One-dimensional ferronematics in a channel: order reconstruction, bifurcations, and multistability

James Dalby, Patrick E. Farrell, Apala Majumdar, Jingmin Xia

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We study a model system with nematic and magnetic order, within a channel geometry modeled by an interval, [−D, D]. The system is characterized by a tensor-valued nematic order parameter Q and a vector-valued magnetization M, and the observable states are modeled as stable critical points of an appropriately defined free energy which includes a nemato-magnetic coupling term, characterized by a parameter c. We (i) derive L bounds for Q and M; (ii) prove a uniqueness result in specified parameter regimes; (iii) analyze order reconstruction solutions, possessing domain walls, and their stabilities as a function of D and c and; (iv) perform numerical studies that elucidate the interplay of c and D for multistability.

Original languageEnglish
Pages (from-to)694-719
Number of pages26
JournalSIAM Journal of Applied Mathematics
Issue number2
Publication statusPublished - 4 May 2022


  • ferronematics
  • bifurcation analysis
  • stability
  • liquid crystals


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