Mathematical Sciences

Research Group: Applied Mathematics

The research focus of Applied Mathematics is on Mathematical Modelling and Mathematical Physics

Currently Active: Yes

Group Overview

Mathematics on large scale

Mathematics on large scale

We carry out internationally leading research in a wide range of areas relating to the Mathematics of Nature. Our main focus is on Mathematical Modelling and Mathematical Physics, and we engage in and collaborate on a wide range of exciting modern problems.

Our research activities form a key part of the new Southampton Centre for Fundamental Science (jointly with colleagues in High-energy Theory and Astronomy), Southampton Initiative for Mathematical Modelling (SIMM), the EPSRC funded Centre for Nanostructured Photonic Metamaterials in Southampton and the University-wide activities on Quantum Coherence.

Solitons

Solitons

The group has an active base of research students and welcomes applications for postgraduate study in any of its fields of interest: more information may be found in the Postgraduate Opportunities section of our website.

Enquiries concerning joint or interdisciplinary research and possible research topics are also very welcome.

You can apply for the PhD programme via this link.

Research groups:

General Relativity. One of the largest classical relativity groups anywhere in the world. Their research is focussed on Einstein's classical theory and its applications to astrophysics with particular interest in the modelling of gravitational-wave sources, and the dynamics of black holes and neutron stars.

Mathematical Modelling. Strong interests in applications of mathematics to medicine and biotechnology, industrial modelling, design of experiments and asymptotics. The group participates in international industrial study groups that provide a rich source of important practical problems.

Mathematical Optical Physics. Research covers a wide range of areas, from fundamental wave phenomena and quantum systems to liquid crystals, ultracold atomic gases, quantum optics and nanofabricated metamaterials.

Key Facts

  • Research projects include a variety of topics from neutron stars to superfluids and to mathematical modelling

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Publications

Selected publications associated with this group from the University of Southampton's electronic library (e-prints):


Key Publications

Dolan, Sam, Barack, Leor and Wardell, Barry (2011) Self-force via m-mode regularization and 2+1D evolution. II. Scalar-field implementation on Kerr spacetime. Physical Review D, 84, (8), 084001-[21pp]. (doi:10.1103/PhysRevD.84.084001).
Ho, Wynn C.G., Maccarone, Thomas J. and Andersson, Nils (2011) Cosmic recycling of millisecond pulsars. Astrophysical Journal Letters, 730, (2), L36-[5pp]. (doi:10.1088/2041-8205/730/2/L36).
Foster, J.m., Please, C.P. and Fitt, A.D. (2011) The slow spreading of a viscous fluid film over a deep viscous pool. Journal of Engineering Mathematics, 71, (4), 393-408. (doi:10.1007/s10665-011-9460-x).
Podoliak, Nina, Buchnev, Oleksandr, D'Alessandro, Giampaolo, Kaczmarek, Malgosia and Sluckin, Timothy J. (2010) Large effect of a small bias field in liquid-crystal magnetic transitions. Physical Review E, 82, (3), 030701-[4pp]. (doi:10.1103/PhysRevE.82.030701).
Radnaev, A. G., Dudin, Y. O., Zhao, R., Jen, H. H., Jenkins, S. D., Kuzmich, A. and Kennedy, T. A. B. (2010) A quantum memory with telecom-wavelength conversion. Nature Physics, 6, (11), 894-899. (doi:10.1038/nphys1773).
Martin, A.D. and Ruostekoski, J. (2010) Quantum and thermal effects of dark solitons in a one-dimensional bose gas. Physical Review Letters, 104, 194102-[4pp]. (doi:10.1103/PhysRevLett.104.194102).
Ho, Wynn C. G. and Heinke, Craig O. (2009) A neutron star with a carbon atmosphere in the Cassiopeia A supernova remnant. Nature, 462, (7269), 71-73. (doi:10.1038/nature08525).
Kunzinger, Michael, Steinbauer, Roland and Vickers, James A. (2009) Sheaves of nonlinear generalized functions and manifold-valued distributions. Transactions of the American Mathematical Society, 361, 5177-5192. (doi:10.1090/S0002-9947-09-04621-2).

Staff

Members of staff associated with this group: