{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,10]],"date-time":"2024-03-10T16:40:03Z","timestamp":1710088803494},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,6,1]],"date-time":"2009-06-01T00:00:00Z","timestamp":1243814400000},"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":[[2009,6]]},"abstract":"<jats:p>Motivated by a recent investigation of Millar and McKay [Director orientation of a twisted nematic under the influence of an in-plane magnetic field.<jats:italic>Mol<\/jats:italic>. Cryst. Liq.<jats:italic>Cryst<\/jats:italic><jats:bold>435<\/jats:bold>, 277\/[937]\u2013286\/[946] (2005)], we study the magnetic field twist-Fr\u00e9edericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre-twist boundary conditions. Despite the pre-twist, the system still possesses \u2124<jats:sub>2<\/jats:sub>symmetry and a symmetry-breaking pitchfork bifurcation, which occurs at a critical magnetic-field strength that, as we prove, is above the threshold for the classical twist-Fr\u00e9edericksz transition (which has no pre-twist). It was observed numerically by Millar and McKay that this instability occurs precisely at the point at which the ground-state solution loses its monotonicity (with respect to the position coordinate across the cell gap). We explain this surprising observation using a rigorous phase-space analysis.<\/jats:p>","DOI":"10.1017\/s0956792509007827","type":"journal-article","created":{"date-parts":[[2009,2,16]],"date-time":"2009-02-16T14:53:59Z","timestamp":1234796039000},"page":"269-287","source":"Crossref","is-referenced-by-count":3,"title":["Bifurcation analysis of the twist-Fr\u00e9edericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions"],"prefix":"10.1017","volume":"20","author":[{"given":"FERNANDO P.","family":"DA COSTA","sequence":"first","affiliation":[]},{"suffix":"JR.","given":"EUGENE C.","family":"GARTLAND","sequence":"additional","affiliation":[]},{"given":"MICHAEL","family":"GRINFELD","sequence":"additional","affiliation":[]},{"given":"JO\u00c3O T.","family":"PINTO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,6,1]]},"reference":[{"key":"S0956792509007827_ref7","first-page":"199","article-title":"Linear operators leaving invariant a cone in banach space (Engl. Transl.)","volume":"10","author":"Krein","year":"1962","journal-title":"Am. Math. Soc. Transl., Ser. 1"},{"key":"S0956792509007827_ref8","volume-title":"Mathematical Modelling of Nematic and Smectic Liquid Crystals","author":"Millar","year":"2007"},{"key":"S0956792509007827_ref4","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.0031"},{"key":"S0956792509007827_ref9","doi-asserted-by":"publisher","DOI":"10.1080\/15421400590955253"},{"key":"S0956792509007827_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511622496"},{"key":"S0956792509007827_ref13","volume-title":"Applied Mathematics and Mathe-matical Computation, Vol. 8","author":"Virga","year":"1994"},{"key":"S0956792509007827_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(81)90077-2"},{"key":"S0956792509007827_ref3","unstructured":"[3] da Costa F. P. , Grinfeld M. , Mottram N. J. & Pinto J. T. (2007) Uniqueness in the Freedericksz transition with weak anchoring (to appear in J. Differ. Equ.)."},{"key":"S0956792509007827_ref5","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198520245.001.0001","volume-title":"The Physics of Liquid Crystals","author":"de Gennes","year":"1993"},{"key":"S0956792509007827_ref6","volume-title":"Topological Methods in the Theory of Nonlinear Integral Equations","author":"Krasnoselskii","year":"1964"},{"key":"S0956792509007827_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0098346"},{"key":"S0956792509007827_ref1","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz","year":"1972"},{"key":"S0956792509007827_ref12","volume-title":"The Liquid Crystals Book Series, Vol. 2","author":"Stewart","year":"2004"}],"container-title":["European Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0956792509007827","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,10]],"date-time":"2024-03-10T16:21:55Z","timestamp":1710087715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0956792509007827\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,6]]}},"alternative-id":["S0956792509007827"],"URL":"https:\/\/doi.org\/10.1017\/s0956792509007827","relation":{},"ISSN":["0956-7925","1469-4425"],"issn-type":[{"value":"0956-7925","type":"print"},{"value":"1469-4425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}