Projects available in 2010-2011
Application forms are available in the link on the right. You can also request a postgraduate brochure.
Details of possible projects are given below.
A study of the Sun's oscillations (R. Jain)
The Sun´s global oscillations are observed very precisely by Earth and Space based instruments. The study of oscillations are interesting in themselves, but their study can also provide important clues to the make-up of the atmosphere in which they occur. Oscillations and waves are also natural means of transmitting energy from one region to the other. They are inevitable when ever and wherever there is a disturbance in the solar atmosphere. Thus, to understand the energy flow in the Sun´s atmosphere, it is vital to understand how the wave motions behave in it.
The Sun has magnetic fields of varying magnitude and they vary with time making it a very challenging time dependent problem to solve in a physical system.The aim of the project is to increase our understanding of the way in which the magnetic fields of the solar atmosphere influence the oscillatory motions. This will help to exploit the diagnostic potential of the waves in determining the Sun´s atmospheric structure.
Heating of the solar corona (R. Jain)
How the Sun's outer atmosphere, also known as the solar corona, is heated to temperatures of millions of degrees is a major issue in solar physics. It is important to understand this issue as it has practical implications here on Earth's climate and `space weather'. Recent space missions reveal that the heating mechanism is connected to the magnetic fields and it is intermittent. This suggests that the heating may be due to superposition of numerous small-scale energy releasing events, known as nanoflares.
This project proposes to simulate them with an aim to understand the process and to investigate their response on the solar corona, such as variability in the X-ray brightness, to predict their observational signatures. Understanding the physical process and predicting the observational signature is crucial to address the issue of hot solar corona.
Turbulent transport in fluids (E. Kim)
Turbulence refers to non equilibrium state of fluids where many spatial and temporal modes are excited. Typical examples of turbulence include water in boiling pots and air flows around airplane wings. These turbulent flows are known to be crucial in enhancing transport level (e.g. mixing) over what is expected based on pure molecular diffusion. For instance, this is why we stir coffee with a spoon after putting sugar in it. This project aims to study turbulence in neutral fluids and in magnetized fluids to understand some of the outstanding problems in astrophysical (e.g. Sun) and laboratory plasmas such as the stellar evolution of rotation and magnetic fields and magnetic activities (e.g. solar cycle, sun spots). It will involve statistical analysis and/or numerical simulations (e.g. by using IDL and Fortran).
Self-Organised Criticality (E. Kim)
Is there a fundamental law that can explain complex phenomena independent of systems? For instance, could volatile magnetic activities on the Sun, earthquakes, forest fires, etc be governed by the same law? One of promising paradigms for such a universal law is the so-called self-organised criticality (SOC), which is based on the property of nonlinear dynamical systems to maintain `quasi-equilibrium' state. The application of SOC has been successful in explaining `seemingly' complex behaviour in many systems (e.g. solar flares, earthquakes, etc) by using extremely simple models (e.g. sand pile). This project aims to learn the basics of SOC and then to use an appropriate model to study the evolution of shear flows and magnetic fields. It will involve statistical analysis and/or numerical simulations (e.g. by using IDL and Fortran). The outcome of the project will be applied to astrophysical and/or laboratory plasmas.
Particle dispersion in stratified and rotating flows (Y. Li)
This project has its background in problems such as the dispersion of pollutant or toxin in the atmosphere, or the microorganisms in the oceans, which has important effects on the ecosystem on the earth. The large scale fluid motion in the atmosphere and the oceans is affected by rotation of the earth and stratification due to the density difference between different layer of the fluid. A lot of problems in such flows are not yet well-understood or lacking accurate models. In this project, the properties of particle motion in such flows will be studied using computer simulations and theoretical modeling.
Lagrangian-Eulerian study of turbulence (Y. Li)
Fluid motion can be studied using two approaches, the Eulerian and Lagrangian approaches. In the Eulerian approach, we observe the changes of the velocity and other properties at fixed points in the flow field, whilst in the Lagrangian approach, one follows the motion of a marker in the fluid and study the changes of the properties seen by the marker. The Eulerian point of view has been adopted as a standard method in most research. However, the Lagrangian method has recently received renewed interests and has led to more realistic models for turbulent motions. In this project, various problems in turbulence will be studied from the Lagrangian point of view, using numerical simulation and theoretical analysis.
