I obtained BS (2009) and PhD (2014) degrees in mathematics from the University of Central Florida (UCF), USA, 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 as a Senior Lecturer.
In my research I seek to better understand how physical phenomena can be described, predicted, and even modified using tools from applied mathematics. I specialize in the trifecta of mathematical modelling (writing down relations between physical quantities within the language of mathematics... this is where all of those equations come from!), analytical and asymptotic solution methods (deriving an exact or approximate solution to a mathematical problem using pen-and-paper approaches), and numerical simulations (using a computer program to solve a mathematical problem). I apply these methods to study physical phenomena, primarily those falling into one of the following areas:
Fluid dynamics
If you're alive, you're interacting with fluids: The air you breathe and the water you drink are examples of fluids. Despite the ubiquitous nature of fluids, there are still many questions we have about their behavior. My interests in fluids include better understanding the dynamics governing fundamental structures – such as vortices, bubbles, waves, and boundary layers – that can then be used as building blocks for more complex fluid flows. What forms can these structures take? Do they persist, or break apart over time? What happens if we attempt to manipulate or control these structures? These are the kinds of questions I am interested in.
Spatial instabilities and pattern formation
Diffusive instabilities – such as the Turing and Benjamin-Feir instabilities – have been proposed as mechanisms for the formation of patterns in many real-world systems, ranging from spot formation on the coats of big cats to optical turbulence in lasers. I am interested in understanding how these instability mechanisms extended to more generic non-autonomous or spatially heterogeneous systems, where they result in messier yet perhaps more realistic patterning. These heterogeneous systems arise from models of reaction-diffusion processes such as chemical reactions in the presence of thermal forcing, fluid flows, or evolving space domains, and are found in applications ranging from physics and chemistry to biology and epidemiology. Under what conditions can spatial or spatiotemporal patterns emerge from such systems? How might these patterns be controlled?
Quantum theory, quantum fluids, and nonlinear waves
My interests in theoretical physics include quantum mechanics and quantum field theory, with a particular focus on modelling problems in low-temperature physics and condensed matter physics as quantum fluids. Some of my work in this area has involved understanding the dynamics Bose-Einstein condensates, quantized vortex filaments in superfluid helium, and confined quantum systems. While these topics are farther removed from our daily experiences, they exhibit exotic and interesting behaviors, providing a number of fascinating scientific challenges. Nonlinear waves arise in these and other applications, and I am interested in understanding how nonlinear waves evolve under various conditions relevant to realistic experimental configurations, such as confined space domains or external forcing.
I am happy to supervise PhD and honours projects in any of these areas.
Publications
Van Gorder, R. A. (2023). Quantum mechanics on time-varying space domains. Proceedings of the Royal Society A, 479, 20220759. doi: 10.1098/rspa.2022.0759
Journal - Research Article
Van Gorder, R. A., & Fisher, P. A. (2023). Spatial eigenvalue problems for stars in hydrostatic equilibrium: Generalized Lane–Emden equations as boundary value problems. Monthly Notices of the Royal Astronomical Society, 523(2), 2059-2073. doi: 10.1093/mnras/stad1506
Journal - Research Article
Van Gorder, R. A. (2022). Compressed hydrogen atoms confined within generic boxes. Proceedings of the Royal Society A, 478(2268), 20220467. doi: 10.1098/rspa.2022.0467
Journal - Research Article
Luckins, E. K., Oliver, J. M., Please, C. P., Sloman, B. M., & Van Gorder, R. A. (2022). Modelling and analysis of an endothermic reacting counter-current flow. Journal of Fluid Mechanics, 949, A21. doi: 10.1017/jfm.2022.702
Journal - Research Article
Luckins, E. K., Oliver, J. M., Please, C. P., Sloman, B. M., Valderhaug, A. M., & Van Gorder, R. A. (2022). Modelling alternating current effects in a submerged arc furnace. IMA Journal of Applied Mathematics, 87, 492-520. doi: 10.1093/imamat/hxac012
Journal - Research Article
Luckins, E. K., Oliver, J. M., Please, C. P., Sloman, B. M., & van Gorder, R. A. (2022). Homogenised model for the electrical current distribution within a submerged arc furnace for silicon production. European Journal of Applied Mathematics, 33, 828-863. doi: 10.1017/s0956792521000243
Journal - Research Article
Ritchie, J. S., Krause, A. L., & Van Gorder, R. A. (2022). Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation. Annals of Physics. Advance online publication. doi: 10.1016/j.aop.2022.169033
Journal - Research Article
Van Gorder, R. A. (2022). Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged. Physics Letters A. Advance online publication. doi: 10.1016/j.physleta.2022.128284
Journal - Research Article
Van Gorder, R. A. (2022). Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state. Proceedings of the Royal Society A, 478(2262), 20220172. doi: 10.1098/rspa.2022.0172
Journal - Research Article
Erban, R., & Van Gorder, R. A. (2021). On the sum of positive divisors functions. Research in Number Theory, 7, 25. doi: 10.1007/s40993-021-00240-6
Journal - Research Article
Van Gorder, R. A. (2021). A theory of pattern formation for reaction–diffusion systems on temporal networks. Proceedings of the Royal Society A, 477, 20200753. doi: 10.1098/rspa.2020.0753
Journal - Research Article
Van Gorder, R. A. (2021). Pattern formation from spatially heterogeneous reaction-diffusion systems. Philosophical Transactions of the Royal Society A, 379, 20210001. doi: 10.1098/rsta.2021.0001
Journal - Research Article
Van Gorder, R. A. (2021). Time-varying Bose–Einstein condensates. Proceedings of the Royal Society A, 477, 20210443. doi: 10.1098/rspa.2021.0443
Journal - Research Article
Van Gorder, R. A., Kamilova, A., Birkeland, R. G., & Krause, A. L. (2021). Locating the baking isotherm in a Søderberg electrode: Analysis of a moving thermistor model. SIAM Journal on Applied Mathematics, 81(4), 1691-1716. doi: 10.1137/20M1314276
Journal - Research Article
Van Gorder, R. A., Klika, V., & Krause, A. L. (2021). Turing conditions for pattern forming systems on evolving manifolds. Journal of Mathematical Biology, 82, 4. doi: 10.1007/s00285-021-01552-y
Journal - Research Article
González-Fariña, R., Münch, A., Oliver, J. M., & van Gorder, R. A. (2020). Modeling microsilica particle formation and growth due to the combustion reaction of silicon monoxide with oxygen. SIAM Journal on Applied Mathematics, 80(2), 1003-1033. doi: 10.1137/19M1287080
Journal - Research Article
Krause, A. L., & Van Gorder, R. A. (2020). A non-local cross-diffusion model of population dynamics II: Exact, approximate, and numerical traveling waves in single- and multi-species populations. Bulletin of Mathematical Biology, 82, 113. doi: 10.1007/s11538-020-00787-y
Journal - Research Article
Sloman, B. M., Please, C. P., & Van Gorder, R. A. (2020). Melting and dripping of a heated material with temperature-dependent viscosity in a thin vertical tube. Journal of Fluid Mechanics, 905, A16. doi: 10.1017/jfm.2020.727
Journal - Research Article
