[{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","ddc":["532"],"date_published":"2026-02-17T00:00:00Z","OA_type":"hybrid","corr_author":"1","author":[{"orcid":"0000-0002-4843-6853","full_name":"Yang, Bowen","id":"71b6ff4b-15b2-11ec-abd3-aef6b028cf7e","first_name":"Bowen","last_name":"Yang"},{"first_name":"Yi","last_name":"Zhuang","full_name":"Zhuang, Yi","id":"3677B57C-F248-11E8-B48F-1D18A9856A87"},{"id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312","last_name":"Yalniz","first_name":"Gökhan"},{"id":"3C5A959A-F248-11E8-B48F-1D18A9856A87","full_name":"Vasudevan, Mukund","last_name":"Vasudevan","first_name":"Mukund"},{"orcid":"0000-0001-7173-4923","id":"0BE7553A-1004-11EA-B805-18983DDC885E","full_name":"Marensi, Elena","last_name":"Marensi","first_name":"Elena"},{"last_name":"Hof","first_name":"Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754"}],"PlanS_conform":"1","day":"17","year":"2026","publication_status":"epub_ahead","status":"public","publisher":"Springer Nature","article_type":"original","date_updated":"2026-02-23T11:36:46Z","arxiv":1,"project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics","grant_number":"662960","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2311.11474"]},"abstract":[{"lang":"eng","text":"Depending on the type of flow, the transition to turbulence can take one of two forms: either turbulence arises from a sequence of instabilities or from the spatial proliferation of transiently chaotic domains, a process analogous to directed percolation. The former scenario is commonly referred to as a supercritical transition and frequently encountered in flows destabilized by body forces, whereas the latter subcritical transition is common in shear flows. Both cases are inherently continuous in a sense that the transformation from ordered laminar to fully turbulent fluid motion is only accomplished gradually with flow speed. Here we show that these established transition types do not account for the more general setting of shear flows subject to body forces. The combination of the two continuous scenarios leads to the attenuation of spatial coupling; with increasing forcing amplitude, the transition becomes increasingly sharp and eventually discontinuous. We argue that the suppression of laminar–turbulent coexistence and the approach towards a discontinuous phase transition potentially apply to a broad range of situations including flows subject to, for example, buoyancy, centrifugal or electromagnetic forces."}],"publication":"Nature Physics","title":"Discontinuous transition to shear flow turbulence","quality_controlled":"1","language":[{"iso":"eng"}],"OA_place":"publisher","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"oa_version":"Published Version","publication_identifier":{"eissn":["1745-2481"],"issn":["1745-2473"]},"_id":"21295","doi":"10.1038/s41567-025-03166-3","date_created":"2026-02-17T11:38:41Z","acknowledgement":"The work was supported by the Simons Foundation (grant number 662960, to B.H.). Open access funding provided by Institute of Science and Technology (IST Austria).","citation":{"short":"B. Yang, Y. Zhuang, G. Yalniz, M. Vasudevan, E. Marensi, B. Hof, Nature Physics (2026).","ieee":"B. Yang, Y. Zhuang, G. Yalniz, M. Vasudevan, E. Marensi, and B. Hof, “Discontinuous transition to shear flow turbulence,” <i>Nature Physics</i>. Springer Nature, 2026.","mla":"Yang, Bowen, et al. “Discontinuous Transition to Shear Flow Turbulence.” <i>Nature Physics</i>, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1038/s41567-025-03166-3\">10.1038/s41567-025-03166-3</a>.","ama":"Yang B, Zhuang Y, Yalniz G, Vasudevan M, Marensi E, Hof B. Discontinuous transition to shear flow turbulence. <i>Nature Physics</i>. 2026. doi:<a href=\"https://doi.org/10.1038/s41567-025-03166-3\">10.1038/s41567-025-03166-3</a>","chicago":"Yang, Bowen, Yi Zhuang, Gökhan Yalniz, Mukund Vasudevan, Elena Marensi, and Björn Hof. “Discontinuous Transition to Shear Flow Turbulence.” <i>Nature Physics</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1038/s41567-025-03166-3\">https://doi.org/10.1038/s41567-025-03166-3</a>.","ista":"Yang B, Zhuang Y, Yalniz G, Vasudevan M, Marensi E, Hof B. 2026. Discontinuous transition to shear flow turbulence. Nature Physics.","apa":"Yang, B., Zhuang, Y., Yalniz, G., Vasudevan, M., Marensi, E., &#38; Hof, B. (2026). Discontinuous transition to shear flow turbulence. <i>Nature Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41567-025-03166-3\">https://doi.org/10.1038/s41567-025-03166-3</a>"},"scopus_import":"1","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"02"},{"status":"public","publication_status":"published","date_updated":"2026-06-18T19:23:35Z","publisher":"Institute of Science and Technology Austria","year":"2025","day":"13","file":[{"creator":"gyalniz","file_size":20058169,"content_type":"application/pdf","date_updated":"2025-05-12T15:13:28Z","relation":"main_file","checksum":"0e452642b79f13633f1595bde71a67e3","date_created":"2025-05-12T15:13:28Z","access_level":"open_access","success":1,"file_name":"Gökhan Yalnız - PhD thesis.pdf","file_id":"19685"},{"file_name":"Movie 2A.1.mp4","file_id":"19686","relation":"supplementary_material","checksum":"921099d76adab2df784ce12ce41cfb22","date_created":"2025-05-12T15:15:59Z","description":"3D visualizations of the turbulent flow (left) and the periodic orbits (middle) that are being shadowed along with the local state space projections (right) onto the principal components of the respective periodic orbit. Shown here are the isosurfaces of velocity (red/blue: ±95% of the instantaneous maximum) and vorticity (purple/green: ±65% of the instantaneous maximum) in the x-direction. Markers along the projections are in sync with the 3D visualizations. The movie corresponds to the initial time interval (up to t = 100) of figure 2.2 (a,b); periodic orbits and the state space projections are shown only through the shadowing events indicated in figure 2.2 (b).","access_level":"open_access","creator":"gyalniz","file_size":37763743,"title":"Chapter 2 - Movie 2A.1","date_updated":"2025-05-12T15:43:28Z","content_type":"video/mp4"},{"file_name":"Movie 3A.1.mp4","file_id":"19687","checksum":"0ae5ac7d9896003c0c4207dd746808dc","date_created":"2025-05-12T15:16:09Z","relation":"supplementary_material","access_level":"open_access","description":"Turbulent flow (left) in HKW domain and its symmetry