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

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.

Impact on Students. The primary impact will be on the 50+ PhD students trained by the Centre. They will be high-quality computational scientists who can develop and implement new methods for modelling complex systems in collaboration with scientists and end-users, who are comfortable working in interdisciplinary environments, have excellent communication skills and be well prepared for a wide range of future careers. The students will tackle and disseminate results from exciting PhD projects with strong potential for direct impact. Exemplar research themes we have identified together with our industrial and international partners: (i) design of electronic devices, (ii) catalysis across scales, (iii) high-performance alloys, (iv) direct drive laser fusion, (v) future medicine exploration, (vi) smart nanofluidic interfaces, (vii) composite materials with enhanced functionality, (viii) heterogeneity of underground systems.

Impact on Industry. Students trained by HetSys will make a significant impact on UK industry as they will be ideally prepared for R&D careers to help to address the skills shortage in science and engineering. They will be in high demand for their ability to (i) work across disciplines, (ii) perform calculations that come along with error estimates, and (iii) develop well-designed software that other researchers can readily use and modify which implements novel solutions to scientific problems. More generally, incorporating error bars into models to take account of incomplete data and insufficient models could lead to significantly enhanced adoption of materials modelling in industry, reducing trial and error, and costly/time-consuming R&D procedures. The global market for simulation software is expected to more than double from now to 2022 indicating a very strong absorptive capacity for graduates. Moreover, a recent European Materials Modelling Consortium report identified a typical eight-fold return on investment for materials modelling research, leading to cost savings of 12M Euros per industrial project.

Impact on Society. Scarcity of resources and high energy requirements of traditional materials processing techniques raise ever-increasing sustainability concerns. Limitations on jet engine fuel efficiency and the difficulties of designing materials for fusion power stations reflect the social and economic cost of our incomplete knowledge of how complex heterogeneous systems behave. High costs of laboratory investigations mean that theory must aid experiment to produce new knowledge and guidance. By training students who can develop the new methodology needed to model such issues, HetSys will support society's long term need for improved materials and processes.

There will also be a direct impact locally and regionally through engagement by HetSys in outreach projects. For example we will encourage CDT students to be involved with annual 'Inspire' residential courses at Warwick for Year 11 girls, which will show what STEM subjects are like at degree level. CDT students will present highlights from projects to secondary-school pupils during these courses and also visit local schools, particularly in areas currently under-represented in the student body, in coordination with relevant professional bodies.

Impact on collaboration. Our international partners have identified the same urgent challenges for computational modelling. We will build flourishing links with research institutes abroad with long term benefit on UK research via our links to computational science networks. Shared research projects will strengthen links between academic staff and industry R&D personnel and across disciplines. The work will also lead to accessible, robust and reusable software. The Centre will achieve cross-disciplinary academic impact on the physical and materials sciences, engineering, manufacturing and mathematics communities at Warwick and beyond, and on the generation of new ideas, insights and techniques.