A positive nematic liquid crystal(5CB)sample is confined in cylindrical cells under strong or weak axial anchoring boundary conditions when a radial nonuniform low-frequency electric field is applied and the flexoelec...A positive nematic liquid crystal(5CB)sample is confined in cylindrical cells under strong or weak axial anchoring boundary conditions when a radial nonuniform low-frequency electric field is applied and the flexoelectric effect is taken into account.Based on the Frank elastic free energy,the surface energy of the Rapini-Papoular approximation,the polarization free energy and the flexoelectric free energy caused by electric field,we obtain the free energy density of the nematic and solve the corresponding Euler-Lagrange equation numerically.We investigate the director distribution,the critical voltage and the critical exponent of nematic liquid crystal in cylindrical cells.It follows that the critical exponent is the classical one.It is also shown that the critical voltage in the system is affected by the flexoelectric effect,the geometric effect and radial weak anchoring effect on the cylindrical surfaces.A new type of director transition caused by the flexoelectric effect,the dielectric coupling effect and the radial weak anchoring effect is found.展开更多
In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an exist...In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.展开更多
文摘A positive nematic liquid crystal(5CB)sample is confined in cylindrical cells under strong or weak axial anchoring boundary conditions when a radial nonuniform low-frequency electric field is applied and the flexoelectric effect is taken into account.Based on the Frank elastic free energy,the surface energy of the Rapini-Papoular approximation,the polarization free energy and the flexoelectric free energy caused by electric field,we obtain the free energy density of the nematic and solve the corresponding Euler-Lagrange equation numerically.We investigate the director distribution,the critical voltage and the critical exponent of nematic liquid crystal in cylindrical cells.It follows that the critical exponent is the classical one.It is also shown that the critical voltage in the system is affected by the flexoelectric effect,the geometric effect and radial weak anchoring effect on the cylindrical surfaces.A new type of director transition caused by the flexoelectric effect,the dielectric coupling effect and the radial weak anchoring effect is found.
基金Supported by the National Natural Science Foundation of China (No. 10771058)the Hunan Provincial Natural Science Foundation (No. 09JJ6013)
文摘In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.
