---
_id: '12259'
abstract:
- lang: eng
text: 'Theoretical foundations of chaos have been predominantly laid out for finite-dimensional
dynamical systems, such as the three-body problem in classical mechanics and the
Lorenz model in dissipative systems. In contrast, many real-world chaotic phenomena,
e.g., weather, arise in systems with many (formally infinite) degrees of freedom,
which limits direct quantitative analysis of such systems using chaos theory.
In the present work, we demonstrate that the hydrodynamic pilot-wave systems offer
a bridge between low- and high-dimensional chaotic phenomena by allowing for a
systematic study of how the former connects to the latter. Specifically, we present
experimental results, which show the formation of low-dimensional chaotic attractors
upon destabilization of regular dynamics and a final transition to high-dimensional
chaos via the merging of distinct chaotic regions through a crisis bifurcation.
Moreover, we show that the post-crisis dynamics of the system can be rationalized
as consecutive scatterings from the nonattracting chaotic sets with lifetimes
following exponential distributions. '
acknowledgement: 'This work was partially funded by the Institute of Science and Technology
Austria Interdisciplinary Project Committee Grant “Pilot-Wave Hydrodynamics: Chaos
and Quantum Analogies.”'
article_number: '093138'
article_processing_charge: No
article_type: original
author:
- first_name: George H
full_name: Choueiri, George H
id: 448BD5BC-F248-11E8-B48F-1D18A9856A87
last_name: Choueiri
- first_name: Balachandra
full_name: Suri, Balachandra
id: 47A5E706-F248-11E8-B48F-1D18A9856A87
last_name: Suri
- first_name: Jack
full_name: Merrin, Jack
id: 4515C308-F248-11E8-B48F-1D18A9856A87
last_name: Merrin
orcid: 0000-0001-5145-4609
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
- first_name: Nazmi B
full_name: Budanur, Nazmi B
id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
last_name: Budanur
orcid: 0000-0003-0423-5010
citation:
ama: 'Choueiri GH, Suri B, Merrin J, Serbyn M, Hof B, Budanur NB. Crises and chaotic
scattering in hydrodynamic pilot-wave experiments. Chaos: An Interdisciplinary
Journal of Nonlinear Science. 2022;32(9). doi:10.1063/5.0102904'
apa: 'Choueiri, G. H., Suri, B., Merrin, J., Serbyn, M., Hof, B., & Budanur,
N. B. (2022). Crises and chaotic scattering in hydrodynamic pilot-wave experiments.
Chaos: An Interdisciplinary Journal of Nonlinear Science. AIP Publishing.
https://doi.org/10.1063/5.0102904'
chicago: 'Choueiri, George H, Balachandra Suri, Jack Merrin, Maksym Serbyn, Björn
Hof, and Nazmi B Budanur. “Crises and Chaotic Scattering in Hydrodynamic Pilot-Wave
Experiments.” Chaos: An Interdisciplinary Journal of Nonlinear Science.
AIP Publishing, 2022. https://doi.org/10.1063/5.0102904.'
ieee: 'G. H. Choueiri, B. Suri, J. Merrin, M. Serbyn, B. Hof, and N. B. Budanur,
“Crises and chaotic scattering in hydrodynamic pilot-wave experiments,” Chaos:
An Interdisciplinary Journal of Nonlinear Science, vol. 32, no. 9. AIP Publishing,
2022.'
ista: 'Choueiri GH, Suri B, Merrin J, Serbyn M, Hof B, Budanur NB. 2022. Crises
and chaotic scattering in hydrodynamic pilot-wave experiments. Chaos: An Interdisciplinary
Journal of Nonlinear Science. 32(9), 093138.'
mla: 'Choueiri, George H., et al. “Crises and Chaotic Scattering in Hydrodynamic
Pilot-Wave Experiments.” Chaos: An Interdisciplinary Journal of Nonlinear Science,
vol. 32, no. 9, 093138, AIP Publishing, 2022, doi:10.1063/5.0102904.'
