This thesis investigates the role of superfluidity in neutron stars and associated phenomena. We model the internal fluid of a neutron star as a two-component system: one of charged particles and one of superfluid neutrons. We derive a set of multi-constituent hydrodynamic equations that allows for a mutual friction between the constituents. We show that when a velocity difference exists between the two constituents the momentum of each constituent is modified by an entrainment parameter. Throughout all of this work we take direction from both theoretical and experimental work on superfluid Helium. This suggests that a force due to vortex lines in the superfluid acts between the two constituents. The hydrodynamic equations are on a scale at which the effect of vortices can be averaged over. The form of the mutual friction between the two constituents depends on the configuration of the vortices. Firstly, we concentrate on an array of vortices. The mutual friction is calculated both for a straight array, and then extended to a ‘moderately’ curved array. We also investigate a turbulent model for the superfluid neutrons in which the vortices are in a tangle. To include rotation in our model we use a phenomenological approach to construct the mutual friction for a polarised tangle. The hydrodynamic equations are used to investigate how entrainment and mutual friction affect plane waves. We show that there are conditions in which the waves are unstable and discuss how this may lead to turbulence. As a first step in considering the neutron star crust we consider how oscillations in the fluid are dissipated on a boundary. As before, we concentrate on the effects of entrainment and mutual friction. Finally, we consider a simple global model of the glitch phenomenon seen in neutron stars in which the important process is a reconfiguration of the vortex array. We use this model to consider how the observational data may constrain parameters.

We investigate equilibrium configurations and oscillation spectra of neutron stars, modelled as rotating magnetised fluid bodies in Newtonian gravity. We also explore the idea that these model neutron stars could have dynamics analogous to rigid-body free precession. In axisymmetry, the equations of magnetohydrodynamics reduce to a purely toroidal-field case and a mixed-field case (with a purely poloidal-field limit). We solve these equations using a nonlinear code which finds stationary rotating magnetised stars by an iterative procedure. We find that despite the general nature of our approach, the mixed-field configurations we produce are all dominated by their poloidal component. We calculate distortions induced both by magnetic fields and by rotation; our results suggest that the relationship between the magnetic energy and the induced ellipticity should be close to linear for all known neutron stars. We then investigate the oscillation spectra of neutron stars, using these stationary configurations as a background on which to study perturbations. This is done by evolving the perturbations numerically, making the Cowling approximation and specialising to purely toroidal fields for simplicity. The results of the evolutions show a number of magnetically-restored Alfv´en modes. We find that in a rotating star pure inertial and pure Alfv´en modes are replaced by hybrid magneto-inertial modes. We also show that magnetic fields appear to reduce the effect of the r-mode instability. Finally, we look at precession-like dynamics in magnetised fluid stars, using both analytic and numerical methods. Whilst these studies are only preliminary, they indicate deficiencies in previous research on this topic. We suggest ways in which the problem of magnetised-fluid precession could be better understood.

Marine anthropogenic noise is increasing, along with concern about its impact on the environment. Hence minimising noise within engineering design is important, including in applications such as ships, submarines and turbines. The desire to mitigate noise may also be related to reducing the detectability of certain types of marine craft. Noise reduction typically focuses on rotating machinery such as propellers, due to the high velocity of the blades. A common source of broadband noise in engineering scenarios is often termed inflow turbulence noise. Resulting from upstream turbulence impinging onto rotor blades, this source typically dominates the low to mid range of the frequency spectrum. This is due to the high turbulence intensity and large length scales present in the inflow turbulence, which exceed those generating competing noise sources. This thesis uses a library of numerical tools to simulate broadband inflow turbulence noise. Synthetic turbulence is generated numerically within the simulations. Turbulence is resolved on the grid by solving the filtered Navier-Stokes equations. Based on the assumption of incompressible flow, noise sources may be predicted without resolving acoustic waves on the grid. This decoupling of hydrodynamic and acoustic processes means that radiated noise may be estimated using an acoustic analogy. Validation of two inflow turbulence generators revealed the importance of obtaining the prescribed turbulence statistics, as well as minimising artificial pressure fluctuations. This is used to simulate homogeneous isotropic turbulence impinging onto a foil, allowing acoustic sources to be located. The far-field sound prediction is in good agreement with experimental measurement data for low frequencies. It is then shown that the effect of foil thickness on noise can successfully be predicted using the proposed methodology. Noise radiation from a tidal turbine is then estimated by fully resolving all turbine blades, both spatially and temporally, in the simulation. A good agreement is seen in comparison to an analytical model, demonstrating that the simulation captures the dominant flow features which affect the acoustic spectrum. These spectral ‘humps’ are a result of turbulence-rotor interaction, which is implicitly included. Full scale noise estimates made from the simulations are then used to inform environmental impact assessment; the turbine hydrodynamic noise is not expected to be an issue in this regard.

