用微极液晶模型研究液晶的Fredericksz磁场效应

用微极液晶模型和Leslie-Eriksen模型讨论向列型液晶的壁面与磁场综合效应，采用垂直和倾斜二类边界条件，主要结果是：⑴指出有半文献中临界磁场强度公式不妥之处，给出修改效果；⑵导出界面指向矢垂直与倾斜锚定条件下，指向矢角度分布的隐式解析解，并通过数值计算给出界面与磁场综合效应；⑶所得结果与Leslie-Ericksen模型相应结果基本箱符，于是，通过二者之比较可给出两类液晶模型材料系数的联系；⑷讨论有关的数学问题，包括用夹逼方法严格论证临界磁场强度公式，对主方程解的多值性与分叉作剖析等。

Microploar Liquid Crystal Model and Fredericksz Magnetic Effects

The present article discusses the synthetic effect of the walls and magnetic field to the nematic liquid crystals by means of the microploar liquid crystal model and the Leslie-Ericksen model,applying perpendicular and slantwise boundary conditions.The main results are:(1)Pointing out the error of the formula of the critical magnetic intensity in the concerned article.(2)Obtaining the implied analytical solution of the director distribution where the perpendicular and slantwise boundary conditions at the walls are used respectively,and presenting the synthetic effect of the walls and magnetic field by numerical calculation.(3)Since the results of this article are consistent with those of the Leslie-Ericksen model,therefore it is possible to find the relations between the coefficients of the two types of liquid cystals models by comparison.(4)Discussing some concerned mathematical problems,including the strict demonstrating of the formula of the critical magnetic intensity by sandwich (or pinching ) method,the analyses of the multi-value properties and bifurcation of the solution of the main equation.