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

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.