The rotational velocities of stars at the edges of galaxies are higher than predicted by Newtonian dynamics. One theory that is capable of explaining this anomaly is called MOdified Newtonian Dynamics
(MOND). To further test this MOND theory, the wide binary test has been suggested. In the wide binary test, the stability of wide binary systems is tested. The MOND theory deviates significantly from the
Newtonian theory when accelerations are smaller than a0 = 1.2·10−10 m/s2 , which is present in wide binary systems. The MOND theory is non-linear, which introduces a non-trivial effect of the external field
(EF) of the Milky Way on the wide binary orbit. To perform the wide binary test, an iterative particle mesh N-body code was used with initial conditions taken from the Gaia mission database. Additionally, the EF was modeled in three ways, where the Newton potential adjustment model was found to be the most realistic. The results include nine simulations, split up into three models and three different regimes. The models include the Newton model, the MOND without EF model, and the MOND with EF model. The regimes consist of the Newtonian regime (ainternal > a0), the transition regime (ainternal ≈ a0), and the deep MOND regime (ainternal < a0). In the Newton model, only the Newtonian regime gave stable orbits. The MOND without EF model gave stable orbits for all regimes, and the MOND with EF model gave stable orbits only for the Newtonian regime. The MOND without EF gave stable wide binary orbits, whereas the other models did not. If additional measurements detect these wide binary systems, then the MOND without EF model gains credibility. The orbits of the Newton model and the MOND with EF model were similar, with only a small difference. This is because the strength of the external field is 1.6 · a0, which makes the external field dominant over the internal accelerations, making the simulation Newtonian-like. To determine which model is correct, additional long-term measurements of Gaia are required. Further research recommendations include improving the performance and accuracy of the code. This is done by better implementation of the fast Fourier transform, translating the code into a faster programming language than Python, using adaptive time steps, and reducing self-interaction. The most important extension to the model is to introduce the galactic tidal effect.

This paper aims to improve the Particle Mesh (PM) method for Newtonian Dynamics (ND) and MOdified Newtonian Dynamics (MOND). The PM method involves discretizing the mass density on a grid using Gaussian smoothing, which is used to calculate the gravitational potential using Fast Fourier Transforms (FFTs). A major downside of Gaussian smoothing is that the mass density of two particles overlaps whenever they are in close proximity, which leads to incorrect orbital dynamics. Hence, the linearity of ND is used to correct the accelerations of particles whenever this overlap in mass density occurs. These short-range corrections involve the use of analytical expressions to eliminate the inaccurate influence of the PM method, correcting the interactions between particle pairs to direct particle-particle interactions. These corrections can introduce instabilities whenever two particles are too close in proximity and the time steps are too large. This issue is mitigated by using a softening parameter in the corrections. In MOND, the linearity in the accelerations is removed, which means that these short-range corrections cannot always be used. They may only be used in the limit of high accelerations, for which MOND reduces to ND. The short-range corrections are tested for circular and elliptical two-body systems, showing a significant reduction in error of their expected orbital trajectories. To test the limitations of the PM method under non-linear accelerations in MOND where no corrections may be applied, a wide binary system is used to determine the minimum distance between particles that still yields somewhat accurate. This also demonstrates that without the use of short-range corrections large grids are required, highlighting a major inefficiency of PM methods. Lastly, the corrections are tested in both ND and MOND using the Plummer and Miyamoto-Nagai models, which represent a sphere and a disk, respectively. The Plummer model showed significant improvements in stability in both ND and MOND. However, the Miyamoto-Nagai model shows less optimistic results in MOND due to the difficulty in placing the particles at a minimum separating particles whenever the accelerations are non-lineair. Overall, careful use of these short-range corrections allows for significant improvements in the PM method for both ND and MOND. Further research into optimizing the computational performance of FFTs and short-range corrections using tree codes is still available. Additionally, a time-adaptive PM can be implemented to prevent possible instabilities due to large time steps when using the corrections.

