Professor Peter Stewart

  • Professor of Applied Mathematics (Mathematics)

telephone: 01413304124
email: Peter.Stewart@glasgow.ac.uk

Room 415, Mathematics and Statistics Building, University Place, Glasgow, G12 8SQ

ORCID iDhttps://orcid.org/0000-0002-0971-8057

Biography

Personal webpage: http://www.maths.gla.ac.uk/~pstewart

I am currently a Professor of Applied Mathematics in the School of Mathematics and Statistics, University of Glasgow. My research focuses on applying continuum mechanics to solve interesting physiological or industrially motivated problems. Before coming to Glasgow, I held Postdoctoral Research Associate positions at the University of Oxford (2011-13) and Northwestern University (2010-2011). I completed my PhD in 2010 from the University of Nottingham, where my thesis was entitled Flows in flexible channels and airways.

Research interests

My research interests lie in the application of continuum mechanics to physiological and industrial problems. In particular I am interested in problems involving interaction between a fluid flow and deformable interfaces, such as liquid-gas free surfaces and elastic solids.

My current research focuses on several topics:

1) Mathematical modelling of the human eye, with a particular interest in retinal blood flow and retinal haemorrhage;

2) The dynamics of gas-liquid foams, with particular application to understanding fracture in crystalling materials and production of high-porosity metallic solids (solid metal foams) as lightweight materials;

3) Mathematical modelling of cell cytoskeleton, with particular application to understanding cell response to mechanical cues;

4) Flow through flexible-walled vessels in the human body, with application to the onset of self-excited oscillations.

Research units

Publications

Selected publications

Wang, D.Y., Luo, X.Y. and Stewart, P.S. (2021) Energetics of collapsible channel flow with a nonlinear fluid-beam model. Journal of Fluid Mechanics, 926, A2. (doi: 10.1017/jfm.2021.642)

Stewart, P. S. (2017) Instabilities in flexible channel flow with large external pressure. Journal of Fluid Mechanics, 825, pp. 922-960. (doi: 10.1017/jfm.2017.404)

Spelman, T.A. and Stewart, P.S. (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. (doi: 10.1098/rspa.2019.0269) (PMID:32201473)

Stewart, P. S. and Hilgenfeldt, S. (2023) Gas-liquid foam dynamics: from structural elements to continuum descriptions. Annual Reviews of Fluid Mechanics, 55, pp. 323-350. (doi: 10.1146/annurev-fluid-032822-125417)

All publications

List by: Type | Date

Jump to: 2023 | 2022 | 2021 | 2020 | 2019 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2010 | 2009
Number of items: 34.

2023

Wang, D., Luo, X. , Liu, Z. and Stewart, P. S. (2023) Flow-induced surface instabilities in a flexible-walled channel with a heavy wall. Journal of Fluid Mechanics, 956, A1. (doi: 10.1017/jfm.2022.1086)

Du, Y. , Stewart, P. , Hill, N. A. , Yin, H. , Penta, R. , Köry, J. , Luo, X. and Ogden, R. (2023) Nonlinear indentation of second-order hyperelastic materials. Journal of the Mechanics and Physics of Solids, 171, 105139. (doi: 10.1016/j.jmps.2022.105139)

Stewart, P. S. and Hilgenfeldt, S. (2023) Gas-liquid foam dynamics: from structural elements to continuum descriptions. Annual Reviews of Fluid Mechanics, 55, pp. 323-350. (doi: 10.1146/annurev-fluid-032822-125417)

2022

Barry, R. G., Hill, N. A. and Stewart, P. S. (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. (doi: 10.1098/rspa.2022.0065)

Griffiths, I. M. and Stewart, P. S. (2022) A hybrid discrete–continuum framework for modelling filtration. Journal of Membrane Science, 647, 120258. (doi: 10.1016/j.memsci.2022.120258)

Herrada, M.A., Blanco-Trejo, S., Eggers, J. and Stewart, P.S. (2022) Global stability analysis of flexible channel flow with a hyperelastic wall. Journal of Fluid Mechanics, 934, A28. (doi: 10.1017/jfm.2021.1131)

Wang, Z., Wang, C., Zhao, F., Qi, N., Lockington, D., Ramaesh, K., Stewart, P. S. , Luo, X. and Tang, H. (2022) Simulation of fluid-structure interaction during the phaco-emulsification stage of cataract surgery. International Journal of Mechanical Sciences, 214, 106931. (doi: 10.1016/j.ijmecsci.2021.106931)

2021

Wang, D.Y., Luo, X.Y. and Stewart, P.S. (2021) Energetics of collapsible channel flow with a nonlinear fluid-beam model. Journal of Fluid Mechanics, 926, A2. (doi: 10.1017/jfm.2021.642)

Wang, D., Luo, X. and Stewart, P. S. (2021) Multiple steady and oscillatory solutions in a collapsible channel flow. International Journal of Applied Mechanics, 13(6), 2150058. (doi: 10.1142/S1758825121500587)

2020

Griffiths, I.M., Mitevski, I., Vujkovac, I., Illingworth, M.R. and Stewart, P.S. (2020) The role of tortuosity in filtration efficiency: a general network model for filtration. Journal of Membrane Science, 598, 117664. (doi: 10.1016/j.memsci.2019.117664)

Spelman, T.A. and Stewart, P.S. (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. (doi: 10.1098/rspa.2019.0269) (PMID:32201473)

2019

Stewart, P. S. and Foss, A. J.E. (2019) Self-excited oscillations in a collapsible channel with applications to retinal venous pulsation. ANZIAM Journal, 61(3), pp. 320-348. (doi: 10.1017/S1446181119000117)

2017

Stewart, P. S. and Hilgenfeldt, S. (2017) Cracks and fingers: dynamics of ductile fracture in an aqueous foam. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 534, pp. 58-70. (doi: 10.1016/j.colsurfa.2017.03.057)

MacTaggart, D. and Stewart, P. (2017) Optimal energy growth in current sheets. Solar Physics, 292(10), 148. (doi: 10.1007/s11207-017-1177-1)

Stewart, P. S. (2017) Instabilities in flexible channel flow with large external pressure. Journal of Fluid Mechanics, 825, pp. 922-960. (doi: 10.1017/jfm.2017.404)

2016

Stewart, P. S. , Waters, S. L., El Sayed, T., Vella, D. and Goriely, A. (2016) Wrinkling, creasing, and folding in fiber-reinforced soft tissues. Extreme Mechanics Letters, 8, pp. 22-29. (doi: 10.1016/j.eml.2015.10.005)

Griffiths, I. M., Kumar, A. and Stewart, P.S. (2016) Designing asymmetric multilayered membrane filters with improved performance. Journal of Membrane Science, 511, pp. 108-118. (doi: 10.1016/j.memsci.2016.02.028)

2015

Stewart, P. S. , Davis, S. H. and Hilgenfeldt, S. (2015) Microstructural effects in aqueous foam fracture. Journal of Fluid Mechanics, 785, pp. 425-461. (doi: 10.1017/jfm.2015.636)

Stewart, P. S. , Feng, J., Kimpton, L. S., Griffiths, I. M. and Stone, H. A. (2015) Stability of a bi-layer free film: simultaneous or individual rupture events? Journal of Fluid Mechanics, 777, pp. 27-49. (doi: 10.1017/jfm.2015.346)

Hermans, T., Bishop, K., Stewart, P. , Davis, S. and Grzybowski, B. (2015) Vortex flows impart chirality-specific lift forces. Nature Communications, 6, p. 5640. (doi: 10.1038/ncomms6640)

Agraval, U., Qi, N., Stewart, P. , Luo, X. , Williams, G., Rotchford, A. and Ramaesh, K. (2015) Optimum size of iridotomy in uveitis. Clinical and Experimental Ophthalmology, 43(7), pp. 692-696. (doi: 10.1111/ceo.12528) (PMID:25881493)

Hermans, T. M., Stewart, P. S. and Grzybowski, B. A. (2015) A pH-oscillator stretched in space but frozen in time. Journal of Physical Chemistry Letters, 6(5), pp. 760-766. (doi: 10.1021/jz502711c)

Stewart, P. S. and Jensen, O. E. (2015) Patterns of recruitment and injury in a heterogeneous airway network model. Journal of the Royal Society: Interface, 12, 20150523. (doi: 10.1098/rsif.2015.0523)

2014

Griffiths, I.M., Kumar, A. and Stewart, P.S. (2014) A combined network model for membrane fouling. Journal of Colloid and Interface Science, 432, pp. 10-18. (doi: 10.1016/j.jcis.2014.06.021) (PMID:25042380)

Stewart, P. S. , Jensen, O. E. and Foss, A. J. E. (2014) A theoretical model to allow prediction of the CSF pressure from observing the retinal venous pulse. Investigative Ophthalmology and Visual Science, 55(10), pp. 6319-6323. (doi: 10.1167/iovs.14-14331)

Lang, G. E., Stewart, P. S. , Vella, D., Waters, S. L. and Goriely, A. (2014) Is the Donnan effect sufficient to explain swelling in brain tissue slices? Journal of the Royal Society: Interface, 11(96), p. 20140123. (doi: 10.1098/rsif.2014.0123) (PMID:24759543)

2013

Davis, M.J., Stewart, P. and Davis, S. (2013) Local effects of gravity on foams. Journal of Fluid Mechanics, 737, pp. 1-18. (doi: 10.1017/jfm.2013.433)

Stewart, P. , Davis, S. and Hilgenfeldt, S. (2013) Viscous Rayleigh–Taylor instability in aqueous foams. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 436(5), pp. 898-905. (doi: 10.1016/j.colsurfa.2013.08.021)

Stewart, P.S. and Davis, S.H. (2013) Self-similar coalescence of clean foams. Journal of Fluid Mechanics, 722, pp. 645-664. (doi: 10.1017/jfm.2013.145)

2012

Stewart, P. S. and Davis, S. H. (2012) Dynamics and stability of metallic foams: Network modeling. Journal of Rheology, 56(3), p. 543. (doi: 10.1122/1.3695029)

2010

Stewart, P. S. , Heil, M., Waters, S. L. and Jensen, O. E. (2010) Sloshing and slamming oscillations in a collapsible channel flow. Journal of Fluid Mechanics, 662, pp. 288-319. (doi: 10.1017/S0022112010003277)

Stewart, P. S. , Waters, S. L., Billingham, J. and Jensen, O. E. (2010) Spatially localised growth within global instabilities of flexible channel flows. In: Schlatter, P. and Henningson, D. S. (eds.) Seventh IUTAM Symposium on Laminar-Turbulent Transition: Proceedings of the Seventh Iutam Symposium on Laminar-turbulent Transition, Stockholm, Sweden, 2009. Series: IUTAM bookseries (18). Springer: Dordrecht, pp. 397-402. ISBN 9789048137220

Stewart, P. S. , Waters, S. L. and Jensen, O. E. (2010) Local instabilities of flow in a flexible channel: Asymmetric flutter driven by a weak critical layer. Physics of Fluids, 22(3), 031902. (doi: 10.1063/1.3337824)

2009

Stewart, P. , Waters, S.L. and Jensen, O.E. (2009) Local and global instabilities of flow in a flexible-walled channel. European Journal of Mechanics - B/Fluids, 28(4), pp. 541-557. (doi: 10.1016/j.euromechflu.2009.03.002)

This list was generated on Thu Jun 8 09:04:46 2023 BST.
Jump to: Articles | Book Sections
Number of items: 34.

Articles

Wang, D., Luo, X. , Liu, Z. and Stewart, P. S. (2023) Flow-induced surface instabilities in a flexible-walled channel with a heavy wall. Journal of Fluid Mechanics, 956, A1. (doi: 10.1017/jfm.2022.1086)

Du, Y. , Stewart, P. , Hill, N. A. , Yin, H. , Penta, R. , Köry, J. , Luo, X. and Ogden, R. (2023) Nonlinear indentation of second-order hyperelastic materials. Journal of the Mechanics and Physics of Solids, 171, 105139. (doi: 10.1016/j.jmps.2022.105139)

Stewart, P. S. and Hilgenfeldt, S. (2023) Gas-liquid foam dynamics: from structural elements to continuum descriptions. Annual Reviews of Fluid Mechanics, 55, pp. 323-350. (doi: 10.1146/annurev-fluid-032822-125417)

Barry, R. G., Hill, N. A. and Stewart, P. S. (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. (doi: 10.1098/rspa.2022.0065)

Griffiths, I. M. and Stewart, P. S. (2022) A hybrid discrete–continuum framework for modelling filtration. Journal of Membrane Science, 647, 120258. (doi: 10.1016/j.memsci.2022.120258)

Herrada, M.A., Blanco-Trejo, S., Eggers, J. and Stewart, P.S. (2022) Global stability analysis of flexible channel flow with a hyperelastic wall. Journal of Fluid Mechanics, 934, A28. (doi: 10.1017/jfm.2021.1131)

Wang, Z., Wang, C., Zhao, F., Qi, N., Lockington, D., Ramaesh, K., Stewart, P. S. , Luo, X. and Tang, H. (2022) Simulation of fluid-structure interaction during the phaco-emulsification stage of cataract surgery. International Journal of Mechanical Sciences, 214, 106931. (doi: 10.1016/j.ijmecsci.2021.106931)

Wang, D.Y., Luo, X.Y. and Stewart, P.S. (2021) Energetics of collapsible channel flow with a nonlinear fluid-beam model. Journal of Fluid Mechanics, 926, A2. (doi: 10.1017/jfm.2021.642)

Wang, D., Luo, X. and Stewart, P. S. (2021) Multiple steady and oscillatory solutions in a collapsible channel flow. International Journal of Applied Mechanics, 13(6), 2150058. (doi: 10.1142/S1758825121500587)

Griffiths, I.M., Mitevski, I., Vujkovac, I., Illingworth, M.R. and Stewart, P.S. (2020) The role of tortuosity in filtration efficiency: a general network model for filtration. Journal of Membrane Science, 598, 117664. (doi: 10.1016/j.memsci.2019.117664)

Spelman, T.A. and Stewart, P.S. (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. (doi: 10.1098/rspa.2019.0269) (PMID:32201473)

Stewart, P. S. and Foss, A. J.E. (2019) Self-excited oscillations in a collapsible channel with applications to retinal venous pulsation. ANZIAM Journal, 61(3), pp. 320-348. (doi: 10.1017/S1446181119000117)

Stewart, P. S. and Hilgenfeldt, S. (2017) Cracks and fingers: dynamics of ductile fracture in an aqueous foam. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 534, pp. 58-70. (doi: 10.1016/j.colsurfa.2017.03.057)

MacTaggart, D. and Stewart, P. (2017) Optimal energy growth in current sheets. Solar Physics, 292(10), 148. (doi: 10.1007/s11207-017-1177-1)

Stewart, P. S. (2017) Instabilities in flexible channel flow with large external pressure. Journal of Fluid Mechanics, 825, pp. 922-960. (doi: 10.1017/jfm.2017.404)

Stewart, P. S. , Waters, S. L., El Sayed, T., Vella, D. and Goriely, A. (2016) Wrinkling, creasing, and folding in fiber-reinforced soft tissues. Extreme Mechanics Letters, 8, pp. 22-29. (doi: 10.1016/j.eml.2015.10.005)

Griffiths, I. M., Kumar, A. and Stewart, P.S. (2016) Designing asymmetric multilayered membrane filters with improved performance. Journal of Membrane Science, 511, pp. 108-118. (doi: 10.1016/j.memsci.2016.02.028)

Stewart, P. S. , Davis, S. H. and Hilgenfeldt, S. (2015) Microstructural effects in aqueous foam fracture. Journal of Fluid Mechanics, 785, pp. 425-461. (doi: 10.1017/jfm.2015.636)

Stewart, P. S. , Feng, J., Kimpton, L. S., Griffiths, I. M. and Stone, H. A. (2015) Stability of a bi-layer free film: simultaneous or individual rupture events? Journal of Fluid Mechanics, 777, pp. 27-49. (doi: 10.1017/jfm.2015.346)

Hermans, T., Bishop, K., Stewart, P. , Davis, S. and Grzybowski, B. (2015) Vortex flows impart chirality-specific lift forces. Nature Communications, 6, p. 5640. (doi: 10.1038/ncomms6640)

Agraval, U., Qi, N., Stewart, P. , Luo, X. , Williams, G., Rotchford, A. and Ramaesh, K. (2015) Optimum size of iridotomy in uveitis. Clinical and Experimental Ophthalmology, 43(7), pp. 692-696. (doi: 10.1111/ceo.12528) (PMID:25881493)

Hermans, T. M., Stewart, P. S. and Grzybowski, B. A. (2015) A pH-oscillator stretched in space but frozen in time. Journal of Physical Chemistry Letters, 6(5), pp. 760-766. (doi: 10.1021/jz502711c)

Stewart, P. S. and Jensen, O. E. (2015) Patterns of recruitment and injury in a heterogeneous airway network model. Journal of the Royal Society: Interface, 12, 20150523. (doi: 10.1098/rsif.2015.0523)

Griffiths, I.M., Kumar, A. and Stewart, P.S. (2014) A combined network model for membrane fouling. Journal of Colloid and Interface Science, 432, pp. 10-18. (doi: 10.1016/j.jcis.2014.06.021) (PMID:25042380)

Stewart, P. S. , Jensen, O. E. and Foss, A. J. E. (2014) A theoretical model to allow prediction of the CSF pressure from observing the retinal venous pulse. Investigative Ophthalmology and Visual Science, 55(10), pp. 6319-6323. (doi: 10.1167/iovs.14-14331)

Lang, G. E., Stewart, P. S. , Vella, D., Waters, S. L. and Goriely, A. (2014) Is the Donnan effect sufficient to explain swelling in brain tissue slices? Journal of the Royal Society: Interface, 11(96), p. 20140123. (doi: 10.1098/rsif.2014.0123) (PMID:24759543)

Davis, M.J., Stewart, P. and Davis, S. (2013) Local effects of gravity on foams. Journal of Fluid Mechanics, 737, pp. 1-18. (doi: 10.1017/jfm.2013.433)

Stewart, P. , Davis, S. and Hilgenfeldt, S. (2013) Viscous Rayleigh–Taylor instability in aqueous foams. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 436(5), pp. 898-905. (doi: 10.1016/j.colsurfa.2013.08.021)

Stewart, P.S. and Davis, S.H. (2013) Self-similar coalescence of clean foams. Journal of Fluid Mechanics, 722, pp. 645-664. (doi: 10.1017/jfm.2013.145)

Stewart, P. S. and Davis, S. H. (2012) Dynamics and stability of metallic foams: Network modeling. Journal of Rheology, 56(3), p. 543. (doi: 10.1122/1.3695029)

Stewart, P. S. , Heil, M., Waters, S. L. and Jensen, O. E. (2010) Sloshing and slamming oscillations in a collapsible channel flow. Journal of Fluid Mechanics, 662, pp. 288-319. (doi: 10.1017/S0022112010003277)

Stewart, P. S. , Waters, S. L. and Jensen, O. E. (2010) Local instabilities of flow in a flexible channel: Asymmetric flutter driven by a weak critical layer. Physics of Fluids, 22(3), 031902. (doi: 10.1063/1.3337824)

Stewart, P. , Waters, S.L. and Jensen, O.E. (2009) Local and global instabilities of flow in a flexible-walled channel. European Journal of Mechanics - B/Fluids, 28(4), pp. 541-557. (doi: 10.1016/j.euromechflu.2009.03.002)

Book Sections

Stewart, P. S. , Waters, S. L., Billingham, J. and Jensen, O. E. (2010) Spatially localised growth within global instabilities of flexible channel flows. In: Schlatter, P. and Henningson, D. S. (eds.) Seventh IUTAM Symposium on Laminar-Turbulent Transition: Proceedings of the Seventh Iutam Symposium on Laminar-turbulent Transition, Stockholm, Sweden, 2009. Series: IUTAM bookseries (18). Springer: Dordrecht, pp. 397-402. ISBN 9789048137220

This list was generated on Thu Jun 8 09:04:46 2023 BST.

Grants

CI on EPSRC SofTMech Statistical Emulation and Translation Hub (2021-2024) (FEC: £1.5M).

CI on EPSRC SofTMech with MIT (USA) and Politechnico di Milano (POLIMI, It) (SofTMechMP) (2020-2023)
(FEC: £2M).

PI on EPSRC First Grant entitled ‘Elastic Jumps on Networks’ (2017-2019) (FEC: £125k).

CI on EPSRC Centre for Multi-scale Soft Tissue Mechanics (2016-2020) (FEC: £2.5M).

Supervision

I am always on the look out for interested PhD students. I would be happy to supervise projects on any of my research interests.

Current PhD students include:

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)

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)

 

Teaching

I am currently the deputy head of Mathematics 1 (2019-2023), where I coordinate our online assessments.

Research datasets

Jump to: 2022 | 2021 | 2020 | 2019 | 2017 | 2015
Number of items: 9.

2022

Wang, D., Luo, X. and Stewart, P. (2022) Flow-induced surface instabilities in a flexible-walled channel with a heavy wall. [Data Collection]

2021

Herrada, M. A., Blanco-Trejo, S., Eggers, J. and Stewart, P. (2021) Global stability analysis of flexible channel flow with a hyperelastic wall. [Data Collection]

Wang, D., Luo, X. and Stewart, P. (2021) Multiple Steady and Oscillatory Solutions in a Collapsible Channel Flow. [Data Collection]

Wang, D., Luo, X. , Cai, Z. and Stewart, P. (2021) Energetics of a collapsible channel flow with a nonlinear fluid-beam model. [Data Collection]

2020

Stewart, P. , Barry, R. and Hill, N. (2020) Continuum soft tissue models from upscaling arrays of hyperelastic cells. [Data Collection]

2019

Stewart, P. and Foss, A. (2019) Self-excited oscillations in a collapsible channel, with applications to retinal venous pulsation. [Data Collection] (Unpublished)

Stewart, P. and Spelman, T. (2019) Shock wave propagation along the central retinal blood vessels. [Data Collection]

2017

Stewart, P. (2017) Instabilities in flexible channel flow with large external pressure. [Data Collection]

2015

Stewart, P. and Jensen, O. (2015) Patterns of recruitment and injury in a heterogeneous airway network model. [Data Collection]

This list was generated on Thu Jun 8 09:04:23 2023 BST.