Numerical computations of generalised functions and their application to fluid dynamics (K. Ohkitani)
By using a recently developed technique of numerical handling generalised functions (Ooura), we attempt numerical computations of fluid equations in the sense of distributions. As an example, we study the inviscid 1D Burgers equation and compare it with the viscous Burgers equation in the vanishing viscosity limit.
Monge-Ampere equation and 2D incompressible fluid dynamics (K. Ohkitani)
An attempt is made to shed some light on the nonlocal nature of the pressure term in incompressible fluid dynamics. We consider the correspondence between the pressure and the stream function on the basis of the Monge-Ampere equation. We aim to alleviate the difficulty associated with nonlocality.
Transverse oscillations of coronal magnetic loops (M.S. Ruderman)
Transverse oscillations of coronal loops were observed by the spacecraft TRACE and SOHO for a few years. Increasingly sophisticated theoretical models were developed to describe these oscillations. The proposed project aims to continue this work. New models of coronal loop oscillations including plasma stratification along the loop, magnetic field twist and loop curvature will be developed. Collective oscillations of two neighbouring coronal loops will be studied.
Helioseismology of the solar activity cycle (M. Thompson)
Solar oscillations observed from the ground and from space enable us to map acoustically the interior the Sun, learning about such things as the internal rotation and sound speed. This project relates theory and data analysis to use high-resolution helioseismic data to study the structure and evolution of solar magnetic activity beneath the Sun's surface, to improve our understanding of the solar cycle. We are involved in all the major missions in helioseismology, giving us access to the full range of data that we need: these missions include the Solar and Heliospheric Observatory (SOHO) and NASA's Solar Dynamics Observatory (SDO) to be launched in 2009. More information about helioseismology can be found at http://soi.stanford.edu/results/heliowhat.html
Inversion techniques for asteroseismology (M. Thompson)
Asteroseismology is a exciting emerging field of study, which provides new and unique tests of our theories of stellar structure and evolution. New developments are being driven rapidly by improvements in ground-based observations and by the launch of new satellite missions - in particular the French mission COROT which launched at Chrismas 2006 and the NASA mission Kepler which launches in 2009. Professor Thompson is on a co-Investigator team to analyse COROT data and is a member of the Kepler Asteroseismology Science Consortium. The aim of this project will be to develop inversion techniques to use the observations to probe the interiors of stars, in particular their internal rotation. This will enable tests of the evolution of stars. More information about asteroseismology can be found at the following site by one of our collaborators, Dr Travis Metcalfe: http://asteroseismology.org .
Dark energy and structure formation (C. van de Bruck)
Studying the interaction between matter (dark matter, neutrinos and/or baryons) and dark energy and the resulting consequences for structure formation. Current and future experiments measuring the anisotropies in the cosmic microwave background radiation and measurements of the distribution of galaxies will put strong constraints on the interaction between dark energy and all forms of matter. This will in turn have important consequences for particle physics models of dark energy.
Models of inflation with multiple fields (C. van de Bruck)
Studying the dynamics of inflation with more than one scalar field and investigating the resulting spectrum of perturbations. Inflation could be driven by more than one field (multiple field inflation). In this case the primordial fluctuations will be more complicated than usual. The background fields could also alter the dynamics of the inflationary phase. Models with background moduli fields will be investigated in particular.
Brane world cosmology (C. Van de Bruck)
Investigating higher dimensional cosmologies, in particular brane worlds. According to the brane world idea, the standard model particles are confined on a surface (brane) embedded in a higher dimensional space (called the bulk). The consequences for the physics of the early universe will be explored, such as inflation and phase transitions.
The mathematical theory of waves in fluids and plasmas (R. von Fay-Siebenburgen)
This project is about the mathematical aspects of linear and nonlinear waves in fluids and plasmas. In particular, we offer a number of exciting approaches, some of them on the famous solitary waves in the context of fluid dynamics or magnetohydrodynamics (MHD). The student would under my supervision, in collaboration with some other colleagues in my group (SP2RC, Solar Physics & Space Plasma Research Center), who are all well-known international experts with serious authority of the field.
MHD waves are paramount in solar, space and some industrial plasmas. Most such applications are dealing with magnetic flux tubes with a cylindrical waveguide geometry. By studying such waves we try to look into the invisible interior of the Sun and stars. We try to model the eruptive and very dynamic phenomena of the solar atmosphere and Space Weather, that ultimately determine life on Earth.