Taylor, N. P., Kim, H., Krause, A. L., & Van Gorder, R. A. (2020). A non-local cross-diffusion model of population dynamics I: Emergent spatial and spatiotemporal patterns. Bulletin of Mathematical Biology, 82, 112. doi: 10.1007/s11538-020-00786-z
Journal - Research Article
Van Gorder, R. A. (2020). Influence of temperature on Turing pattern formation. Proceedings of the Royal Society A, 476(2240), 20200356. doi: 10.1098/rspa.2020.0356
Journal - Research Article
Van Gorder, R. A. (2020). Perturbation theory for Bose-Einstein condensates on bounded space domains. Proceedings of the Royal Society A, 476, 20200674. doi: 10.1098/rspa.2020.0674
Journal - Research Article
Van Gorder, R. A. (2020). Turing and Benjamin–Feir instability mechanisms in non-autonomous systems. Proceedings of the Royal Society A, 476(2238). doi: 10.1098/rspa.2020.0003
Journal - Research Article
Van Gorder, R. A., Krause, A. L., Malomed, B. A., & Kaup, D. J. (2020). Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices. Communications in Nonlinear Science & Numerical Simulation, 85, 105244. doi: 10.1016/j.cnsns.2020.105244
Journal - Research Article
Xu, Y., Krause, A. L., & Van Gorder, R. A. (2020). Generalist predator dynamics under Kolmogorov versus non-Kolmogorov models. Journal of Theoretical Biology, 486, 110060. doi: 10.1016/j.jtbi.2019.110060
Journal - Research Article
Conti, F., & Van Gorder, R. A. (2019). The role of network structure and time delay in a metapopulation Wilson-Cowan model. Journal of Theoretical Biology, 477, 1-13. doi: 10.1016/j.jtbi.2019.05.010
Journal - Research Article
Fadai, N. T., Please, C. P., & Van Gorder, R. A. (2019). Modelling structural deformations in a roasting coffee bean. International Journal of Non-Linear Mechanics, 110, 123-130. doi: 10.1016/j.ijnonlinmec.2018.12.006
Journal - Research Article
Fussell, E. F., Krause, A. L., & Van Gorder, R. A. (2019). Hybrid approach to modeling spatial dynamics of systems with generalist predators. Journal of Theoretical Biology, 462, 26-47. doi: 10.1016/j.jtbi.2018.10.054
Journal - Research Article
Horner, C. L., & Van Gorder, R. A. (2019). Dynamics of quantized vortex filaments under a local induction approximation with second-order correction. Physics of Fluids, 31(6), 065103. doi: 10.1063/1.5091567
Journal - Research Article
Hua, T., & Van Gorder, R. A. (2019). Wave propagation and pattern formation in two-dimensional hexagonally-packed granular crystals under various configurations. Granular Matter, 21, 3. doi: 10.1007/s10035-018-0852-8
Journal - Research Article
Kiradjiev, K. B., Halvorsen, S. A., Van Gorder, R. A., & Howison, S. D. (2019). Maxwell-type models for the effective thermal conductivity of a porous material with radiative transfer in the voids. International Journal of Thermal Sciences, 145, 106009. doi: 10.1016/j.ijthermalsci.2019.106009
Journal - Research Article
Perkins, M., & Van Gorder, R. A. (2019). Closed-form calculation of infinite products of Glaisher-type related to Dirichlet series. Ramanujan Journal, 49, 371-389. doi: 10.1007/s11139-018-0037-4
Journal - Research Article
Sachak-Patwa, R., Fadai, N. T., & Van Gorder, R. A. (2019). Modeling multi-group dynamics of related viral videos with delay differential equations. Physica A, 521, 197-217. doi: 10.1016/j.physa.2019.01.052
Journal - Research Article
Van Gorder, R. A. (2019). Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations. Numerical Algorithms, 81, 181-196. doi: 10.1007/s11075-018-0540-0
Journal - Research Article
Van Gorder, R. A., Kim, H., & Krause, A. L. (2019). Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains. Journal of Fluid Mechanics, 877, 759-823. doi: 10.1017/jfm.2019.620
Journal - Research Article
Van Gorder, R. A., Krause, A. L., & Kwiecinski, J. A. (2019). Amplitude death criteria for coupled complex Ginzburg–Landau systems. Nonlinear Dynamics, 19, 151-159. doi: 10.1007/s11071-019-04961-3
