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

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

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Abstract

We study a model system with nematic and magnetic orders, within a channel geometry modelled by an interval, [−D, D]. The system is characterised by a tensor-valued nematic order parameter Q and a vector-valued magnetisation M, and the observable states are modelled as stable critical points of an appropriately defined free energy. In particular, the full energy includes a nemato-magnetic coupling term characterised by a parameter c. We (i) derive L∞ bounds for Q and M; (ii) prove a uniqueness result in parameter regimes defined by c, D and material- and temperature-dependent correlation lengths; (iii) analyse 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
Number of pages33
JournalSIAM Journal of Applied Mathematics
Publication statusAccepted/In press - 4 Nov 2021

Keywords

  • ferronematics
  • bifurcation analysis
  • stability
  • liquid crystals

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