Quantum Batteries (QBs) are quantum-mechanical devices for energy storage, gaining interest due to a potential quantum advantage in power. Recently, the first experimental implementations of QBs were realised. This study characterises the superconducting transmon qubits of Starmon-5 as QBs using the Quantum Inspire platform. In addition to direct charging of a QB, our focus is on charger-mediated energy transfer and parallel charging of an array of transmon qubits. The figures of merit include the average stored energy, the charging time and the charging power.

The results from direct charging of the qubits align with existing literature. Charger-mediated energy transfer is demonstrated through the characterisation of the CNOT gate as an interaction gate, gaining the same amount of stored energy, but with a significant increase in the charging time, resulting in a lower charging power. Furthermore, our findings demonstrate that parallel charging of an array of qubits preserves the quality of direct charging of the individual qubits.

To our knowledge, this work presents the first results of charger-mediated energy transfer in real quantum devices. Charger-mediated energy transfer can be interesting for specific applications such as quantum metrology, where preserving the quantum state is critical. Additionally, this is the first demonstration of parallel charging of superconducting transmon qubits in the QB context, giving promising results for the scalability of superconducting transmon qubits as QB. Our study paves the way forward to implementing quantum batteries for energy management in quantum technologies, a near-term future application of quantum batteries.

The rotational velocities of stars in galaxies indicate that either Newtonian gravity breaks down on this scale, or that there is extra mass in the universe that has not been observed. The former is known as Modified Newtonian Dynamics (MOND), whereas the latter option is known as the dark matter paradigm. In this thesis a version of MOND is considered where the field equation for gravity is modified and becomes nonlinear. To simulate MOND, new N-body codes are needed due to the field equation not being linear anymore and in this thesis a new particle mesh method is developed. This new particle mesh method follows the same steps as the normal particle mesh method, except at the step where the acceleration field on the grid is calculated. This step is replaced by an iterative method to find the MONDian acceleration field on the grid. The code was then tested in the deep MOND regime using four cases of which analytical solutions of the MOND Poisson equation are known. These cases are: linear motion, the two-body problem, a ring system and an isothermal sphere. Using these test cases, numerous conclusions were drawn. From the linear motion test it was found that in the code bodies can interact with themselves, resulting in non-physical accelerations. The two-body test showed that the magnitude of the relative error in the force as calculated by the particle mesh code is roughly on the same order as the same error when calculating the Newtonian force using a particle mesh code. Furthermore, all tests showed that energy is conserved quite well, even though momentum need not be conserved due to the self interactions, and that generally the conservation of angular momentum is violated by the code. The tests also showed that the analytical formulae that were derived for these systems gave largely the same predictions as the algorithm, hence verifying both the formulae as the algorithm. The code could be sped up by writing it in C, the accuracy can be improved by reducing self-interactions and it can be extended by adding a method to handle close encounters. Some applications of the code are given, including: simulating the solar system, wide binary stars, tidal dwarf galaxies and galaxy clusters.

In this thesis the behaviour of a Bose Einstein condensate is explored that consists of bosons that annihilate. In order to do this a system where bose einstein condensation occurs is modeled as a Zero Range process which is a special case of a Markov process.
First we made a single slow site Zero range process with uniform rates and see how this would be influenced by annihilating particles. For this system it is shown that, in the large system limit, the number of particles in the slow site is given by a differential equation. A series of realization of different sizes of this system are done to support that the fraction of the particles in the ground state converges
to the differential equation.
In order to relate this mathematical approach to physical Bose Einstein condensates it is established that the equilibrium distributions of multiple bosons in one system is the same as the detailed balance of a zero range process where the transition rates depend on the occupation of a site, with an indication function, that is equal to 0 when there are no particles at that site and some constant 𝑐 if there is one
or more particles at that site.
In statistical physics we need to take the energy of the state of the system into account. If the particles do not have interaction with each other this is the sum over all particles of the energy of the particle site. As a zero range model only has rates with one particle hop we can see that the difference in energy of the system is equal to the difference in energy of the sites of hop. In order to stay in detailed
balance the rate for the specific hop must be exp(BΔ𝐸) times the opposite rate, where B = 1 / 𝑘_b 𝑇.
Now we can go from any system with a set of spin orbitals and energies of those spin orbitals and design a zero range model where the spin orbitals correspond to sites of the zero range model with rates between those sites, such that the systems detailed balance distribution is the same distribution as the equilibrium of the physical system. In this zero range model an annihilation term is introduced.
This can be any function of occupation for the site, but in this report a simple relation that decreases when Δ𝐸 increases is used.
In order to see the effect on such systems the system is numerically approached for a 100 particles system in a 3 dimensional harmonic potential. This system is too complicated to get an differential equation that can be easily solved. Therefore it is approximated. This numerical approximation appears to have similar behaviour to the numerical approximation done in [3]. However the results are not identical.
The advantage of the model in this thesis is that an annihilation therm can be implemented. This approximation of a 3 dimensional harmonic oscillator with annihilating particles is done. If annihilation is slow enough, the exited sites form a different equilibrium compared to a Bose Einstein condensate of non annihilating particles. This happens as long as there is a condensate in the ground state.

The Bullet Cluster is a galaxy cluster, which is often used as evidence for dark matter [10]. In this thesis, Modified Newtonian Dynamics (MOND) is studied for various interpolation functions on a model of the Bullet
Cluster. MOND is a theory proposed by Milgrom which modifies the Newtonian gravity law, such that it explains the flat rotation curves observed in all the galaxies and galaxy clusters [13]. It is an alternative theory
to the dark matter model and in this thesis, the results of MOND are compared to results from the paper of
Paraficz et al which have studied the Bullet Cluster with the dark matter model [15]. In MOND, the Newtonian
gravity law is changed at low accelerations, for a around and below the value of 1.2 · 10^-10  m/s²
, which is introduced as a constant a₀ by Milgrom. Accelerations much smaller than a₀ are in the deep MOND regime and
should satisfy certain conditions. Combining the low acceleration regime (a ≪ a₀) and the Newton regime
(a ≫ a₀), an interpolation function is needed. The following interpolation functions are studied: the standard
interpolation function, the Verlinde interpolation function and the Angus interpolation function.
First the Newtonian gravitational potential Φ_N is introduced which can be calculated for a certain mass
distribution ρ using the Poisson equation. Also the acceleration field can be obtained from ΦN . It could
be seen that in the model used in this thesis for the Bullet Cluster, the strength of the acceleration field a
is mostly below a₀, but not much. Similarly the MOND potential Φ_M can also be calculated for ρ with the
MOND equations, which are different equations for each interpolation function. The MOND equations are
non-linear and can not be solved analytically in most cases. Thus a numerical iterative method is introduced
to solve the MOND equations and to obtain Φ_M . After obtaining Φ_M for each interpolation function, the acceleration field f can also be calculated. We found that Φ_M is steeper than Φ_N for all interpolation functions.
Also the acceleration field f is larger than a, and f is mostly above a₀ in the model of the Bullet Cluster used
in this thesis.
By substituting Φ_M in the Poisson equation, another mass distribution could be obtained: apparent matter. This would be the matter distribution needed to give the acceleration field f using the Newtonian gravity
law. From this matter distribution, the apparent dark matter could be obtained. We can compare this apparent dark matter distribution with the dark matter model found in the paper in Paraficz et al. Also the apparent
matter distribution can be compared to the image of the Bullet Cluster. For both apparent dark matter and
apparent matter, the MOND model is not in agreement with the dark matter model and the observation respectively. In general, the dark matter did not spatially coincide with the galaxies. By increasing the number
of galaxies or increasing the mass of the galaxies, dark matter distributions that spatially coincide with the
galaxies can be obtained

Over the past century various different discrepancies in the expected and observed behaviour of galaxies and galaxy clusters were found. Together this is called the missing mass problem and the most well known theory trying to explain these differences states that there is additional undetectable mass in the form of dark matter. Modified Newtonian Dynamics (MOND) is another theory that tries to explain these discrepancies in a different way then by introducing dark matter. Instead the theory changes Newtons law of gravity for low accelerations, smaller than Milgroms constant a0. In this bachelor thesis we look at a discrete model to simulate MOND in galaxy clusters. To simplify calculations we will not be looking at full MOND, which holds for all accelerations but instead we look at the so called deep MOND, which only holds for accelerations much smaller than a0. We use two different versions of the Poisson equation, the standard version for Newtonian dynamics and a modified version for MOND, to compute the gravitational potential fields caused by a mass density distribution. This is done by using the discrete Fourier transform on an discretized region of space. The initial mass density distribution consists of a number  of galaxies ranging between 50 and 1000 per cluster. Each galaxy is modelled as a sphere of constant density. To calculate the potential with MOND we use an iterative process starting from the potential we get using Newtonian dynamics. In this iterative process we made use of the Helmholtz decomposition. From the MOND potential we can compute an apparent mass distribution, which is the mass distribution that would result in the same MOND potential using Newtonian dynamics. This apparent matter distribution we use to predict at what distance of a galaxy most apparent dark matter is located. Lastly we also look at the apparent mass distributions when the galaxy cluster is projected on a 2d plane. All of these calculations were made in Python on a discrete grid of 256 × 256 × 256 points.
When looking at the total amount of apparent mass in concentric spheres around galaxies in our cluster we saw that this increases in three distinct phases. The middle phases, where a linear increase was seen, had a slope in the same order of magnitude as the theoretical value. We found that the average apparent mass density is the highest in the center of galaxies and decreases very quickly at higher distance to the galaxy. When the distance becomes high enough to reach neighbouring galaxies in the same cluster the average apparent mass density stabilizes and becomes almost constant, but still slightly decreases. For the projected mass density a similar pattern was found.

The main goal of this thesis is to better understand the photochromic mechanism in rare-earth (RE) oxyhydride thin films. When illuminated, these materials have shown to darken, and bleach to a transparent state when the illumination source is removed. The RE oxyhydride thin films used in this thesis are deposited using magnetron sputtering and are YOxHy and GdOxHy films with different storage (air and vacuum) and oxidation (air and dry air) conditions. The films were probed using Doppler broadening positron annihilation spectroscopy, spectrophotometric (optical) measurements, X-ray diffraction and spectroscopic ellipsometry, measured before, during and after in or ex situ ultraviolet illumination.

Series of illumination and bleaching cycles have shown to permanently induce vacancy defects, which are most likely divacancies. The photochromic effect is seen as a reversible process, which leads us to believe that the changes seen in the defects are not directly responsible for the photochromic effect. During in-situ photodarkening and bleaching partially reversible changes are seen, whereby systematic shifts in the positron annihilation Doppler parameters are exhibited. This shift correlates with the photochromic effect, where the irreversible formation of vacancies is seen as a result of UV illumination. This leads us to the idea of the formation of metallic domains that may be attributed to H- ions that become mobile under illumination and may cluster to form metallic domains. Furthermore, the formation of the vacancy defects correlates with an increase in bleaching times seen from optical measurements, suggesting that they could play a role in the memory effect. Another optical property seen is a change in the band gap. We have seen that during photodarkening, the band gap tends to widen and decrease during bleaching. This phenomenon can be associated with the Burstein-Moss effect and can be used to estimate the photo-induced electron density in the conduction band. Despite the changes observed from positron annihilation techniques and optical measurements, no significant differences were observed by X-ray diffraction. The lattice constants of the film before and after illumination were shown to be constant.

