at Google ScholarTitle data
Chemnitz, Robin ; Engel, Maximilian ; Koltai, Peter:
Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups.
ArXiv
,
2024
DOI: https://doi.org/10.48550/arXiv.2403.19274
Abstract in another language
Coherent sets are time-dependent regions in the physical space of nonautonomous flows that exhibit little mixing with their neighborhoods, robustly under small random perturbations of the flow. They thus characterize the global long-term transport behavior of the system. We propose a framework to extract such time-dependent families of coherent sets for nonautonomous systems with an ergodic driving dynamics and (small) Brownian noise in physical space. Our construction involves the assembly and analysis of an operator on functions over the augmented space of the associated skew product that, for each fixed state of the driving, propagates distributions on the corresponding physical-space fibre according to the dynamics. This time-dependent operator has the structure of a semigroup (it is called the Mather semigroup), and we show that a spectral analysis of its generator allows for a trajectory-free computation of coherent families, simultaneously for all states of the driving. Additionally, for quasi-periodically driven torus flows, we propose a tailored Fourier discretization scheme for this generator and demonstrate our method by means of three examples of two-dimensional flows.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data > Chair Dynamical Systems and Data - Univ.-Prof. Dr. Peter Koltai Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 500 Science > 510 Mathematics |
| Date Deposited: | 09 Apr 2024 06:46 |
| Last Modified: | 23 Oct 2024 08:19 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/89173 |
Available Versions of this Item
- Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups. (deposited 09 Apr 2024 06:46) [Currently Displayed]