Journal - Research Article
Zhou, Z., & Van Gorder, R. A. (2019). Turing instability and colony formation in spatially extended Rosenzweig-MacArthur predator-prey models with allochthonous resources. Bulletin of Mathematical Biology, 81, 5009-5053. doi: 10.1007/s11538-019-00667-0
Journal - Research Article
Baines, L. W. S., & Van Gorder, R. A. (2018). Soliton wave-speed management: Slowing, stopping, or reversing a solitary wave. Physical Review A, 97, 063814. doi: 10.1103/PhysRevA.97.063814
Journal - Research Article
Bakhtiari, P., Abbasbandy, S., & Van Gorder, R. A. (2018). Reproducing kernel method for the numerical solution of the 1D Swift–Hohenberg equation. Applied Mathematics & Computation, 339, 132-143. doi: 10.1016/j.amc.2018.07.006
Journal - Research Article
Bakhtiari, P., Abbasbandy, S., & Van Gorder, R. A. (2018). Solving the Dym initial value problem in reproducing kernel space. Numerical Algorithms, 78(2), 405-421. doi: 10.1007/s11075-017-0381-2
Journal - Research Article
Bhatt, A., & Van Gorder, R. A. (2018). Chaos in a non-autonomous nonlinear system describing asymmetric water wheels. Nonlinear Dynamics, 93(4), 1977-1988. doi: 10.1007/s11071-018-4301-3
Journal - Research Article
Eide, R. M., Krause, A. L., Fadai, N. T., & Van Gorder, R. A. (2018). Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays. Journal of Theoretical Biology, 451, 19-34. doi: 10.1016/j.jtbi.2018.04.038
Journal - Research Article
Fadai, N. T., Please, C. P., & Van Gorder, R. A. (2018). Asymptotic analysis of a multiphase drying model motivated by coffee bean roasting. SIAM Journal on Applied Mathematics, 78(1), 418-436. doi: 10.1137/16M1095500
Journal - Research Article
Flora Meng, X., Van Gorder, R. A., & Porter, M. A. (2018). Opinion formation and distribution in a bounded-confidence model on various networks. Physical Review E: Statistical, Nonlinear, & Soft Matter Physics, 97(2), 022312. doi: 10.1103/PhysRevE.97.022312
Journal - Research Article
Jansen, J. E., & Van Gorder, R. A. (2018). Dynamics from a predator-prey-quarry-resource-scavenger model. Theoretical Ecology, 11(1), 19-38. doi: 10.1007/s12080-017-0346-z
Journal - Research Article
Kekić, A., & Van Gorder, R. A. (2018). Wave propagation across interfaces induced by different interaction exponents in ordered and disordered Hertz-like granular chains. Physica D, 384-385, 18-33. doi: 10.1016/j.physd.2018.07.007
Journal - Research Article
Kennedy, D. T., & Van Gorder, R. A. (2018). Motion of open vortex-current filaments under the Biot-Savart model. Journal of Fluid Mechanics, 836, 532-559. doi: 10.1017/jfm.2017.826
Journal - Research Article
Kleanthous, A., Hua, T., Manai, A., Yawar, K., & Van Gorder, R. A. (2018). Dynamics from a mathematical model of a two-state gas laser. Physica A, 497, 26-40. doi: 10.1016/j.physa.2017.12.110
Journal - Research Article
Krause, A. L., Beliaev, D., Van Gorder, R. A., & Waters, S. L. (2018). Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media. International Journal of Bifurcation & Chaos, 28(11), 1830037. doi: 10.1142/S0218127418300379
Journal - Research Article
Krause, A. L., Burton, A. M., Fadai, N. T., & Van Gorder, R. A. (2018). Emergent structures in reaction-advection-diffusion systems on a sphere. Physical Review E: Statistical, Nonlinear, & Soft Matter Physics, 97(4), 042215. doi: 10.1103/PhysRevE.97.042215
Journal - Research Article
Krause, A. L., Kurowski, L., Yawar, K., & Van Gorder, R. A. (2018). Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies. Journal of Theoretical Biology, 449, 35-52. doi: 10.1016/j.jtbi.2018.04.023
Journal - Research Article
Kwiecinski, J. A., & Van Gorder, R. A. (2018). Dynamics of nearly parallel interacting vortex filaments. Journal of Fluid Mechanics, 835, 575-623. doi: 10.1017/jfm.2017.792
