Research Opportunities

I am currently looking to take on 1 or 2 PhD students and one postdoctoral researcher. Unless otherwise indicated, funding is provided through the Department of Applied Mathematics and Theoretical Physics, as detailed here and here. Please note the required qualifications and deadlines given on those pages.

Modelling of novel metal forming processes (1×PhD, 1×postdoc)

Our current modelling of metal deformation, particularly of sheet metal, is not sufficient for use in the control of metal forming in engineering practice, yet computer simulations are far too slow to be used in real-time for control of metal forming. I am looking for 1 PhD student and 1 postdoctoral researcher to work on the mathematical modelling of novel metal forming manufacturing processes as part of a collaborative multi-disciplinary project funded by EPSRC. The mathematics developed will be used by researchers in the Cambridge University Engineering Department and elsewhere to develop and control flexible forming machinery.

Other partners on this project include the Department of Engineering Sciences at the University of Oxford, Siemens Metals Technologies, Firth Rixson and Jaguar Land Rover.

Applicants should have a mathematics background, or an engineering background with a strong mathematical component. Familiarity with asymptotics is essential, while familiarity with solid mechanics, plasticity and elasticity would be helpful. While the emphasis is on mathematics, some familiarity with computing (either C, Fortran or Matlab) would be advantageous.

Acoustics and stability of flow over acoustic linings (1×PhD)

Noise limits are a serious engineering restriction on the design of civilian aircraft engines. One popular noise reduction technique is to line the inside of the engine intake with a sound-absorbing structure. However, the simple commonly-used model of this situation has recently been shown to be incorrect for technical mathematical reasons. The problem appears to be correctable by accounting for the boundary layer over the acoustic lining. While the effect of viscosity within the boundary layer is important for stability and accuracy, it does not in itself appear to correct the problem.

There are many way a PhD on this topic could proceed. Further details, including relevant references, are available on request.

For this project, familiarity with asymptotics is essential and familiarity with fluid dynamics (particularly waves in compressible fluids) is highly recommended.

Shock waves in curved cylindrical tube (1×PhD)

Shock waves in a straight shock tube are very well understood, and are well modelled by 1D gas dynamics. Little is known about the propagation of shock waves in curved tubes, however, and no comparable complete mathematical description exists.

Two major applications of shock waves in curved tubes are in musical instruments (effectively without an underlying fluid flow) and curved aircraft engine intakes (with a strong underlying fluid flow). Nonlinear sound propagation and shock waves are now thought to be important within brass instruments when played at loud volumes, giving rise to their ``brassy'' sound. Since curved tubes are predicted to have little effect on linear sound waves but potentially a more major effect on shock waves, the study of shock waves in curved tubes is important to answer the question of how the curved shape of a musical instrument affects the sound it produces. Moreover, the focusing effect of curved cylindrical tubes may lead to qualitatively different behaviour than curved rectangular or 2D tubes. For curved aircraft engine intakes, the understanding of the propagation of surge waves is an important design consideration, but is little understood. Preliminary work indicates a planar shock wave remains almost planar while moving through a 2D model of such an intake, although the 3D focusing effect of a cylindrical geometry may well affect this.

For this project, familiarity with asymptotics is essential and familiarity with fluid dynamics (particularly compressible fluids and shock waves) is highly recommended. Further details, including relevant references, are available on request.

© Ed Brambley 2006