There are two hypotheses explaining the photochromic mechanism: the segregation of metallic domains as a result of H- ion mobility and an Anderson-Mott insulator-to-metal transition as a result of overlapping electron wave functions. Using spectroscopic ellipsometry, these models were tested for YOxHy. It is shown that the mechanism leading to the darkening of the films is best described by the formation of Y or YHx metallic domains and voids. The percentage of metallic domains and voids grows with illumination time and starts stabilising after 90 minutes of illumination. The fraction of metallic domains (1.9-2.6% after 150 minutes of illumination) is similar in magnitude as seen in previous studies. Furthermore, the voids probed by ellipsometry are much larger than the vacancy-related defects probed by positrons. Such voids could give rise to the formation of positronium in the films, as could be examined in future positron annihilation lifetime spectroscopy (PALS) experiments.

Qualitatively GdOxHy and YOxHy behave similarly when it comes to optical measurements, XRD and DB-PAS data. For both systems, an increase in bleaching time as a function of illumination and bleaching cycles, a widening and shrinking of the band gap and a decrease in contrast are observed. However, there are quantitative differences between these films. The bleaching constant is shorter for GdOxHy and the contrast is higher, which makes it seem more attractive for potential applications. However, GdOxHy could not yet be satisfactorily modelled, in contrast to the case of YOxHy using spectroscopic ellipsometry. The GdOxHy film could not be described by a single homogeneous layer and therefore requires more complex models to describe the behaviour of the film in future work.

In this thesis Modified Newtonian Dynamics (MOND) is explored in galaxy clusters similar to the Virgo cluster. MOND is a theory proposed to explain the flat rotation curves of galaxies and the velocities of galaxies within galaxy clusters, as an alternative to the Dark Matter (DM) model. MOND states that Newton’s law of gravitation is incorrect at accelerations of the order of and smaller than Milgrom’s constant a_0 = 1.2 · 10^−10m/s^2 [1]. 
The MOND potential φ_M created by a certain mass distribution ρ satisfies the MOND equation, a non-linear partial differential equation. For accelerations much smaller than a0 this equation gives a quadratic relation between the gradient of the potential (∇φ_M) and the mass distribution ρ, this is called deep MOND. This is much different from the Poisson equation, that infers a linear relation between ∇φ_M and the mass sources, and which still holds for accelerations much larger than a_0 [1], referred to as Newtonian Dynamics (ND). For accelerations around a0 an interpolation of deep MOND and ND is used. It appears that the potential and acceleration in Virgo-like clusters is according to ND at the center, and approaches deep MOND at the edge. Therefore an interpolation function µ is necessary to model such clusters accurately.
When the MOND potential φ_M is substituted into the Poisson equation, a new mass distribution is found, the apparent mass distribution ρ_AM, which would need to match the actual mass distribution in DM models, which use the Poisson equation. This apparent mass distribution ρ_AM is the sum of the actual mass distribution ρ extracted from optical observations and the apparent dark mass distribution ρ_ADM, a distribution that is interpreted as a theoretical DM halo. This allows us to compare MOND and DM. With our method, realistic mass configurations of galaxy clusters that are Virgo-like, generate apparent mass distributions ρ_AM with regions containing negative mass. The existence, shapes and locations of these regions are in agreement with what Milgrom found [2]. The total mass of the actual mass distribution is M = 10^15M_sun, while the sum of the negative mass is M_negative ≈ −0.09 · 10^15M_sun = −0.09M is approximately 9% of the total mass. Since negative mass is not acceptable, this gives us the opportunity to create conditions to falsify either the MOND model or the DM model. 

