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

Publications

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

Anjos, Miguel F., Cheng, Russell C.H. and Currie, Christine S.M. (2005) Optimal pricing for perishable products. European Journal of Operational Research, 166, (1), 246-254. (doi:10.1016/j.ejor.2004.02.015).
Avramidis, A.N., Deslauriers, A. and L'Ecuyer, P. (2004) Modeling daily arrivals to a telephone call center. Management Science, 50, (7), 896-908. (doi:10.1287/mnsc.1040.0236).
Avramidis, A.N. and L'Ecuyer, P. (2006) Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance gamma model. Management Science, 52, (12), 1930-1944. (doi:10.1287/mnsc.1060.0575).
Avramidis, Athanassios N., Chan, Wyean and L'Ecuyer, Pierre (2009) Staffing multi-skill call centers via search methods and a performance approximation. IIE Transactions, 41, (6), 483-497. (doi:10.1080/07408170802322986).
Avramidis, Athanassios N., Channouf, Nabil and L'Ecuyer, Pierre (2009) Efficient correlation matching for fitting discrete multivariate distributions with arbitrary marginals and normal-copula dependence. INFORMS Journal on Computing, 21, (1), Winter Issue, 88-106. (doi:10.1287/ijoc.1080.0281).
Avramidis, Athanassios N. and Wilson, James R. (1998) Correlation-induction techniques for estimating quantiles in simulation experiments. Operations Research, 46 , (4), 574-591. (doi:10.1287/opre.46.4.574).
Baldacci, Roberto, Battarra, Maria and Vigo, Daniele (2009) Valid inequalities for the fleet size and mix vehicle routing problem with fixed costs. Networks, 54, (4), 178-189. (doi:10.1002/net.20331).
Battarra, M., Monaci, M. and Vigo, D. (2009) An adaptive guidance approach for the heuristic solution of a minimum multiple trip vehicle routing problem. Computers and Operations Research, 36, (11), 3041-3050. (doi:10.1016/j.cor.2009.02.008).
Battarra, Maria, Erdogan, Gunes, Laporte, Gilbert and Vigo, Daniele (2010) The traveling salesman problem with pickups, deliveries and handling costs. Transportation Science, 44, (3), 383-399. (doi:10.1287/trsc.1100.0316).
Battarra, Maria, Erdogan, Gunes and Vigo, Daniele (2014) Exact algorithms for the clustered vehicle routing problem. Operations Research (doi:10.1287/opre.2013.1227).
Battarra, Maria, Pessoa, Artur Alves, Subramanian, Anand and Uchoa, Eduardo (2013) Exact algorithms for the traveling salesman problem with draft limits. European Journal of Operational Research, n/a (doi:10.1016/j.ejor.2013.10.042).
Beullens, Patrick and Janssens, Gerrit K. (2011) Holding costs under push or pull conditions - the impact of the Anchor Point. European Journal of Operational Research, 215, (1), 115-125. (doi:10.1016/j.ejor.2011.06.005).
Beullens, Patrick, Muyldermans, Luc, Cattrysse, Dirk and Van Oudheusden, Dirk (2003) A guided local search heuristic for the capacitated arc routing problem. European Journal of Operational Research, 147, (3), 629-643. (doi:10.1016/S0377-2217(02)00334-X).
Currie, C.S.M., Cheng, R.C.H. and Smith, H.K. (2008) Dynamic pricing of airline tickets with competition. Journal of the Operational Research Society, 59, (8), 1026-1037. (doi:10.1057/palgrave.jors.2602425).
Currie, Christine S.M., Williams, Brian G., Cheng, Russell C.H. and Dye, Christopher (2003) Tuberculosis epidemics driven by HIV: is prevention better than cure? AIDS: Official Journal of the International AIDS Society, 17, (17), 2501-2508.
Erdogan, Gunes, Battarra, Maria and Laporte, Gilbert (2014) Scheduling twin robots on a line. Naval Research Logistics (NRL), 1-23. (In Press).
Fleischmann, Moritz, Beullens, Patrick, Bloemhof-Ruwaard, Jacqueline M. and Van Wassenhove, Luk N. (2001) The impact of product recovery on logistics network design. Production and Operations Management, 10, (2), 156-173. (doi:10.1111/j.1937-5956.2001.tb00076.x).
Fliege, Joerg (2011) Multicriteria optimization add-on for the FGS toolbox: technical note. Paris, FR, European Space Agency
Fliege, Joerg, Drummond, Mauricio G. and Svaiter, Benar F. (2009) Newton’s method for multicriteria optimization. SIAM Journal on Optimization, 20, (2), 602-626. (doi:10.1137/08071692X).
Fliege, Joerg, Kaparis, Konstantinos and Khosravi, Banafsheh (2012) Operations research in the space industry. European Journal on Operations Research, 217, (2), 233-240. (In Press).
Fliege, Joerg and Xu, Huifu (2011) Stochastic multiobjective optimization: sample average approximation and applications. Journal on Optimization Theory and Applications, 151, (1), 135-162. (doi:10.1007/s10957-011-9859-6).
Hammond, David and Beullens, Patrick (2007) Closed-loop supply chain network equilibrium under legislation. European Journal of Operational Research, 183, (2), 895-908. (doi:10.1016/j.ejor.2006.10.033).
Izady, Navid and Mahlooji, Hashem (2008) Developing a wide easy-to-generate class of bivariate copulas. Communications in Statistics - Theory and Methods, 37, (12), 1919-1929. (doi:10.1080/03610920801893814 ).
Izady, Navid and Worthington, Dave (2011) Approximate analysis of non-stationary loss queues and networks of loss queues with general service time distributions. European Journal of Operational Research, 213, (3), 498-508. (doi:10.1016/j.ejor.2011.03.029).
