The Fréedericksz transition in twist cells of cholesteric liquid crystals with a finite surface energy is considered. It is shown that this transition can be either of the second order or of the first order depending on the values of the Frank constants, pitch, surface energies, and the cell thickness. A simple criterion that determines the order of the phase transition is obtained. By numerica...

We describe a recipe to generate “nonlocal” constants of motion for ODE Lagrangian systems. As sample application, we recall nonlocal constant dissipative mechanical systems, from which can deduce global existence and estimates solutions under fairly general assumptions. Then review generalization Euler–Lagrange ODEs order higher than two, leading first integrals the Pais–Uhlenbeck oscillator o...