{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:53:48Z","timestamp":1785412428371,"version":"3.56.0"},"reference-count":60,"publisher":"National Academy of Sciences","issue":"28","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMR-2225543"],"award-info":[{"award-number":["DMR-2225543"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0025803"],"award-info":[{"award-number":["DE-SC0025803"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["MRI-2019144"],"award-info":[{"award-number":["MRI-2019144"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,7,14]]},"abstract":"<jats:p>\n                    Active nematics in two dimensions stir themselves efficiently through internally generated chaotic flows, largely driven by motile\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mo>+<\/mml:mo>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:mo stretchy=\"false\">\/<\/mml:mo>\n                          <mml:mn>2<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    disclinations.We investigate how this tendency toward chaotic fluid stirring can, counterintuitively, produce certain ordered, periodic flows in confinement, characterized by stable periodic orbits of\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mo>+<\/mml:mo>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:mo stretchy=\"false\">\/<\/mml:mo>\n                          <mml:mn>2<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    disclinations. We computationally study two-dimensional active nematics in systems with boundary conditions requiring a prescribed number\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    of excess\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mo>+<\/mml:mo>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:mo stretchy=\"false\">\/<\/mml:mo>\n                          <mml:mn>2<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    disclinations, using Beris-Edwards nematohydrodynamics simulations alongside an agent-based simulation approach. We find that when confinement is sufficiently strong to prevent defect pair-nucleation, but not strong enough to arrest all flow, then\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:mo>=<\/mml:mo>\n                          <mml:mn>3<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    defects generically follow a \u201cgolden braid\u201d orbit as observed recently in experiments, and we predict a \u201csilver braid\u201d orbit of\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:mo>=<\/mml:mo>\n                          <mml:mn>4<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    defects. For these results and for greater numbers of defects, we show that the periodic or chaotic nature of the dynamics is determined by a balance between the number of defects and the number of vortices in the flow field, suggesting a design criterion for ordered flows in active nematics.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2516670123","type":"journal-article","created":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T17:38:23Z","timestamp":1783532303000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Chaos-generating periodic orbits of topological defects in confined active nematics"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0211-3968","authenticated-orcid":false,"given":"Brandon","family":"Klein","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics and Astronomy, Johns Hopkins University","place":["Baltimore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alejandro J. Soto","family":"Franco","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics and Astronomy, Johns Hopkins University","place":["Baltimore"]},{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Biomedical Engineering, Johns Hopkins University","place":["Baltimore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8774-1028","authenticated-orcid":false,"given":"Md Mainul Hasan","family":"Sabbir","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00d9ah105","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, University of California","place":["Merced"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6915-2454","authenticated-orcid":false,"given":"Matthew J.","family":"Deutsch","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/049pfb863","id-type":"ROR","asserted-by":"publisher"}],"name":"Advanced Materials and Liquid Crystal Institute, Kent State University","place":["Kent"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-2176-7363","authenticated-orcid":false,"given":"Ross","family":"Kliegman","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics and Astronomy, Johns Hopkins University","place":["Baltimore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6519-9685","authenticated-orcid":false,"given":"Robin L. 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