Throughout my career, I have advanced scientific theories and industrial practices, using mathematical modelling to understand complex problems in real-world contexts. My expertise lies in interdisciplinary collaborative research, having used applied mathematics and data science in application to biology, healthcare, and industry. Also, I have broad teaching experience at undergraduate and postgraduate levels. My work spans from the deep scientific and mathematical study of the natural world to the development of models for analysis and decision making in industry.

My biologically focussed research relates to the modelling of the mechanosensory systems of arthropods (i.e., insects and arachnids such as bees and spiders) to understand the newly discovered sense of aerial electroreception. Together with biologists, physicists and mathematicians, I investigate the mechanical response of sensory hairs to electrical stimuli in order to understand the biological implications of this sense. Importantly, the electroreceptive capability of the hairs lies in a wider multi-modal sensory context in which hairs may mechanically respond to other stimuli such as to sound and air flow. To date, I have made several findings of biological significance, revealing novel aspects of electroreception.

1) I analysed the biologically relevant parameter space of arthropod electro-sensory hairs to understand electroreception's fundamental mechanics (Journal of Theoretical Biology). My main findings show how sensory hairs are inseparably sensitive to aero-acoustic and electrical stimuli, indicating the necessity of considering both modalities together.

2) I investigated how electrical interactions between hairs change their dynamics (Journal of the Royal Society Interface), highlighting how electromechanical sensitivity and interactions vary with hair configuration.

3) I have demonstrated how electroreception enables location detection and object identification via electrical fields (under review), a novel ability within sensory biology.

My fluid dynamics research consists of analytical and numerical studies of coupled fluid-body motion in a range of physical settings, whilst my industrially focussed work has involved developing methods for modelling the physics of droplets and ice crystals, as well as models for decision making in healthcare systems. Together these include: the modelling of the skimming mechanics of arbitrarily shaped bodies (Palmer and Smith, 2020 (JEM); Palmer and Smith, 2022 (JFM)); the use asymptotic and numerical analysis to investigate the coupled fluid-body motion of bodies in boundary layer flow (Palmer and Smith, 2019; Smith and Palmer, 2019; Palmer and Smith, 2020 (JFM)); the modelling of non-spherical particles in aircraft icing (Palmer et al., 2019 (SAE)) and investigations into how mathematical modelling and data visualisation can help inform the organisation and operation of healthcare services (Palmer, Fulop, Utley, 2018; Palmer et al., 2019 (HIJ); Palmer and Utley, 2019).