Associate 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. An old public lecture about the challenges of understanding turbulence can be found here.

MS Applied Mathematics, Columbia University, 2009

BS Applied Mathematics, University of Colorado Boulder, 2007

BS Aerospace Engineering, University of Colorado Boulder, 2007

MATH 444/550, Topics in fluid dynamics

- Q. Wang, D. Goluskin, D. Lohse

*Lifetimes of metastable windy states in two-dimensional Rayleigh—Bénard convection with stress-free boundaries*

J. Fluid Mech. Rapids 976, R2. 2023. arXiv, JFM (open access) - H. Oeri, D. Goluskin

*Convex computation of maximal Lyapunov exponents*

Nonlinearity 36, 5378-5400. 2023. arXiv, Nonlinearity - A. Chernyavsky, J. Bramburger, G. Fantuzzi, D. Goluskin

*Convex relaxations of integral variational problems: pointwise dual relaxation and sum-of-squares optimization*

SIAM J. Opt. 33, 481-512. 2023. arXiv, SIOPT - S. Kazemi, R. Ostilla-Mónico, D. Goluskin

*Transition between boundary-limited scaling and mixing-length scaling of turbulent transport in internally heated convection*

Phys. Rev. Lett. 129, 024501. 2022. arXiv, PRL - F. Fuentes, D. Goluskin, S. Chernyshenko

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

Phys. Rev. Lett. 128, 204502. 2022. arXiv, PRL,**talk** - B. Wen, D. Goluskin, C. R. Doering

*Steady Rayleigh—Bénard convection between no-slip boundaries*

J. Fluid Mech. Rapids 933, R4. 2022. arXiv, JFM (open access),**talk** - J. P. Parker, D. Goluskin, G. M. Vasil

*A study of the double pendulum using polynomial optimization*

Chaos 31, 103102. 2021. arXiv, Chaos - B. Wen, D. Goluskin, M. LeDuc, G. P. Chini, C. R. Doering

*Steady Rayleigh–Bénard convection between stress-free boundaries*

J. Fluid Mech. Rapids 905, R4. 2020. arXiv, JFM - M. Olson, D. Goluskin, W. W. Schultz, C. R. Doering

*Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization*

Physica D 415, 132748. 2020. arXiv, Physica D - J. J. Bramburger, D. Goluskin

*Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization*

Proc. R. Soc. A 476, 20200450. 2020. arXiv, Proc A - G. Fantuzzi, D. Goluskin

*Bounding extreme events in nonlinear dynamics using convex optimization*

SIAM J. Appl. Dyn. Syst. 19, 1823-1864. 2020. arXiv, SIADS - D. Goluskin

*Bounding extrema over global attractors using polynomial optimization*

Nonlinearity 33, 4878-4899. 2020. arXiv, Nonlinearity - 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

*Internally heated convection and Rayleigh–Bénard convection*

Springer. 2016. arXiv, Springer

- 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