reduction (right). Shown here are the isosurfaces of streamwise velocity (red/blue: u = 0.5 max/min u) and streamwise vorticity (green/purple: ω_x = 0.5 max/min ω_x).","creator":"gyalniz","title":"Chapter 3 - Movie 3A.1","file_size":3902655,"content_type":"video/mp4","date_updated":"2025-05-12T15:43:28Z"},{"access_level":"open_access","description":"Turbulent flow (left) in P2K domain and its symmetry reduction (right). Shown here are the isosurfaces of streamwise velocity (red/blue: u = 0.5 max/min u) and streamwise vorticity (green/purple: ω_x = 0.5 max/min ω_x).","relation":"supplementary_material","checksum":"ef8d270e066c1a9c3cb5ae46acf945e6","date_created":"2025-05-12T15:16:21Z","title":"Chapter 3 - Movie 3A.2","file_size":7043169,"date_updated":"2025-05-12T15:43:28Z","content_type":"video/mp4","creator":"gyalniz","file_id":"19688","file_name":"Movie 3A.2.mp4"},{"date_created":"2025-05-12T15:16:36Z","checksum":"7ed871f428100d6827ac9b0e8ca8e985","relation":"supplementary_material","description":"Relative periodic orbit RPO_79.4 (left) of the plane-Couette flow (HKW domain) and its symmetry reduction (right). Shown here are the isosurfaces of streamwise velocity (red/blue: u = 0.5 max/min u) and streamwise vorticity (green/purple: ω_x = 0.5 max/min ω_x).","access_level":"open_access","creator":"gyalniz","date_updated":"2025-05-12T15:43:28Z","content_type":"video/mp4","file_size":7748659,"title":"Chapter 3 - Movie 3A.3","file_name":"Movie 3A.3.mp4","file_id":"19689"},{"description":"Symmetry-reduced flow (left), its SRDMD approximation (middle), and state space projection (right) showing the spiral-out episode in P2K domain (figure 3.6 (b) and figure 3.8 (b)). Shown here are the isosurfaces of streamwise velocity (red/blue: u = 0.5 max/min u) and streamwise vorticity (green/purple: ω_x = 0.5 max/min ω_x).","access_level":"open_access","checksum":"dd5a252e1da00c8f303588e22e2baeef","relation":"supplementary_material","date_created":"2025-05-12T15:16:50Z","title":"Chapter 3 - Movie 3A.4","file_size":5873052,"date_updated":"2025-05-12T15:43:28Z","content_type":"video/mp4","creator":"gyalniz","file_id":"19690","file_name":"Movie 3A.4.mp4"},{"checksum":"5ac58b86810698db28cbfc28f351ff70","date_created":"2025-05-12T15:17:11Z","relation":"supplementary_material","access_level":"open_access","description":"Movie demonstrating the quasi-steady Reynolds number descent from turbulence to a periodic orbit.","creator":"gyalniz","file_size":9209327,"title":"Chapter 4 - Movie 4A.1","content_type":"video/mp4","date_updated":"2025-05-12T15:43:28Z","file_name":"Movie 4A.1.mp4","file_id":"19691"},{"content_type":"video/mp4","date_updated":"2025-05-12T15:43:28Z","title":"Chapter 5 - Movie 5A.1","file_size":5893993,"creator":"gyalniz","access_level":"open_access","description":"Streamwise velocity fluctuations (from laminar) of plane-Couette flow (Re^C =335) at the y = 0 wall-normal plane in coordinates stationary with respect to the bulk velocity. Here, x is the streamwise direction (the wall at y = 1 moves to the right) and z is the spanwise direction. Time is in advectime time units. Shown is the full (L_x = L_z = 400) domain.","date_created":"2025-05-12T15:17:43Z","relation":"supplementary_material","checksum":"ac877f1e1ef39439911bf37cb1793b8e","file_id":"19692","file_name":"Movie 5A.1.mp4"},{"checksum":"fd17eabb70129ceaa414e40924d1d2fe","relation":"supplementary_material","date_created":"2025-05-12T15:17:49Z","description":"Streamwise velocity fluctuations (from laminar) of plane-Poiseuille flow (Re^P =660) at the y = 0.5 wall-normal plane in coordinates stationary with respect to the bulk velocity. Here, x is the streamwise direction (the mean negative pressure gradient is to the right) and z is the spanwise direction. Time is in advectime time units. Shown is the full (L_x = L_z = 400) domain.","access_level":"open_access","creator":"gyalniz","title":"Chapter 5 - Movie 5A.2","file_size":3990352,"date_updated":"2025-05-12T15:43:28Z","content_type":"video/mp4","file_name":"Movie 5A.2.mp4","file_id":"19693"},{"file_id":"19694","file_name":"Movie 5A.3.mp4","access_level":"open_access","description":"Streamwise velocity fluctuations (from laminar) of plane-Poiseuille flow (Re^P=660) at the y = 0.5 wall-normal plane in coordinates stationary with respect to the average velocity of the downstream tip of the stripe. Here, x is the streamwise direction (the mean negative pressure gradient is to the right) and z is the spanwise direction. Time is in advectime time units. Shown is a zoom-in of the full (L_x = L_z) domain.","relation":"supplementary_material","checksum":"32f904497ab0bbee38f0788d96b91454","date_created":"2025-05-12T15:17:58Z","date_updated":"2025-05-12T15:43:28Z","content_type":"video/mp4","file_size":5171009,"title":"Chapter 5 - Movie 5A.3","creator":"gyalniz"},{"file_id":"19695","file_name":"Gökhan Yalnız - PhD thesis.zip","access_level":"closed","date_created":"2025-05-12T15:27:10Z","checksum":"f313261b9bb12dfb943fead8318954c6","relation":"source_file","date_updated":"2025-05-12T15:43:28Z","content_type":"application/x-zip-compressed","file_size":18991996,"creator":"gyalniz"}],"corr_author":"1","date_published":"2025-05-13T00:00:00Z","ddc":["514","519","532","004"],"author":[{"id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312","last_name":"Yalniz","first_name":"Gökhan"}],"has_accepted_license":"1","acknowledgement":"The work in this thesis was supported by a grant from the Simons Foundation (662960, BH).\r\n","date_created":"2025-05-12T15:12:28Z","doi":"10.15479/AT-ISTA-19684","_id":"19684","publication_identifier":{"issn":["2663-337X"]},"related_material":{"record":[{"id":"9558","relation":"part_of_dissertation","status":"public"},{"id":"12105","status":"public","relation":"part_of_dissertation"},{"id":"13274","relation":"part_of_dissertation","status":"public"},{"id":"14466","relation":"part_of_dissertation","status":"public"},{"id":"7563","status":"public","relation":"part_of_dissertation"}]},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","month":"05","type":"dissertation","degree_awarded":"PhD","citation":{"ama":"Yalniz G. Transition to turbulence : Data-, solution-, and pattern-driven approaches. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-19684\">10.15479/AT-ISTA-19684</a>","chicago":"Yalniz, Gökhan. “Transition to Turbulence : Data-, Solution-, and Pattern-Driven Approaches.