Applied Mathematics Research Areas

Dr Grant Cox

• Developing continuum mechanical theories of real-life problems
• Modelling the flow of granular materials
• Moving boundaries
• Operations research

Dr Maureen Edwards

• Lie symmetry analysis and the application of Lie groups to nonlinear differential equations. In particular, diffusion-convection equations.

Dr Joanna Goard

• Financial mathematics
• Lie group analysis of differential equations and its generalizations:
  • Constructing new solutions to classes of nonlinear partial differential equations;
  • Comparing the range of applicability of various classical and nonclassical symmetry methods;
  • Placing various ad-hoc methods on the firmer foundations of classical Lie symmetry theory.

Professor James M Hill

• Applied mathematics and nonlinear continuum mechanics including large elastic deformations of rubberlike materials
• Heat transfer
• Diffusion
• Applied probability
• Moving boundaries
• Granular materials
• Nonlinear partial differential equations.

Associate Professor Philip Laird

• Rail development - primarily freight, with emphasis on rail track
  interaction with trains.
• Road pricing, with emphasis on cost recovery from heavy vehicles.
• Energy use in freight transport.
• Rail research has included studies of the adverse effect on transit times and energy efficiency of both terrain and track alignment.

Dr Xiao-Ping Lu

• Elasticity and fracture mechanics: analysis of interacting cracks in elastic media and interface cracks between dissimilar media.
• Numerical methods: boundary element methods (BEM) in elasticity and fracture, and diffusion equations.

Associate Professor Timothy R. Marchant

• Nonlinear waves. The KdV equation and its higher-order approximations. High-order solitary wave interaction. Development of numerical schemes, using finite-difference methods to model solitary wave interactions.
  
• Microwave heating. Development of approximate analytical solutions. Control of thermal runaway. New efficient numerical schemes.
  
• Combustion theory. Accurate approximate analytical solutions for coupled reaction-diffusion equations.
  
• Modelling chemical reactions and combustion theory.

Dr Mark Nelson

• Bioreactor Engineering
• Chemical Reactor Engineering
• Combustion Theory
• Applied Non-Linear Dynamical Systems

Dr Keith Tognetti

• Applied number theory (integer part sequences)
• Equitable sequences and the stick breaking problem
• Periodic points and symmetries of iterates of the gauss map
• Pattern theory (moire patterns)
• Artificial life (2 base dna)
• A re-examining of the nature of scholarly publications as a result of the many new options opened up now that electronic publication has become economically feasible

Dr Annette Worthy

• The development of mathematical techniques which enable the propagation of signals in optical fibres to be described with a high degree of accuracy.
• The development and implementation of computer aided learning (CAL) modules and mathematical engineering projects for engineering students enrolled in mathematics.

Associate Professor Song-Ping Zhu

• Financial Modelling and Computational Finance: Particularly interested in the pricing of various financial derivatives such as options and convertible bonds. Developing new analytical and numerical solutions.
  
• Computational Mathematics and Numerical Methods: Developing boundary element techniques including the dual reciprocity boundary element method to numerically solve PDEs;
  
• Computational Wave Modeling and Nonlinear Wave Theory: Studying nonlinear waves generated by floating and submerged objects and their interactions; using finite element and boundary element methods to model ocean and coastal water waves;
  
• Applied Mathematical Modeling and Industrial Mathematics: Developing models to study the spread and confinement of oil spills, modeling the pollutant transportation in estuaries and coastal seas and studying environment-related fluid flow problems.