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School Board Finder. Homes Nearby. Schools that create a positive culture help all students thrive. Van Gorder, Dynamics of nearly parallel interacting vortex filaments , Journal of Fluid Mechanics Van Gorder, Dynamics of the Rayleigh-Plesset equation modelling a gas-filled bubble immersed in an incompressible fluid , Journal of Fluid Mechanics Pattern formation Pioneering work in the middle of the 20th century lead to the Turing and Benjamin-Feir instabilities, which give routes for spatially homogeneous solutions to transition into spatially heterogeneous patterns or spatiotemporal structures, and have been suggested as mechanisms for the formation of patterns in many systems.
My work has involved understanding how these instability mechanisms are properly extended to more generic non-autonomous systems systems which have an explicit time dependence and spatially heterogeneous systems systems which have an explicit dependence on space variables.
These kinds of systems arise from studies of reaction-diffusion processes in the presence of thermal forcing, fluid flows, or spatial domains which evolve in time.
Biologically motivated applications have included biochemistry, epidemiology, and ecology, and I've ended up supervising a number of students on projects related to these areas. These kinds of systems arise on both continuum e.
Selected Recent Publications: R. Van Gorder, Pattern formation from spatially heterogeneous reaction-diffusion systems, Philosophical Transactions of the Royal Society A Van Gorder, A theory of pattern formation for reaction-diffusion systems on temporal networks , Proceedings of the Royal Society A Van Gorder, V. Klika, and A. Krause, Turing conditions for pattern forming systems on evolving manifolds , Journal of Mathematical Biology 82 4.
Theoretical and mathematical physics My interests in mathematical physics include quantum mechanics and quantum field theory, with particular application to low-temperature physics and condensed matter physics.
Specific applications of interest include Bose-Einstein condensates and dynamics of quantized vortex filaments in superfluid helium. Nonlinear waves feature frequently in mathematical physics, and current interests on this topic involve the control of nonlinear waves through non-autonomous terms, waves which are dissipative, and waves on bounded space domains.
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
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