Abstract
We consider a continuum theoretical description of a Smectic C monolayer\r made of molecules that can undergo cis-trans isomerization when subject to\r photo-activation. We use analytical and numerical methods to investigate the\r dynamics of this system. We show that this system exhibits self-regulation\r and the existence of propagating solitary waves, central features of an\r active fluid. Thus we demonstrate that this system can serve as an\r experimental platform to investigate the physics of this inherently\r out-of-equilibrium class of materials. The specific results obtained in this\r study are as follows : a) An equilibrium Smectic C monolayer can exist in\r one of two states - a homogeneous state and a striped state. b) In the\r presence of photo-activation the system develops propagating orientation\r waves. These waves are not a pattern but are rather solitary waves resulting\r from the self-regulating nature of the dynamics of the system. c) The\r properties of these waves are characterized as a function of two system\r parameters, the strength of spontaneous splay and the relaxation rate for\r the equilibration process of the molecular isomerization. We find that the\r speed of propagation increases as a function of both these parameters. c) We\r localize the activation by illuminating the monolayer using slits of various\r widths. In this case we find that the localization leads to the formation of\r a domain wall at the edge of the activated region and propagating waves are\r set up moving away from this domain wall. In the absence of diffusion, the\r waves remain confined to the slit of illumination. When diffusion is ramped\r up, the waves penetrate into the dark regions of the system and hence can\r potentially serve for controlled pattern generation and stabilization in\r this liquid crystal system.