--- _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' ...