Recent events in the UK (eg the 2019 London Bridge Attack, in which 2 people were killed, and the Terror Related Streatham Incident, where 2 people were stabbed) have highlighted the need for improved early stand-off detection of threats, which include knives, guns and improvised explosive devices. To be able to characterise and identify these small objects at stand-off distances in the order of 10s metres from the sensor using electromagnetic field measurements requires frequencies in the 300MHz to 12GHz range, where wave propagation effects are important. Frequencies in this range have also been traditionally been used in radar (radio detection and ranging) for large objects (eg ships, aircraft and air borne threats) over much larger distances from the sensor using far field scattering pattens. However, while radar is traditionally associated with the positioning and detection of objects in the far field, radar can also used be for the classification of objects in the near field (such as in autonomous vehicles, parking sensors, and ground penetrating radar (GPR) for finding landmines and unexploded ordnance, archaeological searches and the location of utilities for the construction industry). Furthermore, there is also considerable interest in improved object positioning given the development of autonomous vehicles by Google, Tesla, Uber and many others as well as related applications in autonomous manufacturing. In all these applications there is also considerable demand to improve the characterisation and identification of small objects that are not impeded by boundaries that can be penetrated by electromagnetic fields (eg walls, ground, clothing, smoke, fog or clouds). This proposal is aimed at improving the characterisation, classification and identification of small objects in the near field using electromagnetic frequencies in the range 300MHz to 12GHz leading to new mathematical results, statistical computing tools for object identification and design recommendations for electromagnetic sensors. Our hypothesis is that a higher tensor description of an object combined with a probabilistic classification approach provides an effective means of identifying small objects using electromagnetic field measurements positioned away from the target, but in the near field, at wave propagation frequencies. To test our hypothesis, we will derive new asymptotic expansions, which lead to new object characterisations in terms of new tensor descriptions. We will investigate new minimal contracted representations of objects using these tensors and understand the information about an object that can be obtained from these minimal representations. We will develop new computational tools for computing these characterisations and classifiers that build on a library of tensor coefficients to make object predictions from practical measurements.

Characterising and identifying hidden metallic objects has important applications in: 1. Security screening at border controls, public events and transport hubs and detecting threats such as knives and firearms. Knife crime is at its highest recorded level in 10 years in the UK and firearm offences are seeing an increase, many being smuggled into the UK from Europe via ferry routes. 2. The identification of the 110 million current unexploded anti-personal landmines, unexplored ordnance (UXO) such as mortar and cluster bombs in areas of former conflicts. Using current techniques, it has been estimated to take over 1000 years to clear them so that the land can be returned to normal use. 3. Improvements to scrap sorting, which has the potential to improve the recycling of valuable metals. Going beyond the planned work in the EPSRC funded project EP/R002134/1, a new form of object charactization called a generalised magnetic polarizabilty tensor (GMPT) has been established for highly conducting objects, offering significant advantages over existing small object characterisations. Specifically: 1. Offering the possibility to better discriminate between objects and, hence, the potential to achieve better classification and identification of objects. 2. Being able to use the non-uniform fields generated by a metal detector in a creative way, overcoming the assumption that field is uniform over the object in current small object characterisations, and, hence, achieving better 1. There is much still to learn about GMPTs and there are open mathematical questions about the appropriate choices of invariants (required for object classification) and using representation theory to determine symmetry groups for symmetrical metallic objects (such as mortar bombs). This project will seek to address these questions, which are required before a revolutionary new type of metal detector offering substantial improvements in the above applications can be built.

A few grams of any material contain a bewildering number of individual particles. Interactions between these particles give rise to a vast array of emergent phenomena which cannot be understood from looking at any of the particles in isolation. An important example of this is superconductivity, which enables materials to conduct electricity without resistance. Novel emergent states also occur out of equilibrium, due to the presence of large external forces or the occurrence of extreme events. Examples include turbulence in fluids and plasmas, the spreading of epidemics and diseases, and shocks in the stock market. The above examples illustrate the breadth of this nationally and internationally recognised "Grand Challenge" in Emergence and Physics Far From Equilibrium. Addressing this Grand Challenge requires a coordinated approach, spanning different areas of physics and related disciplines. The Network will facilitate cross-cutting workshops and advanced working groups to enable UK researchers to plan and carry out targeted research programmes. Pump-prime initiatives and interaction with industry will stimulate collaborative research, ensuring UK competitiveness in this far-reaching field.