237 citations · 1.5k across the 36 of their papers we have counts for
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Jacobian-Free Variational Method for Constructing Connecting Orbits in Nonlinear Dynamical Systems
Omid Ashtari, Tobias M. Schneider
In a dynamical systems description of spatiotemporally chaotic PDEs including those describing turbulence, chaos is viewed as a trajectory evolving within a network of non-chaotic,…
Predicting chaotic statistics with unstable invariant tori
Jeremy P. Parker, Omid Ashtari, Tobias M. Schneider
It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic…
Invariant tori in dissipative hyperchaos
Jeremy P Parker, Tobias M Schneider
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's c…
Adjoint-based variational method for constructing periodic orbits of high-dimensional chaotic systems
Sajjad Azimi, Omid Ashtari, Tobias M. Schneider
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatio-temporal systems including fluid turbulence is supported by non…
Increasing lifetimes and the growing saddles of shear flow turbulence
Tobias Kreilos, Bruno Eckhardt, Tobias M. Schneider
In linearly stable shear flows turbulence spontaneously decays with a characteristic lifetime that varies with Reynolds number. The lifetime sharply increases with Reynolds number…
Basin boundary, edge of chaos, and edge state in a two-dimensional model
J. Vollmer, T. M. Schneider, B. Eckhardt
In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When…