Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Pingwen Zhang,School of Mathematical Sciences, Peking University
Inviter:
Feimin Huang
Title:
The Mathematical Problems of Liquid Crystals (I)
Time & Venue:
2015.6.23 14:00-15:00 N620
Abstract:
Liquid crystals represent a vast and diverse class of anisotropic soft matter materials which are intermediate between isotropic liquids and crystalline solids. The mathematicians work on the theory of liquid crystals by its intriguing mathematical structure and connections to different branches of mathematics. A wide spectrum of mathematical problems of Liquid Crystals will be considered, related to the modeling of liquid crystals with varying detail and at different length scales. One set of problems to be considered is the relationship between these different levels of modeling; for example how one can make a rigorous passage from molecular/statistical descriptions to continuum theories. On the continuum level, we will address the dynamics of various liquid crystal phases and the systematic derivation of various equations of motion, and will aim to clarify the accuracy of different descriptions and their applicability to different liquid crystal systems. Special consideration will be given to the existence, uniqueness and regularity of the solutions of these equations, as well as the bifurcation and properties of equilibrium and periodic solutions and dynamic switching, and to how well the equations describe phase transitions. An important problem is to find effective approximations which can be used to overcome the challenges posed by the complexity of liquid crystal phases with biaxial and more complicated order, which are becoming important in emerging applications.
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