Applied Mathematics

Research Areas in Applied Mathematics

• Crystal Growth (Jian-Jun Xu): On the right you see a snow flake. When nature generates such a snow flake, it is solving a moving boundary value problem. Next to it you can see on top experimental data of a growing branch of a snow flake and below the solution of the governing equations obtained by asymptotic analysis. Click on the images to see a blowup.
• Mathematical Physics (Charles Roth): Theoretical Atomic, Nuclear and Molecular Spectroscopy.
• Physiology and Nonlinear Dynamics (Leon Glass M. Mackey)
• Computational Fluid Dynamics (Sherwin Maslowe, Jian-Jun Xu, Peter Bartello): The sequence of images below shows the simulation of a rising atmospheric thermal. The colours show the potential temperature variation from blue to red, representing cold to warm fluid. The simulation was initialised (left panel) with a warm layer of fluid near the relatively cooler surface. Buoyancy induces the upwards motion depicted in the other three panels.

• Computational Electromagnetics (Nilima Nigam): The image shows a finite element simulation of a cavity problem. If you click on the image, the triangular mesh is clearly visible; the quantity plotted is the electric potential for a cavity with an inclusion of different electrical properties.
• Computational Biology (David Bryant, Nilima Nigam): Computational mathematical sciences are now having a huge impact on the biological sciences, from models of disease-spread to gene transcription to evolutionary biology.
• Computational Statistical Mechanics (Paul Tupper) Practical and theoretical issues in the simulation of complex systems. Methods for multiscale simulation in materials science.
• Biomolecular networks: (Peter Swain): The ability to process and act on information is fundamental to life. Complex biochemical networks in all living cells transduce signals from the outside world to the genome. Through modelling and collaborative experiment, my research is aimed at uncovering the `design' of these networks, to explore why one network architecture has been adopted by evolution over another, and ultimately to understand how cells `think'.
  
• Control Theory for Partial Differential Equations (Georg Schmidt): Controlling the behaviour of physical systems modelled by partial differential equations through the choice of boundary data. Recent interests are centered on vibrating flexible systems.


• Optimization (Sanjo Zlobec, Neville Sancho, J.-L. Goffin): The figure on the right was discovered in a cave in Spain. It is about 13 millennia old and it depicts the oldest optimization problem we are aware of. The range of the caveman's arrow depends on the projection angle (parameter). The problem of determining the angle that yields the maximal range, subject to the gravitational force, can be formulated and studied as a stable convex parametric programming model. The parallel arrows on the right of the caveman appear to depict the solution (optimal projection angle). In a modern version of this problem, a businessman wants to determine prices of products, subject to economics constraints, that yield the maximal profit. Problems like these can be formulated and solved as mathematical programming (optimization, parametric) models.
• Dynamical Systems (Tony Humphries):The image you see on the left is the attractor of a simple discrete dynamical system arising when one tries to solve a system of ordinary differential equations describing the evolution of a prey and a predator in a common habitat. The exact solution is known to be cyclic, so the numerical scheme should have this property as well. Inside the orange area the chosen numerical scheme has this property, outside it becomes useless. But what is the structure of the boundary ?

 

Research Seminars  

• Applied Mathematics seminar.
• Computational Science and engineering seminar.
• Nonlinear Dynamics in Physiology and Medicine seminar.