Computational fluid dynamics (CFD) based Fire Field Modelling (FFM) codes offer powerful tools for fire safety engineers but their operation requires a high level of skill and an understanding of the mode of operation and limitations, in order to obtain meaningful results in complex scenarios. This problem is compounded by the fact that many FFM cases are barely stable and poor quality set-up can lead to solution failure. There are considerable dangers of misuse of FFM techniques if they are used without adequate knowledge of both the underlying fire science and the associated numerical modelling. CFD modelling can be difficult to set up effectively since there are a number of potential problems: it is not always clear what controls are needed for optimal solution performance, typically there will be no optimal static set of controls for the whole solution period to cover all stages of a complex simulation, there is the generic problem of requiring a high quality mesh - which cannot usually be ascertained until the mesh is actually used for the particular simulation for which it is intended and there are potential handling issues, e.g. for transitional events (and extremes of physical behaviour) which are likely to break the solution process. In order to tackle these key problems, the research described in this thesis has identified and investigated a methodology for analysing, applying and automating a CFD Expert user's knowledge to support various stages of the simulation process - including the key stages of creating a mesh and performing the simulation. This research has also indicated an approach for the control of a FFM CFD simulation which is analogous to the way that a FFM CFD Expert would approach the modelling of a previously unseen scenario. These investigations have led to the identification of a set of requirements and appropriate knowledge which have been instantiated as the, so called, Experiment Engine (EE). This prototype component (which has been built and tested within the SMARTFIRE FFM environment) is capable, both of emulating an Expert users' ability to produce a high quality and appropriate mesh for arbitrary scenarios, and is also able to automatically adjust a key control factor of the solution process.

Hong Kong is a British colony, a world trade centre, and a world banking and financial centre. The highly successful city is strongly linked with education in Hong Kong. However, education in Hong Kong is much influenced by education in Britain: Sixth Form education is a bridge crossing from school to tertiary education or from school to society. Mathematics is a foundation for all subjects. In addition, mathematics and physics are most popular subjects in the Hong, Kong A-level examination. The mathematical and physical sciences have changed significantly during the past few decades. The most conspicuous and impressive development in mathematics is the enormous increase in the amount of new subject matter being created. In physical science, the coming of relativity theory and quantum theory have revolutionised the traditional concepts. Almost all the new technologies in the world are based on modern physics theory. Such developments have resulted in a complete revision of the content of university courses and school curricula. More generally, changes at one level of education are almost certain to cause changes at other levels and problems at the relevant interfaces. The author's study investigated the transition in mathematics and physics education from school to Hong Kong Polytechnic(s). The first part of this study mainly dealt with the mathematics and physics education in school, particularly the relationship between these two disciplines as well as their A-level syllabuses. The second part of this study dealt with the students' academic performance in mathematics and physics at polytechnic in relation to their entry qualifications and the medium of instruction in school. In addition, a number of surveys on the use of mathematics and physics topics conducted among students in the polytechnic was studied in. order to help the author to propose new A-level syllabuses to fit the modern tertiary education in Hong Kong. Finally, a set of recommendations for the improvement of the Hong Kong education system in general as well as mathematics and physics education in particular are suggested.

