Dr William J. Parnell

I am a Faculty Research Fellow and Lecturer in Applied Mathematics in the School of Mathematics at the University of Manchester.

My research is concerned with modelling the constitutive behaviour of complex inhomogeneous materials, using and developing the theories of homogenization and micromechanics. I am also interested in multiple scattering theory and canonical wave scattering problems. See my research page for more details.

I work with Professor David Abrahams, also in the School of Mathematics at Manchester. Together we have developed various models of composite media and in particular have a close working relationship with the Theoretical Acoustics Group at Thales Underwater Systems with whom we currently have a number of ongoing research projects including a CASE PhD studentship.

Together with Dr Quentin Grimal from the Laboratoire d'Imagerie Parametrique at the Universite Pierre et Marie Curie in Paris, I have developed models of wave propagation through cortical bone. Specifically we are interested in how homogenization techniques can be used to validate experimental ultrasound data to measure wavespeeds in cortical bone.

I am heavily involved in the recent efforts to collaborate with French based researchers who also work on wave propagation problems. This is being done primarily through the channels of the Mathmondes workshops and the GDR. With respect to the latter I am the UK theme leader of the "nonlinearity" theme.

I am particularly interested in the problem of wave propagation through an inhomogeneous material which has undergone pre-stress (finite deformation). In relation to this I have recently started a programme of experimentation on rubbery composite media. This has been achieved via a collaboration with Dr Joao Fonseca from the School of Materials , Manchester.

I have also recently done some work on multiple scattering in pre-stressed rubbery media when visiting Prof Jon Chapman in OCIAM, University of Oxford.