{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:05:38Z","timestamp":1764173138582},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2002,2]]},"abstract":"<jats:p> Nonlinear two-dimensional Rayleigh\u2013B\u00e9nard convection with periodic boundary conditions in the horizontal is studied for spatial periods near the 1:2 steady state mode interaction. The boundary conditions at the bottom are no-slip, and convection is driven by a fixed imposed temperature difference across the layer. Homotopic continuation is used to continue the boundary conditions at the top from no-slip (\u03b2=0) to stress-free (\u03b2=1). When \u03b2=0 and non-Boussinesq effects are absent the system has midplane reflection symmetry and the 1:2 resonance is weak. When \u03b2=1 this symmetry is strongly broken and the resonance is strong. The transition between these two cases is explored for two Prandtl numbers, \u03c3=10 and \u03c3=0.1, representing behavior typical of large and low Prandtl numbers, respectively. <\/jats:p>","DOI":"10.1142\/s0218127402004401","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T10:58:59Z","timestamp":1027767539000},"page":"281-308","source":"Crossref","is-referenced-by-count":13,"title":["THE 1:2 MODE INTERACTION IN RAYLEIGH\u2013B\u00c9NARD CONVECTION  WITH AND WITHOUT BOUSSINESQ SYMMETRY"],"prefix":"10.1142","volume":"12","author":[{"given":"JOANA","family":"PRAT","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tica Aplicada IV, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ISABEL","family":"MERCADER","sequence":"additional","affiliation":[{"name":"Departament de F\u00edsica Aplicada,  Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EDGAR","family":"KNOBLOCH","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Leeds,  Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(87)90042-X"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(88)90032-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90093-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1063\/1.1329905"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112067001661"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00945433"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.53.R2037"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(96)00041-3"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/1\/4\/007"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fl.23.010191.002013"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4574-2"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(84)90179-9"},{"key":"rf13","volume-title":"Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields","author":"Guckenheimer J.","year":"1990"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(87)90008-9"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/056\/855091"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1988.0003"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.42.4693"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1063\/1.868921"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1063\/1.868121"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1017\/S002211209200020X"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127401002006"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112091000605"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(01)00340-2"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1063\/1.868732"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.58.3145"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112088000746"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100056759"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500019223"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-5793-3_36"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127402004401","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:12:37Z","timestamp":1565136757000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127402004401"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,2]]},"references-count":29,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2002,2]]}},"alternative-id":["10.1142\/S0218127402004401"],"URL":"https:\/\/doi.org\/10.1142\/s0218127402004401","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,2]]}}}