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Publications associées (10)

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

Invariant tori in dissipative hyperchaos

Tobias Schneider, Jeremy Peter Parker

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 chaotic attractor. The significance of zero-dimensional unstable fixed points ...

AIP Publishing2022

Variational methods for finding periodic orbits in the incompressible Navier Stokes equations

Tobias Schneider, Jeremy Peter Parker

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 unstable periodic orbits for the incompressible Navier-Stokes equations, bas ...

CAMBRIDGE UNIV PRESS2022

Periodic orbits exhibit oblique stripe patterns in plane Couette flow

Tobias Schneider, Florian Reetz

Spatiotemporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A recent dynamical syst ...

AMER PHYSICAL SOC2021

Fully automated gridding reconstruction for non-Cartesian x-space magnetic particle imaging

Ahmet Alacaoglu

Magnetic particle imaging (MPI) is a fast emerging biomedical imaging modality that exploits the nonlinear response of superparamagnetic iron oxide (SPIO) nanoparticles to image their spatial distribution. Previously, various scanning trajectories were ana ...

2019

Unstable periodic orbits in the Lorenz attractor

We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than ...

2011

New variational principles for locating periodic orbits of differential equations

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerica ...

2011

Realization of a solid-propellant based microthruster using low temperature co-fired ceramics

Peter Ryser, Thomas Maeder, Yannick Sébastien Fournier, Jaya Thakur

The introduction of micro-spacecrafts in the space industry has led to the development of various micro-propulsion techniques. Microthrusters are micropropulsion devices used in a microspacecraft for precise station keeping, orbit adjustment, attitude cont ...

2010

Autoregressive moving average model for analyzing edge localized mode time series on Axially Symmetric Divertor Experiment (ASDEX) Upgrade tokamak

Hartmut Zohm

An approach to analysis of time series of edge localized modes (ELMs) is proposed. It is based on the use of the autoregressive moving average model, which decomposes time series into deterministic and noise components. Despite the inclusion of nonlinearit ...

2004

Exploring Unstsable Periodic Orbits Using Super Stable Ones

This paper deals with Super Stable Orbits (SSOs) of the logistic map, and how they can be used to describe Unstable Periodic Orbits (UPOs).~We will show that Unstable Periodic Orbits have almost the same correlation properties as Super Stable ones from whi ...

2002

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