I am a founding member of the SofTMech consortium, funded as an EPSRC Maths-in-Healthcare centre (2016-2021). This project has recently diversified into a EPSRC Centre-to-Centre partnership with Massachusetts Institute of Technology and Politecnico Milano (2020-2023) and the SofTMech Statistical Emulation Hub, funded as an EPSRC Maths-in-Healthcare centre (2021-2024).

I held an EPSRC First Grant on `Elastic jumps on networks' (2017-2019). As part of this I organised a Dialogue with Clinicians event, gathering expert clinicians and modellers to discuss challenges in quantifying the onset and severity of retinal haemorrhage, along with its likely cause.

I am involved in the Special Interest Group for the Fluid Mechanics of the Eye. See recent case study video here.

• the onset of retinal haemorrhage following traumatic brain injury;

  Spelman TA and Stewart PS (2020), Shock wave propagation along the central retinal blood vessels. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 476(2234), 20190269. link

• the onset of the Retinal Venous Pulse, as a basis for a non-invasive measure of intracranial pressure;

  Stewart PS and Foss A (2019), Self-excited oscillations in a collapsible channel with applications to retinal venous pulsation. ANZIAM Journal, 61(3), pp. 320-348. link

  Stewart PS, Jensen OE and Foss A (2014), A theoretical model to allow prediction of the CSF pressure from observing the retinal venous pulse, Investigative Ophthalmology and Visual Science 55(10) 6320. link

Soft tissue mechanics

• indentation of second-order hyperelastic materials;

  Du Y, Stewart PS, Hill NA, Yin H, Penta R, Kory J, Luo XY and Ogden RW (2023), Nonlinear indentation of second-order hyperelastic materials. Journal of the Mechanics and Physics of Solids, 171, 105139. link

• rational upscaling of individual cell models to soft tissue models;

  Barry R, Hill NA and Stewart PS (2022), Continuum soft tissue models from upscaling of arrays of hyperelastic cells. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478(2266), 20220065. link

• fluid-structure interaction during phaco-emulsification.

  Wang Z, Wang C, Zhao F, Qi N, Lockington D, Ramaesh K, Stewart PS, Luo, XY and Tang H (2022), Simulation of fluid-structure interaction during the phaco-emulsification stage of cataract surgery, International Journal of Mechanical Sciences, 214, 106931 link

• the influence of axonal fibres on the development of cerebral cortex folding;

  Stewart PS, Waters SL, El Sayed T, Vella D, Goriely A (2016), Wrinkling, creasing, and folding in fiber-reinforced soft tissues, Extreme Mechanics Letters, 8, 22-29 link

• the dynamics of neonatal airway recruitment in Respiratory Distress Syndrome;

  Stewart PS and Jensen, OE (2015), Patterns of recruitment and injury in a heterogeneous airway network model. Journal of The Royal Society Interface, 12, 20150523 link

• the optimal size of peripheral iridotomoy in uveitis;

  Agraval U, Qi N, Stewart PS, Luo XY, Williams G, Rotchford A, Ramaesh K (2015), Optimum size of iridotomy in uveitis, Clinical and Experimental Ophthalmology 43 (7), 692-696 link

• the role of the Donnan effect in the swelling of brain tissue;

  Lang GE, Stewart PS, Vella D, Waters SL, Goriely A (2014), Is the Donnan effect sufficient to explain swelling in brain tissue slices? Journal of The Royal Society Interface 11 (96), 20140123 link

Fluid flow through collapsible tubes and channels

Fluid flow through a flexible-walled channel or tube can exhibit self-excited oscillations, which can be studied by considering:

• the global stability in a finite-length flexible-walled channel;

  Herrada MA, Blanco-Trejo S, Eggers J, Stewart PS (2022), Global stability analysis of flexible channel flow with a hyperelastic wall, Journal of Fluid Mechanics, 934, A28 link

  Wang DY, Luo XY, Stewart PS (2021), Energetics of collapsible channel flow with a nonlinear fluid-beam model, Journal of Fluid Mechanics, 926, A2 link

  Wang DY, Luo XY, Stewart PS (2021), Multiple steady and oscillatory solutions in a collapsible channel flow, International Journal of Applied Mechanics, 13, 2150058 link

  Stewart PS (2017), Instabilities in flexible channel flow with large external pressure, Journal of Fluid Mechanics, 825, 922-960 link

  Stewart PS, Heil M, Waters SL, Jensen OE (2010), Sloshing and slamming oscillations in a collapsible channel flow, Journal of Fluid Mechanics, 662, 288-319 link

  Stewart PS, Waters SL, Jensen OE (2009), Local and global instabilities of flow in a flexible-walled channel, European Journal of Mechanics B/Fluids, 28, 541-557 link

• the local stability of Poiseuille flow in a long flexible-walled channel.

  Wang DY, Luo XY, Liu ZS, Stewart PS (2023), Flow-induced surface instabilities in a flexible-walled channel with a heavy wall, Journal of Fluid Mechanics, link

  Stewart PS, Waters SL, Jensen OE (2010), Local instabilities in a flexible channel: asymmetric flutter driven by a weak critical layer, Physics of Fluids 22, 031902 link

  Stewart PS, Waters SL, Billingham J, Jensen OE (2010), Spatially localised growth within global instabilities of flexible channel flows, Proceedings of the Seventh IUTAM Symposium on Laminar-Turbulent Transition (Stockholm 2009) link

Dynamics and stability of gas-liquid foams

Using fluid mechanics to understand the dynamics and stability of gas-liquid foams, including:

• a review highlighting the importance of mesoscale structural elements for the description of foam dynamics;

  Stewart PS, Hilgenfeldt S (2023), Gas-liquid foam dynamics: From Structural Elements to Continuum Descriptions, Annual Review of Fluid Mechanics

• fracture of an aqueous foam under an applied driving pressure, which is qualitatively similar to fracture of crystalline atomics solids like metals;

  Stewart PS, Hilgenfeldt S, Explaining the Fracture Velocity Gap: Cracks and Dissipation in Foams, to be submitted

  Stewart PS, Hilgenfeldt S (2017), Cracks and Fingers: Dynamics of ductile fracture in an aqueous foam, Colloids and Surfaces A: Physicochemical and Engineering Aspects 534, 58-70. link

  Stewart PS, Davis SH, Hilgenfeldt S (2015), Microstructural effects in aqueous foam fracture, Journal of Fluid Mechanics 785, 425-461 link

  Stewart PS, Davis SH, Hilgenfeldt S (2013), Viscous Rayleigh--Taylor instability in aqueous foams, Colloids and Surfaces A: Physicochemical and Engineering Aspects 436, 898-905 link

• bursting of a rising gas bubble at the surface of an oil-covered water bath, which can enhance oil dispersal;

  Stewart PS, Feng J, Kimpton LS, Griffiths IM, Stone HA (2015), Stability of a bi-layer free film: simultaneous or individual rupture events? Journal of Fluid Mechanics 777, 27-49 link

• a large scale network model to understand bubble coalescence in metallic foams;

  Stewart PS and Davis SH (2013), Self-similar coalescence of clean foams, Journal of Fluid Mechanics 722, 645-664 link

  Stewart PS and Davis SH (2012), Dynamics and stability of metallic foams: Network modeling, Journal of Rheology 56, 543-574 link

• the stability of a foam film draining under gravity.

  MJ Davis, PS Stewart and SH Davis (2013), Local effects of gravity on foams, Journal of Fluid Mechanics 737, 1-18 link

Industrial modelling

Using the methods of continuum mechanics to improve industrial protocols, including:

• tailoring the efficency of membrane filtration;

  Griffiths IM, Stewart PS (2022), A hybrid discrete-continuum framework for modelling filtration, Journal of Membrane Science 647, 120258 link

  Griffiths IM, Mitevski I, Vujkovac I, Illingworth MR, Stewart PS (2020), The role of tortuosity in filtration efficiency: A general network model for filtration, Journal of Membrane Science 598, 117664 link

  Griffiths IM, Kumar A, Stewart PS (2016), Designing asymmetric multilayered membrane filters with improved performance, Journal of Membrane Science 511, 108-118 link

  Griffiths IM, Kumar A, Stewart PS (2014), A combined network model for membrane fouling, Journal of Colloid and Interface Science 432, 10-18 link

• using fluid flow to enhance chiral separation;

  Hermans TM, Bishop KJM, Stewart PS, Davis SH, Grzybowski BA (2015), Vortex flows impart chirality-specific lift forces, Nature communications 6, 5640 link

• transforming a chemical oscillator from the temporal domain to the spatial domain.

  Hermans TM, Stewart PS, Grzybowski BA (2015), pH Oscillator Stretched in Space but Frozen in Time, The Journal of Physical Chemistry Letters 6 (5), 760-766 link

Hydrodynamic stability theory

Study of fundamental hydrodynamic instabilities, including:

• the role of non-normal growth in the instability of current sheets.

  MacTaggart D, Stewart PS (2017), Optimal energy growth in current sheets, Solar Physics 292(10), 1-20. link

Current PhD students

Sunday Ifeanyi Onah (2020-), The Riemann problem at a bifurcation in a collapsible tube (with David MacTaggart)

Gordon McNicol (2020-), A mathematical model for nanokicking (with Matt Dalby)

Atrayee Bhattacharya (2021-), Mathematical modelling of retinal vein occlusion (with Hao Gao and Dirk Husmeier)

Former PhD students

Dr Danyang Wang (2014-2018), The energetics of self-excited oscillations in collapsible channel flow (with Xiaoyu Luo)

Dr Ahmed Mostafa Abdelhady Ismaeel (2015-2019), Mathematical modelling of cancer treatment by photothermal ablation (with Xiaoyu Luo)

Dr Roxanna Barry (2016-2020), Discrete-to-continuum modelling of cells to tissues (with Nick Hill)

Current Postdocs

Dr Jakub Koery (2020-) (with Nick Hill and Xiaoyu Luo)

Dr Namshad Thekkethil (2020-) (with Nick Hill and Xiaoyu Luo)

Dr Yangkun Du (2020-) (with Nick Hill, Xiaoyu Luo and Raimondo Penta)

Dr Jay Mackenzie (2021-) (with Nick Hill)

Former Postdocs

Dr Tamsin Spelman (2017-2018) , now University of Cambridge

Dr Danyang Wang (2020-2021), now Xi'an Jiaotong University

Teaching

(2019/20, 2020/21, 2021/22) Mathematics 1 (deputy course head)

(2018/19, 2017/18, 2016/17) 2B Linear Algebra (course head)

(2016/17, 2015/16, 2014/15) 5M Advanced Numerical Methods

(2015/16, 2014/15) 4H Fluid Mechanics

(2013/14) 3H Dynamical Systems