Among others, the student will work towards obtaining a solution to the Lebovich-Roberts equation governing weakly nonlinear dispersive MHD waves in magnetic flux tubes (sounds scary, but it is not!). Suitability and application of the Inverse Scattering Method will be investigated initially to weakly nonlinear MHD waves described by the famous KdV or Benjamin-Ono equations. Generalisation of these investigations will be made to incorporate the Leibovic-Roberts-Ruderman equation.
Needless to say, the project has absolutely beautiful mathematics (and not the easiest on the planet) with exciting new avenues, transferable skills and with great potentials for a future career.
The spiky Sun: the secrets of spicule formation (R. von Fay-Siebenburgen)
Spicules are dynamic narrow jets propelled upwards (at speeds of approx 20 km/s) from the solar surface into the magnetized atmosphere of the Sun. Spicules carry a mass flux of 100 times that of the solar wind into the low solar corona. With diameters close to observational limits (<500 km), spicules have been largely unexplained since their discovery in 1877. The project aims to develop a novel model of spicule formation in which these plasma jets. For more details see in Nature, vol. 430, pp.536-539
MHD solitons in solar magnetic flux tubes (R. von Fay-Siebenburgen)
Magnetic flux tubes are the building blocks of the solar atmosphere. It is of great importance to understand wave propagation is solar flux tubes. This project aims at investigating a special class of nonlinear waves called solitons in flux tubes where magnetic twist and loop structuring is considered. Applications will be made to coronal loops where it will be aimed at deriving diagnostic information about the loops using the method of inverse scattering method.
Linear MHD standing oscillations in structured coronal loops (R. von Fay-Siebenburgen)
The current wealth of satellite oscillations have revailed that solar atmospheric magnetix flux tubes, mostly called coronal loops support standing wave oscillations when the magnetic loops are exposed to blast waves generated by flare explosions. Analysing such oscillations can give as details about the geometry and internal structure of the loops. In this project we aim at investigating the standing modes of loops that contain and internal loop embedded in a magnetic environment, i.e. we will study the loop-in-loop problem. The eigenmodes of such structures will be compared to data from Solar-B and SDO observations.
The leakage of motion from photosphere to outer corona (R. von Fay-Siebenburgen)
Observations of the Transition Region And Coronal Explorer (TRACE) have shown that photospheric motions can leak into the solar chromosphere and transition region causing transition region moss oscillations.
Surprisingly, it was also shown that moss oscillations a show strong correlation with longitudinal wave propagations into the lower corona. In this project we aim to investigate MHD wave propagation in vertically stratified magnetic flux tubes subject to typical boundary conditions at photospheric heights. Results will be compared to observations of oscillations in the outer corona by the UVCS instrument on-board of the SOHO satellite.
Heating of coronal loops (R. von Fáy-Siebenbürgen)
The solar corona has temperatures of the order of a few million K. In spite of the multitude of efforts spent over half a century it is still not clearly understood how energy is dissipated in the atmosphere of Sun and other late type stars. In this project we study the heating of the magnetic corona due to the mechanism of resonant absortion. Resonant absoprtion is a very popular and efficient heating mechanism in inhomogenenous plasmas. The mechanism is successfully used to explain the damping of loops oscillations, the scattering of acoustic waves in active regions, and, certain aspects of coronal heating. Previous modelling efforts focussed on a 1-D approach while there is an urgent need to extend the theoretical investigations to more realistic structures. This project will investigate the mechanism of resonant absortion in multi-dimensional magnetic configurations. We will use analytical approximations and aim to derive the generalised connection formulae - key concept of resonant waves in inhomogneneous media.
Classical hairy black holes (E. Winstanley)
Hairy black holes are solutions of the Einstein equations with unusual types of matter. Current interest involves looking for black holes with unlimited amounts of `hair', particularly in models arising from string theory or supergravity. Black holes with an unconventionally-shaped event horizon could also be investigated. Key properties of these black holes, such as their stability, thermodynamics, and relation to the AdS/CFT correspondence in string theory, would make excellent PhD projects.
Quantum field theory on black hole spacetimes (E. Winstanley)
The main quantity studied in this approach to semi-classical quantum gravity is the renormalized expectation value of the stress-energy tensor (RSET). We regard the background geometry as fixed, and study quantum fields propagating on this background. The RSET then tells us how the quantum fields affect the geometry. Higher-dimensional black holes are currently attracting much interest in the literature, so a good project would be to develop techniques for computing the RSET in higher dimensions.
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