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RA5a: Structure,environment and staffing policyResearch Structure and EnvironmentThe Applied Mathematics Unit forms part of the Department of Mathematical Sciences, which also includes Pure Mathematics and Probability/Statistics. The Unit focuses on two areas, Mathematical Physics and Numerical Analysis, and produces worldclass research in each. Significant recruitment since the last RAE has further strengthened our international standing.
The MATHEMATICAL PHYSICS group is internationally prominent, and has produced 350 highquality research papers in the assessment period. Its work covers several interrelated topics. NonPerturbative Field Theory: Peter Bowcock, Patrick Dorey, Davide Fioravanti, Clifford Johnson, Valya Khoze, Paul Mansfield, Bernard Piette, Anne Taormina, Wojtek Zakrzewski, Roberto Tateo (Visiting Fellow), and 9 research students. String Theory and Gravity: Steven Abel [Institute for Particle Physics Phenomenology], Peter Bowcock, ChongSun Chu, David Fairlie, Ruth Gregory, Bert Janssen, Clifford Johnson, Valya Khoze, Paul Mansfield, Simon Ross, Douglas Smith, Anne Taormina, Dominic Brecher (PDRA), Paul Saffin (PDRA), and 10 research students. Topological Solitons and Nonlinear Dynamics: Davide Fioravanti, Ruth Gregory, Bernard Piette, Richard Ward, Wojtek Zakrzewski, and 8 research students. The Mathematical Physics group forms the major part of a University Research Centre, the Centre for Particle Theory. This is the largest particle theory group in the UK; it is prominent in training graduate students and postdocs, who form an integral part of research activity; a large proportion of them go on to take up permanent academic posts. The current membership of this Centre (staff and graduate students) is 88, comprising 52 in this unit, and 36 in the Department of Physics. In addition, our international standing attracts many visitors. The Mathematical Physics group focuses on the more mathematical aspects, and spans a wide range: from the interface with pure mathematics, through computational mathematics, to quantum field theory, cosmology, statistical mechanics and condensedmatter physics. The Centre for Particle Theory is set to grow significantly in the near future, as a result of the establishment (in October 2000) of the Institute for Particle Physics Phenomenology at Durham. This Institute is jointly funded by PPARC and the University; its resources allow for a new building, four new HEFCEfunded permanent posts, nine shorterterm postdoctoral posts, and extensive visitor, workshop and summerschool programmes. Its Director, James Stirling FRS (returned in UoA 19), is a member of the Department. Both the Mathematical Physics group, and the Particle Theory group in the Department of Physics, will be closely involved in its activities and operation. Indeed, one of the new appointments is in the Mathematics Department, and will strengthen the interactions between the various areas of research in the Centre. The Mathematical Physics group focuses on the more mathematical aspects, and spans a wide range: from the interface with pure mathematics, through computational mathematics, to quantum field theory, cosmology, statistical mechanics and condensedmatter physics.
The purpose of the Centre is to coordinate research, and the postgraduate programme, in Mathematical Physics and Elementary Particle Theory. Its activities include: In addition to this general weekly colloquium, there are several weekly working groups in Mathematical Physics: one on solitons, one on strings and branes, one organized by the postgraduate students, and a more general mathematical physics seminar in which external speakers, postdocs and graduate students give talks; there are also many occasional seminars by visitors. The group is involved in two MSc degrees by advanced study and dissertation: one in Elementary Particle Theory (in collaboration with the Department of Physics), and one in Geometry and Physics (in collaboration with Pure Mathematics). The interests of the NUMERICAL ANALYSIS group centre on partial differential and stochastic equations and their computational treatment. The group runs a weekly seminar in term time. Its work covers a variety of topics which include the following.
