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

非线性但受控：操纵液膜的分层建模方法

• 批准号: 2588409
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2588409
• 关键词: Nonlinear; but; under; control; hierarchical

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.

在我们的日常生活中，我们周围的情况取决于控制结果，从控制人群疏散到有效的药物输送，或者计算中心内的冷却系统。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，无法通过分析或计算来解决。利用一个美丽而丰富的物理问题提供的框架-控制下降液膜中的非线性波-该项目将提供开发分析和计算多物理工具的机会。他们第一次联手行动，变得足够强大，能够将强大的理论策略转化为现实的技术解决方案。虽然本质上是基础性的，但该项目汇集了现代应用数学不同领域的元素，旨在为复杂物理系统的控制理论分层建模提供一个新的框架，本质上是跨学科的。要开发的方法可以概括为：1。弱非线性模型：我们考虑的简单模型，高度通用和高效。它们提供了一个数学分析、控制设计和快速数值计算的环境。但是，它们只适用于非常简单的机器人。2.高级降阶模型：更真实的模型，但其复杂性使得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，并且最近证明由此产生的控制是可靠的。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。该项目将在建模、新颖的分析方法和高性能计算之间的界面上蓬勃发展，自然与透镜和微芯片制造、先进涂层系统和下一代冷却技术中的几个应用联系在一起。