Background

In July 2013 a two-year collaborative EPSRC funded project (EP/K039865/1) with Professor Lionheart, School of Mathematics, University of Manchester, started. The project intends to build links with the world leaders in the field of characterization of objects by means of asymptotic formulae and polarisation tensors. This mathematical description allows the shape and material properties of the inclusion to be described and offers possibilities for the low-cost solution of inverse problems.

Currently the focus is the metal detection problem and investigating how the sensitivity of field measurements due to magnetic induction associated with a conducting object can be expressed in terms of new classes of polarization tensors. The ability to form a library of these tensors for different objects has important implications for the identification of metallic targets in applications such as airport and event security, the detection of unexploded ordnance, improvement of food safety by the detection of foreign bodies and the location of archaeological artefacts.

Links have been established with Professor Ammari, Ecole Normale Supérieure, France; Professor Kang, Inha University, South Korea; Professor Peyton, University of Manchester; and Professor Volkov, Worcester Polytechnic Institute, USA.

Research Outputs

Our work has been presented at the following conferences and research seminars:

  • MAFELAP Conference, Brunel University, London 2013
  • Applied Inverse Problems Conference, Daejeon, South Korea 2013
  • Inverse Problems Seminar Series, The University of Manchester, 2013
  • Applied Mathematics Colloquim, Cardiff University, 2014
  • British Applied Mathematics Colloquim, Cardiff University, 2014
  • British Applied Mathematics Colloquim, The University of Cambridge, 2015
  • Engineering Mechanics Institute Conference, Stanford, USA, 2015
  • IMA Conference for Numerical Simulation, The University of Oxford, 2015

The following papers have appeared in peer reviewed journals:

  • P.D. Ledger and W.R.B. Lionheart, The perturbation of electromagnetic fields at distances that are large compared with the object's size, IMA Journal of Applied Mathematics, volume 80 (3): 865-892, 2015 doi: 10.1093/imamat/hxu009
  • P.D. Ledger and W.R.B. Lionheart, Characterising the shape and material properities of hidden targets from magnetic induction data, IMA Journal of Applied Mathematics, volume 80(6): 1776-1798 2015 doi:10.1093/imamat/hxv015.
  • P.D. Ledger and W.R.B. Lionheart, Understanding the magnetic polarizability tensor, IEEE Transactions on Magnetics, in print, 
    doi:10.1109/TMAG.2015.2507169