Associate Professor Diane Donovan

Reader

Mathematics
Faculty of Science
dmd@maths.uq.edu.au
+61 7 336 51354

Overview

Associate Professor Diane Donovan received her PhD from The University of Queensland in 1987 and has been an integral member of the Discipline of Mathematics and assoicated Schools since that time.

She has two main research streams.

1) The application of polynomial chaos expansions for the modeling of physical problems involving uncertain parameters. We are developing methods to accurately and efficiently explore subsurface geometry. The current work is focussed on problems related to groundwater levels, gas extraction and storage. This work is joint with the Centre for Coal Seam Gas at the University of Queensland.

2) The study of mathematics structures, both discrete and continuous, and their applications to problems in science and engineering. Of particular interest is the development and testing of methods for robust sampling techniques. This interests is supported by a long history of publishing on experimental design, block designs, latin squares and associated algebraic structures.

Research Interests

  • Applications of Continuous Mathematical Structures
    Computer simulations are being developed based on mathematical models that seek to forecasts natural processes, such as rainfall patterns or capacity of subsurface water/gas reservoirs. Scientifically two problems arise: It is hard to build computer simulations that capture the full complexity of physical processes. For instance, how do we model the movement of water through interconnecting aquifers deep underground? In addition, often there is a shortage of field data, which can vary across regions. For instance, can we accurately quantify local rainwater runoff rates, seepage rates and penetration depths? Traditional scientific methods struggle to capture the uncertainty in these natural processes. My research takes an alternate approach. Using polynomial chaos expansion technqiues I use a smallish amount of field data, couple it with a few implementations of the complex model, and construct “approximate” forecasting tools. The interplay of the mathematical theory results in fast and accurate forecasting tools.
  • Applications of Discrete Mathematical Structures
    Discrete structures, such as latin squares, have many diverse applications, some of the best known being in the design of experiments, in biotechnology and in information security. One area of interest is the identification of defining sets (or critical sets) for these structures; that is, a minimal subset of entries which uniquely defines the structure. One of the most fundamental and interesting questions relating to defining sets is that of the spectrum or the set of allowable sizes. Other areas of research interest involve applying combinatorial techniques to problems in information security, and to applications in biotechnology, energy markets and cognitive reasoning.

Qualifications

  • Fellow, Australian Mathematical Society
  • FTICA
  • PhD, The University of Queensland
  • Bachelor of Arts (Honours), La Trobe University
  • Diploma of Education, La Trobe University

Publications

View all Publications

Available Projects

  • Modelling and simulation problems for water/gas reservoir estimation

    Experimental design for problems in geosciences and petroleum engineering

    The study of orthogonal designs for enhanced computer experiments, with particular the study of quasigroups, orthogonal latin squares and orthogonal arrays

    The study of trades and their use in establishing existence results for discrete structures

View all Available Projects

Publications

Book Chapter

  • Donovan, D. M., Mahmoodian, E., Ramsay, C. and Street, A. P. (2003). Defining sets in combinatorics: a survey. In C.D. Wensley (Ed.), Surveys in Combinatorics 2003 (pp. 115-174) UK: Cambridge University Press.

  • Donovan, D. M., Khodkar, A. and Street, A. P. (2003). On minimal defining sets in AG( D, 3). In W.D. Wallis (Ed.), Designs 2002: Further Computational and Constructive Design Theory (pp. 103-131) Massachusetts, USA: Kluwer Academic Press.

Journal Article

Conference Publication

  • Burrage, Kevin, Burrage, Pamela, Donovan, Diane and Thompson, Bevan (2015). Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal sampling. In: International Conference On Computational Science, ICCS 2015 — Computational Science at the Gates of Nature. International Conference On Computational Science, ICCS 2015, Reykjavik, Iceland, (1762-1771). 1-3 June 2015. doi:10.1016/j.procs.2015.05.383

  • Hall, Joanne L., Rao, Asha and Donovan, Diane (2012). Planar difference functions. In: 2012 IEEE International Symposium on Information Theory Proceedings (ISIT 2012). ISIT 2012: IEEE International Symposium on Information Theory, Cambridge, MA, USA, (1082-1086). 1-6 July, 2012. doi:10.1109/ISIT.2012.6283019

  • Wood, Leigh N., Vu, Tori, Bower, Matt, Brown, Natalie, Skalicky, Jane, Donovan, Diane, Loch, Birgit, Joshi, Nalini and Bloom, Walter (2011). Professional development for teaching in higher education. In: Mike Thomas and John Hannah, Selected Papers from Volcanic Delta 2011: The Eighth Southern Hemisphere Conference on Teaching and Learning Undergraduate Mathematics and Statistics. Volcanic Delta 2011: The 8th Delta Conference on Teaching and Learning Undergraduate Mathematics and Statistics, Rotorua, New Zealand, (997-1009). 27 November-2 December, 2011. doi:10.1080/0020739X.2011.608864

  • Donovan, D. M., Lefevre, J. G. and Simpson, L. (2008). A discussion of constrained binary embeddings with applications to cryptanalysis of irregularly clocked stream ciphers. In: R. Balakrishnan and C. E. Veni Madhavan, International Conference on Discrete Mathematics (ICDM 2006), Bangalore, India, (73-85). 15-18 December 2006.

