Erosion has a long history in science and is used in many different fields today, for example in geology for coastal erosion and in the oil industry for pipe erosion. It is very difficult to study erosion both analytically. Numerically it is difficult due to moving and shape-changing boundaries. Here we develop a numerical model in 3D using the Lattice-Boltzmann method, which is good at simulating complex moving boundaries, and erosion capabilities are implemented. Both laminar and turbulent flow can be modelled with this program. Using an experimentally derived model for the mass change due to erosion in clay and mud-type objects, one can derive equations predicting that the volume of a sphere should, due to erosion, scale as V ∼ −t2. This is also observed with simulations. The shapes of a double sphere with different orientations and a cube in laminar flow we find to have similar power law exponent P, P = 2±0.1. But a cube eroding in Re = 800 had no power law behaviour, meaning that the current analytical framework is incomplete. The possibility of a more general framework is presented for future research. Different Reynolds number also affected the power law behaviour and the shape change over time for the different solids. Very little research has been made for erosion of planetesimals, but it has been argued that erosion can be relevant to their fate. Using the same erosion model, an equation of the erosion time is found for laminar flows and for a sphere. Simulation results find that the equation works within an order of magnitude for turbulent flows, a double sphere and a cube. This gives an estimate of the erosion time t∗ of planetesimals to be t∗ ∼ 1s, given a size of radius equal to 10cm and 1km, an orbital eccentricity e > 10−2 and a distance at r = 1 a.u. Implying that orbits for planetesimals with low eccentricity might be favoured.

It is well-known that in 2 + 1 dimensions the flux attachment transmutes the statistics of a particle.The aim of this master thesis is to study the dualities between bosons and fermions induced by Abeliantopological gauge fields in 2 + 1 dimensions. Chapter 1 and 2 are reviews of known results about thepath integral quantization of Chern-Simons theory and the regularization of the fermionic path integral.In the following chapters, we will derive the statistical transmutation and various Abelian dualities in2 + 1 dimensions.

Adaptive optics work to reduce optical losses in the LIGO detectors, making them more sensitive to gravitational wave events. Mode-mismatch between the coupled optical cavities, caused by uncertainty in the radii of curvature and orientation of the interferometer optics, is one of the main sources of loss in Advanced LIGO. Thermal actuators are used to dynamically change the radius of curvature of certain interferometer optics, allowing mode mismatches to be reduced. Finely tunable astigmatic mirrors have the potential to be very useful in gravitational wave detectors for beam reflections at non-normal incidence, but have never been tested. These astigmatic composite mirrors are constructed by bonding a fused silica mirror to a non-axially-symmetric metal plate. When heated, the mirror is differentially distorted in the x- and y-directions due to its asymmetric design, resulting in an elliptical reflected beam profile. We model and test an initial mirror design, finding that it does, in fact, act as an astigmatic mirror. This finding opens a new avenue towards development of adaptive optics for current and next-generation gravitational wave detectors.

Introduced in this paper is the time difference of arrival (TDoA) conic approximation method (TCAM), a technique for passive localization in three dimensions with unknown starting conditions. The TDoA of a mutually detected signal across pairs of detectors is used to calculate the relative angle between the signal source and the center point of the separation between the detectors in the pair. The relative angle is calculated from the TDoA using a mathematical model called the TDoA approximation of the zenith angle (TAZA). The TAZA angle defines the opening angle of a conic region of probability that contains the signal source, produced by each detector pair. The intersecting region of probability is determined from the conic regions of probability and represents the volumetric region with the highest probability of containing the signal source. TCAM was developed and tested using synthetic data in a simulated environment.

Spacecraft pointing accuracy and structural longevity requirements often necessitate auxiliary vibration dissipation mechanisms. However, temperature sensitivity and material degradation limit the effectiveness of traditional damping techniques in space. Robust particle damping technology offers a potential solution, driving the need for microgravity characterization. A 1U cubesat satellite presents a low cost, low risk platform for the acquisition of data needed for this evaluation, but severely restricts available mass, volume, power and bandwidth resources. This paper details the development of an instrument subject to these constraints that is capable of capturing high resolution frequency response measurements of highly nonlinear particle damper dynamics.

