Module Outlines
Here are brief outlines of all the modules that may be taken by 3rd year MPhys physics students.
Term 1
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The basic principles of quantum mechanics will be applied to a range of problems in atomic physics. The intrinsic property of spin will be developed and its relation to the indistinguishability of identical particles in quantum mechanics discussed. Perturbation theory and variational methods will be described and applied to several problems. The hydrogen and helium atoms will be analysed and the ideas that come out from this work will be applied to obtain a good qualitative understanding of the periodic table.
LECTURER: Martin Lees
BOOKS: SM McMurry, Quantum Mechanics, Addison-Wesley
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The module builds on the first and second year modules on electromagnetism by using Maxwell's equations to describe the generation and propagation of electromagnetic waves and their interaction with matter and, in particular, plasmas. The module will introduce at the start the magnetic vector potential, A, which is defined so that the magnetic field B=curl A. Although this appears at first sight to be a technical device, it will prove very useful in later modules particularly in quantum mechanics. It is also the natural variable to consider when exploring how electric and magnetic fields are affected under Lorentz transformations (special relativity).
Plasmas are 'fluids' of charged particles. The motion of these charged particles (usually electrons) is controlled by the electromagnetic fields which are imposed from outside and by the fields which the moving charged particles themselves set up. This module will cover the key equations which describe plasmas, both in the collisionless case (where scattering of particles off each other can be neglected) and in the collisional regime. It will examine some predictions derived on the basis of these equations and compare these with results from laboratory experiments and with observations from in situ measurements of solar system plasmas and remote observations of astrophysical systems.
LECTURER: Bogdan Hnat
BOOKS: IS Grant and WR Philips, Electromagnetism, Wiley
R. O. Dendy. Plasma Dynamics, OUP 1990.
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The diffusion, convection, chemical reactions and the interaction with living organisms which take place in or at the boundaries of the atmosphere determine the weather patterns we observe. The module will look at some of these processes. The module will also treat the phenomenon of cloud-formation and the role of the earth's rotation in determining flow patterns in the atmosphere.
LECTURER: David Leadley
BOOK: JFR McIlveen, Fundamentals of Weather and Climate, Chapman and Hall
J. M. Wallace and P. V. Hobbs, Atmospheric science : an introductory survey (2nd ed), Academic Press, 2006.
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This module should help you develop the C programming skills beyond the level of the introductory second year module PX270 C Programming. The module will consist of some lectures and a series of programming exercises designed to illustrate important aspects of program design. The module will also cover some important numerical techniques used in data processing in physics. Aspects relating to the reliability, accuracy and efficiency of these techniques will be discussed, as well as other issues such as making software user friendly, and data transfer between platforms. The module will be assessed on the basis of the exercises completed during the module and some project work.
LECTURER: Ben McMillan
BOOKS:
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The laboratory is designed to enable you to further develop your experimental skills and group working skills on some project like experiments.
ORGANISER: Oleg Petrenko
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Questions about the origin of the universe, where it is going and how it may get there are the domain of cosmology. One of the questions we will address is whether the universe will continue to expand or ultimately contract. Relevant experimental data include those on the Cosmic Microwave Radiation, the distribution of galaxies and the distribution of mass in the universe. We will discuss the implications of these in some detail. The module will outline Einstein's General Theory of Relativity and the setting up of Einstein's field equations. This is the 'full' theory of relativity. It starts from the apparently simple Principle of Equivalence, which states (roughly speaking) that the laws of physics are the same in all frames of reference including those accelerating in a gravitational field (special relativity is special as it is restricted to frames moving at constant speed).
The cosmological problem will be approached through the Cosmological Principle. This will lead us to the Robertson-Walker metric, Hubble's law and the Cosmological Red Shift. The application of the Einstein equations is then shown to lead irrevocably to the Big Bang Model, with singular behaviour at the origin of the universe. The evolution of the Primeval fireball and the synthesis of Helium is described and the module concludes with a discussion of gravitational collapse, event horizons and black holes.
LECTURER: Andrew Levan
BOOK: M Roos, Introduction to Cosmology , Wiley
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Fluctuations play an essential role in nature. Statistical mechanics is, in essence, a description of the role played by these fluctuations. It allows us to understand the physics of such seemingly diverse problems as diffusion, phase transitions and Fermi-Dirac and Bose-Einstein statistics. We will also give examples from Polymer physics where the behaviour of the polymer chains is driven by configurational entropy, rather than energy.
