Mathematical Theory of Radiation Transport: Nuclear Technology Frontiers (MaThRad)

根据定义，核技术是建立在亚原子物理学原理和辐射粒子与材料相互作用的基础上的。虽然这些系统的微观行为已经被很好地理解，但所涉及的不均匀性程度意味着在宏观（人类）尺度上预测粒子通过复杂物理环境的通量的能力是一个重大挑战。这是我们如何设计、管理和操作21世纪一些最重要技术的核心。这包括建造新的反应堆（裂变和聚变反应堆）、使旧反应堆退役、医疗放射治疗，以及开辟进入空间技术的道路，例如为世界以外的基地开发空间微型反应堆，以及保护暴露在高能辐射下的高科技设备，如卫星和太空服。辐射如何与周围物质相互作用的准确预测是基于所谓的玻尔兹曼输运方程（BTE）的建模。该领域使用的许多现有方法可以追溯到几十年前，并且依赖于通过蒙特卡罗和其他数值方法获得的模拟（例如中子）粒子计数原理。自20世纪80年代以来，来自数学科学界的投入一直很有限。与此同时，各种各样的数学理论出现了，为全新的方法提供了机会。结合强大的现代HPC和更智能的算法，它们有能力处理更复杂的场景，例如时间依赖性，稀有事件采样和方差减少以及多物理场建模。这个为期五年的跨学科研究项目将结合概率论的现代数学方法、先进的蒙特卡罗方法和反问题，开发辐射输运理论和应用的新方法。我们将追求基础、转化和应用驱动研究的互动探索；开发具有可量化准确性的预测模型和软件原型，为能源，医疗保健和空间核工业的实际实施做好准备。该方案赠款将联合来自数学、工程和医学物理学的互补研究小组，从而在学术知识和专业知识方面产生持续的临界质量。通过一个多元化的研究团队，我们将引领辐射建模的进步，颠覆当前的范式，确保英国走在21世纪核工业的前沿。

Nuclear technology is, by definition, based around the principle of subatomic physics and the interaction of radiation particles with materials. Whilst the microscopic behaviour of such systems is well understood, the degree of inhomogeneity involved means that the ability to predict the flux of particles through complex physical environments on the macroscopic (human) scale is a significant challenge. This lies at the heart of how we design, regulate and operate some of the most important technologies for the twenty-first century. This includes building new reactors (fission and fusion), decommissioning old ones, medical radiation therapy, as well as opening the way forward into space technologies through e.g. the development of space-bound mini-reactors for off-world bases and protection for high-tech equipment exposed to high-energy radiation such as satellites and spacesuits. Accurate prediction of how radiation interacts with surrounding matter is based on modelling through the so-called Boltzmann transport equation (BTE). Many of the existing methods used in this field date back decades and rely on principles of simulated (e.g. neutron) particle counting obtained by Monte Carlo and other numerical methods. Input from the mathematical sciences community since the 1980s has been limited. In the meantime, various mathematical theories have since emerged that present the opportunity for entirely new approaches. Together with powerful modern HPC and smarter algorithms, they have the capacity to handle significantly more complex scenarios e.g. time dependence, rare-event sampling and variance reduction as well as multi-physics modelling.This five-year interdisciplinary programme of research will combine modern mathematical methods from probability theory, advanced Monte Carlo methods and inverse problems to develop novel approaches to the theory and application of radiation transport. We will pursue an interactive exploration of foundational, translational and application-driven research; developing predictive models with quantifiable accuracy and software prototypes, ready for real-world implementation in the energy, healthcare and space nuclear industries. This programme grant will unite complementary research groups from mathematics, engineering and medical physics, leading to sustained critical mass in academic knowledge and expertise. Through a diverse team of researchers, we will lead advances in radiation modelling that are disruptive to the current paradigm, ensuring that the UK is at the forefront of the 21st century nuclear industry.