Topological Aspect and Bifurcation of Disclination Lines in Two-Dimensional Liquid Crystals**The project supported by the Science Foundation from the Education Commission of Shanghai under Grant Nos 2000QN64 and 2000A15

Abstract

Using -mapping method and topological current theory, the topological structure and bifurcation of disclination lines in two-dimensional liquid crystals are studied. By introducing the strength density and the topological current of many disclination lines, the total disclination strength is topologically quantized by the Hopf indices and Brouwer 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 are studied in the neighborhoods of the limit points and bifurcation points, respectively. The branch solutions at the limit point and the different directions of all branch curves at the bifurcation point are calculated with the conservation law of the topological quantum numbers. It is pointed out that a disclination line with a higher strength is unstable and it will evolve to the lower strength state through the bifurcation process.