---
_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
arxiv: 1
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. <i>Chaos: An Interdisciplinary
    Journal of Nonlinear Science</i>. 2022;32(9). doi:<a href="https://doi.org/10.1063/5.0102904">10.1063/5.0102904</a>'
  apa: 'Choueiri, G. H., Suri, B., Merrin, J., Serbyn, M., Hof, B., &#38; Budanur,
    N. B. (2022). Crises and chaotic scattering in hydrodynamic pilot-wave experiments.
    <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. AIP Publishing.
    <a href="https://doi.org/10.1063/5.0102904">https://doi.org/10.1063/5.0102904</a>'
  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.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>.
    AIP Publishing, 2022. <a href="https://doi.org/10.1063/5.0102904">https://doi.org/10.1063/5.0102904</a>.'
  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,” <i>Chaos:
    An Interdisciplinary Journal of Nonlinear Science</i>, 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.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>,
    vol. 32, no. 9, 093138, AIP Publishing, 2022, doi:<a href="https://doi.org/10.1063/5.0102904">10.1063/5.0102904</a>.'
  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
arxiv: 1
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. <i>Physical Review Letters</i>.
    2020;125(6). doi:<a href="https://doi.org/10.1103/physrevlett.125.064501">10.1103/physrevlett.125.064501</a>
  apa: Suri, B., Kageorge, L., Grigoriev, R. O., &#38; Schatz, M. F. (2020). Capturing
    turbulent dynamics and statistics in experiments with unstable periodic orbits.
    <i>Physical Review Letters</i>. American Physical Society. <a href="https://doi.org/10.1103/physrevlett.125.064501">https://doi.org/10.1103/physrevlett.125.064501</a>
  chicago: Suri, Balachandra, Logan Kageorge, Roman O. Grigoriev, and Michael F. Schatz.
    “Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic
    Orbits.” <i>Physical Review Letters</i>. American Physical Society, 2020. <a href="https://doi.org/10.1103/physrevlett.125.064501">https://doi.org/10.1103/physrevlett.125.064501</a>.
  ieee: B. Suri, L. Kageorge, R. O. Grigoriev, and M. F. Schatz, “Capturing turbulent
    dynamics and statistics in experiments with unstable periodic orbits,” <i>Physical
    Review Letters</i>, 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.” <i>Physical Review Letters</i>, vol. 125, no.
    6, 064501, American Physical Society, 2020, doi:<a href="https://doi.org/10.1103/physrevlett.125.064501">10.1103/physrevlett.125.064501</a>.
  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
arxiv: 1
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. <i>Physical Review E</i>. 2019;100(1).
    doi:<a href="https://doi.org/10.1103/physreve.100.013112">10.1103/physreve.100.013112</a>
  apa: Suri, B., Pallantla, R. K., Schatz, M. F., &#38; Grigoriev, R. O. (2019). Heteroclinic
    and homoclinic connections in a Kolmogorov-like flow. <i>Physical Review E</i>.
    American Physical Society. <a href="https://doi.org/10.1103/physreve.100.013112">https://doi.org/10.1103/physreve.100.013112</a>
  chicago: Suri, Balachandra, Ravi Kumar Pallantla, Michael F. Schatz, and Roman O.
    Grigoriev. “Heteroclinic and Homoclinic Connections in a Kolmogorov-like Flow.”
    <i>Physical Review E</i>. American Physical Society, 2019. <a href="https://doi.org/10.1103/physreve.100.013112">https://doi.org/10.1103/physreve.100.013112</a>.
  ieee: B. Suri, R. K. Pallantla, M. F. Schatz, and R. O. Grigoriev, “Heteroclinic
    and homoclinic connections in a Kolmogorov-like flow,” <i>Physical Review E</i>,
    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.” <i>Physical Review E</i>, vol. 100, no. 1, 013112, American Physical Society,
    2019, doi:<a href="https://doi.org/10.1103/physreve.100.013112">10.1103/physreve.100.013112</a>.
  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
arxiv: 1
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. <i>Physical Review E</i>.
    2018;98(2). doi:<a href="https://doi.org/10.1103/PhysRevE.98.023105">10.1103/PhysRevE.98.023105</a>
  apa: Suri, B., Tithof, J., Grigoriev, R., &#38; Schatz, M. (2018). Unstable equilibria
    and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow. <i>Physical
    Review E</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevE.98.023105">https://doi.org/10.1103/PhysRevE.98.023105</a>
  chicago: Suri, Balachandra, Jeffrey Tithof, Roman Grigoriev, and Michael Schatz.
    “Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like
    Flow.” <i>Physical Review E</i>. American Physical Society, 2018. <a href="https://doi.org/10.1103/PhysRevE.98.023105">https://doi.org/10.1103/PhysRevE.98.023105</a>.
  ieee: B. Suri, J. Tithof, R. Grigoriev, and M. Schatz, “Unstable equilibria and
    invariant manifolds in quasi-two-dimensional Kolmogorov-like flow,” <i>Physical
    Review E</i>, 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.” <i>Physical Review E</i>, vol. 98, no. 2, American Physical
    Society, 2018, doi:<a href="https://doi.org/10.1103/PhysRevE.98.023105">10.1103/PhysRevE.98.023105</a>.
  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'
...