Glasstone Research Fellow in Science (October 2015 - September 2018)
- Stipendiary Lecturer, Christ Church College, University of Oxford (October 2015 - December 2016)
- Research Fellow in Nonlinear Dynamics, OCIAM, Mathematical Institute, University of Oxford (October 2014 - October 2015)
- NSF Research Fellow, UCF (August 2011 - May 2014)
- Trustee's Research Fellow, UCF (Augut 2009 - August 2011)
+44 1865 611513
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Much of my general research interests lie in applications of mathematics and the analysis of nonlinear differential equations. These include approximation, perturbation, and numerical methods, nonlinear PDEs, dynamical systems, fluid dynamics and turbulence, mathematical physics, integrable systems and nonlinear waves, solid mechanics, game theory and mathematical economics, mathematical biology and chemistry. I occasionally work in more pure mathematical areas, and prior interests have included pure analysis, elementary number theory, and combinatorics.
Previous Oxford teaching includes the following.
College tutorials (1st and 2nd year UG at either Christ Church and/or Oriel colleges):
- Fourier Series and PDEs
- Numerical Analysis
- Probability II
- Fluids and Waves
- Quantum Theory
- Special Relativity
Intercollegiate classes within the Mathematical Institute:
- 3rd year (Part B): Viscous Flow
- 4th year MMath (Part C): Applied Complex Variables, Perturbation Methods,
- MSci MMSC Intercollegiate Classes: Applied Partial Differential Equations, Techniques of Applied Mathematics
- MSci MMSC Modelling Case Study
Prizes, Awards, and Scholarships:
- Violette and Samuel Glasstone Research Fellow in Science, 2015-2018
(Non-Stipendiary) Junior Research Fellow, Oriel College, 2015- 2018
National Science Foundation Research Fellow, 2011-2014
UCF Trustee's Doctoral Research Fellow, 2009-2011
Hernandez Mathematics Award, 2009
Major / Recent Publications:
For a complete list of publications, view my website or Google Scholar. Some recent publications include:
- R. A. Van Gorder, Dynamics of the Rayleigh-Plesset equation modelling a gas-filled bubble immersed in an incompressible fluid, Journal of Fluid Mechanics 807 (2016) 478-508.
- R. A. Van Gorder, Self-similar vortex filament motion under the non-local Biot–Savart model, Journal of Fluid Mechanics 802 (2016) 760-774.
- R. A. Van Gorder, Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation, Physical Review E 93 (2016) 052208.
- R. A. Van Gorder, Exact closed-form solution to jet flow of a polymer arising in the electrospun nanofiber elaboration process, Carbohydrate Polymers 135 (2016) 187-190.
- R. A. Van Gorder, The Biot-Savart description of Kelvin waves on a quantum vortex filament in the presence of mutual friction and a driving fluid, Proceedings of the Royal Society A 471 (2015) 20150149.
- K. Mallory and R. A. Van Gorder, Stationary solutions for the nonlinear Schrödinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials, Physical Review E 92 (2015) 013201.
- R. A. Van Gorder, Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation, Physics of Fluids 27 (2015) 095104.
- K. Mallory and R. A. Van Gorder, Competitive modes for the detection of chaotic parameter regimes in the general chaotic bilinear system of Lorenz type, International Journal of Bifurcation and Chaos 25 (2015) 1530012 (32pp).
- R. A. Van Gorder, Continuous periodic solution of a nonlinear pseudo-oscillator equation in which the restoring force is inversely proportional to the dependent variable, Physica Scripta 90 (2015) 085208.
- R. A. Van Gorder, Quantum Hasimoto transformation and nonlinear waves on a superfluid vortex filament under the quantum local induction approximation, Physical Review E 91 (2015) 053201.
- R. A. Van Gorder, Non-local dynamics governing the self-induced motion of a planar vortex filament, Physics of Fluids 27 (2015) 065105.
- R. A. Van Gorder, Helical vortex filament motion under the non-local Biot-Savart model, Journal of Fluid Mechanics 762 (2015) 141-155.
- R. A. Van Gorder, Does the Riemann zeta function satisfy a differential equation?, Journal of Number Theory 147 (2015) 778-788.
Selected recent papers arising from student projects I've supervised include:
N. T. Fadai, J. Melrose, C. P. Please, A. Schulman, R. A. Van Gorder, A heat and mass transfer study of coffee bean roasting, International Journal of Heat and Mass Transfer 104 (2017) 787-799.
V. C. Lowry, R. A. Van Gorder, Asymptotic solutions for a relativistic formulation of the generalized nonextensive Thomas–Fermi model, Annals of Physics, in press, (2017).
J. P. Taylor-King, R. Klages, S. Fedotov, R. A. Van Gorder, Fractional diffusion equation for an n-dimensional correlated Lévy walk, Physical Review E 94 (2016) 012104.
D. Levy, H. A. Harrington, and R. A. Van Gorder, Role of seasonality on predator-prey-subsidy population dynamics, Journal of Theoretical Biology 396 (2016) 163-181.
G. P. Benham, K. Hildal, C. P. Please, and R. A. Van Gorder, Solidification of silicon in a one-dimensional slab and a two-dimensional wedge, International Journal of Heat and Mass Transfer 98 (2016) 530-540.