Journal - Research Article
Kwiecinski, J. A., Kovacs, A., Krause, A. L., Planella, F. B., & Van Gorder, R. A. (2018). Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations. International Journal of Bifurcation & Chaos, 28(5), 1830013. doi: 10.1142/S0218127418300136
Journal - Research Article
Kwiecinski, J. A., Krause, A. L., & Van Gorder, R. A. (2018). Effects of tidal torques on 1I/2017 U1 (‘Oumuamua). Icarus, 311, 170-174. doi: 10.1016/j.icarus.2018.04.005
Journal - Research Article
Luckins, E. K., & Van Gorder, R. A. (2018). Bose–Einstein condensation under the cubic–quintic Gross–Pitaevskii equation in radial domains. Annals of Physics, 388, 206-234. doi: 10.1016/j.aop.2017.11.009
Journal - Research Article
Planella, F. B., Please, C. P., & Van Gorder, R. A. (2018). Instability in the self-similar motion of a planar solidification front. IMA Journal of Applied Mathematics, 83(1), 106-130. doi: 10.1093/imamat/hxx037
Journal - Research Article
Sachak-Patwa, R., Fadai, N. T., & Van Gorder, R. A. (2018). Understanding viral video dynamics through an epidemic modelling approach. Physica A, 502, 416-435. doi: 10.1016/j.physa.2018.02.083
Journal - Research Article
Sloman, B. M., Please, C. P., & Van Gorder, R. A. (2018). Asymptotic analysis of a silicon furnace model. SIAM Journal on Applied Mathematics, 78(2), 1174-1205. doi: 10.1137/17M1122335
Journal - Research Article
Van Gorder, R. A., Krause, A. L., Brosa Planella, F., & Burton, A. M. (2018). Coupled complex Ginzburg–Landau systems with saturable nonlinearity and asymmetric cross-phase modulation. Annals of Physics, 396, 397-428. doi: 10.1016/j.aop.2018.07.003
Journal - Research Article
Wu, R., & Van Gorder, R. A. (2018). Nonlinear dynamics of discrete time multi-level leader–follower games. Applied Mathematics & Computation, 320, 240-250. doi: 10.1016/j.amc.2017.09.034
Journal - Research Article
Adusumilli, S., & Van Gorder, R. A. (2017). Hyperchaos from a model of coupled stratosphere-troposphere dynamics. International Journal of Bifurcation & Chaos, 27(2), 1730007. doi: 10.1142/S0218127417300075
Journal - Research Article
Bassett, A., Krause, A. L., & Van Gorder, R. A. (2017). Continuous dispersal in a model of predator–prey-subsidy population dynamics. Ecological Modelling, 354, 115-122. doi: 10.1016/j.ecolmodel.2017.02.017
Journal - Research Article
Fadai, N. T., Melrose, J., Please, C. P., Schulman, A., & Van Gorder, R. A. (2017). A heat and mass transfer study of coffee bean roasting. International Journal of Heat & Mass Transfer, 104, 787-799. doi: 10.1016/j.ijheatmasstransfer.2016.08.083
Journal - Research Article
Harrington, H. A., & Van Gorder, R. A. (2017). Reduction of dimension for nonlinear dynamical systems. Nonlinear Dynamics, 88(1), 715-734. doi: 10.1007/s11071-016-3272-5
Journal - Research Article
Kleanthous, A., & Van Gorder, R. A. (2017). Heat and mass transfer within a vertical pipe with a surface heating element of variable size. International Communications in Heat & Mass Transfer, 85, 70-75. doi: 10.1016/j.icheatmasstransfer.2017.05.004
Journal - Research Article
Kleanthous, A., & Van Gorder, R. A. (2017). Influence of boiler size and location on one-dimensional two-phase vertical pipe flow. International Journal of Thermal Sciences, 121, 150-162. doi: 10.1016/j.ijthermalsci.2017.07.007
Journal - Research Article
Kurowski, L., Krause, A. L., Mizuguchi, H., Grindrod, P., & Van Gorder, R. A. (2017). Two-species migration and clustering in two-dimensional domains. Bulletin of Mathematical Biology, 79(10), 2302-2333. doi: 10.1007/s11538-017-0331-0
Journal - Research Article
Lowry, V. C., & Van Gorder, R. A. (2017). Asymptotic solutions for a relativistic formulation of the generalized nonextensive Thomas–Fermi model. Annals of Physics, 376, 311-323. doi: 10.1016/j.aop.2016.12.009
