Maths Research Associates 2021 Manchester

Lead Research Organisation: University of Manchester
Department Name: Mathematics

Abstract

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

Publications

10 25 50
 
Description This award funded 5 postdoctoral research fellows on short positions following their PhDs. This funding was extremely useful for the development of the careers of the researchers in question, particularly during the period when we were emerging from covid, allowing them all an additional short period of time to focus on research and their next directions. The funding had very positive influence on their careers. 3 of the researchers have continued into research careers in academia, including to international destinations. One has moved into industry and one into a teaching position. Although no publications have yet come out of the award we anticipate that they will come with time.
Exploitation Route With regard the project of JF: Development of methods for data selection for stress-strain test to destruction experiments. In these types of experiments, the material is stretched beyond its elastic limit, causing damage and changing the properties of the material, until the material fails. When fitting mechanistic models to the data, which do not take account of that damage, it is important to only fit to the data collected before damage occurs. Usually this data selection is done by hand, the subjectivity of which can adversely affect the quality of the inference on the physical parameters of the material (e.g. Youngs modulus). In this work we developed a Bayesian methodology for data selection in these types of experiments, based on previous work by JF and SC on data selection for a cell matching problem in developmental biology. This method was used to learn the fidelity of each of the observations, ensuring that the model was only fit to data before damage has had a significant effect on the properties of the material. This fidelity was parameterised over the observation space, and a big part of this work was the development of appropriate Gaussian Process priors for the fidelity field. In particular, we developed priors which encouraged high levels of fidelity at low strains where we expect the material to be undamaged. This work was successful, and the findings of the application of the methodology to a set of experiments on horse tendons, where we additionally apply mixed effects models in order to find population-level distributions for material properties, will shortly be submitted to a top international peer reviewed journal. This methodology can be taken forward by any engineers or modellers who wish to fit an elastic model to stress-strain data that goes beyond the elastic limit of the material.
Sectors Healthcare
 
Description With regard to the postdoc of JF: The potential impact of this work is the improvement of inference for materials. In particular, the data selection enables the maximisation of useful information gain from experimental work, leading to better understanding of materials and their properties. The impact is limited at this stage as the work has not been published, but we foresee that these methods have the potential to be applied to a large number of applications in inverse problems for materials and beyond.
First Year Of Impact 2023
Sector Aerospace, Defence and Marine,Healthcare
Impact Types Societal
 
Description JF: Co-leader and mentor of the Women and Minority in Maths Scheme 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Worked to develop the resources available to our members, working with mentees to discuss future career steps and general well-being.
Year(s) Of Engagement Activity 2022