26 citations · 35 across the 6 of their papers we have counts for
7 papers
The Origin of Imperfection Sensitivity in the Buckling of Cylindrical Shells
Tian Yang, Tobias M. Schneider
Buckling of thin cylindrical shells under axial compression, a classical example of a subcritical instability, is highly sensitive to small imperfections, with minute geometric var…
Identifying recurrent flows in high-dimensional dissipative chaos from low-dimensional embeddings
Pierre Beck, Tobias M. Schneider
Unstable periodic orbits (UPOs) are the non-chaotic, dynamical building blocks of spatio-temporal chaos, motivating a first-principles based theory for turbulence ever since the di…
Ghost states underlying spatial and temporal patterns: how non-existing invariant solutions control nonlinear dynamics
Zheng Zheng, Pierre Beck, Tian Yang +3
Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longe…
Data-driven guessing and gluing of unstable periodic orbits
Pierre Beck, Jeremy P. Parker, Tobias M. Schneider
Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatio-temporal chaos and turbulence. Finding these UPOs is however notoriously difficult.…
The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation
Marie Abadie, Pierre Beck, Jeremy P. Parker +1
The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, fo…
Following marginal stability manifolds in quasilinear dynamical reductions of multiscale flows in two space dimensions
Alessia Ferraro, Gregory P. Chini, Tobias M. Schneider
A two-dimensional extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities is derived. Prior work has demonstrated that the…
Variational methods for finding periodic orbits in the incompressible Navier-Stokes equations
Jeremy P Parker, Tobias M Schneider
Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such…