Generalised Magnetic Polarizability Tensors: Invariants and Symmetry Groups

表征和识别隐藏的金属物体在以下方面有重要应用：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。英国持刀犯罪达到10年来的最高水平，枪支犯罪也在增加，其中许多是通过渡轮从欧洲走私到英国的。查明现有的1.1亿枚未爆杀伤人员地雷、迫击炮和集束炸弹等未探明弹药。使用目前的技术，估计需要1000多年的时间才能清理干净，使土地恢复正常使用。除了EPSRC资助的项目EP/R002134/1中计划的工作之外，已经为高导电物体建立了一种被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著的优势。具体地说：1.提供更好地区分物体的可能性，从而有可能更好地对物体进行分类和识别。能够创造性地使用金属探测器产生的非均匀场，克服了当前小物体表征中物体上的场是均匀的假设，从而取得了更好的效果1.关于GMPTS还有很多需要了解的东西，关于适当选择不变量(物体分类所需的)和使用表示理论来确定对称金属物体(如迫击炮)的对称群，仍然存在公开的数学问题。该项目将寻求解决这些问题，在能够制造出革命性的新型金属探测器之前，这些问题是必需的，该新型金属探测器在上述应用中具有实质性的改进。

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.