Fluctuations Near Bifurcations in Spatially Extended Non-Equilibrium Systems
by
Guenter Ahlers
University of California, Santa Barbara

In spatially-extended nonlinear dissipative systems far from equilibrium, bifurcations 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 Rayleigh-Bénard convection (RBC). There is then a sharp bifurcation point at a critical value of the control parameter R = R_c 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. Above the bifurcation the ``ordered" state is also influenced by the noise and shows excitations including "phonons", amplitude excitations, and dislocations. This talk will review relevant experimental measurements and discuss some analogies to fluctuation-induced critical phenomena near equilibrium second-order phase transitions.

Date received: September 25, 2003