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-19684\">https://doi.org/10.15479/AT-ISTA-19684</a>.","short":"G. Yalniz, Transition to Turbulence : Data-, Solution-, and Pattern-Driven Approaches, Institute of Science and Technology Austria, 2025.","mla":"Yalniz, Gökhan. <i>Transition to Turbulence : Data-, Solution-, and Pattern-Driven Approaches</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-19684\">10.15479/AT-ISTA-19684</a>.","ieee":"G. Yalniz, “Transition to turbulence : Data-, solution-, and pattern-driven approaches,” Institute of Science and Technology Austria, 2025.","apa":"Yalniz, G. (2025). <i>Transition to turbulence : Data-, solution-, and pattern-driven approaches</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-19684\">https://doi.org/10.15479/AT-ISTA-19684</a>","ista":"Yalniz G. 2025. Transition to turbulence : Data-, solution-, and pattern-driven approaches. Institute of Science and Technology Austria."},"OA_place":"publisher","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"department":[{"_id":"GradSch"},{"_id":"BjHo"}],"abstract":[{"lang":"eng","text":"The overarching goal of this thesis is to break down the complexity of turbulent flows in terms of enumerable, coherent structures and patterns. In a five-paper series, we adopt a variety of perspectives and techniques to relate the properties of systems of increasing complexity to their underlying coherent structures. \r\n\r\nInitially, we take a dynamical systems point of view, seeing turbulent flow as a chaotic trajectory bouncing between exact unstable solutions of the underlying equations of motion. Using persistent homology, the main tool of topological data analysis capturing the persistence across scales of topological features in a point cloud, we introduce a method that quantifies visits of turbulent trajectories to unstable time-periodic solutions, also called periodic orbits. We demonstrate this method first in the Rössler and Kuramoto–Sivashinsky systems. Using this method in 3D Kolmogorov flow, we extract a Markov chain from turbulent data, where each node corresponds to the neighbourhood of a periodic orbit. The invariant distribution of this Markov chain reproduces expectation values on turbulent data when it is used to weight averages on the respective periodic orbits.\r\n\r\nIn more realistic, wall-bounded settings, such as plane-Couette flow (pcf) driven by the relative motion of the walls, or plane-Poiseuille flow (ppf) driven by a pressure gradient, finding exact solutions is difficult. We use dynamic mode decomposition (DMD), a dimensionality reduction method for sequential data, to identify and approximate low-dimensional dynamics without knowing any exact solutions. Most spatially-extended systems are equivariant under translations, and in such cases spatial drifts dominate DMD, hindering its use in the search for and modelling of low-dimensional dynamics. We augment DMD with a symmetry reduction method trained on turbulent data to stop it from seeing translations as a feature, improving its ability to extract dynamical information in translation-equivariant systems. We find segments of turbulent trajectories that linearize well with their symmetry-reduced DMD spectra, akin to dynamics near exact solutions. Searching for harmonics in the spectra gives leads for periodic orbits with spatial drifts, one of which converges to a new solution.\r\n\r\nIn larger domains, turbulence can localize and coexist with surrounding laminar flow. Our preceding approaches are global, taking all of a domain into account at once, and cannot readily treat each localized patch individually. Working first in a minimal oblique domain that can host a single 1D-localized turbulent patch, we find that turbulence in ppf is connected to a stable periodic orbit at a flow velocity much lower than when turbulence is first onset. We show that, well in advance of sustained turbulence, chaos sets in explosively, and for long time horizons, time series are consistent with that of a random process.\r\n\r\nFinally, in much larger domains, we study and compare 2D-localized turbulence that appears as large-scale inclined structures, called stripes, in ppf and pcf. While appearing similar, we find that stripes in these two settings differ significantly in terms of how they sustain themselves, and in higher velocities, how they proliferate."}],"alternative_title":["ISTA Thesis"],"file_date_updated":"2025-05-12T15:43:28Z","title":"Transition to turbulence : Data-, solution-, and pattern-driven approaches","acknowledged_ssus":[{"_id":"ScienComp"}],"page":"155","article_processing_charge":"No","supervisor":[{"full_name":"Hof, Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754","first_name":"Björn","last_name":"Hof"}],"project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","grant_number":"662960"}]},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"isi":1,"intvolume":"        16","has_accepted_license":"1","ddc":["532"],"APC_amount":"7068 EUR","date_published":"2025-09-26T00:00:00Z","corr_author":"1","OA_type":"gold","author":[{"last_name":"Vasudevan","first_name":"Mukund","id":"3C5A959A-F248-11E8-B48F-1D18A9856A87","full_name":"Vasudevan, Mukund"},{"full_name":"Paranjape, Chaitanya S","id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87","first_name":"Chaitanya S","last_name":"Paranjape"},{"full_name":"Sitte, Michael Philip","id":"0ba0f1f2-9cfe-11f0-bee6-f95318d225b0","first_name":"Michael Philip","last_name":"Sitte"},{"last_name":"Yalniz","first_name":"Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312"},{"first_name":"Björn","last_name":"Hof","full_name":"Hof, Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754"}],"PlanS_conform":"1","day":"26","year":"2025","file":[{"file_id":"20403","file_name":"s41467-025-63044-7.pdf","file_size":2226082,"date_updated":"2025-09-27T13:32:03Z","content_type":"application/pdf","creator":"gyalniz","access_level":"open_access","date_created":"2025-09-27T13:32:03Z","checksum":"945926ead9cde464435d456427e2869e","relation":"main_file"}],"publication_status":"published","status":"public","publisher":"Springer Nature","article_type":"original","date_updated":"2026-05-20T07:56:59Z","arxiv":1,"project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics","grant_number":"662960","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"external_id":{"arxiv":["2112.06537"],"isi":["001582555200041"]},"article_processing_charge":"Yes","file_date_updated":"2025-09-27T13:32:03Z","volume":16,"publication":"Nature