Applications of the Elastic Continuum Theory

The basic principle involved in the application of the fundamental equations to the solution of actual problems is that the equilibrium state of the director field is always given by that director configuration that minimizes the free energy of the system with specified boundary conditions. 

Before getting into actual calculations we first simplify Eq. [5] by setting Kii = K22 = 33 = K. This greatly facilitates the mathematics but does not affect the qualitative behavior of the results. Neglecting the term tt/Xq for the moment, we have 

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