Nonlinear, but under control: a hierarchical modelling approach to manipulating liquid films

我们周围的情况取决于我们日常生活中可控的结果，从控制人群的疏散，到高效的药物输送，或者计算机中心内的冷却系统。大多数现实生活中的场景依赖于复杂的模型，这些模型太复杂了，无法通过分析或计算来处理。利用一个美丽而丰富的物理问题--控制下落液膜中的非线性波--提供的框架，该项目将提供开发分析和计算多物理工具的机会。它们第一次协同行动，变得足够强大，可以将强大的理论战略转化为现实的技术解决方案。虽然该项目本质上是基本的，但它汇集了现代应用数学中不同领域的元素，旨在为本质上跨学科的复杂物理系统控制理论中的分层建模提供一个新的框架。拟开发的方法可概括为：1.弱非线性模型：我们认为较简单的模型，具有高度的通用性和有效性。它们提供了一个进行数学分析、控制设计和快速数值计算的环境。然而，它们只适用于非常简单的场景。高级降阶模型：更逼真的模型，但其复杂的性质使分析结果几乎不可能。然而，基于某些假设的控制开发仍然是可行的，所产生的控制最近被证明是可靠的。直接数值模拟：提供完整模型的高精度解决方案，不依赖于任何建模假设。然而，除非得到有效的指导，否则它们的成本是有限的。该项目将在建模、新颖的分析方法和高性能计算之间的接口上蓬勃发展，自然地与透镜和微芯片制造、先进镀膜系统和下一代冷却技术的几个应用相联系。

We are surrounded by situations that depend on a controlled outcome in our day-to-day lives, ranging from controlling the evacuation of crowds, to efficient drug delivery, or cooling systems inside computing centres. Most real-life scenarios rely on complicated models which are too complex to tackle analytically or computationally. Using the framework provided by a beautiful and rich physical problem - controlling nonlinear waves in falling liquid films - the project will provide opportunities to develop analytical and computational multi-physics tools. Acting in tandem for the first time, they become sufficiently powerful to translate robust theoretical strategies into realistic technological solutions.Whilst fundamental in nature, the project brings together elements from diverse areas in modern applied mathematics and it aims to provide a new framework for hierarchical modelling in control theory for complex physical systems that is intrinsically interdisciplinary. The methodology to be developed can be summarised as:1. Weakly nonlinear models: the simpler models we consider, highly versatile and efficient. They provide an environment where mathematical analysis, control design and rapid numerical calculations are possible. However they are only applicable for very simple scenarios.2. Advanced reduced-order models: more realistic models, but their complex nature renders analytical results almost impossible. However control development based on certain assumptions is still viable, and the resulting controls were recently shown to be reliable.3. Direct numerical simulations: provide highly accurate solutions of the full model and do not rely on any modelling assumptions. However they are restrictively expensive unless efficiently guided.The project will thrive at the interface between modelling, novel analytical approaches and high performance computing, being naturally linked to several applications in lens and microchip manufacturing, advanced coating systems and next-generation cooling technologies.