We report experimental results for convection near onset in a thin layer of a homeotropically aligned nematic liquid crystal heated from below as a function of the temperature difference $\Delta T$ and the applied vertical magnetic field $H$ and compare them with theoretical calculations. The experiments cover the field range $8 \alt h \equiv H/ H_{ F} \alt 80$ ($H_F =$ is the Fr\'eedericksz field). For $h$ less than a codimension-two field $h_{ ct} \simeq 46$ the bifurcation is subcritical and oscillatory, with travelling- and standing-wave transients. Beyond $h_{ ct}$ the bifurcation is stationary and subcritical until a tricritical field $h_t= 57.2$ is reached, beyond which it is supercritical. The bifurcation sequence as a function of $h$ found in the experiment confirms the qualitative aspects of the theoretical predictions. However, the value of $h_{ ct}$ is about 10% higher than the predicted value and the results for $k_c$ are systematically below the theory by about 2% at small $h$ and by as much as 7% near $h_{ ct}$. At $h_{ ct}$, $k_c$ is continuous within the experimental resolution whereas the theory indicates a 7% discontinuity. The theoretical tricritical field $h_t^{ th} = 51$ is somewhat below the experimental one. The fully developed flow above $R_c$ for $h < h_{ ct}$ is chaotic. For $h_{ ct} < h < h_t$ the subcritical stationary bifurcation also leads to a chaotic state. The chaotic states persist upon reducing the Rayleigh number below $R_c$, i.e. the bifurcation is hysteretic. Above the tricritical field $h_t$, we find a bifurcation to a time independent pattern which within our resolution is non-hysteretic.
Categories: patt-sol nlin.PS