Ferronematics in Confinement -Modelling, Analysis and Simulations for New Applications

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Nematic liquid crystals (NLCs) are partially ordered materials that are intermediate between conventional solids and isotropic liquids. NLCs exhibit preferred directions of averaged molecular alignment and typically have a strong direction-dependent response to external electric fields. However, NLCs have relatively weak responses to external magnetic fields. Ferronematics describe suspensions of magnetic particles in a nematic host and have substantially enhanced responses to external magnetic fields. Experimental research in ferronematics is booming but rigorous mathematical underpinnings are slim. In this project, we will study continuum phenomenological free energies for ferronematics, with attention to nature of the coupling between the NLC host and the suspended magnetic particles. The experimentally observable equilibria correspond to energy minimizers, which are solutions of a nonlinear coupled system of partial differential equations. We will study the qualitative properties of the energy minimizers in different asymptotic regimes. This will be supplemented by detailed numerical studies of the solution landscapes. This project aims to provide sound theoretical foundations for the emerging field of ferronematics and composite materials, that can guide further investigations of novel tunable materials, and is squarely within the University's strategic themes of "Measurement Science and Enabling Technologies" and "Advanced Manufacturing and Materials".