Publications de Omid Ashtari | EPFL Graph Search

Search for Unstable Relative Periodic Orbits in Channel Flow Using Symmetry-reduced Dynamic Mode Decomposition

In the dynamical systems approach to turbulence, unstable periodic orbits (UPOs) provide valuable insights into system dynamics. Such UPOs are usually found by shooting-based Newton searches, where constructing sufficiently accurate initial guesses is diff ...

CAMBRIDGE UNIV PRESS2025

Ghost States Underlying Spatial and Temporal Patterns: How Nonexistent Invariant Solutions Control Nonlinear Dynamics

Tobias Schneider, Omid Ashtari, Pierre Beck, Jeremy Peter Parker, Zheng Zheng

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 longer present at the chosen parameter value. For bifurcating equilibria in low-d ...

AMER PHYSICAL SOC2025

Adjoint-based variational methods for computing invariant solutions in spatio-temporally chaotic PDEs

Omid Ashtari

One approach for describing spatio-temporally chaotic dynamical systems, including fluid turbulence, is to study non-chaotic but unstable invariant solutions embedded within the chaotic attractor of the system. These include steady, periodic, and quasi-per ...

EPFL2024

Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques

Tobias Schneider, Omid Ashtari

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 solutions, their identification remains a computational challenge, rendering many ...

Cambridge University Press2023

Predicting chaotic statistics with unstable invariant tori

Tobias Schneider, Omid Ashtari, Jeremy Peter Parker

It has recently been speculated that long-time average quantities of hyperchaotic dissipative systems may be approximated by weighted sums over unstable invariant tori embedded in the attractor, analogous to equivalent sums over periodic orbits, which are ...

American Institute of Physics2023

Jacobian-free variational method for computing connecting orbits in nonlinear dynamical systems

Tobias Schneider, Omid Ashtari

One approach for describing spatiotemporal chaos is to study the unstable invariant sets embedded in the chaotic attractor of the system. While equilibria, periodic orbits, and invariant tori can be computed using existing methods, the numerical identifica ...

American Institute of Physics2023

Symmetry-reduced low-dimensional representation of large-scale dynamics in the asymptotic suction boundary layer

Omid Ashtari

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 designed to detect spatio-temporal coherence, to construct optimal low-dime ...

Elsevier2023

Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method

Tobias Schneider, Sajjad Azimi, Omid Ashtari

Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations ...

2022