[{"article_number":"A21","arxiv":1,"has_accepted_license":"1","date_updated":"2024-02-15T09:06:23Z","ddc":["530"],"publication_identifier":{"issn":["0022-1120"],"eissn":["1469-7645"]},"oa":1,"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","oa_version":"Published Version","type":"journal_article","status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"title":"Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows","isi":1,"citation":{"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.","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.","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>.","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>","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>","short":"E. Marensi, G. Yalniz, B. Hof, Journal of Fluid Mechanics 974 (2023).","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>."},"article_processing_charge":"Yes (via OA deal)","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"acknowledgement":"E.M. acknowledges funding from the ISTplus fellowship programme. G.Y. and B.H. acknowledge a grant from the Simons Foundation (662960, BH).","quality_controlled":"1","_id":"14466","intvolume":"       974","doi":"10.1017/jfm.2023.780","external_id":{"isi":["001088363700001"],"arxiv":["2212.12406"]},"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,"date_published":"2023-11-10T00:00:00Z","author":[{"id":"0BE7553A-1004-11EA-B805-18983DDC885E","full_name":"Marensi, Elena","orcid":"0000-0001-7173-4923","last_name":"Marensi","first_name":"Elena"},{"full_name":"Yalniz, Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","orcid":"0000-0002-8490-9312","last_name":"Yalniz","first_name":"Gökhan"},{"orcid":"0000-0003-2057-2754","last_name":"Hof","first_name":"Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87","full_name":"Hof, Björn"}],"file_date_updated":"2024-02-15T09:05:21Z","keyword":["turbulence","transition to turbulence","patterns"],"day":"10","year":"2023","language":[{"iso":"eng"}],"publication":"Journal of Fluid Mechanics","publisher":"Cambridge University Press","file":[{"success":1,"access_level":"open_access","file_size":2804641,"file_name":"2023_JourFluidMechanics_Marensi.pdf","content_type":"application/pdf","date_updated":"2024-02-15T09:05:21Z","checksum":"17c64c1fb0d5f73252364bf98b0b9e1a","relation":"main_file","creator":"dernst","date_created":"2024-02-15T09:05:21Z","file_id":"14996"}],"date_created":"2023-10-30T09:32:28Z","article_type":"original","project":[{"_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","grant_number":"662960"}]},{"oa":1,"publication_status":"published","date_updated":"2023-12-13T11:40:19Z","publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"month":"07","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"034002","arxiv":1,"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.).","quality_controlled":"1","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"doi":"10.1103/physrevlett.131.034002","external_id":{"isi":["001052929900004"],"arxiv":["2306.05098"]},"_id":"13274","intvolume":"       131","title":"Direct path from turbulence to time-periodic solutions","type":"journal_article","status":"public","article_processing_charge":"No","citation":{"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.","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.","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>.","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>","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).","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>"},"isi":1,"keyword":["General Physics and Astronomy"],"publication":"Physical Review Letters","day":"21","language":[{"iso":"eng"}],"year":"2023","author":[{"full_name":"Paranjape, Chaitanya S","id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87","last_name":"Paranjape","first_name":"Chaitanya S"},{"last_name":"Yalniz","first_name":"Gökhan","orcid":"0000-0002-8490-9312","full_name":"Yalniz, Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425"},{"full_name":"Duguet, Yohann","first_name":"Yohann","last_name":"Duguet"},{"first_name":"Nazmi B","last_name":"Budanur","orcid":"0000-0003-0423-5010","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","full_name":"Budanur, Nazmi B"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","full_name":"Hof, Björn","last_name":"Hof","first_name":"Björn","orcid":"0000-0003-2057-2754"}],"volume":131,"abstract":[{"lang":"eng","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."}],"date_published":"2023-07-21T00:00:00Z","issue":"3","project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","grant_number":"662960"}],"date_created":"2023-07-24T09:43:59Z","article_type":"original","publisher":"American Physical Society","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.05098","open_access":"1"}]},{"article_type":"original","project":[{"grant_number":"662960","name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"}],"date_created":"2023-01-08T23:00:53Z","file":[{"content_type":"application/pdf","date_updated":"2023-02-02T12:34:54Z","access_level":"open_access","file_size":1931647,"file_name":"2023_JourFluidMechanics_Marensi.pdf","file_id":"12489","checksum":"9224f987caefe5dd85a70814d3cce65c","relation":"main_file","creator":"dernst","date_created":"2023-02-02T12:34:54Z","success":1}],"publisher":"Cambridge University Press","scopus_import":"1","year":"2023","language":[{"iso":"eng"}],"day":"10","publication":"Journal of Fluid Mechanics","file_date_updated":"2023-02-02T12:34:54Z","date_published":"2023-01-10T00:00:00Z","abstract":[{"lang":"eng","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."}],"volume":954,"author":[{"first_name":"Elena","last_name":"Marensi","full_name":"Marensi, Elena","id":"0BE7553A-1004-11EA-B805-18983DDC885E"},{"full_name":"Yalniz, Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","last_name":"Yalniz","first_name":"Gökhan","orcid":"0000-0002-8490-9312"},{"last_name":"Hof","first_name":"Björn","orcid":"0000-0003-2057-2754","full_name":"Hof, Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-0423-5010","first_name":"Nazmi B","last_name":"Budanur","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","full_name":"Budanur, Nazmi B"}],"intvolume":"       954","_id":"12105","external_id":{"arxiv":["2101.07516"],"isi":["000903336600001"]},"doi":"10.1017/jfm.2022.1001","department":[{"_id":"BjHo"}],"quality_controlled":"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).","isi":1,"article_processing_charge":"Yes (via OA deal)","citation":{"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.","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.","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>.","short":"E. Marensi, G. Yalniz, B. Hof, N.B. Budanur, Journal of Fluid Mechanics 954 (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>.","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>"},"status":"public","type":"journal_article","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"title":"Symmetry-reduced dynamic mode decomposition of near-wall turbulence","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","month":"01","publication_identifier":{"eissn":["1469-7645"],"issn":["0022-1120"]},"ddc":["530"],"date_updated":"2023-08-01T12:53:23Z","publication_status":"published","oa":1,"arxiv":1,"has_accepted_license":"1","article_number":"A10"},{"project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","grant_number":"662960"}],"article_type":"letter_note","date_created":"2021-06-16T15:45:36Z","publisher":"American Physical Society","main_file_link":[{"url":"https://arxiv.org/abs/2007.02584","open_access":"1"}],"day":"18","year":"2021","language":[{"iso":"eng"}],"publication":"Physical Review Letters","issue":"24","abstract":[{"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","lang":"eng"}],"volume":126,"date_published":"2021-06-18T00:00:00Z","author":[{"full_name":"Yalniz, Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","first_name":"Gökhan","last_name":"Yalniz","orcid":"0000-0002-8490-9312"},{"full_name":"Hof, Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn","last_name":"Hof","orcid":"0000-0003-2057-2754"},{"last_name":"Budanur","first_name":"Nazmi B","orcid":"0000-0003-0423-5010","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","full_name":"Budanur, Nazmi B"}],"_id":"9558","intvolume":"       126","doi":"10.1103/PhysRevLett.126.244502","external_id":{"arxiv":["2007.02584"],"isi":["000663310100008"]},"department":[{"_id":"GradSch"},{"_id":"BjHo"}],"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.","quality_controlled":"1","isi":1,"acknowledged_ssus":[{"_id":"ScienComp"}],"citation":{"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.","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.","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>.","short":"G. Yalniz, B. Hof, N.B. Budanur, Physical Review Letters 126 (2021).","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>","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>","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>."},"article_processing_charge":"No","status":"public","type":"journal_article","title":"Coarse graining the state space of a turbulent flow using periodic orbits","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","related_material":{"link":[{"url":"https://ist.ac.at/en/news/turbulent-flow-simplified/","description":"News on IST Homepage","relation":"press_release"}]},"oa_version":"Preprint","month":"06","date_updated":"2023-08-08T14:08:36Z","publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"oa":1,"publication_status":"published","arxiv":1,"article_number":"244502"},{"publication_identifier":{"eissn":["1089-7682"],"issn":["1054-1500"]},"date_updated":"2023-08-18T06:47:16Z","publication_status":"published","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","month":"03","article_number":"033109","arxiv":1,"department":[{"_id":"BjHo"}],"quality_controlled":"1","intvolume":"        30","_id":"7563","external_id":{"isi":["000519254800002"],"arxiv":["1910.04584"]},"doi":"10.1063/1.5122969","status":"public","type":"journal_article","title":"Inferring symbolic dynamics of chaotic flows from persistence","isi":1,"citation":{"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>","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>.","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>","short":"G. Yalniz, N.B. Budanur, Chaos 30 (2020).","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.","ista":"Yalniz G, Budanur NB. 2020. Inferring symbolic dynamics of chaotic flows from persistence. Chaos. 30(3), 033109."},"article_processing_charge":"No","language":[{"iso":"eng"}],"year":"2020","day":"03","publication":"Chaos","date_published":"2020-03-03T00:00:00Z","volume":30,"abstract":[{"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.","lang":"eng"}],"author":[{"id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","full_name":"Yalniz, Gökhan","last_name":"Yalniz","first_name":"Gökhan","orcid":"0000-0002-8490-9312"},{"id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","full_name":"Budanur, Nazmi B","orcid":"0000-0003-0423-5010","last_name":"Budanur","first_name":"Nazmi B"}],"issue":"3","date_created":"2020-03-04T08:06:25Z","article_type":"original","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1063/1.5122969"}],"publisher":"AIP Publishing"}]