Elastic constants of nematic liquid crystals of uniaxial symmetry

We study in detail the influence of molecular interactions on the Frank elastic constants of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. A brief summary of the status of theoretical development for the elastic constants of nematics is presented. Considering a pair potential having both repulsive and attractive parts numerical calculations are reported for three systems MBBA, PAA and 8OCB. For these systems the length-to-width ratio ${x_0}$ is estimated from the experimentally proposed structure of the molecules. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution (HER) and the attractive potential is represented by the quadrupole and dispersion interactions. From the numerical results we observe that in the density range of nematics the contribution of the quadrupole and dispersion interactions are small as compared to the repulsive HER interaction. The inclusion of attractive interaction reduces the values of elastic constants ratios. The temperature variation of elastic constants ratios are reported and compared with the experimental values. A reasonably good agreement between theory and experiment is observed

Viscosities of the Gay-Berne nematic liquid crystal

We present molecular dynamics simulation measurements of the viscosities of the Gay-Berne phenomenological model of liquid crystals in the nematic and isotropic phases. The temperature dependence of the rotational and shear viscosities, including the nonmonotonic behavior of one shear viscosity are in good agreement with experimental data. The bulk viscosities are significantly larger than the shear viscosities, again in agreement with experiment.Comment: 11 pages, 4 Postscript figures, Revte

Моделювання поширення небезпечної домішки в атмосфері з урахуванням її поглинання водним середовищем

The mathematical model has been developed for additives distribution in the atmospheric air considering its interaction with aqueous medium. It has been developed as a practical component of assessing the ecological safety level. A comparison of the model analytical and numerical solutions is represented. The model is applicable for solving educational and practical problems on prevention and elimination of negative effect from human activity.Для оценки уровня экологической безопасности разработана математическая модель распространения примеси в атмосферном воздухе с учетом ее взаимодействия с водной средой. Представлено сравнение аналитического решения с численным. Модель пригодна для решения учебных и практических задач по предупреждению и ликвидации негативных последствий хозяйственной деятельности.The mathematical model has been developed for additives distribution in the atmospheric air considering its interaction with aqueous medium. It has been developed as a practical component of assessing the ecological safety level. A comparison of the model analytical and numerical solutions is represented. The model is applicable for solving educational and practical problems on prevention and elimination of negative effect from human activity.