Concept

Periodic point

Related publications (43)

Swirling against the forcing: Evidence of stable counterdirected sloshing waves in orbital-shaken reservoirs

François Gallaire, Alessandro Bongarzone, Alice Evelyne Julienne Marcotte

We investigate the response of the free liquid surface in a partially filled circular cylindrical container undergoing a planar elliptic and time-periodic orbit while maintaining fixed its orientation. For small forcing amplitudes and deep liquid layers, w ...

College Pk2023

Signatures of a sampling quantum advantage in driven quantum many-body systems

A crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can perform a computation task that is classically intractable. A key question is to identify setups that can achieve such goal within current te ...

IOP Publishing Ltd2023

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

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

Koopmans Spectral Functionals in Periodic Boundary Conditions

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Riccardo De Gennaro

Koopmans spectral functionals aim to describe simultaneously ground-state properties and charged excitations of atoms, molecules, nanostructures, and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically ...

AMER CHEMICAL SOC2022

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

Learning dynamical systems with bifurcations

Aude Billard, Farshad Khadivar, Ilaria Lauzana

Trajectory planning through dynamical systems (DS) provides robust control for robots and has found numerous applications from locomotion to manipulation. However, to date, DS for controlling rhythmic patterns are distinct from DS used to control point to ...

2021

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

Geometric mixing

Nicolas Piro Mastracchio

Mixing fluids often involves a periodic action, like stirring one's tea. But reciprocating motions in fluids at low Reynolds number, in Stokes flows where inertia is negligible, lead to periodic cycles of mixing and unmixing, because the physics, molecular ...

ROYAL SOC2020

Invariant solutions underlying small- and large-scale structures in turbulent boundary layers

Sajjad Azimi

Flows of gases and liquids interacting with solid objects are often turbulent within a thin boundary layer. As energy dissipation and momentum transfer are dominated by the boundary layer dynamics, many engineering applications can benefit from an improved ...

EPFL2020

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