LECTURER: Marco Polin
BOOKS: David Chandler, Introduction to Modern Statistical Mechanics, OUP; F. Mandl, Statistical Physics, Wiley; P de Gennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press
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The module continues with themes introduced in PX384 Electrodynamics. The radiation (em-waves) emitted by accelerating charges will be described in more detail using retarded potentials (these are just time-dependent analogs of the usual electrostatic potential and its vector equivalent used to describe magnetic fields) which have the wave-like nature of light built in. The scattering of light by free electrons (Thompson scattering) and by bound electrons (Rayleigh scattering) will also be described. Understanding the bound electron problem led Rayleigh to his celebrated explanation of why the sky is blue and why sunlight appears redder at sunrise and sunset.
The module will also continue to discuss plasmas. The treatment of light scattering will be developed to discuss the interaction of lasers with plasmas. A fluid-mechanical description (magnetohydrodynamics) will be introduced to tackle the tough problem of how to describe the motion of charged particles when interacting with electromagnetic fields they themselves generate.
LECTURER: Valery Nakariakov
BOOKS: IS Grant and WR Philips, Electromagnetism, Wiley
R. O. Dendy. Plasma Dynamics, OUP 1990.
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One third of this module is on the calculus of variations and two thirds on complex variables. The calculus of variations is concerned with the minimisation of integrals over sets of differentiable functions. Such integrals crop up in many contexts. For example, the ground state wavefunction of a quantum system minimises the expectation value of the energy. The classical equations of motion for both particles and fields can be obtained by minimising what is called the action functional (which may be familiar if you took Hamiltonian Mechanics).
Requiring functions of complex variables to be analytic (differentiable with respect to their complex argument in some domain) turns out to constrain such functions very strongly. As we will see: only the constant function is differentiable everywhere, analytic functions are actually equal to their Taylor series and not just approximated by them, a function that is once differentiable is differentiable infinitely many times ... . Complex differentiable functions are clean, they are fun and they are important in physics. For example, response functions like the dielectric response function are analytic functions with the domain in which the function is analytic being related to causality.
LECTURER: Nicholas d'Ambrumenil
BOOK: KF Riley,MP Hobson and SJ Bence, Mathematical Methods for Physics and Engineering: a Comprehensive Guide, Wadsworth.
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This module will cover the structure and properties of crystalline solids. The structure of crystalline materials is important in determining their mechanical and electronic properties. For example, the different cubic crystal ordering in iron and copper is what makes one more brittle (Fe) and the other more malleable (Cu). The structure of the crystal also determines the allowed quantum numbers of the conduction electrons in the material, while the vibrational excitations of the lattice, called phonons, play an important part in determining properties like the heat capacity and electrical conductivity of a material. The module discusses the experimental techniques used in crystallography and the classification by symmetry of ordered structures. We will also discuss the quantum theory of the elementary excitations of the lattice, the phonons.
LECTURER: Oleg Petrenko
BOOKS: JR Hook and HE Hall, Solid State Physics, Wiley
Term 2
A number of modules taught by outside departments continue from term 1.
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In recent years considerable progress has been made in the application of physics and physical measurement techniques to medicine. This module concentrates on five major areas of medical physics: X-rays, radionuclide imaging, ultrasound, neuroelectromagnetism and radiotherapy. The aim of the module is to demonstrate the application of basic physical principles to these important areas of medical physics.
LECTURER: Adrian Wilson
BOOK: S. Webb (Ed), The Physics of Medical Imaging, Hilger
B.H. Brown et. al., Medical Physics and Biomedical Engineering, IOPP; G. Steele, Basic Clinical Radiobiology, Arnold; Bomford et. al., Walter and Miller's textbook of radiotherapy, Churchill.
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This module introduces the most important physical processes and detection methods required for understanding the broad range emission spectra of astrophysical objects from the radio regime to X-rays and gamma rays. It will provide a basis for any further studies in observational astrophysics.
