Generalised Magnetic Polarizability Tensors:Invariants and Symmetry Groups

Lead Research Organisation: University of Manchester
Department Name: Mathematics

Abstract

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Description New mathematical results were developed to underpin future new types of metal detection technology, which has the potential to detect threat items (such as firearms and knives) in security screening at border controls, public events and transport hubs, as well as important application in the clearance of anti-personal landmines and unexploded ordnance and the sorting of scrap to recover valuable metals. This involved developing new forms of object characterisations with minimal representations in terms of harmonic polynomials first for a scalar problem relevant for finding hidden magnetic objects in magnetometry and then for the vectorial eddy current problem relevant for finding hidden conducting magnetic objects with metal detection. For the latter, the behaviour of the new forms of object characterisation with frequency was investigated. Computational approaches for computing the basis needed for new forms of minimal object characterisation were released as open source scripts on github. In collaboration with group led by Professor Peyton, The University of Manchester, measurement of the new forms of object characterisation were undertaken and their spectral (frequency behaviour) was shown to be in close agreement with the computed characterisations for a range of different materials.
Yes


This award has shown for the first time that generalised magnetic polarizability tensors can be both measured and computed. These new forms of object characterisation have the potential to lead to new forms of metal detection technology aimed at identifying hidden conducting objects with greater accuracy. This has potential important uses in the defence, manufacturing and security industries.
Exploitation Route We are continuing our colaboration with engineers developing demining equipment, scrap metal sorting, civil engineering, severity, forensics and archeology to develop improved metal detection and identification methods
Sectors Aerospace

Defence and Marine

Agriculture

Food and Drink

Construction

Environment

Culture

Heritage

Museums and Collections

Security and Diplomacy
 
Description This project has developed new minimal object characterisations using harmonic polynomials. Compared to previous generalised polarizabilty tensor characterisations, these require fewer coefficients to characterise an object to a given rank. Furthermore, an approach has been developed to determine those coefficients that are invariant to object rotation when an object is a member of a given symmetry group. This approach has the potential to provide invariants for object characterisations using higher polarizabilty tensors and has the potential to be used in the next-generation of detection technology for finding unexploded ordnance and landmines. The results of this research have been published in a number of research articles and have been promoted in research seminars and at conferences. The mathematical developments have been used to develop the Mathematica notebooks that are released as open software on a GitHub page.
First Year Of Impact 2022
Sector Aerospace, Defence and Marine,Agriculture, Food and Drink,Construction,Environment,Government, Democracy and Justice,Manufacturing, including Industrial Biotechology,Security and Diplomacy
Impact Types Societal

Economic
 
Title MPT Calculator (new version) 
Description Python code using FEM to calculate magnetic polarizability tensors 
Type Of Technology Software 
Year Produced 2023 
Open Source License? Yes  
Impact Used by metal detector researchers in engineering 
 
Description Rich and Nonlinear Tomography - a multidisciplinary approach, Newton Institute programme 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Industry/Business
Results and Impact Rich and Nonlinear Tomography - a multidisciplinary approach was a 6 month programme at the Isaac Newton Institute for Mathematical Sciences in Cambridge. Around 70 participants came for visits from 3 weeks to 6 months to collaborate, and we held 4 workshops with on average 100 participants. We had participants from academia, industry and government from around the world working on Astronomy, radar, medical imaging, non-destructive testing, cancer treatment, materials science. They worked together with mathematical specialists on theory, numerical analysis and statistics.
Year(s) Of Engagement Activity 2023
URL https://www.newton.ac.uk/event/rnt/
 
Description School talk Manchester 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Schools
Results and Impact Talk to sixformers in Manchester on mathematics of demiining
Year(s) Of Engagement Activity 2019
 
Description Talk at IMA Conference on Inverse Problems from Theory to Application 2022 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Around 50 attendees from academia and industry attended my talk at the IMA Conference on Inverse Problems from Theory to Application that was held in Edinburgh, which sparked questions and discussion afterwards, and led to requests for further information.
Year(s) Of Engagement Activity 2020