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.
|Number of pages||33|
|Journal||SIAM Journal of Applied Mathematics|
|Publication status||Accepted/In press - 4 Nov 2021|
- bifurcation analysis
- liquid crystals