LECTURER: Boris Gaensicke
BOOKS: H Bradt, Astronomical Methods: A Physical Approach to Astronomical Observations, CUP; J Frank, AR King, DJ Raine, Accretion Power in Astrophysics, CUP; C Hellier, Cataclysmic Variables: How and why they vary, Springer
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You have probably heard about the use of Magnetic Resonance Imaging (MRI) in medical diagnosis. In fact, magnetic resonance in nuclei - Nuclear Magnetic Resonance (NMR) - and in electrons - Electron Paramagnetic Resonance (EPR) - had existed as powerful tools used across science for several decades before being applied in the medical arena. This module will describe the physics behind the magnetic resonance techniques - NMR and EPR are excellent experimental evidence for the existence of nuclear and electron spin - and will show why these techniques have found numerous applications in fields as diverse as medicine, materials science, chemistry and biology.
LECTURER: Andy Howes
BOOK: Levitt, Spin Dynamics: Basic principles of Nuclear Magnetic Resonance Spectroscopy, Wiley
J. A. Weil, Electron Paramagnetic Resonance, Wiley-Interscience
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The electronic properties of solids and liquids are determined by the quantum and statistical mechanics of their electrons and their study is (and has always been) central to physics. Progress gained over the last century in the understanding of magnetism, superconductivity, semiconductors and semiconductor devices has been substantial and has come as understanding of quantum phenomena in many-electron systems has improved.
The module will cover the free, and nearly free, electron models of metals and insulators (introduced in the second year module Quantum Mechanics and its Applications) and introduce an alternative model, the tight-binding model, which is more appropriate for systems with the tightly bound conduction and valence band orbitals found, for example, in transition metals, insulators and semiconductors. The module will discuss the relationship between the crystalline structure of a material and the allowed electronic states and, in particular, the shape of the Fermi surface in metals. We will also see how the properties of electrons are affected if they are constrained to move in two dimensions, for example at the interface between two semiconductors. This turns out to be both surprising and very important in device physics.
In the second part of the module we will consider electronic properties of materials which arise out of interactions between electrons. Some condensed matter phenomena cannot be accounted for by assuming that electrons sense each other only through some average potential due to the ions and all the other electrons. The main example we will study will be magnetism.
LECTURER: Rudolf Roemer
BOOKS: JR Hook and HE Hall, Solid State Physics, Wiley; C. Kittel, Introduction to Solid State Physics, Wiley
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This module shows how the properties of the stable nucleus can be understood in terms of elementary models using basic physics from earlier modules, but with the introduction of the strong nuclear force. It is shown that the main features of the decay of unstable nuclei can also be understood on the basis of these ideas, but that a further interaction, the weak interaction, has to be postulated.
LECTURER: Michal Kreps
BOOK: KS Krane, Introduction to Nuclear Physics, Wiley, or, WSC Williams, Nuclear and Particle Physics, OUP
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The researching, evaluation and presentation of scientific information are important skills that you used in the 2nd year Physics Skills module. This project is designed to further develop these skills.
Your class will be divided into groups each of about six members. Each group will then be assigned a topic to be researched and reported on, and they will also each be allocated a member of Academic Staff who will act as a both a mentor and an assessor. The group will then meet regularly (at least weekly on a formal basis but probably more regularly informally) to assign individual tasks and collate information. Towards the end of the ten weeks you will give an oral presentation on the part of the problem you have investigated to the rest of your group (and perhaps others). The group will then organise the production of the final written report which will be assessed.
The overall assessment will be based on the oral presentation and the report mark, as apportioned by the group members.
ORGANISER: Sandra Chapman
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This module follows on from PX264 Physics of Fluids. The lectures will provide the student with a solid background in the mathematical description of fluid dynamics. You will be introduced to the method of deducing the equations of motion from conservation laws (mass, momentum, energy), the value of dimensional analysis in finding scale-invariant solutions and universal turbulence spectra, role of the gravity and rotation in atmospheric and oceanic dynamics, and deriving approximate equations of motion (e.g. boundary layer equations).
An important aim of the module is to provide an appreciation of the complexities and beauty of fluid motion. This will be brought out in lectures, computer demonstrations and visualisations, web pages. Students are also encouraged to attend seminars on fluid dynamics put on by the Fluid Dynamics Research Centre (Engineering Dept and Maths) and by MIR@W (Maths) where they can learn about current research by physicists, engineers and mathematicians.
