The defect structures of s = ±1/2 twist disclinations in twisted nematic and twisted chiral liquid crystals have been investigated within the Landau-de Gennes theory numerically. Our results show that there exist...The defect structures of s = ±1/2 twist disclinations in twisted nematic and twisted chiral liquid crystals have been investigated within the Landau-de Gennes theory numerically. Our results show that there exists eigenvalue exchange across the defect core of both the two models. The defect core is essentially biaxial and never isotropic. The defect centre is uniaxial and is surrounded by a strong biaxial region.展开更多
Confined geometry can change the defect structure and its properties.In this paper,we investigate numerically the dynamics of a dipole of ±1/2 parallel wedge disclination lines in a confined geometry：a thin hybr...Confined geometry can change the defect structure and its properties.In this paper,we investigate numerically the dynamics of a dipole of ±1/2 parallel wedge disclination lines in a confined geometry：a thin hybrid aligned nematic（HAN） cell,based on the Landau-de Gennes theory.When the cell gap d is larger than a critical value of 12ξ（where ξis the characteristic length for order-parameter change）,the pair annihilates.A pure HAN configuration without defect is formed in an equilibrium state.In the confined geometry of d ≤ 12ξ,the diffusion process is discovered for the first time and an eigenvalue exchange configuration is formed in an equilibrium state.The eigenvalue exchange configuration is induced by different essential reasons.When 10ξ 〈 d ≤ 12ξ,the two defects coalesce and annihilate.The biaxial wall is created by the inhomogeneous distortion of the director,which results in the eigenvalue exchange configuration.When d≤ 10ξ,the defects do not collide and the eigenvalue exchange configuration originates from the biaxial seeds concentrated at the defects.展开更多
The stability of thermohaline convection problems of Veronis and Stern types for stationary convection is studied for quite general nature of boundaries. It is shown by means of an appropriately chosen linear transfor...The stability of thermohaline convection problems of Veronis and Stern types for stationary convection is studied for quite general nature of boundaries. It is shown by means of an appropriately chosen linear transformation, that in case of stationary convection the equations describing the eigenvalue problem for thermohaline convection problems are identical to equations describing the eigenvalue problem for classical Bénard convection problem. As a consequence, the values of the critical Rayleigh numbers for the onset of stationary convection in thermohaline convection problems are obtained. Also, necessary conditions for the validity of principle of exchange of stabilities for thermohaline convection problems are derived using variational principle.展开更多
文摘The defect structures of s = ±1/2 twist disclinations in twisted nematic and twisted chiral liquid crystals have been investigated within the Landau-de Gennes theory numerically. Our results show that there exists eigenvalue exchange across the defect core of both the two models. The defect core is essentially biaxial and never isotropic. The defect centre is uniaxial and is surrounded by a strong biaxial region.
基金supported by the National Natural Science Foundation of China(Grant No.11374087)the Key Subject Construction Project of Hebei Province University
文摘Confined geometry can change the defect structure and its properties.In this paper,we investigate numerically the dynamics of a dipole of ±1/2 parallel wedge disclination lines in a confined geometry：a thin hybrid aligned nematic（HAN） cell,based on the Landau-de Gennes theory.When the cell gap d is larger than a critical value of 12ξ（where ξis the characteristic length for order-parameter change）,the pair annihilates.A pure HAN configuration without defect is formed in an equilibrium state.In the confined geometry of d ≤ 12ξ,the diffusion process is discovered for the first time and an eigenvalue exchange configuration is formed in an equilibrium state.The eigenvalue exchange configuration is induced by different essential reasons.When 10ξ 〈 d ≤ 12ξ,the two defects coalesce and annihilate.The biaxial wall is created by the inhomogeneous distortion of the director,which results in the eigenvalue exchange configuration.When d≤ 10ξ,the defects do not collide and the eigenvalue exchange configuration originates from the biaxial seeds concentrated at the defects.
文摘The stability of thermohaline convection problems of Veronis and Stern types for stationary convection is studied for quite general nature of boundaries. It is shown by means of an appropriately chosen linear transformation, that in case of stationary convection the equations describing the eigenvalue problem for thermohaline convection problems are identical to equations describing the eigenvalue problem for classical Bénard convection problem. As a consequence, the values of the critical Rayleigh numbers for the onset of stationary convection in thermohaline convection problems are obtained. Also, necessary conditions for the validity of principle of exchange of stabilities for thermohaline convection problems are derived using variational principle.
