Fluctuations near bifurcations in non-equilibrium systems
Guenter Ahlers, Department of Physics, University of California, Santa Barbara
In spatially-extended nonlinear dissipative systems far from equilibrium, transitions occur from a spatially uniform state to a state with spatial variation, i.e. to a pattern. These transitions are usually discussed in terms of deterministic equations for the macroscopic variables which neglect the "microscopic" degrees of freedom. An example is the use of the Navier-Stokes equation for convection in a thin horizontal layer of fluid heated from below [Rayleigh-B\'enard convection (RBC)].
There is then a sharp point at a critical value of a control parameter (e.g. the temperature difference in RBC) at which an exchange of stability occurs between the spatially-uniform state and the state with spatial variation. There are many analogies to equilibrium second-order phase transitions in systems which can be described by mean-field theories.
If the system is subjected to external (thermal) noise, then even below the bifurcation there are fluctuations of the macroscopic variables away from the uniform state. The relevant fields then each have zero mean but a positive mean square. This talk will review experimental measurements using RBC and electro-convection in a thin layer of a nematic liquid crystal subjected to an electric field. It will discuss some analogies to fluctuation-induced critical phenomena near equilibrium second-order phase transitions.