9 citations · 23 across the 6 of their papers we have counts for
6 papers
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…
Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques
Omid Ashtari, Tobias M. Schneider
Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solut…
Symmetry-reduced low-dimensional representation of large-scale dynamics in the asymptotic suction boundary layer
Matthias Engel, Omid Ashtari, Moritz Linkmann
An important feature of turbulent boundary layers are persistent large-scale coherent structures in the flow. Here, we use Dynamic Mode Decomposition (DMD), a data-driven technique…
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…
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…