NON LINEARITIES CLOSE TO THE THERMAL THRESHOLD IN A PLANAR NEMATIC LIQUID-CRYSTAL

Nonlinearities in the thermal instability induced by heating a nematic liquid crystal from below are studied. First a model with free-free boundary conditions is studied. Critical behavior of the free-free model is analyzed. Properties above the threshold are determined with use of perturbation analysis. One shows that the first expansion coefficient R**(**1**) of the critical number vanishes. One determines in an approximate manner the amplitude of the disturbances above the threshold and finds that for most nematics the bifurcation is normal.