Journal - Research Article
Luckins, E. K., & Van Gorder, R. A. (2017). Linear stability analysis of steady-state tropical cyclones with single or double eyewalls. Quarterly Journal of the Royal Meteorological Society, 143(708), 2949-2959. doi: 10.1002/qj.3154
Journal - Research Article
Prasad, K. V., Vajravelu, K., Vaidya, H., & Van Gorder, R. A. (2017). MHD flow and heat transfer in a nanofluid over a slender elastic sheet with variable thickness. Results in Physics, 7, 1462-1474. doi: 10.1016/j.rinp.2017.03.022
Journal - Research Article
Ruks, L., & Van Gorder, R. A. (2017). On the inverse problem of competitive modes and the search for chaotic dynamics. International Journal of Bifurcation & Chaos, 27(10), 1730032. doi: 10.1142/S0218127417300324
Journal - Research Article
Shen, L., & Van Gorder, R. A. (2017). Predator–prey–subsidy population dynamics on stepping-stone domains. Journal of Theoretical Biology, 420, 241-258. doi: 10.1016/j.jtbi.2017.03.013
Journal - Research Article
Shi, B., & Van Gorder, R. A. (2017). Nonlinear dynamics from discrete time two-player status-seeking games. Journal of Dynamics & Games, 4(4), 335-359. doi: 10.3934/jdg.2017018
Journal - Research Article
Sloman, B. M., Please, C. P., Van Gorder, R. A., Valderhaug, A. M., Birkeland, R. G., & Wegge, H. (2017). A heat and mass transfer model of a silicon pilot furnace. Metallurgical & Materials Transactions B, 48(5), 2664-2676. doi: 10.1007/s11663-017-1052-3
Journal - Research Article
Theaker, K. A., & Van Gorder, R. A. (2017). Multicomplex wave functions for linear and nonlinear Schrödinger equations. Advances in Applied Clifford Algebras, 27(2), 1857-1879. doi: 10.1007/s00006-016-0734-2
Journal - Research Article
Theaker, K. A., & Van Gorder, R. A. (2017). Solutions to forced and unforced Lin-Reissner-Tsien equations for transonic gas flows on various length scales. Communications in Theoretical Physics, 67(3), 309-316. doi: 10.1088/0253-6102/67/3/309
Journal - Research Article
Van Gorder, R. A. (2017). Asymptotic solutions for the Föppl – von Kármán equations governing deflections of thin axisymmetric annular plates. International Journal of Non-Linear Mechanics, 91, 8-21. doi: 10.1016/j.ijnonlinmec.2017.02.004
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Van Gorder, R. A. (2017). Breathers and nonlinear waves on open vortex filaments in the nonrelativistic Abelian Higgs model. Physical Review D, 95(9), 096007. doi: 10.1103/PhysRevD.95.096007
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Van Gorder, R. A. (2017). Exact solution to a generalized model for compact stars. European Physical Journal C, 77, 74. doi: 10.1140/epjc/s10052-017-4632-0
Journal - Research Article
Van Gorder, R. A. (2017). Motion of isolated open vortex filaments evolving under the truncated local induction approximation. Physics of Fluids, 29(11), 115105. doi: 10.1063/1.5005113
Journal - Research Article
Waldron, O., & Van Gorder, R. A. (2017). A nonlinear Klein-Gordon equation for relativistic superfluidity. Physica Scripta, 92(10), 105001. doi: 10.1088/1402-4896/aa86fa
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Benham, G. P., Hildal, K., Please, C. P., & Van Gorder, R. A. (2016). Penetration of molten silicon into a bed of fines. International Journal of Heat & Mass Transfer, 75, 323-327. doi: 10.1016/j.icheatmasstransfer.2016.03.029
Journal - Research Article
Bhrawy, A. H., Doha, E. H., Abdelkawy, M. A., & Van Gorder, R. A. (2016). Jacobi-Gauss-Lobatto collocation method for solving nonlinear reaction-diffusion equations subject to Dirichlet boundary conditions. Applied Mathematical Modelling, 40(3), 1703-1716. doi: 10.1016/j.apm.2015.09.009
Journal - Research Article
Bhrawy, A. H., Zaky, M. A., & Van Gorder, R. A. (2016). A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation. Numerical Algorithms, 71(1), 151-180. doi: 10.1007/s11075-015-9990-9
