MA; MSc; DPhil (Oxford)

Academic background

I was a mathematics undergraduate and graduate student at St Anne’s College (Oxford) in the 1990s. My DPhil thesis was about “The mathematics of foam”. I spent two years at Sheffield University working in the Department of Pathology, where I constructed some of the first mathematical models for vascular tumour growth. I returned to Oxford in 2001 to a position at the Mathematical Institute as a Research Facilitator (the first of its kind) which combined research with getting grants.  This was a very successful role and in 2008 we won a $25M grant from KAUST in Saudi Arabia to set up the Oxford Centre for Collaborative Applied Mathematics (OCCAM).  I was appointed to a faculty position in 2008 and was OCCAM’s Associate Director from 2008-2014 (when the money ran out).

I was the lead academic in the preparation of the Mathematical Sciences submission to REF 2014. We had the very pleasing result of coming top in every submeasure that the government used, as well as coming overall top (Yes, Oxford Mathematics is officially better than Cambridge Mathematics).

I am currently the co-Director of the EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling InFoMM, which is an 8-year endeavour to train 60 applied maths DPhil students in the skills needed to tackle 21st Century industrial problems using cutting edge mathematical techniques. Our centre, which launched in 2014, currently has over 60 company partners.

I am an elected member of the University’s Delegacy for Military Instruction, and of the Council of the Institute of Mathematics and Its Applications.

On the teaching front, I joined Christ Church’s teaching team in October 2004.

Undergraduate teaching

I teach first and second year applied mathematics – calculus, dynamics, ODEs/PDEs, calculus of variations, fluid mechanics and mathematical biology. I occasionally teach intercollegiate classes in fluid mechanics or applied partial differential equations for third years. 

Research interests

My research is centred around explaining phenomena arising in industry and medicine. Often these involve fluid mechanics or heat and mass transfer. One key area of my work has been the study of surface-active agents, such as washing up liquid, which modify the surface tension of air-liquid interfaces and can fundamentally change fluid flows. I’m currently working on modelling surfactants in systems out of thermodynamic equilibrium, tear films during blinking, glass manufacture, enhanced oil recovery, silicon manufacture, and filtering.

Featured publications

Here are some recent publications, which indicate my research interests:

Wilmott ZM, Breward CJW and Chapman SJ. (2018) Slip flow through channels of varying elliptic cross section. IMA J. Appl. Math. (To appear)

O'Kiely D, Breward CJW, Griffiths IM, Howell PD and Lange U. (2018) Glass sheet redraw through a long heater zone. IMA J. Appl. Math. (To appear)

Wilmott ZM, Breward CJW and Chapman SJ. (2018) The effect of ions on the motion of an oil slug through a charged capillary. J. Fluid Mech. 841, 310-350. DOI://doi.org/10/1017/jfm.2018.13

Black JP, Breward CJW and Howell PD (2017) Quantum mechanical effects in continuum charge flow models IMA J. Appl. Math., 82(2), 251-269 (doi:10.1093/imamat/hxw037).

Hennessy M, Breward CJW and Please CP (2016) A two-phase model for evaporating solvent-polymer mixtures SIAM J. Appl. Math. 76(4):1711-1736.

O'Kiely D, Breward CJW, Griffiths IM, Howell PD and Lange U (2015)  Edge behaviour in the glass redraw process. J. Fluid Mech., 785, 248-269. 

Breward CJW, Griffiths IM, Howell PD and Morgan M (2015)  Straining flow of a weakly interacting polymer-surfactant solution. Euro. J. Appl. Math., 26 (5), 743-772.

Morgan CE, Breward CJ, Griffiths IM and Howell PD (2015) Mathematical Modelling of Surfactant Self-Assembly at Interfaces. SIAM J. Appl. Math., 75(2), 836-860. 

Black JP, Breward CJ, and Howell PD (2015) Two-dimensional modelling of electron flow through a poorly conducting layer. SIAM J. Appl. Math., 75(2), 289-312. DOI:10.1137/140984105. 

Bruna M and Breward CJW (2014) The influence of nonpolar lipids on tear film dynamics. J Fluid Mech., 746, 565-605. DOI: 10.1017/jfm.2014.106  

Other interests and activities

I hold a Cadet Forces Commission, and currently command seven Air Training Corps Squadrons in South and West Oxfordshire.