Solar cells can play a key role in the transition towards a sustainable future. This transition is one of the major challenges our society faces during the coming decades. Development of high-efficiency photovoltaic solutions at reasonable costs will help accelerating the transformation of our energy system. In this respect, perovskite solar cells are very promising due to their outstanding opto-electronical properties and low-cost fabrication. Obtaining a complete understanding of the device physics and charge transfer mechanisms inside perovskites is crucial for further device improvements. This thesis focuses on the notorious hysteresis in the current-voltage characteristics of perovskite solar cells. So far, this remarkable phenomenon has usually been explained using ion migration, despite the lack of clear experimental evidence. We implement a simulation platform of perovskite solar cells to analyse the charge transfer mechanisms among energy states including those with energy within the forbidden bandgap. We evaluate transient behaviour and identify the limiting physical mechanisms. To explain anomalous hysteresis in perovskite solar cells we use a novel approach in which charge accumulates near the material interfaces due to defects with relatively low capture cross-sections. Defects in lead halide perovskites create shallow sub-gap energy states, that act as charge carrier traps. Near the interfaces, this leads to accumulation of trapped charge carriers, effectively screening the electric field inside the perovskite layer. This reduces the device performance. A slow release of trapped charge due to low capture cross-sections results in hysteresis in the current-voltage curve at commonly used scan rates. TCAD Sentaurus is used as a platform to simulate J-V scans of a planar non-inverted architecture based on the archetypal perovskite MAPbI3, with TiO2 as electron transport layer and spiro-OMeTAD as hole transport layer. This thesis presents a systematic study of different trap distributions, both in the spatial and energetic domain. The capture cross-sections, densities, energy levels and locations of traps are varied and also the effect of scan rate is analysed. This work analyses both tail state defects and deep defects, based on reported values in literature. It is found that defects near the ETL/perovskite interface potentially cause anomalous hysteresis in the current-voltage curve. These defects have their transition energy around 0.25 eV and are possibly attributed to iodine interstitials.

This Bachelor thesis is on Covariant Emergent Gravity (CEG): a covariant formulation by Sabine Hossenfelder of the ideas of Erik Verlinde on gravity as an emergent force. In this work, the ideas of Erik Verlinde are presented as well as the field equations of CEG. The aim of this thesis is to find experimentally verifiable results for CEG. From the field equations we derive a general gravitational lensing formalism for CEG that is applicable to general lensing systems. This thesis also includes an attempt at an expanding universe model for a vacuum or matter dominated universe. Subsequently, a numerical algorithm is presented to solve for the non-linear differential equations in CEG and MOND in Newtonian regimes for general matter distributions using Fourier transformations. A faster version of this algorithm for cylindrical symmetric matter distributions using Fourier-Bessel transformations is also presented. This algorithm is tested on both the Sun and galaxy NGC6503. Next, the rotation curves as predicted by CEG and MOND of 132 galaxies are compared to the observed velocities using the SPARC data set. The velocities are fitted using three fit parameters and a Markov Chain Monte Carlo algorithm. Both theories show good fits to the observed velocities. We conclude that no differences between the predictions of CEG and MOND can be made on the basis of rotation curves, but that covariant features (such as gravitational lensing) might be used to distinguish between the two theories. An important test for both theories can be provided by a comparison between strong lensing measurements and rotation curves for a single galaxies.

A time of flight MIEZE spectrometer, which employs radio frequency spin flippers with square pole shoes and a magnetic yoke is presented. These flippers can achieve higher fields than conventional resonant RF flippers, which employ an air core. High fields are crucial for the construction of a high resolution and compact MIEZE spectrometer. Setups using conventional and novel flippers are constructed for comparison and a variety of experiments to characterize MIEZE instruments. Evidence is presented which indicates that high field flippers are capable of generating a 100kHz MIEZE signal comparable to that obtained with a conventional setup. Furthermore the need for a fast and thin detector is demonstrated. In addition the shape of the MIEZE focal spot is determined to be Gaussian. Finally the importance of stable timing for time of flight MIEZE is demonstrated. This research is relevant for the implementation of MIEZE on the Larmor instrument at ISIS pulsed neutron source in the UK.