Associate Professor Wayne Read

Head of School Room: MP152 Phone: +61 7 4781 4117 Email: wayne.read@jcu.edu.au

CAREER PROFILE:

I completed an Honours degree in Mathematics at James Cook University in 1982, and then commenced doctoral studies in the School of Engineering (Civil and Systems) in 1983. The title of my thesis was Wave Groups in the Time and Frequency Domains, and the degree was conferred in 1987. During the final stages of writing up my thesis in late 1985, I accepted a lecturing position in the Department of Computer Science (now the School of Information Technology). In 1989 I transferred to the Mathematics Department, where I was promoted to Senior Lecturer in 1993. I have been the Head of the School of Mathematical and Physical Sciences since June 2002.

TEACHING:

I have taught a wide variety of subjects in Computer Science (Information Technology) and pure and applied Mathematics since I commenced lecturing in 1985. My main teaching responsibilities over the past five years have been MA1000 (Mathematical Foundations), MA1721 (Computing Mathematics) and part of PH3003 (Classical Mechanics). Currently I am teaching parts of MA3109 (Applied Complex Variable Theory), MA3605 (Operations Research and Modelling) and PH3003 (Classical Mechanics). Please visit http://www.amsi.org.au/ to see the range of job opportunities available for a trained mathematician.

RESEARCH INTERESTS:

• Modelling transport processes in porous media
  I started research on solving groundwater flow problems not long after I finished my doctorate. This is an excellent area for a mathematical modeller to research in, to help quantify our understanding of the physical processes involved. This is particularly so, when we consider that experimental and field data is of limited help. Although this may seem counter-intuitive, it is very difficult to capture anything other than the bulk macroscopic features of the flow, due to the difficulty of estimating parameters like the hydraulic conductivity in field data or eliminating unwanted parameter variability in experiments. Mathematical models provide a detailed quantitative understanding of the macroscopic features of flow at comparatively little or no cost. Saturated soil can be modelled by linear elliptic equations, whereas unsaturated soil is dominated by strongly non-linear processes that depend on the percentage of moisture present in the soil. However, some linear techniques are applicable in the vadoze zone, as the unsaturated soil profile is sometimes called. My research is this area is primarily focused on finding series solutions for two and three-dimensional saturated flow (or seepage) problems. These solutions provide the water table location and the seepage face length (when the entire soil profile is not saturated), the flow paths that the fluid takes through the soil and the velocity of the fluid in the soil. Once the flow field is known, the advection and diffusion of solutes such as salt can be quantified by solving the transport (ie, advection-diffusion) equation. I am currently investigating series methods for solving transport problems in the saturated zone. In the vadoze zone, steady unsaturated flow (or infiltration) can be modelled using the quaisi-linear approximation and I am researching series methods for this class of problem.
• Series solutions to partial differential equations
  This research area is closely related to my main research area, discussed above. I conduct research into series solutions to partial differential equations, with the primary focus on elliptic free boundary problems. Locating the water table in a hillslope subject to steady recharge is an example of an elliptic free boundary problem. The techniques that I have developed allow the use of classical series solutions, obtained directly using separation of variables, on arbitrary geometries. These ‘analytic’ series methods are related to (but not the same as) spectral methods. In conjunction with other members of the school, I am developing general methods for free boundary problems with applications in porous media, as well as flow over topography. Both these types of problem are challenging computationally, for different reasons. For groundwater problems, the very long aspect ratios typical in practical applications make it difficult to resolve the water table location, even though it is smoothly varying. Equally, the nonlinear boundary condition and standing wave solutions are difficult to obtain for steady flow over relatively high mountains.
• Restricted occupancy models
  Restricted occupancy models are a generalization of the classic problem of enumerating the number of ways of placing like coloured balls in a set of urns. In the more general problem, there is a maximum and minimum number of balls that any urn can take. The restricted occupancy model can be used to analyse the storage complexity of secondary memory data structures on a computer, where large data sets are stored on magnetic or optical disk. The main storage method used is called a B-tree, a type of m-way search tree. I am interested in applying these models to other data structures and to biological processes.

RELEVANCE OF RESEARCH:

• Before we can treat soil salinity and acidity, we need to quantify flow paths and velocities through the soil. My research in this area is covered by two of National Research Priority Goals: A1 “Water – a critical resource” and “A3 “Overcoming soil loss, salinity and acidity”. My research in this area also is aligned with two of James Cook University’s areas of research strength: E “Earth Sciences” and M “Marine Sciences”.
• My research interest in restricted occupancy problems has some coverage in the National Research Priority Goals: A5 “Sustainable use of Australia’s biodiversity” and B4 “Smart Information Use”. The application to biological modelling is covered by one of James Cook University’s areas of research strength: M “Marine Sciences”.
• At a personal level, my research allows me to apply theoretical, mathematical models to real world problems and so enhance our understanding and knowledge of these problems.

For detailed information on the National Research Priority Areas, go to the JCU web page http://www.jcu.edu.au/office/research_office/Codes/NRP-G.html.
For detailed information on James Cook University’s areas of research strength, go to the JCU web page http://www.jcu.edu.au/office/research_office/Codes/AoRF.html.

