Introducing ICIAM's New Officer-at-Large Yvonne Stokes

I am an applied mathematician at The University of Adelaide, Australia. In 2023 I was elected as an Officer-at-large on the International Council of Industrial and Applied Mathematics (ICIAM). I also represent Australian and New Zealand Industrial and Applied Mathematics (ANZIAM), a division of the Australian Mathematics Society, on the ICIAM Board. I have a keen interest in applied mathematics and developing a better understanding of its value in the general population. I joined the ICIAM Board to both contribute to and learn about applied mathematics on the international scene and have become a member of ICIAM’s International Science Council Committee.

Brief Biography

I obtained a BSc from Murdoch University, Australia, and a BSc(Hons) and PhD from the University of Adelaide, Australia. Over my academic career, commenced in 1999 as an Assistant Lecturer at the University of Adelaide, I have held an Australian Research Council Postdoctoral Fellowship (2000-2002) and an Australian Research Council Future Fellowship (2017-2021). My research and contributions to applied mathematics have been recognised by two ANZIAM medals: the J.H. Michell Medal in 2007 which recognises outstanding new researchers, and the E.O. Tuck Medal in 2018 for outstanding research and distinguished service to the field of Applied Mathematics. Since 2012 I have been a Member of the Australian Academy of Sciences National Committee for Mechanical and Engineering Sciences. I am also a member of the ANZIAM Executive Committee. I have 70 peer reviewed journal and conference papers and have been awarded five highly competitive ARC Discovery Project grants. I have also been awarded three ARC Linkage Project grants which include an industry partner.

Research 

I enjoy using mathematics to solve real-world problems and have made significant contributions in the fields of fluid dynamics and mathematical biology. I develop physically grounded and elegant mathematical models using a range of sophisticated and inventive mathematics to obtain insightful and predictive results. These results provide fundamental understanding of complex processes. My models are important design tools for improving scientific understanding and developing new industrial processes across diverse areas including optical fibre fabrication, isolation of specific particles from others in a fluid, manufacture of novel components for mass-spectrometry, and assisted reproduction technologies.

My research on the drawing of optical fibres illustrates the type of research I enjoy. Thin optical fibres, ranging from axisymmetric tubes through to complex non-axisymmetric geometries with many air channels, have many uses in modern technologies, including communications systems, and biological, chemical and physical sensing. Accurate fabrication, by making an initial preform and pulling this to a fibre with the desired geometry, is crucial. But geometrical changes during fabrication make this very challenging. Predictive tools to replace costly experimental iteration are of significant value. 3D numerical simulation is not a viable option because of the number of free boundaries in even a quite simple fibre. I and my team, including applied mathematicians and experimentalists, have made ground-breaking contributions to provide such tools. With novel use of a variable transformation we solved a 30-year-old problem to show that extensional flow theory gives a semi-explicit solution for the change in geometry in drawing a preform to fibre for an arbitrary cross-sectional geometry (see figure, taken from reference [2]). The solution agrees well with experiments. Its form enables determining preform geometry and draw parameters to give a desired final fibre geometry. We showed that the same fibre will be obtained for a given pulling tension, regardless of the temperature profile, where the preform and other parameters are the same, a finding of enormous practical benefit because knowledge of the temperature is not needed provided furnace temperature can be adjusted to achieve the tension required for a desired fibre. From this the importance of equipping fibre-draw towers with tension measuring devices has been recognised. Our experimentally-validated mathematical models [1-5] provide highly-efficient, practically-useful, predictive tools with accuracy and power far exceeding what has gone before. More recent work has answered long-standing open questions on the effect of surface tension and an arbitrary number of internal holes on the stability of fibre drawing [6]. 

  1. Y.M. Stokes, P. Buchak, D.G. Crowdy and H. Ebendorff-Heidepriem (2014) Drawing of micro-structured fibres: circular and non-circular tubes. J. Fluid Mech. 755, 176-203. doi:10.1017/jfm.2014.408 
  2. P. Buchak, D.G. Crowdy, Y.M. Stokes and H. Ebendorff-Heidepriem (2015) Elliptical pore regularisation of the inverse problem for microstructured optical fibre fabrication, J. Fluid Mech. 778, 5-38. doi:10.1017/jfm.2015.337
  3. M.J. Chen, Y.M. Stokes, P. Buchak, D.G. Crowdy and H. Ebendorff-Heidepriem (2015) Microstructured optical fibre drawing with active pressurisation. J. Fluid Mech. 783, 137–165. doi:10.1017/jfm.2015.570 
  4. M. Chen, Y.M. Stokes, P. Buchak, D.G. Crowdy and H. Ebendorff-Heidepriem (2016) Asymptotic modelling of a six-hole MOF. J. Lightwave Technol. 34, 5651–5656. doi:10.1109/JLT.2016.2628438 
  5. M.J. Chen, Y.M. Stokes, P. Buchak, D.G. Crowdy, H.T.C. Foo, A. Dowler and H. Ebendorff-Heidepriem (2016) Drawing tubular fibres: experiments versus mathematical modelling. Optical Mater. Express 6, 166–180. doi:10.1364/OME.6.000166
  6. Y.M. Stokes, J.J. Wylie, M.J. Chen (2019). Coupled fluid and energy flow in fabrication of microstructured optical fibres. J. Fluid Mech. 874, 548–572. doi:10. 1017/jfm.2019.466
  7. J.J. Wylie, N.N. Papri, Y.M. Stokes, D. He (2023). Stability of drawing of microstructured optical fibres. J. Fluid Mech. 962, A12 (30pp). doi:10.1017/jfm. 2023.267
Author: 

Yvonne Stokes

Yvonne Stokes is Professor of Mathematics at the University of Adelaide, Australia. She is a member of the Executive Committee of ANZIAM, and became an Officer-at-Large of ICIAM in 2003. Her research areas are fluid dynamics and mathematical biology.
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