Dynamics of kinks in smectic-Cliquid crystals in periodically varying external fields

Abstract

We have considered the dynamics of kinks in smectic-$C$ liquid crystal in uniformly rotating and oscillating electric or magnetic fields. In tilted oscillating fields our results are at variance with those of earlier investigations which predict chaos in this geometry for a $\ensuremath{\pi}$ kink. On the other hand, we find that the velocity and the structure of a $\ensuremath{\pi}$ kink are oscillatory with the frequency of the varying field. The average velocity as a function of the tilt angle of the field indicates a threshold angle beyond which there is a crossover in velocity selection with the system choosing from a family of solutions. Surprisingly, in a nonoscillating field rotating in a plane normal to the layers, a $\ensuremath{\pi}$ kink has a drift velocity whose direction is dependent upon the sense of rotation. As a result of this, a $2\ensuremath{\pi}$ kink could be in a bound oscillating state or it could split itself into two oppositely drifting oscillating $\ensuremath{\pi}$ kinks. In a nonoscillating tilted field rotating about the layer normal, in the synchronous regime we find an instability of a kink connecting a stable state and a metastable state. In the asynchronous regime, a kink connecting two stable states has aperiodic motion. Interestingly, in the same geometry in oscillating fields, we find that a kink joining a stable state and a metastable state is more stable. In this geometry, periodic and aperiodic fluctuating kink structures are also possible. We have suggested a simple way of understanding the general dynamical features of a kink on the basis of the dynamics of the uniform director state which is found to be very sensitive to parameters of the system.