Keaton J. Burns

Hello! I'm a postdoc at the Flatiron Institute interested in scientific computing and fluid dynamics. I'm developing the spectral PDE solver Dedalus and utilizing it to study diverse problems in astrophysical, geophysical, and biological fluids.

Current Research

Spectral methods for PDEs with Dedalus

I'm the lead developer of Dedalus, an open-source framework for solving differential equations with modern spectral methods. Dedalus is composed of generalized algorithms that can accomodate a broad range of custom equation sets and spectral domains. It's written in Python 3 and is easy to use on a laptop, yet calls compiled libraries for performance-critical routines and can scale to thousands of cores with MPI.

Collaborators: Ben Brown, Daniel Lecoanet, Jeff Oishi, Geoff Vasil

Nonlinear tides in neutron stars

I am currently using Dedalus to study the nonlinear stability and saturation of tides in astrophysical bodies, particularly neutron stars. Orbiting bodies generate tides in their companions, and the dissipation of these tides can modify the orbital evolution of such systems over time. We're using direct numerical simulations to test theories of nonlinear instabilities and estimates of tidal dissipation rates in inspiralling neutron star binaries, like those recently observed by LIGO and VIRGO.

Collaborators: Nevin Weinberg

Glacial meltwater plumes

I'm also using Dedalus to model turbulent flows at the edges of marine-terminating glaciers. The fresh melt from the submerged face of such glaciers is buoyant with respect to the surrounding fluid, and forms a rising plume along the glacier's edge. The turbulent characteristics of these plumes may ultimately control the heat transport between the ambient water and the glacier, thereby influencing the melt rate and evolution of the glacier.

Collaborators: Glenn Flierl, Andrew Wells

Rolling resistance on granular media

During the 2016 Geophysical Fluid Dynamics program at the Woods Hole Oceanographic Institute, I performed experiments examining the dynamics of rolling objects on sand and other granular materials.

Collaborators: Neil Balmforth, Ian Hewitt

Selected Publications

Journal publications

  • "Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods"
    Burns et al.,, 2019. [arxiv]
  • "The 'Sphered Cube': A New Method for the Solution of Partial Differential Equations in Cubical Geometry"
    Burns et al.,, 2019. [arxiv]
  • "Tensor calculus in spherical coordinates using Jacobi polynomials. Part-II: Implementation and examples"
    Lecoanet et al., Journal of Computational Physics, 2019. [doi]
  • Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: Mathematical analysis and derivations"
    Vasil et al., Journal of Computational Physics, 2019. [doi]
  • "Anomalous Chained Turbulence in Actively Driven Flows on Spheres"
    Mickelin et al., Physical Review Letters, 2018. [ads] [doi]
  • "Rolling resistance of shallow granular deformation"
    Burns et al., Proceedings of the Royal Society A, 2017. [ads] [doi]
  • "Conversion of Internal Gravity Waves into Magnetic Waves"
    Lecoanet et al., MNRAS, 2016. [ads] [doi]
  • "Turbulent Chemical Diffusion in Convectively Bounded Carbon Flames"
    Lecoanet et al., Astrophysical Journal, 2016. [ads] [doi]
  • "Tensor calculus in polar coordinates using Jacobi polynomials"
    Vasil et al., Journal of Computational Physics, 2016. [ads] [doi]
  • "A validated nonlinear Kelvin-Helmholtz benchmark for numerical hydrodynamics"
    Lecoanet et al., MNRAS, 2016. [ads] [doi]
  • "Numerical simulations of internal wave generation by convection in water"
    Lecoanet et al., Physical Review E, 2015. [ads] [doi]
  • "Conduction in Low Mach Number Flows. I. Linear and Weakly Nonlinear Regimes"
    Lecoanet et al., Astrophysical Journal, 2014. [ads] [doi]
  • "FIRST, a fibered aperture masking instrument. I. First on-sky test results"
    Huby et al., Astronomy & Astrophysics, 2012. [ads] [doi]

Conference presentations

  • "The Automatic Sparse Spectral Discretization of Tensorial PDEs"
    Burns et al., NAHOMCon, 2019.
  • "Nonlinear tidal instabilities in compressible atmospheres"
    Burns et al., APS DFD, 2018.
  • "Dedalus: A parallel spectral framework for multidimensional PDEs"
    Burns et al., ICOSAHOM, 2017.
  • "Turbulent Heat Transfer from a Thermally Forced Boundary in a Stratified Fluid"
    Burns et al., AGU Fall Meeting, 2017.
  • "Dedalus: A spectral solver for PDEs with diverse applications to CFD"
    Burns et al., APS DFD, 2017.
  • "Sidewall-driven convection in a thermally and compositionally stratified fluid"
    Burns et al., APS DFD, 2016.
  • "Turbulent structures in convection from a heated sidewall in a stratified fluid"
    Burns et al., APS DFD, 2015.
  • "Numerical simulations of nonlinear wall-mode convection"
    Burns et al., AGU Fall Meeting, 2014.
  • "Orbital Stability of Spacecraft Exploring Multiple Asteroid Systems"
    Burns et al., AAS 218th Meeting, 2011.

Other works

  • "Flexible Spectral Algorithms for Simulating Astrophysical and Geophysical Flows"
    Burns, Doctoral Thesis, 2018. [pdf]
  • "Perspectives on Reproducibility and Sustainability of Open-Source Scientific Software from Seven Years of the Dedalus Project"
    Oishi et al.,, 2018. [arxiv]
  • "Chebyshev Spectral Methods with Applications to Astrophysical Fluid Dynamics"
    Burns, Cambridge Part III Essay, 2013. [pdf]
  • "Ionocraft Lifter"
    Burns & Pope, Undergraduate Project, 2011. [pdf] [youtube]