Content: The module will cover the following topics:
Kinematics of Fluid Motion.. Specification of the flow by field variables; vorticity; stream function; strain tensor; stress tensor.
Conservation Laws.. Conservation of mass, momentum and energy and equations of motion deduced from these laws; Bernoulli's equation.
Vorticity.. Vortex lines and vortex tubes, Kelvin's circulation theorem, vorticity equation, interaction of vortices, vortex sheet.
Dimensional analysis.. Reynolds number, Rayleigh number, Ekman number, Rossby number, etc.
Laminar flow.. Flow in a pipe; shear flows; flow due to an oscillating plate; Stokes flows of very viscous fluids.
Boundary layers.. Prandtl's boundary layer theory; flow separation. Taylor-Proudman theorem and Eckman boundary layer in rotating fluids.
Instability and waves.. Releigh-Taylor and Kelvin-Helmholtz instabilities; stability of parallel flows. Inertia-gravity and internal waves. Waves on a deep water. Sound. Time permitting, lectures will be given on material selected from the following.
Geophysical Fluid Dynamics.. Rotating reference frames; shallow water equations; geostrophic equations; potential vorticity; Rossby waves and vortices.
Turbulence. Onset of turbulence; energy cascade and the Kolmogorov spectrum. Inverse energy cascade and the enstrophy cascade in 2D fluids. Turbulent boundary layer; log-profile.
Books:
D.J. Acheson, Elementary Fluid Dynamics, OUP. (The main text. Excellent and affordable.); L.D. Landau and E.M. Livshitz, Fluid Dynamics, OUP. (A classic.); D.J. Tritton, Physical Fluid Dynamics (Second Edition), Oxford Science Publs. (Another classic. The emphasis is on the physical phenomena and less on the mathematics.); A.R. Paterson, A First Course in Fluid Dynamics, CUP. (Affordable and easier than Acheson.)
Assessment: 3 hour exam
Lecturer: Sergei Nazarenko
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The development of lasers during the last thirty years has been extremely rapid and with the appearance of semiconductor lasers they have become very important in optoelectronic communication. This module combines the treatment of the basic physics of laser action in the various types of laser which now exist with a coverage of their applications in optoelectronics.
LECTURER: Steve Dixon
BOOK: J Wilson and JFB Hawkes, Optoelectronics, an Introduction, Prentice-Hall; CC Davis, Laser and Electro-optics, Fundamentals and Engineering, CUP
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The module introduces non-linear phenomena in science. Examples from physics, chemistry and biology will be discussed (little previous knowledge of these subjects will be assumed).
A discussion of phase transitions and the elements of bifurcation theory will be followed by the theory of first and second order non-linear differential equations. Such phenomena as simple attractors (limit cycles) will be discussed.
It will be shown how non-linear systems can `self-organize' to produce structures which have interesting time and space dependences. The main ideas from the theory of chaos will also be introduced using one-dimensional difference equations as working examples.
LECTURER: Sandra Chapman
BOOKS: George Rowlands, Non-Linear Phenomena in Science and Engineering, Ellis Horwood
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The Standard Model describes elementary particles (the quarks, leptons, and bosons) using gauge theories. Although a full quantitative description of the SM requires the machinery of quantum field theory and is not easily accessible, it is quite possible to develop a good qualitative understanding of what is meant by a gauge theory and how this contrains the predictions of the model. A lot of this follows from symmetry. We will look at Noether's theorem (for any continuous symmetry property there is a conserved quantity, eg conservation of charge and invariance under gauge transformations are the same thing), flavour symmetry, parity (P) and others. We will show how these aspects of the model are tested against experiment. We will also look at the reasons for quark confinement and the concept of a momentum-transfer dependent coupling, the Higgs mechanism, quark mixing and questions about unification.
LECTURER: Sinead Farrington
BOOK: Introduction to Elementary Particles, David Griffiths, Wiley
Modern Elementary Particle Physics, Gordon Kane, Addison Wesley
Particle Physics, B.R. Martin and G. Shaw, Wiley
Introduction to High Energy Physics, Donald Perkins, Addison Wesley
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