5 papers
Domain-filling rolls in two-dimensional fixed-flux Rayleigh-Bénard convection
Mathew D. B. Lewis, Zehan Zheng, David Goluskin
Rayleigh-Bénard convection of large horizontal extent sometimes self-organizes into domain-filling structures. In two dimensions, domain-filling rolls persist - from some but not a…
Computation of minimal periods for ordinary differential equations
Jeremy P. Parker, David Goluskin
A framework is presented for lower-bounding periods among periodic solutions to an autonomous dynamical system governed by ordinary differential equations. For a chosen dynamical s…
Quartic Lyapunov functions for global fluid stability
David Darrow, Elizabeth Carlson, David Goluskin
A fluid system is 'globally stable' if all initial conditions eventually converge to the same state. Since Reynolds (1895) and Orr (1907), the standard way to show global stability…
Computation of attractor dimension and maximal sums of Lyapunov exponents using polynomial optimization
Jeremy P Parker, David Goluskin
Two approaches are presented for computing upper bounds on Lyapunov exponents and their sums, and on the Lyapunov dimension, among all trajectories of a dynamical system governed b…
Bounds on dissipation in three-dimensional planar shear flows: reduction to two-dimensional problems
Farid Rajkotia-Zaheer, David Goluskin
Bounds on turbulent averages in shear flows can be derived from the Navier--Stokes equations by a mathematical approach called the background method. Bounds that are optimal within…