Communications","abstract":[{"lang":"eng","text":"The recent classification of the onset of turbulence as a directed percolation (DP) phase transition has been applied to all major shear flows including pipe, channel, Couette and boundary layer flows. A cornerstone of the DP analogy is the memoryless (Poisson) property of turbulent sites. We here show that, for the classic case of channel flow, neither the decay nor the proliferation of turbulent stripes is memoryless. As demonstrated by a standard analysis of the respective survival curves, isolated channel stripes, in the immediate vicinity of the critical point, age. Consequently, the one to one mapping between turbulent stripes and active DP-sites is not fulfilled in this low Reynolds number regime. In addition, the interpretation of turbulence as a chaotic saddle with supertransient properties, the basis of recent theoretical progress, does not apply to individual localized stripes. The discrepancy between channel flow and the transition models established for pipe and Couette flow, illustrates that seemingly minor geometrical differences between flows can give rise to instabilities and growth mechanisms that fundamentally alter the nature of the transition to turbulence."}],"title":"Aging and memory of transitional turbulence","article_number":"8447","quality_controlled":"1","language":[{"iso":"eng"}],"OA_place":"publisher","department":[{"_id":"BjHo"}],"DOAJ_listed":"1","oa_version":"Published Version","oa":1,"publication_identifier":{"eissn":["2041-1723"]},"_id":"20402","doi":"10.1038/s41467-025-63044-7","date_created":"2025-09-27T13:27:31Z","acknowledgement":"This work was supported by a grant from the Simons Foundation (662960, BH). We thank Yohann Duguet for helpful discussions, Baofang Song for the initial adaptation of openpipeflow57 to the channel geometry, and Ashley P. Willis for openpipeflow57.","citation":{"apa":"Vasudevan, M., Paranjape, C. S., Sitte, M. P., Yalniz, G., &#38; Hof, B. (2025). Aging and memory of transitional turbulence. <i>Nature Communications</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41467-025-63044-7\">https://doi.org/10.1038/s41467-025-63044-7</a>","ista":"Vasudevan M, Paranjape CS, Sitte MP, Yalniz G, Hof B. 2025. Aging and memory of transitional turbulence. Nature Communications. 16, 8447.","chicago":"Vasudevan, Mukund, Chaitanya S Paranjape, Michael Philip Sitte, Gökhan Yalniz, and Björn Hof. “Aging and Memory of Transitional Turbulence.” <i>Nature Communications</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1038/s41467-025-63044-7\">https://doi.org/10.1038/s41467-025-63044-7</a>.","ama":"Vasudevan M, Paranjape CS, Sitte MP, Yalniz G, Hof B. Aging and memory of transitional turbulence. <i>Nature Communications</i>. 2025;16. doi:<a href=\"https://doi.org/10.1038/s41467-025-63044-7\">10.1038/s41467-025-63044-7</a>","ieee":"M. Vasudevan, C. S. Paranjape, M. P. Sitte, G. Yalniz, and B. Hof, “Aging and memory of transitional turbulence,” <i>Nature Communications</i>, vol. 16. Springer Nature, 2025.","mla":"Vasudevan, Mukund, et al. “Aging and Memory of Transitional Turbulence.” <i>Nature Communications</i>, vol. 16, 8447, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1038/s41467-025-63044-7\">10.1038/s41467-025-63044-7</a>.","short":"M. Vasudevan, C.S. Paranjape, M.P. Sitte, G. Yalniz, B. Hof, Nature Communications 16 (2025)."},"scopus_import":"1","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"09"},{"article_processing_charge":"Yes","external_id":{"arxiv":["2504.12472"],"isi":["001616473700003"]},"project":[{"_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","grant_number":"850899","call_identifier":"H2020","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control"},{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund","call_identifier":"FWF"}],"arxiv":1,"title":"Finding periodic orbits in projected quantum many-body dynamics","article_number":"040333","ec_funded":1,"volume":6,"publication":"PRX Quantum","abstract":[{"text":"Describing general quantum many-body dynamics is a challenging task due to the exponential growth of the Hilbert space with system size. The time-dependent variational principle (TDVP) provides a powerful tool to tackle this task by projecting quantum evolution onto a classical dynamical system within a variational manifold. In classical systems, periodic orbits play a crucial role in understanding the structure of the phase space and the long-term behavior of the system. However, finding periodic orbits is generally difficult, and their existence and properties in generic TDVP dynamics over matrix product states have remained largely unexplored. In this work, we develop an algorithm to systematically identify and characterize periodic orbits in TDVP dynamics. Applying our method to the periodically kicked Ising model, we uncover both stable and unstable periodic orbits. We characterize the Kolmogorov-Arnold-Moser tori in the vicinity of stable periodic orbits and track the change of the periodic orbits as we modify the Hamiltonian parameters. We observe that periodic orbits exist at any value of the coupling constant of the kicked Ising model between prethermal and fully thermalizing regimes, but their relevance to quantum dynamics and imprint on quantum eigenstates diminishes as the system leaves the prethermal regime. Our results demonstrate that periodic orbits provide valuable insights into the TDVP approximation of quantum many-body evolution and establish a closer connection between quantum and classical chaos.","lang":"eng"}],"file_date_updated":"2025-11-14T09:44:10Z","oa_version":"Published Version","oa":1,"department":[{"_id":"GradSch"},{"_id":"BjHo"},{"_id":"MaSe"}],"DOAJ_listed":"1","OA_place":"publisher","language":[{"iso":"eng"}],"quality_controlled":"1","issue":"4","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","citation":{"apa":"Petrova, E., Ljubotina, M., Yalniz, G., &#38; Serbyn, M. (2025). Finding periodic orbits in projected quantum many-body dynamics. <i>PRX Quantum</i>. American Physical Society. <a href=\"https://doi.org/10.1103/tldp-kvkd\">https://doi.org/10.1103/tldp-kvkd</a>","ista":"Petrova E, Ljubotina M, Yalniz G, Serbyn M. 2025. Finding periodic orbits in projected quantum many-body dynamics. PRX Quantum. 