This report investigates the sensitivity of the control rod depletion coefficients, Sg, to different input parameters and how this affects the accumulated 10B depletion, β. Currently the coefficients are generated with PHOENIX4, but the geometries can be more accurately simulated in McScram. McScram is used to calculate Control Rod Worth, which in turn is used to calculate Nuclear End Of Life, and Sg cannot be generated in the current version of McScram. Therefore, it is also analyzed whether the coefficients can be related to CRW and thus be studied indirectly through it. Simulations of the coefficients were done in PHOENIX4, simulations of CRW were done in both PHOENIX4 and McScram and simulations of β were done in POLCA7. All simulations were performed for a CR99 in a BWR reactor. The control rod coefficients were found to be sensitive to the enrichment of the fuel, void fraction of the water and the width of the gap, and these effects were also seen in the results of β. As a result, one of three steps could be taken. First, the parameter values should not be set arbitrarily, instead default values could be chosen such that Sg is calculated more accurately. Second, a set of tables of Sg could be generated for different parameter values so that β can be calculated with Sg from the current conditions, although this would mean that PHOENIX4 needs to be updated. Third, McScram can be updated to be able to calculate Sg directly. It has been concluded that Sg cannot be studied indirectly through CRW since the trends and the sensitivity to the different parameters were not consistent between Sg, CRW calculated with PHOENIX4 and CRW calculated with McScram, where PHOENIX4 was more sensitive than McScram. The results can instead be used to bench-mark the PHOENIX4 results.

The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing, quantum communication and detecting phase transitions, among others. The amount of entanglement can be quantified via the von Neumann and Rényi entropies, which have their origins in information theory. In this work, the quantum entanglement between subsystems of a one dimen- sional lattice model of fermions is quantified. The von Neumann and Rényi entropies were calculated for two types of subsystems. In the first study, the subsystems were treated as two subsets of particles, and in the second, as two spatial subregions. Finally, by considering particle superselection rules, the amount of entanglement that can actually be accessed as a resource was calcu- lated. In all cases, the quantum entanglement served to detect phase transitions in the model.

From Birkoff's theorem, the geometry in four spacetime dimensions outside a spherically symmetric and static, gravitating source must be given by the Schwarzschild metric. This metric therefore satisfies the Einstein vacuum equations. If the mass which gives rise to the Schwarzschild spacetime geometry is concentrated within a radius of r=2M, a black hole will form. Non-accelerating particles (freely falling) traveling through this geometry will do so along parametrized curves called geodesics, which are curved space generalizations of straight paths. These geodesics can be found by solving the geodesic equation. In this thesis, the geodesic structure in the Schwarzschild geometry is investigated with an attempt to generalize the solution to higher dimensions.

Representations (such as pictures, diagrams, word descriptions, equations, etc.) are critical tools for learning, problem solving, and communicating in science, particularly in physics where multiple representations often serve as intermediate steps, a means to evaluate a solution, and highlight different aspects a physical phenomenon. This dissertation explores the representation choices made by students in the University Modeling Instruction (MI) courses on problems from across introductory physics content. Modeling Instruction is a two-semester introductory, calculus-based physics sequence that was designed to guide students through the process of building, testing, applying, and refining models. As a part of this modeling cycle, students have explicit instruction and practice in building, evaluating, and coordinating representations in introductory physics. Since I am particularly interested in representations across all of introductory physics, this work was situated in the second semester of MI. To address students' representation choices, the Problem Solving and Representation Use Survey (PSRUS) was developed as modified card sort survey, which asked students to simply list the representations that they would use on 25 physics questions from across introductory physics. Using non-parametric statistical tests (Mann-Whitney-Wilcox, Wilcoxon-Ranked Sign, and Cliff's Delta), I compare the number and variety of representations that students choose. Initially, students who took the first semester of MI use significantly more representations in their problem solving when compared to those who did not; however, there are significant gains in the number of representations that these students choose over the semester across the introductory physics content. After significant changes to the second semester MI curriculum, the difference between these two groups disappears, with both groups increasing their representation choices when compared to the previous semester. Using network analysis to compare students' concurrent representation choices, I also show that students use a consistent set of representations on mechanics problems; whereas, they choose a wider variety on electricity and magnetism (EM) problems. In both mechanics and EM, pictures serve as an important connecting representation between the others. I use these results to make suggestions for instructors, curriculum developers, and physics education researchers.

Of many modern constructions in geometry Calabi Yau manifolds hold special relevance in theoretical physics. These manifolds naturally arise from the study of compactification of certain string theories. In particular Calabi Yau manifolds of dimension three, commonly known as threefolds, are widely used for compactifications of heterotic string theories. Among the many constructions, that of complete intersection Calabi Yau manifolds (CICY) is generally regarded to be the simplest. Furthermore, CICY threefolds have been proven to exist only in finite number. In the following text CICY manifolds will be analyzed, with particular attention to threefolds. A general description of some of their topological quantities and their calculation is offered. Lastly, a proof of the finiteness of CICY threefolds is given.