SCHOLARLY ACTIVITIES:

• Member of the Australian Mathematical Society and ANZIAM, its Applied Mathematics branch, the American Geophysical Union and the ACM (Association for Computing Machinery).
• Awarded the G.N. Alexander medal in Hydrology (jointly with Prof. R.E. Volker) in 1991, by the Australian Institute of Engineers.
• Voted the best non-student paper presented at the Queensland Mathematics Society Conference (QANZIAM ’93), held at Alexander Headlands, in 1993, one of the best six non student papers presented at the Australian & New Zealand Industrial & Applied Mathematics Conference (ANZIAM'96), held in Masterton (New Zealand),in 1996.
• Invited to chair sessions at the Australian & New Zealand Industrial & Applied Mathematics Conferences ANZIAM’95, ANZIAM’96, ANZIAM’97, ANZIAM’99 and the International Conferences on Computational Techniques & Applications CTAC'95, CTAC'99, CTAC'01, CTAC’03, CTAC’04.
• Program committee member CTAC’01, CTAC’03, CTAC’04, CTAC’06.
• Committee member on the CTAC management group, 2001--present.
• Invited to present a paper at the Queensland Mathematics Society Conference (QANZIAM’03) held on Stradbroke Island, in 2003.
• I have refereed papers for the following Journals: The ANZIAM Journal, AMS Gazette, Information Processing Letters, ANZIAM Journal (E), AMS Bulletin, Computational Techniques and Applications, Mathematical and Computer Modelling.

STUDENT PROJECTS

PUBLICATIONS (Last 5 years & Career Best):

REFEREED JOURNAL PAPERS AND BOOK CHAPTERS:

1. Read W.W., Sneddon G.E. & Bode L., A Series Method for the Eigenvalues of the Advection Diffusion Equation, The ANZIAM Journal, 45(E), 2004, pp. C773--C786.

2. Read W.W., Belward, S.R. & Higgins P.G., A Potential Update Method for Series Methods in Steady Seepage, The ANZIAM Journal, 45(E), 2004, pp. C759--C772.

3. Belward, S.R., Read W.W. & Higgins P.G., Accurate Series Solutions for Non-Linear Flow Over Topography, The ANZIAM Journal, 44(E), 2003, pp. C96--C113.

4. Read W.W., Higgins P.G. & Belward, S.R., An Efficient Iterative Scheme for Series Solutions to Laplacian Free Boundary Problems, The ANZIAM Journal, 44(E), 2003, pp. C644--C663.

5. Read, W.W. & Sneddon G.E., A Little Known Result on Systems of Ordinary Differential Equations, The Australian Mathematical Society Gazette, 28 (2), 2001, pp.63--66.

6. Tritscher, P., Read, W. W., Broadbridge, P. & Knight, J.H., Steady Saturated-Unsaturated Flow in Irregular Porous Domains, Mathematical and Computer Modelling, 34 (1&2), 2001, pp. 177--194.

7. Read W.W., An Iterative Analytic Series Method for Laplacian Problems with Free and Mixed Boundary Conditions, The ANZIAM Journal, 42(E), 2000, pp. C1238--C1259.

8. Tritscher P., Read W. W. & Broadbridge P., Specific Yield for a Two-Dimensional Flow, Water Resources Research 36 (6), 2000, pp. 1393--1402.

9. Hollins S.E., Ridd P.V. & Read W.W. (2000), Measurement of the Diffusion Coefficient for Salt in Salt Flat and Mangrove Soils, Wetlands Ecology and Management 8, 2000, pp. 257--262.

CONFERENCE ABSTRACTS:

1. Read W.W., Belward, S.R. & Higgins, P.J., Steady Seepage in Three--Dimensional Aquifers, Proceedings 41st ANZIAM Conference (Napier, N.Z.), 2005.

2. Belward, S.R., Read W.W. & Higgins, P.J., Series Methods for Atmospheric Interfacial Waves, Proceedings 41st ANZIAM Conference (Napier, N.Z.), 2005.

3. Higgins, P.J., Read W.W. & Belward, S.R., Flow Over Topography with Various Upstream Velocity Profiles, Proceedings 41st ANZIAM Conference (Napier, N.Z.), 2005.

4. Read W.W., Seepage Face Lengths and Flow Paths for Hillslopes With a Horizontal Aquiclude, Proceedings 40th ANZIAM Conference (Hobart), 2004.

5. Read W.W., Belward, S.R. & Higgins P.J., Series Methods For Steady Seepage With Mixed Boundary Conditions, Proceedings 5th International Congress on Industrial & Applied Mathematics (ICIAM 2003) (Sydney), 2003.

6. Read W.W., Sneddon G.E. & Bode L., A Spectral Method for Transport in Irregular Aquifers, Proceedings 5th International Congress on Industrial & Applied Mathematics (ICIAM 2003) (Sydney), 2003.

7. Read W.W., Belward, S.R. & Higgins P.J., Accurate Derivatives of Analytic Series Solutions, Proceedings 38th ANZIAM Conference (Canberra), 2002.

8. Read W.W., Analytic Series Solutions for Laplacian Mixed Boundary Value Problems, Proceedings 37th ANZIAM Conference (Barossa Valley), 2001.

CAREER BEST PUBLICATIONS:

1. Tritscher, P., Read, W. W., Broadbridge, P. & Knight, J.H., Steady Saturated-Unsaturated Flow in Irregular Porous Domains, Mathematical and Computer Modelling, 34 (1&2), 2001, pp. 177--194.

2. Read W.W., Hillside Seepage and the Steady Water Table I: Theory, Advances in Water Resources 19 (2), 1996, pp. 63--73.

3. Volker R.E. & Read W.W., Solutions for Water Table Shape andSeepage Face Location on Long Hillslopes Under Irrigation, Civil Engineering Transactions, I.E.Aust. CE 32 (1), 1990, pp. 1–6.