{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:36:48Z","timestamp":1787225808205,"version":"build-2736575974"},"reference-count":52,"publisher":"National Academy of Sciences","issue":"21","license":[{"start":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T00:00:00Z","timestamp":1779408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,5,26]]},"abstract":"<jats:p>\n                    In suspensions of swimming bacteria, individual cells interact via long-range hydrodynamic forces and self-organize into collective states that drive large-scale chaotic flows, commonly referred to as \u201cbacterial turbulence.\u201d Despite extensive experimental and theoretical work, it remains unclear whether an intrinsic length scale underlies the observed patterns. To directly address this question and shed light on the mechanisms driving active turbulence, we investigate the emergence of large-scale flows in\n                    <jats:italic toggle=\"yes\">E. coli<\/jats:italic>\n                    suspensions confined within flat cylindrical chambers, systematically varying the confinement height over more than two orders of magnitude. We first demonstrate that the critical density for the onset of collective motion scales inversely with the confinement height without saturation. Near the onset, both the observed length and time scales increase sharply, with the length scale limited only by the vertical confinement. Importantly, both scales exhibit clear power-law dependence on the confinement height, demonstrating the absence of an intrinsic length scale in bacterial collective motion. Close to the instability onset, we observed transient coherent vortices, reaching up to 4,000 times the size of a single bacterium and spanning the full chamber width, further reinforcing the conclusion that bacterial turbulence is scale-free. Our experimental results, which characterize the onset of collective motion and demonstrate that bacterial turbulence is scale-free, discriminate between competing theoretical models and provide essential input for theories seeking to capture the dynamics and constitutive relations of wet active matter.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2600266123","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T17:39:57Z","timestamp":1779471597000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":1,"title":["Collective motion in bacterial suspensions is scale-free"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-9382-2877","authenticated-orcid":false,"given":"Benjam\u00edn","family":"P\u00e9rez-Estay","sequence":"first","affiliation":[{"name":"Physique et M\u00e9canique des Milieux H\u00e9t\u00e9rog\u00e8nes, \u00c9cole sup\u00e9rieure de physique et de chimie industrielles Paris, Universit\u00e9 Paris Sciences et Lettres, Universit\u00e9 Paris Cit\u00e9, Sorbonne Universit\u00e9, CNRS","place":["Paris, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2395-5929","authenticated-orcid":false,"given":"Vincent","family":"Martinez","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01nrxwf90","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Physics and Astronomy, The University of Edinburgh","place":["Edinburgh, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5216-8997","authenticated-orcid":false,"given":"Carine","family":"Douarche","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03xjwb503","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratoire Fluides, Automatique et Syst\u00e8mes Thermiques, CNRS, Universit\u00e9 Paris-Saclay","place":["Orsay, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jana","family":"Schwarz-Linek","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01nrxwf90","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Physics and Astronomy, The University of Edinburgh","place":["Edinburgh, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4152-5896","authenticated-orcid":false,"given":"Jochen","family":"Arlt","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01nrxwf90","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Physics and Astronomy, The University of Edinburgh","place":["Edinburgh, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre-Henri","family":"Delville","sequence":"additional","affiliation":[{"name":"Physique et M\u00e9canique des Milieux H\u00e9t\u00e9rog\u00e8nes, \u00c9cole sup\u00e9rieure de physique et de chimie industrielles Paris, Universit\u00e9 Paris Sciences et Lettres, Universit\u00e9 Paris Cit\u00e9, Sorbonne Universit\u00e9, CNRS","place":["Paris, France"]},{"id":[{"id":"https:\/\/ror.org\/03xjwb503","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratoire Fluides, Automatique et Syst\u00e8mes Thermiques, CNRS, Universit\u00e9 Paris-Saclay","place":["Orsay, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gail","family":"McConnell","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00n3w3b69","id-type":"ROR","asserted-by":"publisher"}],"name":"Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde","place":["Glasgow, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0760-7940","authenticated-orcid":false,"given":"Wilson C. 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