76 citations · 669 across the 27 of their papers we have counts for
28 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…
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…
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…
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…
Lifetimes of metastable windy states in two-dimensional Rayleigh-Bénard convection with stress-free boundaries
Qi Wang, David Goluskin, Detlef Lohse
Two-dimensional horizontally periodic Rayleigh-Bénard convection between stress-free boundaries displays two distinct types of states, depending on the initial conditions. Roll sta…
Convex computation of maximal Lyapunov exponents
Hans Oeri, David Goluskin
We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formula…
Steady Rayleigh--Bénard convection: strongly nonlinear high-wavenumber rolls
Baole Wen, Alexander Takla, David Goluskin +1
In Rayleigh--Bénard convection, two-dimensional steady rolls bifurcate supercritically at a Rayleigh number that depends on their horizontal-to-vertical aspect ratio , and…
Transition between Boundary-Limited Scaling and Mixing-Length Scaling of Turbulent Transport in Internally Heated Convection
Sina Kazemi, Rodolfo Ostilla-Mónico, David Goluskin
Heat transport in turbulent thermal convection increases with the thermal forcing, but in almost all studies the rate of this increase is slower than it would be if transport becam…
Convex relaxations of integral variational problems: pointwise dual relaxation and sum-of-squares optimization
Alexander Chernyavsky, Jason J. Bramburger, Giovanni Fantuzzi +1
We present a method for finding lower bounds on the global infima of integral variational problems, wherein is minimized over functions $u\col…
A study of the double pendulum using polynomial optimization
Jeremy P Parker, David Goluskin, Geoffrey M Vasil
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtain…
Steady Rayleigh--Bénard convection between no-slip boundaries
Baole Wen, David Goluskin, Charles R. Doering
The central open question about Rayleigh--Bénard convection -- buoyancy-driven flow in a fluid layer heated from below and cooled from above -- is how vertical heat flux depends on…
Steady Rayleigh--Bénard convection between stress-free boundaries
Baole Wen, David Goluskin, Matthew LeDuc +2
Steady two-dimensional Rayleigh--Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls…
Minimum wave speeds in monostable reaction-diffusion equations: sharp bounds by polynomial optimization
Jason J. Bramburger, David Goluskin
Many monostable reaction-diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are…
Heat transport bounds for a truncated model of Rayleigh-Bénard convection via polynomial optimization
Matthew L. Olson, David Goluskin, William W. Schultz +1
Upper bounds on time-averaged heat transport are obtained for an eight-mode Galerkin truncation of Rayleigh's 1916 model of natural thermal convection. Bounds for the ODE model---a…
Global stability of fluid flows despite transient growth of energy
Federico Fuentes, David Goluskin, Sergei Chernyshenko
Verifying nonlinear stability of a laminar fluid flow against all perturbations is a central challenge in fluid dynamics. Past results rely on monotonic decrease of a perturbation…
Bounding extreme events in nonlinear dynamics using convex optimization
Giovanni Fantuzzi, David Goluskin
We study a convex optimization framework for bounding extreme events in nonlinear dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs). This fram…
Bounding extrema over global attractors using polynomial optimisation
David Goluskin
We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bo…
Bounds on mean energy in the Kuramoto-Sivashinsky equation computed using semidefinite programming
David Goluskin, Giovanni Fantuzzi
We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov fun…
Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems
Ian Tobasco, David Goluskin, Charles R. Doering
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories,…
Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system
David Goluskin
We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain pro…
Internally heated convection beneath a poor conductor
David Goluskin
We consider convection in an internally heated layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled…
Bounds for convection between rough boundaries
David Goluskin, Charles R. Doering
We consider Rayleigh-Bénard convection in a layer of fluid between rough no-slip boundaries where the top and bottom boundary heights are functions of the horizontal coordinates wi…
Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization
Giovanni Fantuzzi, David Goluskin, Deqing Huang +1
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynami…