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

向列型液晶（NLC）是介于常规固体和各向同性液体之间的部分有序材料。NLC表现出平均分子排列的优选方向，并且通常对外部电场具有强烈的方向依赖性响应。然而，NLC对外部磁场的响应相对较弱。亚铁磁悬浮液描述了磁性颗粒在磁性主体中的悬浮液，并且对外部磁场具有显著增强的响应。铁电学的实验研究正在蓬勃发展，但严格的数学基础却很薄弱。在这个项目中，我们将研究连续唯象自由能的铁离子，与注意之间的NLC主机和悬浮的磁性粒子的耦合的性质。实验观察到的平衡对应于能量最小化，这是一个非线性耦合系统的偏微分方程的解决方案。我们将研究在不同的渐近制度的能量极小的定性性质。这将是补充的解决方案景观的详细数值研究。该项目旨在为铁磁体和复合材料的新兴领域提供良好的理论基础，可以指导对新型可调材料的进一步研究，并完全符合大学的“测量科学和使能技术”和“先进制造和材料”的战略主题。

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".