Journal - Research Article
Kaup, D. J., & Van Gorder, R. A. (2016). Resonant solitons from the 3 × 3 operator. Mathematics & Computers in Simulation, 127, 131-150. doi: 10.1016/j.matcom.2012.11.004
Journal - Research Article
Levy, D., Harrington, H. A., & Van Gorder, R. A. (2016). Role of seasonality on predator-prey-subsidy population dynamics. Journal of Theoretical Biology, 396, 163-181. doi: 10.1016/j.jtbi.2016.02.005
Journal - Research Article
Saberi Nik, H., Van Gorder, R. A., & Gambino, G. (2016). The chaotic Dadras-Momeni system: Control and hyperchaotification. IMA Journal of Mathematical Control & Information, 33(2), 497-518. doi: 10.1093/imamci/dnu050
Journal - Research Article
Shah, R., & Van Gorder, R. A. (2016). Localized nonlinear waves on quantized superfluid vortex filaments in the presence of mutual friction and a driving normal fluid flow. Physical Review E: Statistical, Nonlinear, & Soft Matter Physics, 93(3), 032218. doi: 10.1103/PhysRevE.93.032218
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Taylor-King, J. P., Klages, R., Fedotov, S., & Van Gorder, R. A. (2016). Fractional diffusion equation for an n-dimensional correlated Lévy walk. Physical Review E: Statistical, Nonlinear, & Soft Matter Physics, 94(1), 012104. doi: 10.1103/PhysRevE.94.012104
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Van Gorder, R. A. (2016). A third-order extension to the Liénard oscillator and it’s competitive modes analysis. Nonlinear Dynamics, 86(1), 235-244. doi: 10.1007/s11071-016-2885-z
Journal - Research Article
Van Gorder, R. A. (2016). Dynamics of the Rayleigh-Plesset equation modelling a gas-filled bubble immersed in an incompressible fluid. Journal of Fluid Mechanics, 807, 478-508. doi: 10.1017/jfm.2016.640
Journal - Research Article
Van Gorder, R. A. (2016). Exact closed-form solution to jet flow of a polymer arising in the electrospun nanofiber elaboration process. Carbohydrate Polymers, 135, 187-190. doi: 10.1016/j.carbpol.2015.08.033
Journal - Research Article
Van Gorder, R. A. (2016). Self-similar vortex filament motion under the non-local Biot-Savart model. Journal of Fluid Mechanics, 802, 760-774. doi: 10.1017/jfm.2016.502
Journal - Research Article
Van Gorder, R. A. (2016). Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation. Physical Review E: Statistical, Nonlinear, & Soft Matter Physics, 93(5), 052208. doi: 10.1103/PhysRevE.93.052208
Journal - Research Article
Abbasbandy, S., Van Gorder, R. A., & Hajiketabi, M. (2015). The Lie-group shooting method for radial symmetric solutions of the Yamabe equation. Computer Modeling in Engineering & Sciences, 104(4), 329-351. doi: 10.3970/cmes.2015.104.329
Journal - Research Article
Abbasbandy, S., Van Gorder, R. A., Hajiketabi, M., & Mesrizadeh, M. (2015). Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system. Communications in Nonlinear Science & Numerical Simulation, 27(1-3), 254-262. doi: 10.1016/j.cnsns.2015.03.016
Journal - Research Article
Baxter, M., Choudhury, S. R., & Van Gorder, R. A. (2015). Zero curvature representation, bi-Hamiltonian structure, and an integrable hierarchy for the Zakharov-Ito system. Journal of Mathematical Physics, 56(6), 063503. doi: 10.1063/1.4922361
Journal - Research Article
Baxter, M., Van Gorder, R. A., & Vajravelu, K. (2015). Analytical construction of peaked solutions for the nonlinear evolution of an electromagnetic pulse propagating through a plasma. Quaestiones Mathematicae, 38(5), 725-748. doi: 10.2989/16073606.2014.981719
Journal - Research Article
Baxter, M., Van Gorder, R. A., & Vajravelu, K. (2015). Several types of similarity solutions for the Hunter-Saxton equation. Communications in Theoretical Physics, 63(6), 675-681. doi: 10.1088/0253-6102/63/6/675
Journal - Research Article