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学术报告(20181009)Geometric theory of defects
发布时间:2018-10-09

报告题目: Geometric theory of defects
报告人: Mikhail Katanaev教授
报告人单位: M. O. Katanaev V. A. Steklov Mathematical Institute, ul. Gubkina 8, 119991 Moscow, Russian Federation
报告时间: 2018年10月09日上午10:00
报告地点: 东七楼,四楼427会议室
报告摘要:

We describe defects -- dislocations and disclinations -- in the framework of the Riemann--Cartan geometry. Curvature and torsion tensors are interpreted as surface densities of Frank and Burgers vectors, respectively. We propose new expression for the free energy describing static distribution of defects. Equations of nonlinear elasticity theory are used to fix the coordinate system. The Lorentz gauge yields equations for the principal chiral SO(3)-field. When defects are absent the geometric model reduces to the elasticity theory for the displacement vector field and to the principal chiral SO(3)-field model for the spin structure. The example of the wedge dislocation shows, that the elasticity theory reproduces only the line.
报告人简介:

Mikhail Katanaev是俄罗斯科学院教授。


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