Generalised Magnetic Polarizability Tensors: Invariants and Symmetry Groups

表征和识别隐藏的金属物体具有重要的应用：1。在边境管制、公共活动和交通枢纽进行安全检查，并检测刀具和枪支等威胁。在英国，持刀犯罪达到了10年来的最高记录，枪支犯罪也在增加，许多枪支是通过渡轮航线从欧洲走私到英国的。查明在以前的冲突地区现有的1.1亿枚未爆炸的杀伤人员地雷、迫击炮和集束炸弹等未探测弹药。根据目前的技术，估计需要1000多年的时间才能清除它们，使土地恢复正常使用。改进废料分选，这有可能改善有价值金属的回收。除了EPSRC资助的项目EP/R 002134/1中的计划工作之外，还为高导电物体建立了一种称为广义磁极化张量（GMPT）的新形式的物体表征，与现有的小物体表征相比具有显着优势。具体而言：1.提供了更好地区分物体的可能性，因此有可能实现更好的物体分类和识别。能够以创造性的方式使用由金属探测器产生的非均匀场，克服了在当前小物体表征中场在物体上是均匀的假设，并且因此，实现更好1.关于GMPTs还有很多东西要学，关于不变量的适当选择还有一些开放的数学问题（物体分类所需）和使用表示理论来确定对称金属物体（如迫击炮弹）的对称群。该项目将寻求解决这些问题，这些问题是在建立一种革命性的新型金属探测器之前所必需的，这种新型金属探测器可以在上述应用中提供实质性的改进。

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.