6(4), 040333.","chicago":"Petrova, Elena, Marko Ljubotina, Gökhan Yalniz, and Maksym Serbyn. “Finding Periodic Orbits in Projected Quantum Many-Body Dynamics.” <i>PRX Quantum</i>. American Physical Society, 2025. <a href=\"https://doi.org/10.1103/tldp-kvkd\">https://doi.org/10.1103/tldp-kvkd</a>.","ama":"Petrova E, Ljubotina M, Yalniz G, Serbyn M. Finding periodic orbits in projected quantum many-body dynamics. <i>PRX Quantum</i>. 2025;6(4). doi:<a href=\"https://doi.org/10.1103/tldp-kvkd\">10.1103/tldp-kvkd</a>","ieee":"E. Petrova, M. Ljubotina, G. Yalniz, and M. Serbyn, “Finding periodic orbits in projected quantum many-body dynamics,” <i>PRX Quantum</i>, vol. 6, no. 4. American Physical Society, 2025.","mla":"Petrova, Elena, et al. “Finding Periodic Orbits in Projected Quantum Many-Body Dynamics.” <i>PRX Quantum</i>, vol. 6, no. 4, 040333, American Physical Society, 2025, doi:<a href=\"https://doi.org/10.1103/tldp-kvkd\">10.1103/tldp-kvkd</a>.","short":"E. Petrova, M. Ljubotina, G. Yalniz, M. Serbyn, PRX Quantum 6 (2025)."},"scopus_import":"1","acknowledgement":"We acknowledge useful discussions with C. Kollath, A. Green, and D. Huse. E.P., M.L., and M.S. acknowledge support by the European Research Council under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899). This research was funded in whole or in part by the Austrian Science Fund (FWF) (Grant No. 10.55776/COE1). For open access purposes, the author has applied a CC BY public copyright license to any author accepted manuscript version arising from this submission. M.L. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111—390814868. This research was supported in part by National Science Foundation (NSF) Grant No. PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP) and by the Erwin Schrödinger International Institute for Mathematics and Physics (ESI).","publication_identifier":{"eissn":["2691-3399"]},"_id":"20646","related_material":{"link":[{"url":"https://ista.ac.at/en/news/reaching-for-the-quantum-scars/","relation":"press_release","description":"News on ISTA website"}]},"date_created":"2025-11-14T09:40:52Z","doi":"10.1103/tldp-kvkd","has_accepted_license":"1","intvolume":"         6","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"author":[{"last_name":"Petrova","first_name":"Elena","id":"0ac84990-897b-11ed-a09c-f5abb56a4ede","full_name":"Petrova, Elena"},{"full_name":"Ljubotina, Marko","id":"F75EE9BE-5C90-11EA-905D-16643DDC885E","orcid":"0000-0003-0038-7068","first_name":"Marko","last_name":"Ljubotina"},{"full_name":"Yalniz, Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","orcid":"0000-0002-8490-9312","first_name":"Gökhan","last_name":"Yalniz"},{"orcid":"0000-0002-2399-5827","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","full_name":"Serbyn, Maksym","last_name":"Serbyn","first_name":"Maksym"}],"OA_type":"gold","corr_author":"1","date_published":"2025-11-12T00:00:00Z","APC_amount":"3599,50 EUR","ddc":["539"],"file":[{"success":1,"file_id":"20647","file_name":"tldp-kvkd.pdf","date_updated":"2025-11-14T09:44:10Z","content_type":"application/pdf","file_size":2504713,"creator":"gyalniz","access_level":"open_access","relation":"main_file","date_created":"2025-11-14T09:44:10Z","checksum":"5d6d04ac518b4118405334e1ddc7a56d"}],"year":"2025","PlanS_conform":"1","day":"12","date_updated":"2026-05-20T07:59:04Z","article_type":"original","publisher":"American Physical Society","publication_status":"published","status":"public"},{"publication_status":"published","status":"public","date_updated":"2026-04-07T11:47:05Z","publisher":"Cambridge University Press","article_type":"original","year":"2023","day":"10","file":[{"success":1,"file_name":"2023_JourFluidMechanics_Marensi.pdf","file_id":"12489","creator":"dernst","content_type":"application/pdf","date_updated":"2023-02-02T12:34:54Z","file_size":1931647,"relation":"main_file","checksum":"9224f987caefe5dd85a70814d3cce65c","date_created":"2023-02-02T12:34:54Z","access_level":"open_access"}],"corr_author":"1","ddc":["530"],"date_published":"2023-01-10T00:00:00Z","author":[{"orcid":"0000-0001-7173-4923","id":"0BE7553A-1004-11EA-B805-18983DDC885E","full_name":"Marensi, Elena","last_name":"Marensi","first_name":"Elena"},{"first_name":"Gökhan","last_name":"Yalniz","orcid":"0000-0002-8490-9312","full_name":"Yalniz, Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425"},{"orcid":"0000-0003-2057-2754","id":"3A374330-F248-11E8-B48F-1D18A9856A87","full_name":"Hof, Björn","last_name":"Hof","first_name":"Björn"},{"last_name":"Budanur","first_name":"Nazmi B","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","full_name":"Budanur, Nazmi B","orcid":"0000-0003-0423-5010"}],"intvolume":"       954","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"isi":1,"has_accepted_license":"1","acknowledgement":"E.M. acknowledges funding from the ISTplus fellowship programme. G.Y. and B.H. acknowledge\r\na grant from the Simons Foundation (662960, BH).","_id":"12105","related_material":{"record":[{"id":"19684","relation":"dissertation_contains","status":"public"}]},"publication_identifier":{"issn":["0022-1120"],"eissn":["1469-7645"]},"doi":"10.1017/jfm.2022.1001","date_created":"2023-01-08T23:00:53Z","type":"journal_article","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"01","citation":{"short":"E. Marensi, G. Yalniz, B. Hof, N.B. Budanur, Journal of Fluid Mechanics 954 (2023).","ieee":"E. Marensi, G. Yalniz, B. Hof, and N. B. Budanur, “Symmetry-reduced dynamic mode decomposition of near-wall turbulence,” <i>Journal of Fluid Mechanics</i>, vol. 954. Cambridge University Press, 2023.","mla":"Marensi, Elena, et al. “Symmetry-Reduced Dynamic Mode Decomposition of near-Wall Turbulence.” <i>Journal of Fluid Mechanics</i>, vol. 954, A10, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/jfm.2022.1001\">10.1017/jfm.2022.1001</a>.","ama":"Marensi E, Yalniz G, Hof B, Budanur NB. Symmetry-reduced dynamic mode decomposition of near-wall turbulence. <i>Journal of Fluid Mechanics</i>. 2023;954. doi:<a href=\"https://doi.org/10.1017/jfm.2022.1001\">10.1017/jfm.2022.1001</a>","chicago":"Marensi, Elena, Gökhan Yalniz, Björn Hof, and Nazmi B Budanur. “Symmetry-Reduced Dynamic Mode Decomposition of near-Wall Turbulence.” <i>Journal of Fluid Mechanics</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/jfm.2022.1001\">https://doi.org/10.1017/jfm.2022.1001</a>.","ista":"Marensi E, Yalniz G, Hof B, Budanur NB. 2023. Symmetry-reduced dynamic mode decomposition of near-wall turbulence. Journal of Fluid Mechanics. 954, A10.","apa":"Marensi, E., Yalniz, G., Hof, B., &#38; Budanur, N. B. (2023). Symmetry-reduced dynamic mode decomposition of near-wall turbulence. <i>Journal of Fluid Mechanics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/jfm.2022.1001\">https://doi.org/10.1017/jfm.2022.1001</a>"},"scopus_import":"1","language":[{"iso":"eng"}],"quality_controlled":"1","oa":1,"oa_version":"Published Version","department":[{"_id":"BjHo"}],"volume":954,"publication":"Journal of Fluid Mechanics","abstract":[{"text":"Data-driven dimensionality reduction methods such as proper orthogonal decomposition and dynamic mode decomposition have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known challenge for these techniques is posed by the continuous symmetries, e.g. translations and rotations, of the system under consideration, as drifts in the data dominate the modal expansions without providing an insight into the dynamics of the problem. In the present study, we address this issue for fluid flows in rectangular channels by formulating a continuous symmetry reduction method that eliminates the translations in the streamwise and spanwise directions simultaneously. We demonstrate our method by computing the symmetry-reduced dynamic mode decomposition (SRDMD) of sliding windows of data obtained from the transitional plane-Couette and turbulent plane-Poiseuille flow simulations. In the former setting, SRDMD captures the dynamics in the vicinity of the invariant solutions with translation symmetries, i.e. travelling waves and relative periodic orbits, whereas in the latter, our calculations reveal episodes of turbulent time evolution that can be approximated by a low-dimensional linear expansion.","lang":"eng"}],"file_date_updated":"2023-02-02T12:34:54Z","article_number":"A10","title":"Symmetry-reduced dynamic mode decomposition of near-wall turbulence","arxiv":1,"external_id":{"arxiv":["2101.07516"],"isi":["000903336600001"]},"article_processing_charge":"Yes (via OA deal)","project":[{"grant_number":"662960","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","name":"Revisiting the Turbulence Problem Using Statistical Mechanics"}]},{"author":[{"first_name":"Chaitanya S","last_name":"Paranjape","full_name":"Paranjape, Chaitanya S","id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Yalniz","first_name":"Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312"},{"first_name":"Yohann","last_name":"Duguet","full_name":"Duguet, Yohann"},{"orcid":"0000-0003-0423-5010","full_name":"Budanur, Nazmi B","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","first_name":"Nazmi B","last_name":"Budanur"},{"orcid":"0000-0003-2057-2754","id":"3A374330-F248-11E8-B48F-1D18A9856A87","full_name":"Hof, Björn","last_name":"Hof","first_name":"Björn"}],"date_published":"2023-07-21T00:00:00Z","corr_author":"1","keyword":["General Physics and Astronomy"],"isi":1,"intvolume":"       131","publisher":"American Physical Society","article_type":"original","date_updated":"2026-04-07T11:47:05Z","publication_status":"published","pmid":1,"status":"public","day":"21","year":"2023","title":"Direct path from turbulence to time-periodic solutions","article_number":"034002","volume":131,"abstract":[{"text":"Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to high-dimensional motion can be rationalized within the framework of the Navier-Stokes equations is not well understood. Exploiting geometrical properties of transitional channel flow we trace turbulence to far lower Reynolds numbers (Re) than previously possible and identify the complete path that reversibly links fully turbulent motion to an invariant solution. This precursor of turbulence destabilizes rapidly with Re, and the accompanying explosive increase in attractor dimension effectively marks the transition between deterministic and de facto stochastic dynamics.","lang":"eng"}],"publication":"Physical Review Letters","project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","grant_number":"662960"}],"external_id":{"pmid":["37540883"],"isi":["001052929900004"],"arxiv":["2306.05098"]},"article_processing_charge":"No","arxiv":1,"citation":{"apa":"Paranjape, C. S., Yalniz, G., Duguet, Y., Budanur, N. B., &#38; Hof, B. (2023). Direct path from turbulence to time-periodic solutions. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevlett.131.034002\">https://doi.org/10.1103/physrevlett.131.034002</a>","ista":"Paranjape CS, Yalniz G, Duguet Y, Budanur NB, Hof B. 2023. Direct path from turbulence to time-periodic solutions. Physical Review Letters. 131(3), 034002.","ama":"Paranjape CS, Yalniz G, Duguet Y, Budanur NB, Hof B. Direct path from turbulence to time-periodic solutions. <i>Physical Review Letters</i>. 2023;131(3). doi:<a href=\"https://doi.org/10.1103/physrevlett.131.034002\">10.1103/physrevlett.131.034002</a>","chicago":"Paranjape, Chaitanya S, Gökhan Yalniz, Yohann Duguet, Nazmi B Budanur, and Björn Hof. “Direct Path from Turbulence to Time-Periodic Solutions.” <i>Physical Review Letters</i>. American Physical Society, 2023. <a href=\"https://doi.org/10.1103/physrevlett.131.034002\">https://doi.org/10.1103/physrevlett.131.034002</a>.","short":"C.S. Paranjape, G. Yalniz, Y. Duguet, N.B. Budanur, B. Hof, Physical Review Letters 131 (2023).","mla":"Paranjape, Chaitanya S., et al. “Direct Path from Turbulence to Time-Periodic Solutions.” <i>Physical Review Letters</i>, vol. 131, no. 3, 034002, American Physical Society, 2023, doi:<a href=\"https://doi.org/10.1103/physrevlett.131.034002\">10.1103/physrevlett.131.034002</a>.","ieee":"C. S. Paranjape, G. Yalniz, Y. Duguet, N. B. Budanur, and B. Hof, “Direct path from turbulence to time-periodic solutions,” <i>Physical Review Letters</i>, vol. 131, no. 3. American Physical Society, 2023."