论文标题
液晶中的近视相位相变：有效几何运动的变异推导
Nematic-Isotropic phase transition in Liquid crystals: a variational derivation of effective geometric motions
论文作者
论文摘要
在这项工作中，我们基于液晶液晶理论的动力学研究了列中异位相变。在临界温度下，Landau--de Gennes的大量电势偏向于各向同性相和列相位。当弹性系数远小于大量电势时，可以通过形式的渐近扩展来得出缩放限制：溶液梯度集中在通过平均曲率流动的封闭表面上。此外，在表面的一侧，溶液趋向于列前相，该相位由谐波地图热流进入球体时，而在另一侧，它趋向于各向同性相。为了严格证明这种缩放限制的合理性，我们通过结合弱收敛方法和调制能量方法来证明收敛的结果。只要有限的平均曲率流保持光滑，我们的证明就适用。
In this work, we study the nematic-isotropic phase transition based on the dynamics of the Landau--De Gennes theory of liquid crystals. At the critical temperature, the Landau--De Gennes bulk potential favors the isotropic phase and nematic phase equally. When the elastic coefficient is much smaller than that of the bulk potential, a scaling limit can be derived by formal asymptotic expansions: the solution gradient concentrates on a closed surface evolving by mean curvature flow. Moreover, on one side of the surface the solution tends to the nematic phase which is governed by the harmonic map heat flow into the sphere while on the other side, it tends to the isotropic phase. To rigorously justify such a scaling limit, we prove a convergence result by combining weak convergence methods and the modulated energy method. Our proof applies as long as the limiting mean curvature flow remains smooth.