Analysis and solution of PDEs: James Blowey, Tony Shardlow, Brian Straughan. Members of the group have a number of very successful ongoing collaborations with leading international and national researchers, for example H Garcke (Inst. Appl. Math, Bonn), J Barrett (Imperial), J King (Nottingham), L E Payne (Cornell), K Hutter (Darmstadt), A Stuart (Warwick), E Buckwar (Manchester) and N Spenley (Unilever). In addition, the group currently has 5 PhD students and is actively recruiting more. Last summer the group hosted the Ninth EPSRC Summer School in Numerical Analysis, which was attended by 56 researchers. James Blowey was an organiser. The Tenth School (in 2002) will again be held in Durham. The work of the group has centred on traditional numerical analysis. Due to recent appointments the emphasis is changing, so while analysis of finite element and spectral methods and derivation of sharp error bounds will still be important, the direction is moving toward accurate computation of applied mathematics problems, including analysis of particle methods in fluid dynamics. Research Support Structures The Department has a Research Committee, the duties of which include promoting the pursuit of research excellence in the department, monitoring research activity, advising on Research Leave applications, and encouraging applications for external funding and Fellowships. A Visiting Fellowship scheme (funded by outside donations) has recently been established; this enables visiting fellows (up to three each year) to spend a term in Durham working within the Department. The unit is able to call on the University's REDSS Office (Research and Economic Development Support Service), which includes specialist teams working on research grant applications and contracts. All postgraduates are members of the University's Graduate School. The Graduate School runs an extensive induction and training programme, tailored to graduate students in the Faculty of Science; and provides an overarching structure for the monitoring of postgraduate student progress. In addition, all fulltime research students are members of one of the University's Colleges or Societies. In the Department, each student prepares an annual report on his/her activity and progress during the preceeding year, and is interviewed by two members of staff (neither of whom is the supervisor). The Department also operates a formal procedure for assessing whether firstyear students may progress to their second year. The Department actively encourages research students to attend conferences and summer schools which will benefit their development, and gives full financial support. To support most effectively its specialised needs, the Department has developed its own highperformance computer facilities. Each researcher has a machine in his or her office (usually a Linux PC) linked to a network of twenty SUN workstations, giving access to a collection of mathematical software and specialised packages. These are connected in turn with the University Ethernet and central facilities. As well as its paper collections, the University library now subscribes to over 100 electronic mathematics journals, including all leading journals and databases, which researchers can access from their offices. The Department has two Computer Officers who maintain and upgrade the network and its outside links. Staffing Policy The Department's staffing policy is guided by the University Strategy of strengthening internationallycompetitive research. We endeavour to enable all staff to achieve their full potential; and we provide particular support to younger members. Two mentors are appointed for all new lecturers. The mentors are experienced permanent members of staff (at least one of them in the same subject area as the new appointee). One mentor is appointed for each research assistant or fellow. Younger members of staff are given a lighter teaching load (for example, new staff have a twothirds load during their first two years), and little administration, so that they may concentrate more time on their research. The University has recently established a Centre for Teaching, Learning and Research in Higher Education which has universitywide responsibility for academic staff development programmes. These include workshops on supervising research students, making research grant applications, career planning for contract research staff and writing up research for publication. In order to allow younger members of staff to become members of the wider community we encourage them to attend seminars, workshops and meetings, or make research visits to other Universities and research institutes, wherever possible. We take as flexible a view as possible to rearranging teaching commitments so that opportunities to attend important conferences or make contacts are not missed. The department has a generous policy of financial support for travel (both UK and overseas) for younger members of staff, administered by the Chairman, who also makes recommendations to the central University Research Committee for research leave (the current entitlement is one term in nine, subject to merit). Since RAE96, there have been many staffing changes in the MATHEMATICAL PHYSICS group. Of three temporary lecturers (Peter Bowcock, Lucien Hardy and Robert Weston), the first has been appointed to a permanent lectureship, while the other two have taken up positions elsewhere. Following