Izady, Navid and Worthington, Dave (2012) Setting staffing requirements for time-dependent queueing networks: the case of accident and emergency departments. [in special issue: Operations Research in Health Care. EURO XXIII, 5-8 July 2009, Bonn. The Past and Present of Optimization. EURO XXIV, 11-14 July 2010, Lisbon] European Journal of Operational Research, 219, (3), 531-540. (doi:10.1016/j.ejor.2011.10.040 ).
Kunegis , Jérôme and Fliege, Joerg (2012) Predicting directed links using nondiagonal matrix decompositions. In, IEEE International Conference on Data Mining, Brussels, BE, 10 - 13 Dec 2012. 6pp. (In Press).
Li, Qingna and Qi, Houduo (2011) A sequential semismooth Newton method for the nearest low-rank correlation matrix problem. SIAM Journal on Optimization, 21, (4), 1641-1666. (doi:10.1137/090771181).
Li, Xiaodong, Beullens, Patrick, Jones, Dylan F. and Tamiz, Mehrdad (2009) An integrated queuing and multi-objective bed allocation model with application to a hospital in China. Journal of the Operational Research Society, 60, (3), 330-338. (doi:10.1057/palgrave.jors.2602565).
Lu, Lanting, Currie, Christine S.M., Cheng, Russell C.H. and Ladbrook, John (2010) Classification analysis for simulation of the duration of machine breakdowns. Journal of the Operational Research Society (doi:10.1057/jors.2010.33).
Mellor, G.R., Currie, C.S.M. and Corbett, E.L. (2011) Incorporating household structure into a discrete event simulation model of tuberculosis and HIV. [in special issue: Healthcare] ACM Transactions on Modeling and Computer Simulation, 21, (4), 26:1-26:17. (doi:10.1145/2000494.2000499).
Meskarian, Rudabeh, Fliege, Joerg and Xu, Huifu (2012) Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization. European Journal of Operational Research, 216, (2), 376-385. (doi:10.1016/j.ejor.2011.07.044).
Muyldermans, Luc, Beullens, Patrick, Cattrysse, Dirk and Van Oudheusden, Dirk (2005) Exploring variants of 2-opt and 3-opt for the general routing problem. Operations Research, 53, (6) (doi:10.1287/opre.1040.0205 ).
Nguyen, T.D. and Welsch, R. (2010) Outlier detection and least trimmed squares approximation using semi-definite programming. Computational Statistics & Data Analysis, 54, (12), 3212-3226. (doi:10.1016/j.csda.2009.09.037).
Nguyen, Tri-Dung (2014) A fast approximation algorithm for solving the complete set packing problem. European Journal of Operational Research (doi:10.1016/j.ejor.2014.01.024). (In Press).
Nguyen, Tri-Dung and Lo, Andrew (2012) Robust ranking and portfolio optimization. European Journal of Operational Research, 221, (2), 407-416. (doi:10.1016/j.ejor.2012.03.023).
Nguyen, Tri-Dzung and Welsch, Roy E. (2010) Outlier detection and robust covariance estimation using mathematical programming. Advances in Data Analysis and Classification, 4, (4), 301-334. (doi:10.1007/s11634-010-0070-7).
Qi, Houduo (2009) Local duality of nonlinear semidefinite programming. Mathematics of Operations Research, 34, (1), 124-141. (doi:10.1287/moor.1080.0315).
Qi, Houduo (2011) A semidefinite programming study of the Elfving theorem. Journal of Statistical Planning and Inference, 141, 3117-3130. (doi:10.1016/j.jspi.2011.03.033).
Qi, Houduo and Sun, Defang (2010) Correlation stress testing for value-at-risk: an unconstrained convex optimization approach. Computational Optimization and Applications, 45, (2), 427-462. (doi:10.1007/s10589-008-9231-4).
Qi, Houduo and Sun, Defeng (2011) An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem. IMA Journal of Numerical Analysis, 31, 491-511. (doi:10.1093/imanum/drp031).
Smith, H.K., Laporte, G. and Harper, P.R. (2009) Locational analysis: highlights of growth to maturity. [in special issue: Milestones in OR] Journal of the Operational Research Society, 60, (S1), S140-S148. (doi:10.1057/jors.2008.172).
Smith, Honora, Harper, Paul and Potts, Chris N. (2012) Bicriteria efficiency/equity hierarchical location models for public service application. Journal of the Operational Research Society, 64, 500-512. (doi:10.1057/jors.2012.68).
Smith, Honora K., Harper, Paul R., Potts, Chris N. and Thyle, Ann (2009) Planning sustainable community health schemes in rural areas of developing countries. European Journal of Operational Research, 193, (3), 768-777. (doi:10.1016/j.ejor.2007.07.031).
Strang, Gilbert and Nguyen, Tri (2004) The interplay of ranks of submatrices. SIAM Review, 46, (4), 637.
Upstill-Goddard, R., Eccles, Diana, Ennis, Sarah, Rafiq, Sajjad, Tapper, William, Fliege, Jörg and Collins, Andrew (2013) Support vector machine classifier for estrogen receptor positive and negative early-onset breast cancer. PLoS ONE, 8, (7), e68606. (doi:10.1371/journal.pone.0068606).
White, Leroy, Smith, Honora K. and Currie, Christine S.M. (2011) OR in developing countries: A review. European Journal of Operational Research, 208, 1-11. (doi:10.1016/j.ejor.2010.02.015).

Article

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).
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).
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).
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: