# 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

## 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 groups

## 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

## 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)

**Agozie**, Bethel

Nonlinear flows in networks**Bhattacharya**, Atrayee

Predicting patterns of retinal haemorrhage**Kumari**, Tanisha

The mathematics of glacial ice sheets and their role in the changing climate**McNicol**, Gordon

Mathematical models for cell-substrate interaction**Onah**, Ifeanyi Sunday

Riemann problems in retinal circulation

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.