the swing equation. First we prove basic properties of the model such as periodicity and existence and uniqueness. Then<br/>we explore the properties of...

Visualising Conformational Changes in HSP90 Protein using Plasmonic Nanoapertures

In this thesis, we demonstrate optical trapping of HSP90 proteins in plasmonic nanoapertures to study the HSP90 conformational change. This technique is label-free and non-destructive. The resonance of the bow tie shaped plasmonic nanoaperture is used to create a very strong electric field gradient force able to trap proteins. The resonance...

Quantum synchronisation and the validity of its derivation

In this bachelor thesis, the paper ”Classical synchronization indicates persistent entanglement in isolated quantum systems” by Dirk Witthaut et al. is looked into and discussed. First, synchronization in a classic sense is explained. The Kuramoto model is introduced, and a few properties of this model are defined. In the next part of the...

Collective dynamics of an active system with binary particle size

Collective dynamics is something that can be found in nature on macro and micro scale. Since the 90s of the previous century researchers have been interested in finding a model for this group behaviour. The dynamics of a group as a whole is only determined by shortrange interactions of the individuals. To better understand the working of this...

Broken Mirrors: The breakdown of the law of reflection in bilayer graphene

As long as a wave has a large enough wavelength, it should reflect off of smooth surfaces specularly: that is what the law of reflection states. This phenomenon is widely known, and used in for instance sonars. Electrons that reflect off of boundaries within conductors should abide this law as well, due to the particle-wave duality. However, it...

Non-imaging optics: Using Laplacian magic windows and Zernike polynomials

In this report a semi-analytic solution to the Laplacian magic window is proposed. The Laplacian magic window is a term recently introduced in 2017[2]. When a uniform wavefront hits a refractive surface, it creates an illumination distribution behind the surface. When the curvature of the surface is sufficiently small, it can be related linearly...

Parameter Estimation of the Hamiltonian of the Nitrogen-Vacancy Center in Diamond

The Hamiltonian of the NV center contains unknown parameters, such as the zero-field splitting and the magnetic field. Knowing how the frequency measurements depend on the parameters will give greater understanding<br/>of the NV center. Including the nitrogen nuclear spin gives us the opportunity to find more parameters such as the quadrupole...

On discrete and continuous state adaptive network models: with an application to self-organisation in swarming systems

We consider adaptive network models with discrete and continuous state sets obeying dynamical rules that enable application to swarming systems. The 2-state adaptive network contains a supercritical pitchfork bifurcation in the transition between ordered and disordered stationary solutions. We derive an adaptive network model that works on a...

Modelling Markovian epidemic and information diffusion over adaptive networks

Modelling the spread of contagious diseases among people has been a research topic for over a hundred years. However, the increase in computation power in the recent years allows for more advanced scientific models. The well-known susceptible-infected-susceptible model is used to describe the spreading of a disease among a group of people. This...

Adaptive Complex Network: An analytical and numerical study of synchronization in complex networks with anti-Hebbian and Hebbian adaptation rules

Synchrony is a phenomenon that pervades all fields of science. The Kuramoto model is a prominent model that describes synchronization in systems (networks). It models each element of the network as an oscillator with an individual phase. Due to global coupling, a phase transition is realized, such that some oscillators of the network synchronize...

Transmembrane signal transduction: A comparison between two opposing receptor mechanisms

In biological cells, information from the external environment of the cell is used to make survival related decisions. For these decisions, it is important that signals are accurately transduced from the outside to the inside of the cell. In \textit{Dictyostelium discoideum}, two opposing mechanisms using G-protein coupled receptors are used for...

The Kuramoto model on ring networks: Cluster synchronization and the size of the Basin of Attraction

The phenomenon of cluster synchronization in ring networks is studied in the first part of this thesis by means of Representation Theory. The second part of this thesis is devoted to the determination of the size of the Basin of Attraction for a stable node.

Analysis of a Nonlinear Rouse Model

Resilience and Synchronization Behaviour within Mean Field Models

The study of the dynamics of large, complex networks is generally very hard. Analytical solutions are rarely available and numerical solutions require immense computation times. Recently, Gao et al. [1]have proposed a new theoretical approach to analyse the average behaviour of complex networks. In this research we discuss the derivation of the...

The Brachistochrone Problem: From Euler to Quantum

In this thesis I take a look at various aspects of the brachistochrone problem. In the first half I consider the classical brachistochrone problem, without friction, after which I generalize to also consider drag; friction proportional to the squared speed. I do this numerically, with the shooting method, and following some papers, which Euler...

Polymer diffusion in a gel network

In this thesis, we model the diusion of a tracer polymer inside of a gel network and simulate it, hoping to nd a connection between the diusion of the polymer and the strength of the gel network. This model is made by using the Rouse model for the gel network and the tracer polymer.<br/>The overdamped Langevin equation is then used to nd a set...

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...