David Goluskin

Photo

Assistant Professor
Department of Mathematics and Statistics
University of Victoria
Email: goluskin at uvic.ca

My research is in the broad area of applied nonlinear dynamics and incorporates both computation and analysis. Much of my work concerns fluid dynamics, but I also study simpler ordinary and partial differential equations. Recently I have been developing ways to use polynomial optimization to study dynamics, for instance to estimate time averages and other properties of attractors. A lecture for the public relating generally to some of my fluid dynamical research can be found here. I currently have funding for another PhD or MSc student to join my research group; a strong mathematical background and computational skills are required.

Education

PhD Applied Mathematics, Columbia University, 2013
MS Applied Mathematics, Columbia University, 2009
BS Applied Mathematics, University of Colorado Boulder, 2007
BS Aerospace Engineering, University of Colorado Boulder, 2007

Teaching: Winter 2021

Math 379, Nonlinear dynamical systems and chaos

Research group

Alexandr Chernyavskiy (postdoc)
Jason Bramburger (postdoc)
Hans Oeri (PhD)
Narges Hosseini (MSc)
Mathew Lewis (undergrad)
Hannah Swan (undergrad)
Xuchen Wu (undergrad)
Zehan Zheng (undergrad)
Eric Wang (undergrad)

Publications (arXiv)

arXiv versions closely reflect published versions.

Book

  1. D. Goluskin
    Internally heated convection and Rayleigh–Bénard convection
    Springer. 2016. arXiv, Springer

Preprints

  1. B. Wen, D. Goluskin, M. LeDuc, G. P. Chini, C. R. Doering
    Steady coherent convection between stress-free boundaries
    arXiv

  2. J. J. Bramburger, D. Goluskin
    Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization
    arXiv

  3. F. Fuentes, D. Goluskin, S. Chernyshenko
    Global stability of fluid flows despite transient growth of energy
    arXiv

  4. M. Olson, D. Goluskin, W. W. Schultz, C. R. Doering
    Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization
    arXiv

Journal articles

  1. G. Fantuzzi, D. Goluskin
    Bounding extreme events in nonlinear dynamics using convex optimization
    SIAM J. Appl. Dyn. Syst. (to appear). arXiv

  2. D. Goluskin
    Bounding extrema over global attractors using polynomial optimization
    Nonlinearity (to appear). arXiv

  3. D. Goluskin, G. Fantuzzi
    Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming
    Nonlinearity 32, 1705-1730. 2019. arXiv, Nonlinearity

  4. D. Goluskin
    Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system
    J. Nonlinear Sci. 28, 621-651. 2018. arXiv, JNLS

  5. I. Tobasco, D. Goluskin, C. R. Doering
    Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems
    Phys. Lett. A 382, 382-386. 2018. arXiv, PLA

  6. G. Fantuzzi, D. Goluskin, D. Huang, S. I. Chernyshenko
    Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization
    SIAM J. Appl. Dyn. Syst. 15, 1962-1988. 2016. arXiv, SIADS (open access)

  7. D. Goluskin, C. R. Doering
    Bounds for convection between rough boundaries
    J. Fluid Mech. 804, 370-386. 2016. arXiv, JFM

  8. D. Goluskin, E. P. van der Poel
    Penetrative internally heated convection in two and three dimensions
    J. Fluid Mech. Rapids 791, R6. 2016. arXiv, JFM

  9. J. von Hardenberg, D. Goluskin, A. Provenzale, E. A. Spiegel
    Generation of large-scale winds in horizontally anisotropic convection
    Phys. Rev. Lett. 115, 134501. 2015. arXiv, PRL

  10. D. Goluskin
    Internally heated convection beneath a poor conductor
    J. Fluid Mech. 771, 36-56. 2015. arXiv, JFM

  11. D. Goluskin, H. Johnston, G. R. Flierl, E. A. Spiegel
    Convectively driven shear and decreased heat flux
    J. Fluid Mech. 759, 360-385. 2014. arXiv, videos, JFM

  12. D. Goluskin, E. A. Spiegel
    Convection driven by internal heating
    Phys. Lett. A 377, 83-92. 2012. arXiv, PLA

Proceedings

  1. D. Goluskin
    Who ate whom: population dynamics with age-structured predation
    in WHOI GFD 2010 program of study: swimming and swirling in turbulence. 2010.

Book review

  1. D. Goluskin
    Review of Exploring ODEs. By Lloyd N. Trefethen, Ásgeir Birkisson, and Tobin A. Driscoll
    SIAM Rev. 61, 392-393. 2019.

Thesis

  1. D. Goluskin
    Zonal flow driven by convection and convection driven by internal heating
    Columbia University. 2013. download