A Game of Order Parameters

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Brief description of the context of the research including potential impactPredicting if, how and when ice crystals will form in clouds (and our own cells!) is important to atmospheric science (and cryopreservation!) and the manufacture of pharmaceuticals. Preventing crystals from nucleating is desirable instead in our brains (where aggregates of proteins can lead to neurological diseases) and for the oil industry (where water-based crystals can block pipelines). Computer modelling can, in principle, design strategies for optimal control over these processes: in fact, advanced atomistic simulation techniques are now able to calculate key properties such as crystal nucleation rates. Unfortunately, the comparison of these rates against experimental data is subject to uncertainties yet to be rigorously quantified. Specifically, the choice of the particular mathematical object we use to identify atoms as part of a crystalline nucleus (the so-called "order parameter") has a major impact. We will use formal uncertainty quantification (which form part of the core HETSYS training) to rectify this, initially using simple models - for which accurate results are available, and then moving onto scenarios of great practical importance - such as the formation of ice. Aims and objectivesThis project seeks to establish what is the uncertainty associated with the choice of a particular order parameter when computing crystal nucleation rate by means of computer simulations. Aside from quantitative results, we also aim to develop a reliable methodology that will allow us to estimate said uncertainty in a robust and reproducible fashion, so as to provide the community with a reliable tool to make sense of computationally obtained nucleation rates. In addition, we intend to move from relatively simple model systems to realistic scenarios such as the heterogeneous formation of ice, which is a hotly debated issue with countless practical reverberations across fields as diverse as atmospheric science and cryopreservation.Novelty of the research methodologyComputing crystal nucleation rates is a challenging task for molecular simulations: as such, very little is known about the uncertainty related to these rates, and the field is presently lacking a robust approach tackle this pitfall. In this project we will leverage an extensive array of different order parameters to systematically investigate their effect on crystal nucleation rates. On top of relatively standard techniques (such as committor analysis) to probe the reliability of these order parameters, we will harness Bayesian inference to provide quantitative, unprecedented estimates of the error associated with the choice of a specific order parameter.Alignment to EPSRC's strategies and research areasThis project fits very well within Computational and Theoretical Chemistry and Surface Science EPSRC Areas. Given the far-reaching implications of this research in the context of ice nucleation and growth, we believe the project has the potential to make a concrete impact with respect to the Healthy Nation prosperity outcome highlighted in the EPSRC strategy for the physical sciences.Any companies or collaborators involvedThe project leverages an extensive network of collaboration, some of which directly involved with the recently awarded "Crystallization in the Real World" EPSRC Program Grant, encompassing several UK institutions; Leeds, Sheffield, UCL as well as Warwick. The supervisors can both boast a large network of existing collaborations directly connected to ice and crystallization, which are bound to maximise the impact of the proposed research.