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.

MS Applied Mathematics, Columbia University, 2009

BS Applied Mathematics, University of Colorado Boulder, 2007

BS Aerospace Engineering, University of Colorado Boulder, 2007

- D. Goluskin

*Internally heated convection and Rayleigh–Bénard convection*

Springer. 2016. arXiv, Springer

- F. Fuentes, D. Goluskin, S. Chernyshenko

*Global stability of fluid flows despite transient growth of energy*

arXiv - G. Fantuzzi, D. Goluskin

*Bounding extreme events in nonlinear dynamics using convex optimization*

arXiv - D. Goluskin

*Bounding extrema over global attractors using polynomial optimization*

arXiv

- D. Goluskin, G. Fantuzzi

*Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming*

Nonlinearity 32, 1705-1730. 2019. arXiv, Nonlinearity - D. Goluskin

*Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system*

J. Nonlinear Sci. 28, 621-651. 2018. arXiv, JNLS - 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 - 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) - D. Goluskin, C. R. Doering

*Bounds for convection between rough boundaries*

J. Fluid Mech. 804, 370-386. 2016. arXiv, JFM - 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 - 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 - D. Goluskin

*Internally heated convection beneath a poor conductor*

J. Fluid Mech. 771, 36-56. 2015. arXiv, JFM - 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 - D. Goluskin, E. A. Spiegel

*Convection driven by internal heating*

Phys. Lett. A 377, 83-92. 2012. arXiv, PLA

- D. Goluskin

*Who ate whom: population dynamics with age-structured predation*

in WHOI GFD 2010 program of study: swimming and swirling in turbulence. 2010.

- D. Goluskin

Review of*Exploring ODEs. By Lloyd N. Trefethen, Ásgeir Birkisson, and Tobin A. Driscoll*

SIAM Rev. 61, 392-393. 2019.

- D. Goluskin

*Zonal flow driven by convection and convection driven by internal heating*

Columbia University. 2013. download