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 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 the convex optimization technique of semidefinite programming to study dynamical systems, 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.

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: Fall 2019


Publications (arXiv)

arXiv versions closely reflect published versions, but I can provide published versions by email also.

Book

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

Preprints

  1. D. Goluskin
    Bounding extreme values on attractors using sum-of-squares optimization, with application to the Lorenz attractor
    arXiv

Journal articles

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

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

  3. 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

  4. 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)

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

  6. 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

  7. 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

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

  9. 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

  10. 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.

Thesis

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