the untimely death of Euan Squires in 1995, the Unit decided not to continue its activity in the Foundations of Quantum Mechanics. Edward Corrigan FRS moved elsewhere in 1999, but continues as Visiting Professor, and his area of research is being actively continued by several other members of staff; he was replaced by two young lecturers (Clifford Johnson and Simon Ross). Anne Taormina, who was here in 1996 as an Advanced Fellow, and subsequently as a Leverhulme Fellow, has now been appointed to a permanent post, as a forward replacement for David Fairlie. The policy of the group has been to appoint young, highlyactive staff, with established research reputations; in addition to Peter Bowcock, six new lecturers have recently taken up positions: Douglas Smith and Simon Ross in 1999; Clifford Johnson and Anne Taormina in 2000; Steven Abel and ChongSun Chu in 2001. Note that Mike Pennington (who was returned in 1996) is this time being returned in UoA19 (Physics); while Valya Khoze was in UoA19 previously, so he is not a new member of staff. Postdocs and research fellows who have been members of the group during the assessment period, include: Kim Baskerville, Christos Charmousis, Anastasia Doikou, Jacek Dziarmaga, Roberto Emparan, Bertrand Eynard, Davide Fioravanti, Georg Gandenberger, Meik Hellmund, Theodora Ioannidou, Marco Rossi, Ivo Sachs, Roberto Tateo, Tatsuya Ueno and Robert Weston. Five of these now have permanent academic positions, while almost all the rest have continued as postdocs/fellows elsewhere; Fioravanti and Tateo, after a period away from Durham, have now returned here. The NUMERICAL ANALYSIS group has begun a significant rebuilding programme, and in 1999 the Department decided to strengthen and enlarge the section, initially by the appointment of a Professor, a new Lecturer, and two teaching assistants (PhD students who undertake a limited amount of teaching). This has necessitated substantial changes, and the group is now focusing on numerical and applied analysis in applied mathematics problems. Professor Brian Straughan took up the Chair (in Computational Mathematics) in September 2000, and a new lecturer (Tony Shardlow) also arrived in September 2000. James Blowey was promoted to Senior Lecturer in March 2001. A PDRA (Stephen Langdon) was here from March 1999 to September 2000. One teaching assistant began in October 1999, and another in January 2001. Tony Ware (temporary lecturer) has moved to a permanent post in Canada. SelfAssessment We have achieved almost all of the objectives set out in RAE96. Two particular aspects are worth commenting on. First, our strategy is to appoint the best available researchers who will fit into our two subgroups, without being too prescriptive about their area of research. This has led to a considerable strengthening of our activity in, for example, string theory and gravity, and computational mathematics. Secondly, we benefited significantly from our membership of the EU networks referred to in RAE96; and we are actively involved in preparation of two new proposals. In MATHEMATICAL PHYSICS, we have made significant contributions during the assessment period to the development of quantum field theory, string theory and gravity. We have played an important part in the testing and extension of SeibergWitten theory and the AdS/CFT correspondence, in the construction of new gauge/gravity duals extending the Maldacena conjecture, and in their use to study black holes and gravity. New gravity solutions have been found describing branes in Mtheory and cosmology extending the RandallSundrum construction, and the noncommutativity of Dbranes in background fields has been demonstrated. We have maintained our strong international profile in the study of exactlysolvable models in two dimensions, both conformal and nonconformal. We have also applied semiclassical methods to elicit many new properties of Skyrmions and solitons. In NUMERICAL ANALYSIS, we have significantly contributed to the numerical analysis of thin film problems, to the ergodic behaviour of numerical approximations of stochastic pdes, and to the analysis and computation of the equations of porous flows. All of this work has had a high international impact, as is reflected in the citations that our papers attract, and the many invitations that members of the unit receive to speak at international conferences and schools. These and related items are detailed in RA6, while further information on our research achievements is available at http://maths.dur.ac.uk/ We believe that the Applied Mathematics Unit is significantly stronger than it was at the last RAE. Our arrangements for facilitating and promoting research are working well. Two of the permanent staff members returned in 1996 are no longer with us; but their place has been taken by eight new longterm staff, all of them distinguished and highlyactive in research. Morale, enthusiasm and vitality are particularly high, partly because of the young age profile of staff. The standing of the Mathematical Physics group attracts a large number of excellent graduate students and postdocs, who contribute to the vibrant environment. The vitality of the Numerical Analysis group has been significantly enhanced by recent appointments and by the greater number of research students. Copyright 2002  HEFCE, SHEFC, ELWa, DEL Last updated 17 October 2003
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