On étudie la limite thermodynamique pour un système de particules quantiques en interaction dans un milieu aléatoire dans le formalisme de l'ensemble microcanonique. L'existence de la limite est démontrée pour l'énergie interne ainsi que pour l'entropie sous des conditions assez générales sur le modèle à une particule. Ensuite, la limite thermodynamique est étudiée pour le modèle des pièces à une dimension dans le cas des fermions et pour une densité de particules faible. On donne une caractérisation de l'état fondamental en terme d'espaces fonctionnels, on démontre sa non dégénérescence presque sûre et on décrit sa fonction d'autocorrélation. Ces résultats permettent d'obtenir une estimée de l'énergie fondamentale par particule comme fonction de la densité de particules dans la limite thermodynamique.

No description available.

Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using symmetric monoidal categories. This leads to an elegant formalism for describing quantum protocols such as quantum teleportation. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow of such protocols in an intuitive way. However, the graphical calculus also reveals surprising features of these protocols; for example, in the quantum teleportation protocol, information appears to flow `backwards-in-time'. This leads to question of how causal structure can be described within categorical quantum mechanics, and how this might lead to insight regarding the structural compatibility between quantum theory and relativity. This thesis is concerned with the project of formalising causal structure in categorical quantum mechanics. We begin by studying an abstract view of Bell-type experiments, as described by `no-signalling boxes', and we show that under time-reversal no-signalling boxes generically become signalling. This conflicts with the underlying symmetry of relativistic causal structure. This leads us to consider the framework of categorical quantum mechanics from the perspective of relativistic causal structure. We derive the properties that a symmetric monoidal category must satisfy in order to describe systems in such a background causal structure. We use these properties to define a new type of category, and this provides a formal framework for describing protocols in spacetime. We explore this new structure, showing how it leads to an understanding of the counter-intuitive information flow of protocols in categorical quantum mechanics. We then find that the formal properties of our new structure are naturally related to axioms for reconstructing quantum theory, and we show how a reconstruction scheme based on purification can be formalised using the structures of categorical quantum mechanics. Finally, we discuss the philosophical aspects of using category theory to describe fundamental physics. We consider a recent argument that category-theoretic formulations of physics, such as categorical quantum mechanics, can be used to support a variant of structural realism. We argue against this claim. The work of this thesis suggests instead that the philosophy of categorical quantum mechanics is subtler than either operationalism or realism.

In the first part of this thesis, we study the duality of Wilson loops and M2-branes in AdS₄/CFT₃. We focus on supersymmetric M-theory solutions on AdS₄xY₇ that have a superconformal dual description on S³ = ?AdS⁴. We will find that the Hamiltonian function h_M for the M-theory circle plays an important role in the duality. We show that an M2-brane wrapping the M-theory circle is supersymmetric precisely at the critical points of h_M, and moreover the value of this function at those points determines the M2-brane actions. Such a configuration determines the holographic dual of a Wilson loop for a Hopf circle in S³. We find agreement in large classes of examples between the Wilson loop and its dual M2-brane and also that the image h_M(Y₇) determines the range of support of the eigenvalues in the dual large N matrix model, with the critical points of h_M mapping to points where the derivative of the eigenvalue density is discontinuous. We will then move away from the three-sphere and construct gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localisation. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories defined on a general class of background three-manifold geometries. To further verify that our gravitational backgrounds are indeed dual to field theories on their boundaries, we compute Wilson loops and their M2-brane duals in this general setting. We find that the Wilson loop is given by a simple closed formula which depends on the background geometry only through the supersymmetric Killing vector field. The supergravity dual M2-brane precisely reproduces this large N field theory result. This constitutes a further check of AdS₄/CFT₃ for a very broad class of examples.