},"scopus_import":"1","type":"journal_article","month":"07","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"id":"19684","status":"public","relation":"dissertation_contains"}]},"_id":"13274","publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"date_created":"2023-07-24T09:43:59Z","doi":"10.1103/physrevlett.131.034002","acknowledgement":"We thank Baofang Song as well as the developers of Channelflow for sharing their numerical codes, and Mukund Vasudevan and Holger Kantz for fruitful discussions. This work was supported by a grant from the Simons Foundation (662960, B. H.).","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.05098"}],"department":[{"_id":"GradSch"},{"_id":"BjHo"}],"oa_version":"Preprint","oa":1,"language":[{"iso":"eng"}],"quality_controlled":"1","issue":"3"},{"article_type":"original","publisher":"Cambridge University Press","date_updated":"2026-04-07T11:47:05Z","status":"public","publication_status":"published","file":[{"file_name":"2023_JourFluidMechanics_Marensi.pdf","file_id":"14996","success":1,"checksum":"17c64c1fb0d5f73252364bf98b0b9e1a","relation":"main_file","date_created":"2024-02-15T09:05:21Z","access_level":"open_access","creator":"dernst","date_updated":"2024-02-15T09:05:21Z","content_type":"application/pdf","file_size":2804641}],"day":"10","year":"2023","author":[{"id":"0BE7553A-1004-11EA-B805-18983DDC885E","full_name":"Marensi, Elena","orcid":"0000-0001-7173-4923","last_name":"Marensi","first_name":"Elena"},{"first_name":"Gökhan","last_name":"Yalniz","full_name":"Yalniz, Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","orcid":"0000-0002-8490-9312"},{"full_name":"Hof, Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754","first_name":"Björn","last_name":"Hof"}],"date_published":"2023-11-10T00:00:00Z","ddc":["530"],"corr_author":"1","keyword":["turbulence","transition to turbulence","patterns"],"has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"isi":1,"intvolume":"       974","scopus_import":"1","citation":{"apa":"Marensi, E., Yalniz, G., &#38; Hof, B. (2023). Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows. <i>Journal of Fluid Mechanics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/jfm.2023.780\">https://doi.org/10.1017/jfm.2023.780</a>","ista":"Marensi E, Yalniz G, Hof B. 2023. Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows. Journal of Fluid Mechanics. 974, A21.","chicago":"Marensi, Elena, Gökhan Yalniz, and Björn Hof. “Dynamics and Proliferation of Turbulent Stripes in Plane-Poiseuille and Plane-Couette Flows.” <i>Journal of Fluid Mechanics</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/jfm.2023.780\">https://doi.org/10.1017/jfm.2023.780</a>.","ama":"Marensi E, Yalniz G, Hof B. Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows. <i>Journal of Fluid Mechanics</i>. 2023;974. doi:<a href=\"https://doi.org/10.1017/jfm.2023.780\">10.1017/jfm.2023.780</a>","mla":"Marensi, Elena, et al. “Dynamics and Proliferation of Turbulent Stripes in Plane-Poiseuille and Plane-Couette Flows.” <i>Journal of Fluid Mechanics</i>, vol. 974, A21, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/jfm.2023.780\">10.1017/jfm.2023.780</a>.","ieee":"E. Marensi, G. Yalniz, and B. Hof, “Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows,” <i>Journal of Fluid Mechanics</i>, vol. 974. Cambridge University Press, 2023.","short":"E. Marensi, G. Yalniz, B. Hof, Journal of Fluid Mechanics 974 (2023)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","type":"journal_article","date_created":"2023-10-30T09:32:28Z","doi":"10.1017/jfm.2023.780","publication_identifier":{"issn":["0022-1120"],"eissn":["1469-7645"]},"_id":"14466","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19684"}]},"acknowledgement":"E.M. acknowledges funding from the ISTplus fellowship programme. G.Y. and B.H. acknowledge a grant from the Simons Foundation (662960, BH).","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"oa_version":"Published Version","oa":1,"quality_controlled":"1","language":[{"iso":"eng"}],"article_number":"A21","title":"Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows","file_date_updated":"2024-02-15T09:05:21Z","publication":"Journal of Fluid Mechanics","abstract":[{"text":"The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes is central to transition, and recent studies proposed an analogy to directed percolation where the stripes’ proliferation is ultimately responsible for the turbulence becoming sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure- and shear-driven planar flows, respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar–turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off/shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes.","lang":"eng"}],"volume":974,"project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics","grant_number":"662960","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"}],"external_id":{"arxiv":["2212.12406"],"isi":["001088363700001"]},"article_processing_charge":"Yes (via OA deal)","arxiv":1},{"issue":"24","quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Preprint","oa":1,"department":[{"_id":"GradSch"},{"_id":"BjHo"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2007.02584"}],"acknowledgement":"We thank the referees for improving this Letter with their comments. We acknowledge stimulating discussions with\r\nH. Edelsbrunner. This work was supported by Grant No. 662960 from the Simons Foundation (B. H.). The numerical calculations were performed at TUBITAK ULAKBIM High Performance and Grid Computing Center (TRUBA resources) and IST Austria High Performance Computing cluster.","date_created":"2021-06-16T15:45:36Z","doi":"10.1103/PhysRevLett.126.244502","related_material":{"link":[{"description":"News on IST Homepage","url":"https://ist.ac.at/en/news/turbulent-flow-simplified/","relation":"press_release"}],"record":[{"relation":"popular_science","status":"returned","id":"19591"},{"status":"public","relation":"dissertation_contains","id":"19684"}]},"_id":"9558","publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"06","type":"journal_article","scopus_import":"1","citation":{"ieee":"G. Yalniz, B. Hof, and N. B. Budanur, “Coarse graining the state space of a turbulent flow using periodic orbits,” <i>Physical Review Letters</i>, vol. 126, no. 24. American Physical Society, 2021.","mla":"Yalniz, Gökhan, et al. “Coarse Graining the State Space of a Turbulent Flow Using Periodic Orbits.” <i>Physical Review Letters</i>, vol. 126, no. 24, 244502, American Physical Society, 2021, doi:<a href=\"https://doi.org/10.1103/PhysRevLett.126.244502\">10.1103/PhysRevLett.126.244502</a>.","short":"G. Yalniz, B. Hof, N.B. Budanur, Physical Review Letters 126 (2021).","chicago":"Yalniz, Gökhan, Björn Hof, and Nazmi B Budanur. “Coarse Graining the State Space of a Turbulent Flow Using Periodic Orbits.” <i>Physical Review Letters</i>. American Physical Society, 2021. <a href=\"https://doi.org/10.1103/PhysRevLett.126.244502\">https://doi.org/10.1103/PhysRevLett.126.244502</a>.","ama":"Yalniz G, Hof B, Budanur NB. Coarse graining the state space of a turbulent flow using periodic orbits. <i>Physical Review Letters</i>. 