{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T16:56:49Z","timestamp":1761929809308},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2016,6,16]],"date-time":"2016-06-16T00:00:00Z","timestamp":1466035200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Eur. J. Appl. Math"],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p>In the paper, <jats:italic>Bifurcation analysis of the twist-Fr\u00e9edericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions<\/jats:italic> (2009 <jats:italic>Eur. J. Appl. Math.<\/jats:italic><jats:bold>20<\/jats:bold>, 269\u2013287) by da Costa <jats:italic>et al.<\/jats:italic> the twist-Fr\u00e9edericksz transition in a nematic liquid-crystal one-dimensional cell of lenght <jats:italic>L<\/jats:italic> was studied, imposing an antisymmetric net twist Dirichlet condition at the cell boundaries. In the present paper, we extend that study to the more general case of net twist Dirichlet conditions without any kind of symmetry restrictions. We use phase-plane analysis tools and appropriately defined time maps to obtain the bifurcation diagrams of the model when <jats:italic>L<\/jats:italic> is the bifurcation parameter, and related these diagrams with the one in the antisymmetric situation. The stability of the bifurcating solutions is investigated by applying the method of Maginu (1978 <jats:italic>J. Math. Anal. Appl.<\/jats:italic><jats:bold>63<\/jats:bold>, 224\u2013243).<\/jats:p>","DOI":"10.1017\/s0956792516000243","type":"journal-article","created":{"date-parts":[[2016,6,22]],"date-time":"2016-06-22T16:48:51Z","timestamp":1466614131000},"page":"243-260","source":"Crossref","is-referenced-by-count":4,"title":["Bifurcations analysis of the twist-Fr\u00e9edericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions: the asymmetric case"],"prefix":"10.1017","volume":"28","author":[{"given":"FERNANDO P.","family":"DA COSTA","sequence":"first","affiliation":[]},{"given":"MARIA ISABEL","family":"M\u00c9NDEZ","sequence":"additional","affiliation":[]},{"given":"JO\u00c3O T.","family":"PINTO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,6,16]]},"reference":[{"key":"S0956792516000243_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792509007827"},{"key":"S0956792516000243_ref8","volume-title":"Fundamentals of Liquid Crystal Devices","author":"Yang","year":"2015"},{"key":"S0956792516000243_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.01.033"},{"key":"S0956792516000243_ref3","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.0031"},{"key":"S0956792516000243_ref7","volume-title":"The Static and Dynamic Continuum Theory of Liquid Crystals","author":"Stewart","year":"2004"},{"key":"S0956792516000243_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(78)90116-6"},{"key":"S0956792516000243_ref5","volume-title":"Asymptotic Behavior of Dissipative Systems","author":"Hale","year":"1988"},{"key":"S0956792516000243_ref4","first-page":"85","article-title":"On the use of a magnetic field in the measurement of the forces tending to orient an anisotropic liquid in a thin homogeneous layer.","volume":"55","author":"Freedericksz","year":"1929","journal-title":"Trans. Am. Electrochem. Soc."}],"container-title":["European Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0956792516000243","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T20:30:23Z","timestamp":1555533023000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0956792516000243\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,16]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,4]]}},"alternative-id":["S0956792516000243"],"URL":"https:\/\/doi.org\/10.1017\/s0956792516000243","relation":{},"ISSN":["0956-7925","1469-4425"],"issn-type":[{"value":"0956-7925","type":"print"},{"value":"1469-4425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,16]]}}}