A física se relaciona intimamente com a matemática, e essa relação pode ser refletida com olhares distintos e complementares. A respeito dessa temática, existem trabalhos que discutem o papel técnico e operacional que a matemática exerce em diferentes níveis de ensino de física, assim como existem trabalhos que refletem sobre o caráter organizacional e estrutural que ela possui no ensino, construção e aprendizagem da ciência. Esse trabalho tem como principal objetivo observar esses dois tipos de relações em um curso introdutório de mecânica na licenciatura em física da Universidade de São Paulo e refletir sobre como as relações da física com a matemática podem ser apresentadas no contato inicial na graduação que o futuro professor de física tem com os conceitos da mecânica. Para isso, foi realizado um estudo de caso na disciplina Fundamentos de Mecânica em duas turmas com professores distintos. Nesse estudo, foram gravados áudios das explicações dos professores e anotadas as formulações matemáticas utilizadas nas aulas, como equações, resolução de exercícios e/ou esboços de gráficos. Em um primeiro momento, foram analisadas as representações matemáticas utilizadas pelos professores em trechos das aulas denominados episódios de ensino. Nesses episódios, se observaram aspectos como a transitividade de representações matemáticas, o aspecto operacional da matemática e as relações explícitas com outros cursos da licenciatura, como o cálculo e a geometria analítica. Em um segundo momento, foram analisados os aspectos organizacionais da matemática na física presentes no estudo de caso que permitem pensar a matemática como estruturante do pensamento físico (PIETROCOLA, 2002): interpretação, significação, abstração e linguagem matemática. Com essas análises, foi possível concluir que a relação da física com a matemática pode ser explorada no início da formação do professor em aspectos que extrapolam o uso técnico e mecânico das operações: a reflexão sobre a utilização das representações, a extração de informações físicas a partir de formulações e o exercício de pensar e ouvir questionamentos sobre o uso da matemática na física. A partir dessas apresentações, emergem outros questionamentos para a área de ensino de física: quando o futuro professor começa a pensar sobre a relação da física com a matemática? Quais as implicações de um curso introdutório em mecânica ser oferecido concomitantemente com um curso matemático de cálculo, por exemplo? Essa dissertação busca oferecer explanações que permitam levantar questões para futuras pesquisas na área e contribuir para a discussão sobre o tema. / Physics is closely related to mathematics, and this relationship can be seen with different and complementary points of view. Regarding this issue, there are studies that discuss the technical and operational role that mathematics plays in different levels of the education of physics, and there are works that focus on the organizational and structural nature that it has in education, construction and learning of science. This work is aimed at evaluate these two types of relationships in an introductory course in the degree in Physics from the University of Sao Paulo and think about on how the relations of Physics and Mathematics can be presented in the initial contact at the beginning of the university studies that the future teachers of Physics with the concepts of mechanics. For this, a case study in Mechanical Fundamentals course was conducted in two classes with different teachers. In this study, the audio recordings of the teachers explanations were made and noted the mathematical formulations, used in class were noted, as equations, problem solving and/or graphic sketches. At first, we analyzed the mathematical representations used by teachers in parts of classes called episodes of education. In those episodes, aspects such as transitivity mathematical representations, the operational aspect of mathematics and relationships with other courses of degree, such as calculus and analytic geometry, were as noted a second step; the organizational aspects of mathematics in Physics were analyzed to consider Mathematics as a structure for the physical thought (PIETROCOLA, 2002): interpretation, meaning, abstraction and mathematical language. With these analyzes, it was concluded that the physical relationship with mathematics can be explored at the beginning of a teacher training in aspects that go beyond the technical and mechanical use of the operations: a reflection on the use of representations, extraction of physical information from formulations and the exercise of thinking and hearing questions about the use of Mathematics in Physics. From these presentations, other questions emerge for the area of physical education: when the future teacher begins think about the physical relationship with Mathematics? What are the implications if an introductory course in Mechanics is offered concurrently with a Mathematical Calculus course, for example? This dissertation seeks to offer explanations that enable the raise of questions for future researches in the area and contribute to discussion on the topic.