This review article offers a survey of the research program focused on a systematic
computational search for extreme and potentially singular behaviour in hydrodynamic …

This study presents a comprehensive review of the automated classification in partial
discharge (PD) source identification and probabilistic interpretation of the classification …

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 …

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 …

We study a convex optimization framework for bounding extreme events in nonlinear
dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs) …

The precise set of parameters governing transition to turbulence in wall-bounded shear
flows remains an open question; many theoretical bounds have been obtained, but there is …

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 …

We present 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 bounded …

Tobasco, Goluskin, and Doering [https://doi. org/10.1016/j. physleta. 2017.12. 023 Phys. Lett.
A, 382 (2018), pp. 382--386}] recently suggested that trajectories of ODE systems that …

We propose a new framework to evaluate input–output amplification properties of nonlinear
models of wall-bounded shear flows, subject to both square integrable and persistent …