short: 'G.H. Choueiri, B. Suri, J. Merrin, M. Serbyn, B. Hof, N.B. Budanur, Chaos:
An Interdisciplinary Journal of Nonlinear Science 32 (2022).'
date_created: 2023-01-16T09:58:16Z
date_published: 2022-09-26T00:00:00Z
date_updated: 2023-08-04T09:51:17Z
day: '26'
ddc:
- '530'
department:
- _id: MaSe
- _id: BjHo
- _id: NanoFab
doi: 10.1063/5.0102904
external_id:
arxiv:
- '2206.01531'
isi:
- '000861009600005'
file:
- access_level: open_access
checksum: 17881eff8b21969359a2dd64620120ba
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T09:41:12Z
date_updated: 2023-01-30T09:41:12Z
file_id: '12445'
file_name: 2022_Chaos_Choueiri.pdf
file_size: 3209644
relation: main_file
success: 1
file_date_updated: 2023-01-30T09:41:12Z
has_accepted_license: '1'
intvolume: ' 32'
isi: 1
issue: '9'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science'
publication_identifier:
eissn:
- 1089-7682
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Crises and chaotic scattering in hydrodynamic pilot-wave experiments
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 32
year: '2022'
...
---
_id: '8634'
abstract:
- lang: eng
text: In laboratory studies and numerical simulations, we observe clear signatures
of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional
flow. We validate the dynamical relevance of such solutions by demonstrating that
turbulent flows in both experiment and numerics transiently display time-periodic
dynamics when they shadow unstable periodic orbits (UPOs). We show that UPOs we
computed are also statistically significant, with turbulent flows spending a sizable
fraction of the total time near these solutions. As a result, the average rates
of energy input and dissipation for the turbulent flow and frequently visited
UPOs differ only by a few percent.
acknowledgement: M. F. S. and R. O. G. acknowledge funding from the National Science
Foundation (CMMI-1234436, DMS1125302, CMMI-1725587) and Defense Advanced Research
Projects Agency (HR0011-16-2-0033). B. S.has received funding from the People Programme
(Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007–2013/
under REA Grant Agreement No. 291734.
article_number: '064501'
article_processing_charge: No
article_type: original
author:
- first_name: Balachandra
full_name: Suri, Balachandra
id: 47A5E706-F248-11E8-B48F-1D18A9856A87
last_name: Suri
- first_name: Logan
full_name: Kageorge, Logan
last_name: Kageorge
- first_name: Roman O.
full_name: Grigoriev, Roman O.
last_name: Grigoriev
- first_name: Michael F.
full_name: Schatz, Michael F.
last_name: Schatz
citation:
ama: Suri B, Kageorge L, Grigoriev RO, Schatz MF. Capturing turbulent dynamics and
statistics in experiments with unstable periodic orbits. Physical Review Letters.
2020;125(6). doi:10.1103/physrevlett.125.064501
apa: Suri, B., Kageorge, L., Grigoriev, R. O., & Schatz, M. F. (2020). Capturing
turbulent dynamics and statistics in experiments with unstable periodic orbits.
Physical Review Letters. American Physical Society. https://doi.org/10.1103/physrevlett.125.064501
chicago: Suri, Balachandra, Logan Kageorge, Roman O. Grigoriev, and Michael F. Schatz.
“Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic
Orbits.” Physical Review Letters. American Physical Society, 2020. https://doi.org/10.1103/physrevlett.125.064501.
ieee: B. Suri, L. Kageorge, R. O. Grigoriev, and M. F. Schatz, “Capturing turbulent
dynamics and statistics in experiments with unstable periodic orbits,” Physical
Review Letters, vol. 125, no. 6. American Physical Society, 2020.
ista: Suri B, Kageorge L, Grigoriev RO, Schatz MF. 2020. Capturing turbulent dynamics
and statistics in experiments with unstable periodic orbits. Physical Review Letters.
