Physics with Astrophysics BSc (Hons)

This module is designed to introduce fundamental concepts in the mathematical area of Fluid Dynamics. You will analyse the equations of continuity and momentum, and will investigate key concepts in this area. We will introduce the Navier-Stokes equations, and case studies will be used to visualise and analyse real-world problems (using appropriate software) as appropriate to delivery of the module. Initially, we will use the inviscid approximation and then utilise analytical and computational techniques to investigate flows. The second half of the module is a specialist course in laminar incompressible viscous flows, encompassing background mathematical theory allied to a case study approach, with solution to problems by both analytical and computational means.

Assessment of the module is by one individual assignment (30%) and one formal examination (70%).

The module is designed to provide you with a useful preparation for employment in an applied mathematical environment, physics environment or engineering environment.

Outline Syllabus
• Introduction of fluid dynamics, Navier-Stokes equations, equations of continuity and momentum for inviscid flow, unsteady one-dimensional flow along a pipe, irrotational flow, Bernouilli's equation, stream function formulation, flow past a cylinder, velocity potential.

• Low Reynolds Number Flow including: (i) lubrication theory, slider bearing, cylinder-plane, journal bearing, Reynolds equation, short bearing approximation; (ii) Flow in a corner, stream function formulation, solution of the biharmonic equation by separation of variables.

• High Reynolds Number Flow including boundary layer equations, skin friction, displacement and momentum thickness, similarity solutions, momentum integral equation, approximate solutions.

The module aims to present an introduction to Dynamical Systems and associated transferable skills, providing the students with tools and techniques needed to understand the dynamics of those systems. You will analyse non-linear ordinary differential equations and maps, focusing on autonomous systems, and will learn analytical and computational methods to solve them. This module offers the additional opportunity of research-orientated learning through a hands-on approach to selected research-based problems.

Topics may include (note this is indicative rather than prescriptive):
1. Autonomous linear systems, fixed points and their classification.
2. 1-dimensional non-linear systems: critical points; local linear approximations; qualitative analysis; linear stability analysis; bifurcations.
3. Multi-dimensional non-linear systems: linearisation about critical points, limit cycles, bifurcations.
4. Discrete systems: maps (such as tent map, logistic map, Henon map, standard map).
5. Numerical schemes for ordinary differential equations, such as the embedded Runge-Kutta method.
6. Numerical applications and programming: generation of the orbit of a map, Lorenz map for a dynamical system, orbit diagrams, cobwebs, simple fractals.
7. Elements of Chaos theory: Lyapunov exponents, sensitive dependence on initial conditions, strange attractors, Hausdorff dimension, self-similarity, fractals.

The aim of this module is to develop knowledge of three main areas of astrophysics:
• Stellar evolution (including star formation, supernovae, white dwarfs, neutron stars, black holes)
• Galaxies (including morphology, spectral properties, Hubble classification, gravitational lensing)
• Cosmology (including Hubble’s law, expansion and curvature of the Universe, Inflation, Cosmic Microwave Background).

The student will be introduced to the big questions in astrophysics, including the mysteries of dark matter and dark energy, the hunt for extra-solar planets and gravitational waves, and consider the ultimate fate of our Universe by looking at the curvature and geometry of space-time.

The module will be taught using a mixture of lectures and seminars. It will be assessed by coursework (30%) and formal examination (70%). Exam feedback will provided individually and also generically to indicate where the cohort has a strong or a weaker answer to examination questions. Written feedback will be provided on the coursework. Formative feedback will be provided during the seminars.

Outline Syllabus

Stellar Evolution
Structure and evolution of stars, including formation and fundamental properties, composition, nucleosynthesis, the Hertzsprung-Russell diagram, spectroscopic classification. Extra-solar planets. Star formation, evolution and death, including supernovae, white dwarfs, neutron stars, pulsars and black holes.

Galaxies
The morphology, spectral properties and population groups of galaxies (including elliptical, spiral and stellar nursery). Hubble classification. Review of apparent and absolute magnitudes, Doppler effect and redshifts. The main-sequence mass-luminosity relationship. Clusters, including chemical composition. The Interstellar Medium and the heliopause. Variable stars. Distance to the Galactic Centre. Galaxy formation and evolution. Gravitational lensing and gravitational waves. Dark matter.

Cosmology
Hubble’s law and the expansion of the Universe. Cosmological Principle. Review of the origin of the Big Bang and age of the Universe. Curvature and expansion of the Universe and curved space-time. Cosmic Microwave Background, Inflation. The curved, expanding universe as well as the geometry and ultimate fate of universes. Dark Energy

The aim of this module is to investigate the Sun, our nearest star, as the energy powerhouse of our solar system. You will consider fundamental solar processes, solar radiation and neutrinos, nuclear fusion reactions, the physics of the solar interior and solar atmosphere, the coronal heating problem, sunspots, solar flares and coronal mass ejections, solar wind and space weather, geomagnetic storms and auroras, solar dangers and the Sun-Earth connection.

