-
Abstract
Light can change the orientation of a liquid crystal. This is the optical Freedericksz transition, discovered by Saupe.
In the Janossy effect, the threshold intensity for the optical Freedericksz transition is dramatically reduced by the
additon of a small amount of dye to the sample. This has been interpreted as an optically pumped orientational
rachet mechanism, similar to the rachet mechanism in biological molecular motors. To interpret the evolution system
proposed for this effect requires an innovative gradient flow. Here we introduce this gradient flow and illustrate how
it also provides the boundary conditions, some unusual coupling conditions, between the liquid crystal and the dye.
An existence theorem for the evolution problem follows as well. Furthermore, we consider the time independent
problem and show its local asymptotic stability. Finally we progress toward showing that the proposed model correctly predicts the
onset of the Janossy effect.
Mathematics Subject Classification: 35K45, 35K50, 35K55, 35K57, 92C37, 92C45.
\begin{equation} \\ \end{equation}
-
Access History
-