  • Donovan, Diane, Loch, Birgit, Thompson, H. B and Thompson, Jayne (2008). Change detection through clustering and spectral analysis.. In: L. Brankovich, Y. Lin and W. F. Smyth, Proceedings of the International Workshop on Combinatorial Algorithms 2007. 18th International Workshop on Combinatorial Algorithms (IWOCA 2007), Newcastle, NSW, Australia, (35-44). 5-9 November 2007.

  • Donovan, D. M., Loch, B., Thompson, H. B. and Thompson, J. (2007). Change detection through clustering and spectral analysis. In: Brankovic, L., Lin, Y. and Smyth, W. F., International Workshop on Combinatorial Algorithms. 18th International Workshop on Combinatorial Algorithms 2007, Lake MacQuarrie, New South Wales, (49-58). 5-9 November, 2007.

  • Donovan, D M, Lefevre, J G and Simpson, L (2006). A discussion of constrained binary embeddings with applications to cryptanalysis of irregularly clocked stream ciphers. In: R Balakrishnan and C E Veni Madhavan, Proceedings of International Conference on Discrete Mathematics (ICDM 2006). International Conference on Discrete Mathematics 2006 (ICDM 2006), Banglaore, India, (75-87). 15-18 December 2006.

  • Vladimirov, I G, Donovan, D M and Thompson, H B (2006). Gibbs equilibrium in interacting particle systems with coordination constrained bonding on Bethe lattices. In: Joe Ryan, AWOCA 2006 17th Australasian Workshop on Combinatorial Algorithms. AWOCA 2006, Uluru & Kings Canyon, Central Austraila, (110-122). July 13 - 19 2006.

  • Cavenagh, N. J., Donovan, D. M. and Hamalainen, C. (2005). Are there three MOLS of Order 10?. In: J Ryan, P Manyem, K Sugeng and M Miller, Proceedings of the sisteenth Australasian Workshop on Combinatorial Algorithms. Australasian Workshop on Combinatorial Algorithms, Ballarat, (57-66). 18 - 21 September 2005.

  • Donovan, D. M., Hamalainen, C. and Khodkar, A. (2004). On greedy critical sets in latin squares. In: Seok-Hee Hong, Proceedings of the Fifteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2004). Fifteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2004), Ballina, N.S.W., Australia, (529-535). 6-9 July 2004.

  • Donovan, D. M., Fu, C.-M. and Khodkar, A. (2002). An investigation of 2-critical sets in Latin squares. In: D. Donovan, Proceedings of the Thirteenth Australasian Workshop on Combinatorial Algorithms. AWOCA 2002, Fraser Island, Queensland, (309-332). 7-10 July, 2002.

  • Donovan, D. M. and Khodkar, A. (2002). Premature partial Latin squares and critical sets. In: E.J. Billington, D.M. Donovan and A. Khodkar, Proceedings of the Thirteenth Australasian Workshop on Combinatorial Algorithms. AWOCA 2002, Fraser Island, Queensland, (115-126). 7-10 July, 2002.

  • Donovan, D. M., Fu, C.-M. and Khodkar, A. (2001). A discussion of 2-critical sets in Abelian 2-groups. In: E.T. Baskoro, Proceeding of the Twelth Australasian Workshop on Combinatorial Algorithms. Australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia, (88-96). 14 July - 17 July 2001.

  • Donovan, D. M. (2000). Interactive Discrete Mathematics. In: R. L. May, G. F. Fitz-Gerald and I. H. Grundy, EMAC 2000. 4th Biennial Engineering Mathematics & Applications Conference EMAC 2000, Royal Melbourne Institute of Technology, Melbourne, (131-133). 10-13th September 2000.

  • Bean, R., Donovan, D. M., Khodkar, A. and Street, A. P. (2000). Steiner trades that give rise to completely decomposable latin interchanges. In: Ljiljana Brankovic and Joe Ryan, Proceedings of the Eleventh Australasian Workshop on Combinatorial Algorithms. Eleventh Australasian Workshop on Combinatorial Algorithms, Hunter Valley, NSW, Australia, (17-30). 20th July - 1st August 2000.

  • Dawson E., Donovan D. and Rahilly A. (1992). Methods for sharing cryptographic keys. In: Conference on Communication Technology, Services and Systems - COMMUNICATIONS '92, Sydney, Aust, (135-139). October 20, 1992-October 22, 1992.

Other Outputs

  • Donovan, Diane Margaret (1987). Topics in balanced ternary designs PhD Thesis, School of Physical Sciences, The University of Queensland. doi:10.14264/uql.2015.44

Grants (Administered at UQ)

PhD and MPhil Supervision

Completed Supervision

Possible Research Projects

Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.

  • Modelling and simulation problems for water/gas reservoir estimation

    Experimental design for problems in geosciences and petroleum engineering

    The study of orthogonal designs for enhanced computer experiments, with particular the study of quasigroups, orthogonal latin squares and orthogonal arrays

    The study of trades and their use in establishing existence results for discrete structures