You will construct and apply mathematical models of the Sun to describe fundamental solar processes and phenomena, including the use of magnetic fluid dynamics and magnetism made visible.

Outline Syllabus

The Sun as a star
Solar radiation, solar constants, spectroscopy of the Sun, the Sun’s place in the Milky Way and universe, nuclear fusion reactions, solar neutrino problem, solar energy transfer, the solar atmosphere, sunspots, solar flares and coronal mass ejections, solar wind and space weather, geomagnetic storms and auroras, solar dangers (including satellites), and the Sun-Earth connection.

The physics of the Sun
Review of magnetism and Maxwell’s equations, fluid description and magnetohydrodynamic (MHD) equations, magnetic induction, magnetic forces (Lorentz force), magnetism made visible, the vector potential, MHD waves (phase and group speeds), Alfvén waves, and mathematical models of the solar wind.

The module aims to provide the student, as an individual, an opportunity to carry out an extended study in a specific area of physics, developing the student's ability to work independently and promoting self-reliance. Guidance to source and assess the appropriateness of information is provided by the module.

A key aim is to encourage students to apply theoretical and analytical techniques to problem solve. The module also aims to develop both verbal and written communication skills. The project will provide practical experience of drawing up a project specification defining aims, objectives and identifying an envisaged endpoint. With their supervisor’s guidance, the student will prepare a project plan that includes a Gantt chart, project background and sourcing previous work and associated theory/simulation to assess whether the aims and objectives are achievable and that their theoretical basis is sound.

To meet University requirements and gain practical experience, students must perform a risk assessment to identify potential risks/hazards associated with the project. The student will follow the defined plan to complete the project that will include, for example, experimental investigations and the application of appropriate theory and simulations

Students will be encouraged to monitor their progress based upon the project plan and, where necessary, adjust timescales/objectives. The student will be required to submit a final project report and present the project verbally to the supervisor, second markers and peers. Contact with the supervisor must be maintained on a regular basis to: discuss/assess progress and obtain advice.

Physicists are increasingly able to exploit quantum mechanical behaviour in new optoelectronic devices that will have a profound impact on our lives. These devices offer unprecedented performance in terms of speed and efficiency. The student will develop knowledge of how these characteristics stem from design at the atomic scale and of the challenges associated with scaling-up for practical applications such as sustainable energy and quantum computing.

Background Quantum Theory
Review of quantum mechanical concepts. Density of states function in one, two and three dimensions. Fermi-Dirac occupation function. Electron gas and the Fermi surface. Band theory of semiconductors and doping. Band structure of important semiconductors.

Low-dimensional Semiconductors
Energy and length scales. Fabrication techniques: top down and bottom up. High electron mobility transistor and the two-dimensional electron gas. Quantum Hall effect. Quantum wires and quantised conductance. Semiconductor quantum dots. Measurement methods for quantum devices.

Quantum Devices
Quantum computing, Quantum cryptography, Single photon and entangled photon emitters, Single electron transistor, Semiconductor quantum dot laser, Quantum cascade laser, Optical cavities, Third generation photovoltaics and quantum efficiency, Light emitting diodes and solid-state lighting, Resonant tunnelling diode, Future opportunities for quantum devices: properties of graphene and graphene-based devices; Scaling up nanotechnology, Sustainability and cost.

The module provides students with skills and knowledge to develop scientific and/or electronic systems for space applications. The topics covered are:

The space environment - launch, orbits, rocket equation, drag, radiation, vacuum, thermal gradients.

Satellite systems and system development for space applications - radio communication, ground stations and link budgets, solar power, data processing, Earth observation, optimisation of systems for space, materials choice for space, component characteristics, mechanical and thermal testing.

Product Acceptance and Qualification Assurance for space – industry standards for space-worthy design, functional testing, simulation of operations, verification and validation processes.

Environmental Testing – theory and practice of vibration testing, resonant sweeps, shock tests and random noise tests. Theory and practice of thermal vacuum testing, the effect of vacuum on electronics and thermal cycling. Theory and practice of radiation testing, how radiation effects electronics, how to design to be radiation tolerant, and testing components in the x-ray irradiator.

You will develop your understanding of academic conventions in UK higher education aligned to your level of study, including expectations around critical analysis, structure, argumentation, evidencing, and referencing. The module focuses on developing communication strategies that will help you express your ideas clearly and coherently in written assignments and spoken activities. You will also reflect on your current academic and language skills and develop strategies for development ahead of your assessments.