One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability - Dalby, J; Farrell, PE; Majumdar, A; Xia, J (Society for Industrial and Applied Mathematics, 2022)
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.