Dr Robert Van Gorder

Dr Robert Van Gorder
Glasstone Research Fellow and Junior Research Fellow in Mathematics
Dr
Robert
Van Gorder

I hold B.S., M.S., and Ph.D. degrees, all in mathematics, and all from the University of Central Florida (UCF).

I was a recipient of the UCF Trustees Doctoral Fellowship (~ 8 awarded in a given year by UCF), and later the National Science Foundation's Graduate Research Fellowship (~ 20 awarded in a given year nationally, in the area of applied mathematics).

I was UCF's Hernandez Mathematics Award winner in 2009. I taught and conducted research in the Department of Mathematics at UCF from 2009 to 2014. In 2014, I joined the Mathematical Institute at the University of Oxford. During the 2014-2015 academic year, I held the position of Research Fellow in Nonlinear Dynamics (Mathematical Institute, Oxford). During the 2015-2018 academic years, I will hold the position of Glasstone Research Fellow in Science (Mathematical Institute, Oxford).

Research interests

My general research interests lie in applied mathematics and nonlinear differential equations. Approximation and perturbation methods, nonlinear PDEs, dynamical systems, fluid dynamics and turbulence, mathematical physics, integrable models and nonlinear waves, game theory and mathematical economics, mathematical biology and chemistry.

Selected publications

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, 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, 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.

R. A. Van Gorder, Dynamics of a planar vortex filament under the quantum local induction approximation, Proceedings of the Royal Society A 470 (2014) 20140341.

R. A. Van Gorder, Quantum vortex dynamics under the tangent representation of the local induction approximation, Journal of Fluid Mechanics 740 (2014) 5-16.

E. H. Doha, A. H. Bhrawy, M. A. Abdelkawy, and R. A. Van Gorder, Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations, Journal of Computational Physics 261 (2014) 244-255.

J. Haussermann and R. A. Van Gorder, Classification of two types of weak solutions to the Casimir equation for the Ito system, Quarterly of Applied Mathematics 72 (2014) 471-490.

K. Mallory and R. A. Van Gorder, Stationary solutions for the 2+1 nonlinear Schrödinger equation modeling Bose-Einstein condensates in radial potentials, Physical Review E 90 (2014) 023201.

D. Karpenko, R. A. Van Gorder and A. Kandel, The Cauchy Problem for Complex Fuzzy Differential Equations, Fuzzy Sets and Systems 245 (2014) 18-29.

R. A. Van Gorder, Decay of helical Kelvin waves on a quantum vortex filament, Physics of Fluids 26 (2014) 075101.