## Robert A. Van Gorder

### Bio-sketch:

I obtained BS (2009) and PhD (2014) degrees in mathematics from the University of Central Florida (UCF), where I held a Trustees Doctoral Fellowship (2009-2011) and then a National Science Foundation Graduate Research Fellowship (2011-2014). After completion of my PhD, I moved to the Mathematical Institute at the University of Oxford, UK, and took up the post of Research Fellow in Nonlinear Dynamics (2014-2015), followed by a Glasstone Research Fellowship in Science (2015-2018). In 2019, I joined the faculty of the Department of Mathematics and Statistics at the University of Otago, New Zealand, as a Senior Lecturer.

### Contact Details:

Physical address: Robert A. Van Gorder, Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand

email: rvangorder at maths dot otago dot ac dot nz

### Employment:

Senior Lecturer, Department of Mathematics and Statistics, University of Otago, New Zealand (2019 - present)

Violette and Samuel Glasstone Research Fellow in Science, Mathematical Institute, University of Oxford, United Kingdom (2015 - 2018)

Research Fellow in Nonlinear Dynamics, Mathematical Institute, University of Oxford, United Kingdom (2014 - 2015)

### Education:

PhD Mathematics (2014); University of Central Florida (UCF), Orlando, Florida, United States

National Science Foundation (NSF) Graduate Research Fellowship (2011-2014)

UCF Trustees Doctoral Fellowship (2009-2011)

B.S. Mathematics (2009); University of Central Florida (UCF), Orlando, Florida, United States

Minor areas of concentration: Economics, Physics, Statistics

### Research Field and Publications:

I am an applied mathematician with interests in several application areas. Mathematically, I specialize in the trifecta of mathematical modelling, analytical and asymptotic solution methods, and numerical simulations, with the focus being on establishing mathematical models for scientific phenomena or engineering problems, and these studying these models using a variety of analytical and numerical techniques.

Roughly half of my work, and much of my recent work, is primarily motivated by specific applications, with any mathematical analysis in the service of better understanding underlying phenomena. The focus of these publications is to say something relevant or useful about a specific problem or family of problems related to an application in science or engineering. In the area of physics, applications of interest have included nonlinear waves, Bose-Einstein condensates, and quantized vortex filaments in superfluids. Work in fluids has involved topics such as vortex dynamics, bubbles, and boundary layer flows in classical fluids, as well as various applications involving a variety of flow configurations and fluid properties. I've studied various heat and mass transfer problems, as well as multi-phase flows, fluid-particle systems, and chemical flows, and some of these have been in collaboration with industrial partners. Biologically motivated applications have included biochemistry, pattern formation, and ecology. Publications in econophysics and network dynamics have concerned problems in economics (including nonlinear dynamics and control), sociology, epidemiology of metapopulations, and game theory.

Roughly half of my work, including much of my earlier work, was focused on analytical approaches for the solution of mathematical models involving differential equations, including exact solution methods, approximate methods such as asymptotic, perturbation, series and related techniques, as well as existence or stability results. Pseudo-analytic techniques, such as homotopy analysis, where optimization or acceleration of a series involves a numerical component, is one example. Some of this work includes numerical methods which involve some sort of analytical component.

I am occasionally interested in problems in elementary analytic number theory and related mathematics.

These days, my papers appear on Google Scholar quickly after they are published, and you can find a publication list sorted in reverse chronological order here:

Feel free to get in touch if you'd like a copy of a published paper emailed to you.

### Research student supervision:

I've supervised the following doctoral students:

E. K. Luckins, Energy Balance Models and the Control of Silicon Furnaces, 2018 - present, DPhil, Oxford InFoMM CDT; co-supervised with J. M. Oliver, C. P. Please; industry sponsor: Elkem

R. González Fariña, Microsilica Particle Formation and Growth, 2017 - 2020, DPhil, Oxford InFoMM CDT; co-supervised with A. Muench, J. M. Oliver; industry sponsor: Elkem

J. Lee, Modelling and Computation for Petroleum Systems in Basins with Complex Structural Geometries, 2015-2019, DPhil, Oxford InFoMM CDT; co-supervised with K. Gillow, J. Whiteley; industry sponsor: Petrotechnical Data Systems

F. Brosa Planella, Modelling Solidification of Binary Alloys, 2015 - 2018, DPhil, Oxford InFoMM CDT; co-supervised with C. P. Please; industry sponsor: Elkem. (Placement: Post-Doc at Warwick)

N. T. Fadai, Multiphase Modelling of Coffee Bean Roasting, Oxford, 2015 - 2018, DPhil, Oxford InFoMM CDT; co-supervised with C. P. Please; industry sponsor: Jacobs Douwe Egberts. (Placement: Post-Doc at QUT, then Lecturer at Nottingham)

B. M. Sloman, Mathematical Modelling of Silicon Furnaces, 2015 - 2018, DPhil, Oxford InFoMM CDT; co-supervised with C. P. Please; industry sponsor: Elkem. (Placement: Research Scientist at Elkem ASA)

A. L. Krause, Network Modelling of Bioactive Porous Media, 2015 - 2017, DPhil, Oxford; co-supervised with S. L. Waters and D. Beliaev. (Placement: Post-Doc at Oxford, then Lecturer at Oxford)

I've also supervised a number of MSc, BSc, and other short-term research projects.

### Teaching

University of Otago

Lectures: MATH170 Mathematics 2 - Calculus and ODEs (S1 2019, S1 & S2 2020, S1 & S2 2021), MATH4AA Asymptotic Analysis (S2 2019, S2 2020, S2 2021), MATH4A1 Techniques in Applied Mathematics 1 (S1 2021), MATH4A2 Techniques in Applied Mathematics 2 (S2 2021)

University of Oxford

Intercollegiate Classes (Mathematical Institute): Applied Complex Variables (2015,2017), Perturbation Methods (2014), Viscous Flow (2015), Applied Partial Differential Equations (2015), Techniques of Applied Mathematics (2014), Modelling Case Study (2016, 2017, 2018)

College Tutorials (including Christ Church College, Oriel College, New College): Geometry (2015,2016), Dynamics (2016), Fluids and Waves (2016), Fourier Series and PDEs (2015), Integration (Measure Theory) (2016), Numerical Analysis (2015, 2016), Probability II (2015), Quantum Theory (2015, 2016), Special Relativity (2015), Statistics and Data Analysis (2016), Topology (2016)

University of Central Florida

Lectures: Calculus 1 (2010), Calculus 2 (2011), Calculus 3 (2010, 2013)

### Miscellaneous:

Erdős Number = 3