125(6), 064501.
mla: Suri, Balachandra, et al. “Capturing Turbulent Dynamics and Statistics in Experiments
with Unstable Periodic Orbits.” Physical Review Letters, vol. 125, no.
6, 064501, American Physical Society, 2020, doi:10.1103/physrevlett.125.064501.
short: B. Suri, L. Kageorge, R.O. Grigoriev, M.F. Schatz, Physical Review Letters
125 (2020).
date_created: 2020-10-08T17:27:32Z
date_published: 2020-08-05T00:00:00Z
date_updated: 2023-09-05T12:08:29Z
day: '05'
department:
- _id: BjHo
doi: 10.1103/physrevlett.125.064501
ec_funded: 1
external_id:
arxiv:
- '2008.02367'
isi:
- '000555785600005'
intvolume: ' 125'
isi: 1
issue: '6'
keyword:
- General Physics and Astronomy
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2008.02367
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Physical Review Letters
publication_identifier:
eissn:
- 1079-7114
issn:
- 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
status: public
title: Capturing turbulent dynamics and statistics in experiments with unstable periodic
orbits
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 125
year: '2020'
...
---
_id: '6779'
abstract:
- lang: eng
text: "Recent studies suggest that unstable recurrent solutions of the Navier-Stokes
equation provide new insights\r\ninto dynamics of turbulent flows. In this study,
we compute an extensive network of dynamical connections\r\nbetween such solutions
in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion
symmetric subspace. In particular, we find numerous isolated heteroclinic connections
between different\r\ntypes of solutions—equilibria, periodic, and quasiperiodic
orbits—as well as continua of connections forming\r\nhigher-dimensional connecting
manifolds. We also compute a homoclinic connection of a periodic orbit and\r\nprovide
strong evidence that the associated homoclinic tangle forms the chaotic repeller
that underpins transient\r\nturbulence in the symmetric subspace."
article_number: '013112'
article_processing_charge: No
article_type: original
author:
- first_name: Balachandra
full_name: Suri, Balachandra
id: 47A5E706-F248-11E8-B48F-1D18A9856A87
last_name: Suri
- first_name: Ravi Kumar
full_name: Pallantla, Ravi Kumar
last_name: Pallantla
- first_name: Michael F.
full_name: Schatz, Michael F.
last_name: Schatz
- first_name: Roman O.
full_name: Grigoriev, Roman O.
last_name: Grigoriev
citation:
ama: Suri B, Pallantla RK, Schatz MF, Grigoriev RO. Heteroclinic and homoclinic
connections in a Kolmogorov-like flow. Physical Review E. 2019;100(1).
doi:10.1103/physreve.100.013112
apa: Suri, B., Pallantla, R. K., Schatz, M. F., & Grigoriev, R. O. (2019). Heteroclinic
and homoclinic connections in a Kolmogorov-like flow. Physical Review E.
American Physical Society. https://doi.org/10.1103/physreve.100.013112
chicago: Suri, Balachandra, Ravi Kumar Pallantla, Michael F. Schatz, and Roman O.
Grigoriev. “Heteroclinic and Homoclinic Connections in a Kolmogorov-like Flow.”
Physical Review E. American Physical Society, 2019. https://doi.org/10.1103/physreve.100.013112.
ieee: B. Suri, R. K. Pallantla, M. F. Schatz, and R. O. Grigoriev, “Heteroclinic
and homoclinic connections in a Kolmogorov-like flow,” Physical Review E,
vol. 100, no. 1. American Physical Society, 2019.
ista: Suri B, Pallantla RK, Schatz MF, Grigoriev RO. 2019. Heteroclinic and homoclinic
connections in a Kolmogorov-like flow. Physical Review E. 100(1), 013112.
mla: Suri, Balachandra, et al. “Heteroclinic and Homoclinic Connections in a Kolmogorov-like
Flow.” Physical Review E, vol. 100, no. 1, 013112, American Physical Society,
2019, doi:10.1103/physreve.100.013112.
short: B. Suri, R.K. Pallantla, M.F. Schatz, R.O. Grigoriev, Physical Review E 100
(2019).
date_created: 2019-08-09T09:40:41Z
date_published: 2019-07-25T00:00:00Z
date_updated: 2024-02-28T13:13:00Z
day: '25'
ddc:
- '532'
department:
- _id: BjHo
doi: 10.1103/physreve.100.013112
ec_funded: 1
external_id:
arxiv:
- '1907.05860'
isi:
- '000477911800012'
intvolume: ' 100'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1907.05860
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Physical Review E
publication_identifier:
eissn:
- 2470-0053
issn:
- 2470-0045
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Heteroclinic and homoclinic connections in a Kolmogorov-like flow
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 100
year: '2019'
...
---
_id: '136'
abstract:
- lang: eng
text: Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes
equation may provide deep insights into fluid turbulence. In this article, we
present a combined experimental and numerical study exploring the dynamical role
of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent,
electromagnetically driven, shallow fluid layer. Identifying instants when turbulent
evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional
model of the flow. We establish the dynamical relevance of these unstable equilibria
by showing that they are closely visited by the turbulent flow. We also establish
the dynamical relevance of unstable manifolds by verifying that they are shadowed
by turbulent trajectories departing from the neighborhoods of unstable equilibria
over large distances in state space.
article_processing_charge: No
author:
- first_name: Balachandra
full_name: Suri, Balachandra
id: 47A5E706-F248-11E8-B48F-1D18A9856A87
last_name: Suri
- first_name: Jeffrey
full_name: Tithof, Jeffrey
last_name: Tithof
- first_name: Roman
full_name: Grigoriev, Roman
last_name: Grigoriev
- first_name: Michael
full_name: Schatz, Michael
last_name: Schatz
citation:
ama: Suri B, Tithof J, Grigoriev R, Schatz M. Unstable equilibria and invariant
manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical Review E.
2018;98(2). doi:10.1103/PhysRevE.98.023105
apa: Suri, B., Tithof, J., Grigoriev, R., & Schatz, M. (2018). Unstable equilibria
and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical
Review E. American Physical Society. https://doi.org/10.1103/PhysRevE.98.023105
chicago: Suri, Balachandra, Jeffrey Tithof, Roman Grigoriev, and Michael Schatz.
“Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like
Flow.” Physical Review E. American Physical Society, 2018. https://doi.org/10.1103/PhysRevE.98.023105.
ieee: B. Suri, J. Tithof, R. Grigoriev, and M. Schatz, “Unstable equilibria and
invariant manifolds in quasi-two-dimensional Kolmogorov-like flow,” Physical
Review E, vol. 98, no. 2. American Physical Society, 2018.
ista: Suri B, Tithof J, Grigoriev R, Schatz M. 2018. Unstable equilibria and invariant
manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical Review E. 98(2).
mla: Suri, Balachandra, et al. “Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional
Kolmogorov-like Flow.” Physical Review E, vol. 98, no. 2, American Physical
Society, 2018, doi:10.1103/PhysRevE.98.023105.
short: B. Suri, J. Tithof, R. Grigoriev, M. Schatz, Physical Review E 98 (2018).
date_created: 2018-12-11T11:44:49Z
date_published: 2018-08-13T00:00:00Z
date_updated: 2023-10-10T13:29:10Z
day: '13'
department:
- _id: BjHo
doi: 10.1103/PhysRevE.98.023105
external_id:
arxiv:
- '1808.02088'
isi:
- '000441466800010'
intvolume: ' 98'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1808.02088
month: '08'
oa: 1
oa_version: Submitted Version
publication: Physical Review E
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like
flow
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 98
year: '2018'
...