Stochastic Effects in Systems Far from Equilibrium

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

This work focuses on quantitative studies of fluctuations caused by thermal noise below and near bifurcations in systems far from equilibrium. Well below the bifurcation it is expected that the measurements will test recent predictions about the structure factor of a fluid in a thermal gradient. Near the bifurcation the nonlinear interactions between the fluctuations should lead to critical phenomena in the sense that the various measurable quantities will deviate non-trivially from mean-field (or linear) predictions. The experiments will focus on Rayleigh-Bernard convection (RBC) in a horizontal layer of a fluid heated from below, and on electro convection (EC) of a nematic liquid crystal in an electric field. It has been predicted that RBC belongs to a universality class first studied theoretically by Brazovskii for which fluctuations change the bifurcation from a second-order to a first-order transition. For electro convection there is at present no theory of the critical behavior, but on general grounds one expects several different universality classes that depend on the relationship between the nematic director and the convection-roll wave director. The experiments will open a new research field of critical phenomena in non-equilibrium systems, and will prepare graduate students and postgraduate researchers for academic or industrial careers. Within an outreach program they will offer opportunities for participation by high school students. Many properties of equilibrium systems exhibit large thermally driven fluctuations near critical points. An example is the density of a fluid near a liquid-gas critical point. Nonlinear interactions between the fluctuations then cause the critical behavior to be different from that which is expected when fluctuations are small. The same phenomena should occur in a very different context, namely near transitions in non-equilibrium systems. For example, the transition from pure conduction to convection in a thin horizontal layer of a fluid heated from below was predicted to be of second order when fluctuations were neglected, but to become a first-order transition when they were considered. This work will determine the critical behavior near transitions in several non-equilibrium systems, including convection in a fluid heated from below and convection in a liquid crystal exposed to an electric voltage. This research will use advanced experimental techniques and sophisticated numerical image analysis, which will provide excellent training of graduate students for careers in academic and industrial positions. It also lends itself well to the participation of undergraduate students. Within an outreach program it is expected that high school students will also participate in some of the experiments.