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

根据定义，核技术是基于亚原子物理学原理和辐射粒子与材料的相互作用。虽然这种系统的微观行为是很好的理解，所涉及的不均匀性的程度意味着预测粒子通过宏观（人类）尺度上的复杂物理环境的通量的能力是一个重大的挑战。这是我们如何设计、管理和操作二十一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），使旧的反应堆退役，医学放射治疗，以及通过例如为地球外基地开发空间微型反应堆和保护暴露于高能辐射的高科技设备（如卫星和宇航服）开辟空间技术的前进道路。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传输方程（BTE）的建模。在这一领域中使用的许多现有方法可以追溯到几十年前，并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）粒子计数的原理。自20世纪80年代以来，数学科学界的投入一直有限。与此同时，各种数学理论已经出现，为全新的方法提供了机会。加上强大的现代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建模。这个为期五年的跨学科研究计划将结合联合收割机现代数学方法，从概率论，先进的蒙特卡罗方法和反问题，以开发新的方法，辐射输运的理论和应用。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。该计划赠款将联合数学，工程和医学物理学的互补研究小组，导致学术知识和专业知识的持续临界质量。通过一个多元化的研究团队，我们将引领辐射建模的进步，这对当前的范式是颠覆性的，确保英国处于21世纪世纪核工业的最前沿。

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.