Based on dynamic theory of liquid crystal and finite-difference iterative method, dynamic response of strong anchoring hybrid aligned nematic (HAN) liquid crystal cell as removing applied voltage was studied. Flexoelectricity of liquid crystal material was considered. Time-dependences of transmittance through a HAN cell were obtained. It indicates that response time decreases with increasing of absolute value of the sum of splay and bend flexoelectric coefficient |e₁₁+e₃₃|. Especially, at |e₁₁+e₃₃|=50 pC·m^-1 response time is half shortened relative to the case with no flexoelectric effect.

Nematic droplets are studied with Monte Carlo simulations with a modified Gruhn-Hess pair potential. The potential is spatially anisotropic and potential parameters are related to elastic constants K₁₁ ,K₂₂ ,K₃₃ and surface-like elastic constant K₁₃. It is assumed that nematic droplet surface is a free surface. Second order parameters and introrse intensity, which describes quantitatively intrinsic anchoring induced by surface at low temperatures, are calculated with a modified Gruhn-Hess pair potential and are compared with those in Gruhn-Hess model I. It is shown that the modified model with K₁₃ induces intrinsic anchoring near droplet surface, orientation and intrinsic anchoring strength depend strongly on K₁₃, and introrse intensity is related to K₃₃/K₁₁. Order degree of nematic droplet is lower from inner shell to outer shell due to incomplete anisotropic nematic-nematic interactions.

Nematic liquid crystal cell with bend distortions is studied in a modified Gruhn-Hess spatially anisotropic pair potential model.Under one-constant approximation,we get continuous form of free energy density formula in a perfect order considering second rank distortions,which is consistent with elastic theory.Strong anchoring nematic liquid crystal cell with bend distortions in the model doesn't show surface discontinuities as in the elastic theory.With Monte Carlo simulation,we find that the k₁₃ term in pair potential increases the fluctuation in the middle cell.

Flexoelectric effect on electro-optical characteristics of a nematic liquid crystal cell is investigated.Differential equations and boundary conditions for director of liquid crystal are obtained with variation theory.Distributions of director of nematic liquid crystal (NLC) cells with strong anchoring and weak anchoring are calculated by a finite-difference iterative method.With Jones matrix method,transmittance-voltage characteristics of liquid crystal cells are obtained.Surface flexoelectric effect and bulk flexoelectric effect are considered.

Nematic droplets are studied with Monte Carlo simulation in a spatially anisotropic molecular pair potential model. The potential is based on a lattice model and dependent on elastic constants of liquid crystals. We assume that nematic droplet surface is a free surface and introduce tangent-introrse intensity to quantitatively describe intrinsic anchoring induced by surface. The tangent-introrse intensity and the second order parameters in different regions of droplets at low temperature are calculated by two schemes with spatially anisotropic potential and are compared with those in Lebwohl-Lasher model. Only one scheme can give intrinsic easy axis near droplets surface and introrse intensity is related to K₃₃/K₁₁. The degree of nematic order in the vicinity of droplet surface becomes lower from inner shell to outer shell due to incomplete anisotropic nematic-nematic interactions.

The cell theory is used to study nematic liquid crystals formed by biaxial molecules. A new numerical method is developed to calculate the nematic order in liquid crystals. Without any functional expansions, accurate orientational distribution functions are obtained by using a newly iterative method to solve the equation of equilibrium state. The temperature dependences of the order parameter and of the internal energy per molecule are calculated, and the values of the relevant physical quantities at the nematic isotropic phase transition are given. Numerical results are in better agreement with the Monte Carlo simulation results than those of the molecular field theory.

The calculations of nematic order in liquid crystals with an external magnetic field are made based on the cell theory.By taking account of the molecular short range correlations,the dependences of order parameter and internal energy on magnetic strengty are in close agreement with those of the simulation.

Some important physical effects appear due to short range order in nematic liquid crystals. On the basis of the cell theory, new numerical method is presented, which are used to calculate these effects.We do not use ann functional expansions but we obtain accurate orientational distribution functions by solving the equation of equilibrium state, using an iterative method. Then various physical quantities can be calculated. The accurate numerical results of order parameter at phase transition and entropy change etc. are given.