2021;126(24). doi:<a href=\"https://doi.org/10.1103/PhysRevLett.126.244502\">10.1103/PhysRevLett.126.244502</a>","ista":"Yalniz G, Hof B, Budanur NB. 2021. Coarse graining the state space of a turbulent flow using periodic orbits. Physical Review Letters. 126(24), 244502.","apa":"Yalniz, G., Hof, B., &#38; Budanur, N. B. (2021). Coarse graining the state space of a turbulent flow using periodic orbits. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevLett.126.244502\">https://doi.org/10.1103/PhysRevLett.126.244502</a>"},"acknowledged_ssus":[{"_id":"ScienComp"}],"arxiv":1,"external_id":{"arxiv":["2007.02584"],"isi":["000663310100008"]},"article_processing_charge":"No","project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics","grant_number":"662960","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"}],"abstract":[{"lang":"eng","text":"We show that turbulent dynamics that arise in simulations of the three-dimensional Navier--Stokes equations in a triply-periodic domain under sinusoidal forcing can be described as transient visits to the neighborhoods of unstable time-periodic solutions. Based on this description, we reduce the original system with more than 10^5 degrees of freedom to a 17-node Markov chain where each node corresponds to the neighborhood of a periodic orbit. The model accurately reproduces long-term averages of the system's observables as weighted sums over the periodic orbits.\r\n"}],"publication":"Physical Review Letters","volume":126,"title":"Coarse graining the state space of a turbulent flow using periodic orbits","article_number":"244502","year":"2021","day":"18","status":"public","publication_status":"published","date_updated":"2026-04-07T11:47:05Z","article_type":"letter_note","publisher":"American Physical Society","intvolume":"       126","isi":1,"corr_author":"1","date_published":"2021-06-18T00:00:00Z","author":[{"full_name":"Yalniz, Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","orcid":"0000-0002-8490-9312","first_name":"Gökhan","last_name":"Yalniz"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754","last_name":"Hof","first_name":"Björn"},{"first_name":"Nazmi B","last_name":"Budanur","full_name":"Budanur, Nazmi B","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0423-5010"}]},{"oa":1,"oa_version":"Published Version","department":[{"_id":"BjHo"}],"language":[{"iso":"eng"}],"quality_controlled":"1","issue":"3","type":"journal_article","month":"03","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Yalniz G, Budanur NB. 2020. Inferring symbolic dynamics of chaotic flows from persistence. Chaos. 30(3), 033109.","apa":"Yalniz, G., &#38; Budanur, N. B. (2020). Inferring symbolic dynamics of chaotic flows from persistence. <i>Chaos</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.5122969\">https://doi.org/10.1063/1.5122969</a>","ieee":"G. Yalniz and N. B. Budanur, “Inferring symbolic dynamics of chaotic flows from persistence,” <i>Chaos</i>, vol. 30, no. 3. AIP Publishing, 2020.","mla":"Yalniz, Gökhan, and Nazmi B. Budanur. “Inferring Symbolic Dynamics of Chaotic Flows from Persistence.” <i>Chaos</i>, vol. 30, no. 3, 033109, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/1.5122969\">10.1063/1.5122969</a>.","short":"G. Yalniz, N.B. Budanur, Chaos 30 (2020).","chicago":"Yalniz, Gökhan, and Nazmi B Budanur. “Inferring Symbolic Dynamics of Chaotic Flows from Persistence.” <i>Chaos</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/1.5122969\">https://doi.org/10.1063/1.5122969</a>.","ama":"Yalniz G, Budanur NB. Inferring symbolic dynamics of chaotic flows from persistence. <i>Chaos</i>. 2020;30(3). doi:<a href=\"https://doi.org/10.1063/1.5122969\">10.1063/1.5122969</a>"},"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1063/1.5122969"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19684"}]},"_id":"7563","publication_identifier":{"issn":["1054-1500"],"eissn":["1089-7682"]},"date_created":"2020-03-04T08:06:25Z","doi":"10.1063/1.5122969","external_id":{"isi":["000519254800002"],"arxiv":["1910.04584"]},"article_processing_charge":"No","arxiv":1,"article_number":"033109","title":"Inferring symbolic dynamics of chaotic flows from persistence","volume":30,"abstract":[{"lang":"eng","text":"We introduce “state space persistence analysis” for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent homology for the characterization of state space projections of chaotic trajectories and periodic orbits. By comparing the shapes along a chaotic trajectory to those of the periodic orbits, state space persistence analysis quantifies the shape similarity of chaotic trajectory segments and periodic orbits. We demonstrate the method by applying it to the three-dimensional Rössler system and a 30-dimensional discretization of the Kuramoto–Sivashinsky partial differential equation in (1+1) dimensions.\r\nOne way of studying chaotic attractors systematically is through their symbolic dynamics, in which one partitions the state space into qualitatively different regions and assigns a symbol to each such region.1–3 This yields a “coarse-grained” state space of the system, which can then be reduced to a Markov chain encoding all possible transitions between the states of the system. While it is possible to obtain the symbolic dynamics of low-dimensional chaotic systems with standard tools such as Poincaré maps, when applied to high-dimensional systems such as turbulent flows, these tools alone are not sufficient to determine symbolic dynamics.4,5 In this paper, we develop “state space persistence analysis” and demonstrate that it can be utilized to infer the symbolic dynamics in very high-dimensional settings."}],"publication":"Chaos","year":"2020","day":"03","date_updated":"2026-06-18T19:23:35Z","publisher":"AIP Publishing","article_type":"original","publication_status":"published","status":"public","intvolume":"        30","isi":1,"author":[{"last_name":"Yalniz","first_name":"Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312"},{"orcid":"0000-0003-0423-5010","full_name":"Budanur, Nazmi B","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","first_name":"Nazmi B","last_name":"Budanur"}],"corr_author":"1","ddc":["530"],"date_published":"2020-03-03T00:00:00Z"}]