In spatially-extended nonlinear dissipative systems far from
equilibrium, bifurcations are usually discussed in terms of
deterministic equations of motion. This yields a sharp bifurcation
point at a critical value $R = R_c$ of the control parameter
at which an exchange of stability occurs between
the spatially-uniform state and the state with spatial variation.
However, 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 and the relevant fields,
although they have zero mean, have a positive (albeit small) mean
square.
This talk will review the measurements
of the properties of these fluctuations. In the case of Rayleigh-B\'enard
convection (RBC) nonlinear interaction between them yields a first-order
transition as predicted by Swift and Hohenberg. The "ordered" state
of convection rolls above the bifurcation exhibits thermally induced
amplitude variations, roll undulations, and dislocations, as envisioned
in part by Toner and Nelson. Electroconvection in nematic liquid
crystals (NLC) does not belong to the same universality class as RBC,
and fluctuation interactions leave the bifurcation supercritical; but the
exponents are renormalized. For a Hopf bifurcation to oblique rolls in
the NLC I52 experiment yields $\gamma \simeq 0.35 < \gamma_{MF} = 1/2$
for the exponent describing the fluctuation intensity,
whereas a stationary bifurcation to oblique rolls in the NLC N4 gives
$\gamma \simeq 0.85 > \gamma_{MF}$. Thus, as in equilibrium systems,
there exist several distinct universality classes.
Work done in collaboration with Michael Scherer, Jaechul Oh, and Xinliang Qiu.
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