UK Graduate Modelling Camp

The UK's Graduate Modelling Camp is a 3-day (virtual) workshop which will run from 15-17 July 2020 that aims to provide participants with hands-on experience of mathematical modelling under the guidance of experienced instructors. The camp is open to all PhD students and designed to promote a broad range of problem-solving skills, such as mathematical modelling & analysis, scientific computation & critical assessment of solutions.

The camp will take place online; attendees will need to commit to attending the camp for the whole duration, and there will be a need to work in the evening on Thursday 16th July. The problems to be considered are inspired by real problems that have arisen in industry or science. The camp begins with presentations from the mentors. Then, according to preference, the participants form teams to work on each problem. Scientific communication is an important part of the camp and all participants are expected to make presentations.

Academic Organiser: Chris Breward

Mentors to include:

  • Ashleigh Hutchinson (Witwatersrand) ''Mismatch of bee behaviour and flowering dates'' Flowers blossom when exposed to stimuli such as changes in mean day length and temperature variations. Bee behaviour is mostly aligned with temperature changes. Usually, the time at which bees begin to leave the hive in search of food in order to replenish their diminishing supply, corresponds to the event at which flowers begin to blossom. A mutually beneficial relationship exists between bees and flowers: bees rely on blossoms for food, and plants require bees for fertilization and propagation allowing for new plants to develop. Climate change has led to an increase in mean temperature values across the globe. Because bee behaviour is sensitive to temperature changes, bees are starting to leave their hives before flowers have begun to blossom, thus upsetting the delicate balance. Our aim will be to develop a mathematical model to describe a bee population in a hive, its interactions with blossoms, and the resulting change in behaviour due to global warming. Data applicable to the Northern Hemisphere will be made available to those choosing this challenge.
  • Graham Benham (Cambridge) ''Optimal ship berthing strategies to reduce tugboat fuel consumption'' In ports all across the world, large freight ships must be pulled into harbours by smaller tugboats. The pulling strategy/trajectory is chosen to keep fuel consumption low, both for environmental and cost reasons, whilst also staying within the safety standards. In this challenge, which originated in ESGI 146, we will use mathematical modelling to study how to use tugboats to pull a large boat into a given harbour space using the minimum amount of fuel possible. 
  • Tori Pereira (Oxford) ''Optimising the performance of a conical ceramic membrane'' Microfiltration is the process of filtering particles with diameters between 0.1 and 100 micrometres. This is a poorly explored field with many important applications from the filtering of blood to the purification of water and air. Current filters are typically fibre-based and have several significant drawbacks including minimal control of the pore structure and a large environmental footprint as the fibres clog up and have to be discarded thereby increasing waste to landfill. Smart Separations Ltd is a UK-based start-up who have developed a reusable ceramic membrane with micron-sized conical pores distinct from the cylindrical pores typically used for filtration. This new technology has the potential to be highly beneficial in many applications. However to fully realize its potential, a comprehensive analysis of the performance and efficiency of the membrane is vital. This project will use mathematical modelling to explore the behaviour of the membrane and the efficiency of filtration, which is inherently linked to the underlying pore structure. We will study how the structure of the membrane relates to the fluid flow rate and microparticle separation through the filter.
  • Galane J. Luo (Birmingham) ''How a plant root generates curvature and why it matters'' Harnessing the power of plant life may help to accelerate sustainable development and enhance technological innovation. For instance, climate-resilient crops can alleviate hunger, optimised natural carbon storage can improve quality of life, and plant-inspired self-growing robotics can transform the manufacturing industry. Relating to the latter example, several ‘plantoid’ robots have been invented recently; but their control capabilities and autonomy are limited. To make further progress towards emulating the complex growth dynamics of plants, the industry needs better mathematical models of growth-driven morphogenesis in plant organs. In this challenge, we will attempt to unlock the mechanisms underlying curvature generation in an elongating plant root. Using continuum mechanics, differential geometry, and numerical simulations (time-permitting), we will derive and solve equations governing the root’s relative elongation rate (RER) and curvature generation rate, based on the simple assumption that the RER of each individual cell is proportional to the excess turgor pressure over some prescribed threshold. We will contemplate the implications of these mechanisms for biomimetic robotics and automation.

Logisitics: Sarah Howle

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