Using φ-mapping method and topological current theory, the topological structure and bifurcation ofdisclination lines in two-dimensional liquid crystals are studied. By introducing the strength density and the topolo...Using φ-mapping method and topological current theory, the topological structure and bifurcation ofdisclination lines in two-dimensional liquid crystals are studied. By introducing the strength density and the topologicalcurrent of many disclination lines, the total disclination strength is topologically quantized by the Hopf indices andBrouwer degrees at the singularities of the director field when the Jacobian determinant of director field does not vanish.When the Jacobian determinant vanishes, the origin, annihilation and bifurcation processes of disclination lines arestudied in the neighborhoods of the limit points and bifurcation points, respectively. The branch solutions at the limitpoint and the different directions of all branch curves at the bifurcation point are calculated with the conservation lawof the topological quantum numbers. It is pointed out that a disclination line with a higher strength is unstable and itwill evolve to the lower strength state through the bifurcation process.展开更多
The ternary phase diagrams of musk ketone, musk xylene and various solvent were obtained by calcu- lations. Moreover, the double saturated lines were found to be curve for the first time. The methods to separate eutec...The ternary phase diagrams of musk ketone, musk xylene and various solvent were obtained by calcu- lations. Moreover, the double saturated lines were found to be curve for the first time. The methods to separate eutectic mixtures of musks by solution crystallization were suggested on the basis of these phase diagrams. A new process was proposed to get musk ketone and musk xylene from the eutectics by adding acetonitrile and heptane in turn, which was verified by experiments. Musk xylene with purity of 97.50% and musk ketone with purity of 98.10% were obtained.展开更多
文摘Using φ-mapping method and topological current theory, the topological structure and bifurcation ofdisclination lines in two-dimensional liquid crystals are studied. By introducing the strength density and the topologicalcurrent of many disclination lines, the total disclination strength is topologically quantized by the Hopf indices andBrouwer degrees at the singularities of the director field when the Jacobian determinant of director field does not vanish.When the Jacobian determinant vanishes, the origin, annihilation and bifurcation processes of disclination lines arestudied in the neighborhoods of the limit points and bifurcation points, respectively. The branch solutions at the limitpoint and the different directions of all branch curves at the bifurcation point are calculated with the conservation lawof the topological quantum numbers. It is pointed out that a disclination line with a higher strength is unstable and itwill evolve to the lower strength state through the bifurcation process.
文摘The ternary phase diagrams of musk ketone, musk xylene and various solvent were obtained by calcu- lations. Moreover, the double saturated lines were found to be curve for the first time. The methods to separate eutectic mixtures of musks by solution crystallization were suggested on the basis of these phase diagrams. A new process was proposed to get musk ketone and musk xylene from the eutectics by adding acetonitrile and heptane in turn, which was verified by experiments. Musk xylene with purity of 97.50% and musk ketone with purity of 98.10% were obtained.
